14
Research Article bcBIM: A Blockchain-Based Big Data Model for BIM Modification Audit and Provenance in Mobile Cloud Rongyue Zheng, 1 Jianlin Jiang, 1 Xiaohan Hao , 2 Wei Ren , 2 Feng Xiong, 3 and Yi Ren 4 1 Faculty of Architecture, Civil Engineering and Environment, Ningbo University, Ningbo, China 2 School of Computer Science, China University of Geosciences, Wuhan, China 3 School of Business Administration, Zhongnan University of Economics and Law, Wuhan, China 4 School of Computing Science, University of East Anglia, Norwich NR4 7TJ, UK Correspondence should be addressed to Wei Ren; [email protected] Received 13 January 2019; Accepted 4 March 2019; Published 18 March 2019 Academic Editor: Ana C. Teodoro Copyright © 2019 Rongyue Zheng et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Building Information Modeling (BIM) is envisioned as an indispensable opportunity in the architecture, engineering, and construction (AEC) industries as a revolutionary technology and process. Smart construction relies on BIM for manipulating information flow, data flow, and management flow. Currently, BIM model has been explored mainly for information construction and utilization, but rare works pay efforts to information security, e.g., critical model audit and sensitive model exposure. Moreover, few BIM systems are proposed to chase aſter upcoming computing paradigms, such as mobile cloud computing, big data, blockchain, and Internet of ings. In this paper, we make the first attempt to propose a novel BIM system model called bcBIM to tackle information security in mobile cloud architectures. More specifically, bcBIM is proposed to facilitate BIM data audit for historical modifications by blockchain in mobile cloud with big data sharing. e proposed bcBIM model can guide the architecture design for further BIM information management system, especially for integrating BIM cloud as a service for further big data sharing. We propose a method of BIM data organization based on blockchains and discuss it based on private and public blockchain. It guarantees to trace, authenticate, and prevent tampering with BIM historical data. At the same time, it can generate a unified format to support future open sharing, data audit, and data provenance. 1. Introduction Building Information Modeling (BIM) is a set of interact- ing policies, processes, and technologies, which produce a methodology to manage the essential building design and project data throughout the building’s life cycle [1]. It can provide a unified presentation, data framework, and organization. In construction automation, the architecture enables information and communication technology (ICT) to manage the life cycle information of buildings. During a whole life of a building, the essential features of BIM can be summarized into four aspects, namely, integrating with various databases, facilitating document management, visualizing analytical processes and results, and providing sustainability analyses and simulation [2]. e most recent ICT architecture application for BIM is the traditional client- server architecture, some of which still work as a single workstation pattern. We argue that the future development of BIM technology must be combined with advanced com- munications technology and computer technology in order to greatly improve the efficiency of the construction industry, such as blockchain, mobile cloud computing, big data, and the Internet of ings. Blockchain is a distributed database system that acts as an “open ledger” to store and manage transactions. Each record in the database is called a block and contains details such as transaction timestamp and links to the previous block. is characteristic makes it impossible for anyone to change the information about the records retro- spectively. In addition, since the same transaction is recorded on multiple distributed database systems, the technology is safe in design. As a hot topic in the world at present, cloud computing has become the strategic direction of the future development of information industry and an impor- tant engine to promote economic growth, which not only Hindawi Mathematical Problems in Engineering Volume 2019, Article ID 5349538, 13 pages https://doi.org/10.1155/2019/5349538

bcBIM: A Blockchain-Based Big Data Model for BIM

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Research ArticlebcBIM A Blockchain-Based Big Data Model for BIMModification Audit and Provenance in Mobile Cloud

Rongyue Zheng1 Jianlin Jiang1 Xiaohan Hao 2 Wei Ren 2 Feng Xiong3 and Yi Ren4

1Faculty of Architecture Civil Engineering and Environment Ningbo University Ningbo China2School of Computer Science China University of Geosciences Wuhan China3School of Business Administration Zhongnan University of Economics and Law Wuhan China4School of Computing Science University of East Anglia Norwich NR4 7TJ UK

Correspondence should be addressed to Wei Ren weirencscugeducn

Received 13 January 2019 Accepted 4 March 2019 Published 18 March 2019

Academic Editor Ana C Teodoro

Copyright copy 2019 Rongyue Zheng et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Building Information Modeling (BIM) is envisioned as an indispensable opportunity in the architecture engineering andconstruction (AEC) industries as a revolutionary technology and process Smart construction relies on BIM for manipulatinginformation flow data flow and management flow Currently BIM model has been explored mainly for information constructionand utilization but rare works pay efforts to information security eg critical model audit and sensitive model exposureMoreoverfew BIM systems are proposed to chase after upcoming computing paradigms such as mobile cloud computing big datablockchain and Internet of Things In this paper we make the first attempt to propose a novel BIM system model called bcBIMto tackle information security in mobile cloud architectures More specifically bcBIM is proposed to facilitate BIM data audit forhistorical modifications by blockchain inmobile cloudwith big data sharingThe proposed bcBIMmodel can guide the architecturedesign for further BIM information management system especially for integrating BIM cloud as a service for further big datasharingWe propose amethod of BIMdata organization based on blockchains anddiscuss it based on private and public blockchainIt guarantees to trace authenticate and prevent tampering with BIM historical data At the same time it can generate a unifiedformat to support future open sharing data audit and data provenance

1 Introduction

Building Information Modeling (BIM) is a set of interact-ing policies processes and technologies which producea methodology to manage the essential building designand project data throughout the buildingrsquos life cycle [1] Itcan provide a unified presentation data framework andorganization In construction automation the architectureenables information and communication technology (ICT)to manage the life cycle information of buildings Duringa whole life of a building the essential features of BIMcan be summarized into four aspects namely integratingwith various databases facilitating document managementvisualizing analytical processes and results and providingsustainability analyses and simulation [2] The most recentICT architecture application for BIM is the traditional client-server architecture some of which still work as a single

workstation pattern We argue that the future developmentof BIM technology must be combined with advanced com-munications technology and computer technology in orderto greatly improve the efficiency of the construction industrysuch as blockchain mobile cloud computing big data andthe Internet of Things Blockchain is a distributed databasesystem that acts as an ldquoopen ledgerrdquo to store and managetransactions Each record in the database is called a blockand contains details such as transaction timestamp and linksto the previous block This characteristic makes it impossiblefor anyone to change the information about the records retro-spectively In addition since the same transaction is recordedon multiple distributed database systems the technologyis safe in design As a hot topic in the world at presentcloud computing has become the strategic direction of thefuture development of information industry and an impor-tant engine to promote economic growth which not only

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 5349538 13 pageshttpsdoiorg10115520195349538

2 Mathematical Problems in Engineering

provides new impetus for transformation and innovationof the information industry itself but also provides greatopportunities for the upgrading of traditional industries andthe development of new industries

With the rapid development of society more and moredifficulties appear in current models The main difficultyis that they cannot safely track revisions For example thedesign may be modified due to budget or host requirementsThe revision of BIM data is usually updated rather thanretaining the revision history Even if the update records arestored it is difficult to guarantee the integrity of historicaldata In addition record updates depend on the full trust ofthe central operator Once the internal operators misbehavethe data will lead to construction rework or even disas-ter

However the marriage of them with BIM has beenexplored by few related work The BIM cloud will signif-icantly reduce the latency of information access makingBIM information available to all users It provides a high-capacity storage fast retrieval and on-demand calculationsfor building information As a result mobile cloud archi-tectures can make BIM information popular and availableto a large number of users Although the mobile cloud forBIM provides conveniences of information accessing it alsoraises several security issues [3ndash5] In this paper we mainlysolve the following problem the audit of BIM modificationThe current challenges are as follows (1) Keep only thelast modification record (2) The source of the modifieditem cannot be traced (3) Attacks from the central operatorcannot be recorded and tracked In order to solve the abovechallenges we combine BIM with blockchain to providea BIM data organization method which can track proveand prevent the tampering of BIM historical data At thesame time a unified format is generated to support theopen sharing of future data In addition BIM models andparameters may be modified during smart construction Ifthe chain of revision history is stored for later audit theprovenance and accountability will be possible Howevercurrent BIM architecture pays insufficient concerns for thedata audit In this paper we propose a bcBIM modelcustomized for BIM data audit and mobile cloud BIMarchitecture The contributions of the paper are listed asfollows

(1) We make the first attempt to propose a bcBIMmodel enhanced by blockchain for BIM data auditprovenance and accountability

(2) We propose traceable and authenticated bcBIMmodel via blockchain that can satisfy traceability bytimestamp for recording BIMmodification history

The rest of the paper is organized as follows Section 2summarizes the related preliminary work In Section 3 weanalyze the audit problem and propose a bcBIM modelvia blockchain In Section 4 we propose a further ICTparadigm for mobile cloud BIM architecture and describethe proposed model bcBIM in detail In Section 5 we analyzebcBIMmodelrsquos security and performance extensively FinallySection 6 concludes the full paper

2 Related Work

In view of the combination of architecture with BIM Nassiriet al [6] combined BIM with decision method (entropy-TOPSIS) to scientifically optimize the choice of sustainablebuilding materials during the conceptual design phase of abuilding project Oti and Tizani et al [7] provided a BIMintegrated system that combined three green metrics lifecycle costs ecological footprint and carbon footprint to helpstructural engineers conduct sustainability assessments ofalternative designs Inyim et al [8] introduced an optimiza-tion tool combining BIM with construction environmentalimpact simulation to help designers achieve multiple sus-tainable goals in the decision-making process such as thoserelated to construction time initial construction costs andCO2 emissions Wang et al [9] discussed and investigatedhowBIM can be extended to the site via the ldquopractical armrdquo ofAR Kokorus et al [10] used Building Information Modeling(BIM) technology to design innovative approach to the sub-station Dawood et al [11] combined Building InformationModeling (BIM) with genetic algorithm (GA) to find theoptimal design with minimum life cycle cost in the servicelife of buildings Pasini et al [12] built information modelingframework for management of cognitive buildings to explorehow BIM practices and technologies could improve a data-driven asset management Zhu et al [13] combined withBIM construction and other building technologies greatlyshortened the time of modeling development and signifi-cantly improved the efficiency of modeling Isikdag et al[14] proposed a BIM-oriented service-oriented architecturedesign pattern Yoon and Park et al [15] put forward a designmethod of energy-saving building based on BIM On thespecific practice of BIM the practical implementation of BIMframework is proposed by Jung and Joo et al [16] Linderothet al [17] understood adoption and used BIM as the creationof actor networks Lu and Li et al [18] established informationmodeling and changed construction practice Desogus et al[19] presented preliminary performance monitoring plan forenergy retrofit The ldquoMandolesi Pavillonrdquo at the University ofCagliari

Considering the combination of big data and BIMArslanet al [20] developed a prototype system using Hadoop fordata storage and processing The results of processing BIMand sensor data in a Hadoop architecture have demonstratedthat the system can effectively provide data visualizationsto facility managers Building life cycle assessment (BLCA)of energy consumption is an important issue in the fieldof sustainable development and green building Yuan et al[21] summarized the features of building life cycle energyconsumption (BLCEC) data proposed the method of infor-mation exchange and integration management by BIM andutilized cloud computing technology to achieve wide-areaBLC energy data management Ferguson et al [22] presentedan application of linked data views (or semantic views) as partof a larger modular and extensible framework that provideda method to automatically query understand and translateBIM instances into linked data for better supporting moreaccurate decision Bottaccioli et al [23] proposed buildingenergy modeling and monitoring through the integration

Mathematical Problems in Engineering 3

Table 1 A comparison of three kinds of blockchain

Application ofDecentralized

DegreeAccess Mechanism Transaction

SpeedTransaction

CostExecutionEfficiency

Applicationexample

private Centralize Specific individualsor entities fast low high Acrblock

consortium Partialdecentralization

Authorizedorganizations orinstitutions

mid mid mid R3 Hyperledger

public Completedecentralization All slow high low BTC ETH NEO

of Internet of Things equipment and building informationmodel Razavi et al [24] proposed using BIM to realize mul-tisensor data fusion of material tracking in construction site

Themobile cloud or blockchain marries with BIMmodelare a new topic and the literatures are very limited Park andASCE et al [25] presented a framework for this safety moni-toring system as a cloud-based real-time on-site applicationThe system integrates Bluetooth low-energy- (BLE-) basedlocation detection technology BIM-based hazard identifica-tion and a cloud-based communication platform Garcia-Fernandez et al [26] discussed the different approaches todate on the BIM generation chain from 3D point cloud datacollection to semantically enriched parametric models Inthis paper we proposed a bcBIMmodel via blockchain whichcan not only satisfy traceability by timestamp for recordingBIM modification history but also enhanced for BIM dataaudit provenance and accountability

3 Problem Formulation

31 System Model In this section we briefly describe howthe bcBIM model implements our proposed scheme beforediscussing the adversary model

BIM can collect a large amount of information through-out the lifecycle of a project by creating a database Throughthe adjustment addition and modification of the data infor-mation the overall status of the project can be accuratelyreflected Through the association with the data fasterdecision-making progress can be achieved and the quality ofdecision-making can be improved thereby improving projectquality and increasing project profit However the mainweaknesses of BIM in terms of security are as follows

The audit and provenance of revised BIM data somerevision for BIM data may not be avoided in constructionfor example design may be revised due to budgets orrequirements of hostsThemajor difficulties in current modelare that the revision can not be traced securely The revisionof BIM data is usually updating not remaining the revisionhistory Even the updating record is stored the integrity forhistorical data is difficult to be guaranteed Furthermorethe updating of record relies on the fully trust of centraloperators Once internal operators conduct misbehavior thedata will lead to construction rework or even disaster

To solve the overcome weakness we consider usingblockchain technology to improve BIM Blockchain can be

roughly divided into three categories public blockchainprivate blockchain and consortium blockchain Publicblockchain is open to all whichmeans anyone can participateit private blockchain is open to individual or entity andconsortium blockchain is open to specific organizations andgroups Although the above three blockchains are all based onconsensus mechanisms to ensure the security and reliabilityof blockchain technology operations satisfying traceableand nontamperable they also have significant differencesFrom private blockchain consortium blockchain to publicblockchain the degree of decentralization has graduallyincreased and the scope of authority has been expandingDifferent levels of information disclosure and central controlhelp blockchain meet different types of application require-ments Table 1 makes comparison of three blockchain

In the basic model we discuss our proposal with privateblockchain which can be signed by a trusted center Howeverif applying in consortium blockchain it can be signed bythe federation node Private blockchain refers to the writerights which are entirely in the hands of an organizationand all the nodes involved in the chain are strictly con-trolled In some cases some rules in the private blockchaincan be modified by the organization such as restoringthe transaction process Compared with public blockchainprivate blockchain have the greatest advantage of encryptingaudit and public identity information That is no one cantamper with data once some errors occur it is possible totrack the source of errors Therefore private blockchain iscommon in internal system or network Due to its privacysome private chains also omit the function of ldquominingrdquowhich greatly improves the efficiency of implementationPrivate blockchain can not only prevent a single node inan organization from deliberately concealing or tamper-ing with data but also quickly identify sources wheneverthere are occurs some errors Different from the open andsemiopen characteristics of public blockchain or consortiumblockchain private blockchain emphasizes privacy which islimited to user access and transactions within an enterprisebetween two organizations such as Acrblock For examplesome financial and auditing institutions are used to storebooks and databases only users with relevant authority canaccess and modify data The advantages of private blockchainare as follows(1) Private blockchain has fast transaction speed Its

transaction progress only requires a few generally recognized

4 Mathematical Problems in Engineering

high-power nodes and rather requires the confirmation of allnetwork nodes(2) Transaction costs are very low compared with public

and consortium blockchain(3) Since the privacy of receipts is limited it is difficult for

participants to obtain data on private blockchain that is theprivacy protection is better than others

The disadvantage of private blockchain is as followsthe risk of receiving attacks is higher because it can bemanipulated price or modified code

Unlike private blockchain consortium blockchain hasseveral organizations or institutions which participating inthe management Each organization or institution controlsone or more nodes and they record transaction data togetherOnly organizations and institutions which have relevantauthorities can read write or send transaction data onconsortium blockchain Since it only opens parts of func-tions to members the permissions and accounting rules onconsortium blockchain are ldquocustomizedrdquo according to theconsortium The consensus process is controlled by prese-lected nodes on consortium blockchain It is suitable for B2Bscenarios such as interagency transactions settlement andliquidation For example many financial institutions connecttheir blockchain networks together to form a consortiumnet-work which facilitates data docking and collaboration Forexample R3 Hyperledger and Golden Chain Consortiumeach node has its corresponding entity or organization onconsortium blockchain Only authorized to join or exit thenetwork which is aiming at reducing costs and improvingefficiency In addition it is also suitable for scenarios suchas transaction and settlement between different entitiesConsortium blockchain is maintained by the participatingmember organizations and provides a complete set of safetymanagement functions such as management certificationauthorization monitoring and auditing of the participatingmembers For example the R3 consortium is a consortiumblockchain of banking industry which was established in2015 At present it has joined more than 40 membersincluding world famous banks such as JPMorgan ChaseHSBC and Goldman Sachs Each bank can become a nodebut the transfer behavior of one bank must be confirmed byother bank nodes (23 number) in order to make the blockeffective Nowadays BIM is usually used internally such asa bridge design institute architectural design institute and alarge group company In addition almost no POWconsensusmechanism is used in consortium blockchain but consensusalgorithms such as proof of rights or PBTF are used Theadvantages of consortium blockchain are as follows(1) Due to the fact that the number of nodes has been

streamlined consortium blockchain has faster transactionspeed and lower cost(2) Compared with public blockchain consortium

blockchain requires more transactions to be confirmed perunit time

The disadvantage of consortium blockchain is as followsthe safety and performance requirements are relatively high

Considering that contemporary green construction isassembled building we discuss how to establish a BIMshared component library One of the applications of public

blockchain is recording BIM database which can be addedby anyone that is it can form BIM shared componentlibrary We propose this scheme as an advanced model withPOWmechanism In addition public blockchain is a kind ofnontampering account book and it is the most widely usedblockchain at present In addition public blockchain estab-lishes a centralized autonomous organization which can bebooks electricity transactions big data transactions or BIMdatabase Bitcoin and Ethernet are the most popular publicblockchain which means the behavior of public blockchainis open However it is not controlled by anyone nor ownedby anyone it is a ldquocompletely decentralizedrdquo blockchain Theadvantages of public blockchain are as follows(1)The access threshold is so low that any user with an

Internet-connected computer can access it(2) Open and transparent since the whole system is

ldquocompletely decentralizedrdquo the process of running the systemis open and transparent(3) Anonymity since nodes do not need to trust each

other all operations can be performed anonymously that isthe privacy is well protected(4) Free from the influence of the developer reading

and writing public blockchain data are not controlled by anyorganization or individual so it can also protect users fromprogrammers

The disadvantages of public blockchain are as follows lowefficiency large power consumption and long time requiredto validate and complete transactions

32 AdversaryModel In this section we identify four poten-tial vulnerabilities that can be exploited by our opponents toundermine our solutions (1) the modified content cannot betraced to its source (2) the integrity of the historical data istampered with the last modification record (3) attacks fromthe central operator cannot be recorded and tracking Somemodifications of BIM data may be unavoidable in construc-tion for example design modifications due to budget or hostrequirements The revision of BIM data is usually updatedrather than retaining the revision historyTherefore attackersmay be able to modify the source of BIM data In our schemewe combine BIMwith blockchain to ensure that the source ofBIM data is not modified

As mentioned above the traditional BIM model onlyretains the last modification record In the process of revisingBIM data even if the update record is stored the historicaldata can be modified by attackers and the integrity of thehistorical data is difficult to guarantee In our model theintegrity of historical data can be guaranteed by using thetraceability of blockchain and the nontampering character-istics of information In traditional BIM model recordingupdates depend on the full trust of the central operatoronce improper behavior of internal operators occurs thedata will lead to construction rework or even disaster Inour scheme we combine BIM with blockchain and takeadvantage of the decentralization of blockchain Since theuse of distributed billing and storage there is no centralizedhardware or management organization that is the rightsand obligations of any node are the same In addition the

Mathematical Problems in Engineering 5

data blocks in BIM system are maintained by the nodes withmaintenance function in the whole system

4 Proposed Scheme

Our solution is briefly described in the above section and thedetails of our solution are detailed in this section

41 Proposed Basic Architecture In this section we pro-pose the mobile cloud BIM architecture for further ICTparadigms

411 BIM as a Service BIMaaS BIMaaS is a cloud service forproviding outsourced BIM data storage and computation Itcan be looked as a united virtual central server by harvestingmultiple computing resources which provides an on-demandstorage and computation service BIMaaS is managed bydedicated cloud computing software It can smoothly respondto any storage and computation requests by migrating orredistributing the tasks to a resource pool which is trans-parent to users Thus users do not need to care about theimplementation details on BIMaaS and just look it as a virtualserver

The BIMaaS can be further classified into two folders(1) BIM data are outsourced to a public cloud that is

provided by cloud service companies such as AWS AzureandAliYun Such public cloud service is paid according to theresource requirements The initial investment for hardwareand software is avoided as both of them are rented from thepublic BIMaaS It can obviously decrease the startup budgetfor small business in AEC industry Besides the managementof BIMaaS can also be outsourced to public BIMaaS thepersonnel enrollments and cost for human resourcesmay alsobe alleviated(2) For some giant companies in AEC industry it may

be possible to integrate private BIMaaS by themselves Suchcompanies have already deployed an information infrastruc-ture such as data center before They usually have their ICTdivision and have a large number of human resources for ICTsupports Thus they construct their private BIMaaS servicesvia some publicly available software tools such as OpenStack

412 Big Data Sharing among BIMaaS With the develop-ment of BIMaaS BIM data is accumulated with time elapsingand project conducting Even for one building a large volumeof BIM data is aggregated Once revision occurs during aconstruction life time all historical data may also be snapshotand stored for further audit For example once a designfor a model is modified all legacy versions may also bestored respectively for tracing revised model locations andparameters When such traceability is required for criticalstructures or components an additive data organization withprovenance capability will be required In addition BIMdata sharing should be a trend once the data is accumulatedsufficiently large For example for different buildings in thesame category BIM data can be mutually accessed or refer-enced among them Some validated best practices and designexperiences can be migrated from one project (building)

to another Some common characteristics in design can beabstracted by data mining or machine learning Informationexchanges between BIM data will let users form a global viewof specific design in multiple projects

413 Pervasively Accessing by Mobile Terminals Anyone canaccess BIM data and revoke the BIM computation servicesuch as model visualization from BIMaaS or big data poolMobile terminal is a convenient tool for mobile usersespecially field engineers in smart construction It is a hand-held device that can access the BIM information any timeanywhere by wireless It can be divided into two folders asfollows(1) Mobile terminals can be hand-held devices such as

smart phones tablets laptops and so on Currently suchdevices are largely used as personal computing tools By themdesigners can verify the conformation of engineering regu-lation the monitors can check the schedules of engineeringprocedures the suppliers can consult the future requirementsfor material resources(2) Mobile terminals can be wearable devices such as

smart watches smart glasses and smart helmets Those areequipped with sensors for instant information collectionor displayers for smooth human-machine interaction Forexample wireless sensors for environmental monitors 3Dinformation presentation such as Virtual Reality (VR) orAugmented Reality (AR) It can improve operational effi-ciency especially for field engineers in a limited space Itcan support smart and automatic construction scenarios Forexample smart helmet for engineers on constructing fieldsmay access BIM data remotely and reconstruct VR by thelatest data Construction robots may access BIM data andcollect sensing information from sensors in constructingfields to evaluate sustainable design parameters for greenhouses

414 Automatically Exchanging by Internet of Things Inter-net of Things (IoTs) is a network with wireless sensors Insmart construction those sensors may deploy with facilitiesin operational fields with Internet accessing via wirelesscommunications such as 4G or NB-IOT Those sensors cancollect the construction environmental data and upload theminto BIMaaS server once those data can help the revisionor improvement of the design in BIM For example windand sunshine design evaluation for green construction canbe justified or amended after analysis from the field sensingdata during the construction This feedback will enhancethe initial design in BIM that only relies on simulationor emulation but also is manipulated from realistic on-site parameters Moreover the construction engineeringmachines (eg crane) that are equipped wireless devicescan also access BIM data in BIMaaS They may access theBIM information automatically and display the result tooperators to guide the future instructions Some equipmentsuch as surveillance video cameras can automatically set upthe direction of lens by fetch specific installation data fromBIMaaS

6 Mathematical Problems in Engineering

In summary BIMaaS provides a storage and computationservice for BIM data including data retrieval data updat-ing and data computation BIM big data is accumulativelymerged and shared to form a unified resource pool forresponding on-demanded requests from traditional desktopPCs or especially mobile terminals in construction fieldsSome special wearable devices such as helmets may providemore enhancement for BIM information presentation BIMdata can be accessed any time anywhere not only by mobiledevices but also by wireless sensors Those sensors createIoTs to collect critical data about on-site construction ontime The analysis on those data can help reevaluate thequality of design or construction and provide amendingfeedback Moreover IoT devices on construction machinecan access and display BIM data to empower the intelligenceof construction machines This architecture not only enablesthe pervasive retrievals of BIM information but also supportsthe ubiquitous information exchanging or cooperativelyconstructing It provides a promising framework for theexchanging and sharing of BIM data in smart construction

415 Structure of Blockchain Blockchain is a distributedledger a technical solution to collectively maintain a reliabledatabase throughdecentralized trustedways and blockchainis a distributed database that is almost impossible to changeldquoDistributedrdquo here is not only a distributed storage of databut also a distributed record of data (ie shared by thesystem participants) blockchain is not a single technologybut a result of a variety of technology integration thesetechnologies are in a new structure together to form a newway of data recording storage and expression Combinedwith these technologies the contents of the scheme afteradopting the present inventionwill be difficult to bemodifiedand the security can be improved

Data stored using blockchain technology is also timeseries tamper-proof forged and privacy-pending which isproven in many documents bcBIM also inherits these fea-tures and guarantees the absolute security of the informationdata from two aspects one is to ensure that the pseudo-blockdoes not appear on the blockchain

Each node in the receipt of the new block will be the blockvalidation pseudo-block because it can not be verified will bediscarded and will not be written into the blockchain if themalicious node would like to use pseudo-branched chain toreplace the correct blockchain which is the computing powerof todayrsquos computer which is almost impossible to achieve thetask the other is to ensure that the data in the chain will notbe modified Because each chunk contains the hash value ofthe previous chunk if the malicious node changes a chunk ofdata you must change the chunk behind all the blocks whichare changed but also in the future with their own pseudo-branched chain to cover the correct blockchain in terms ofmodern computer capabilities this is also an impossible task

The basic processing unit of blockchain technology is adata block that stores all transaction data and related verifica-tion information for a certain period of time The blockchainis combined into a specific data structure in chronologicalorder which forms the nontamper and nonfalsification data

sharing information guaranteed by cryptography and usesthe SHA 256 algorithm and theMerkle tree to realize the datamanagement system with simple and safe storage successiverelation efficient and fast verification [27]

Block is the basic unit of block chain which is composedof blocks and blocks The block header contains blockID version number previous block hash value timestampMerkle root the block target hash value and so onThemainbody of the block contains the main data information ofthe block including identity certificate transaction contentamount of breach of contract and so on (Figure 1)

The characteristic of BIM data organization methodbased on blockchain is that each newly generated block savesthe hash value of the previous block Therefore we combineBIM with blockchain to provide BIM data organizationmethod which can track prove and prevent tampering ofBIM historical data At the same time it can generate unifiedformat to support open sharing of future data

42 Blockchain-Based Model for Audit and Provenance Inthis section we propose to use blockchain to facilitate theaudit and provenance of historical BIM data

Blockchain consists of a data structurewith cryptographichash value to guarantee the integrity of a serial data Themajor items in proposed blockchain-based model are asfollows (= denotes that ldquois defined asrdquo)

(1) Block = ⟨119861119897119900119888119896119867119890119886119889119863119886119905119886⟩ 119861119897119900119888119896119867119890119886119889 guaran-tees the integrity (nonmodification) of 119863119886119905119886 andmodifying history of 119863119886119905119886

(2) BlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎNonce Difficulty Timestamp⟩ The 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ is the hash value of the intermediate previousblock head 119863119886119905119886119867119886119904ℎ is the hash value of 119863119886119905119886 inthis block 119873119900119899119888119890 is a value to be determined byrandomly checking whetherZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 119885119890119903119900(sdot) is afunction that returns the number of left consecutivezeros in an inputting string in bytes 119863119894119891119891119894119888119906119897119905119910 isan integer to tell the requirement on how manyconsecutive zeros in the head of hash result Forexample 119863119894119891119891119894119888119906119897119905119910 = 2 means the first 2 bytes oftarget hash outputting is 0 That is the first 2 bytesof 119867119886119904ℎ(sdot) is 0 119879119894119898119890119904119905119886119898119901 is the time snapshot ofcurrent packaging block

(3) Data = ⟨119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886⟩ 119872119890119905119886119889119886119905119886 is anoptional tuple for data description on 119861119868119872119889119886119905119886which can be empty The 119861119868119872119889119886119905119886 is a mandatorytuple for concrete BIM data Once BIM data ismodified 119863119886119905119886 will be created and wait for beingappended into blockchain in a batch

(4) 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) where119861119897119900119888119896119867119890119886119889 is the previous blockhead where119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ tuple is located That is the hashvalue of previous blockhead is embedded into nextblock head It can also be looked as a link of twoadjacent block heads

Mathematical Problems in Engineering 7

Block Header

Field Description

Version Block Version Number

Previous Block HashHash of the previous block

in the chain

Merkle Tree RootHash of the Merkle tree root

Timestamp Creation time of this block

Targeted Difficultye Proof-Of-Work

difficulty target

Nonce

2IIN-

A counter for the Proof-Of-Work

Figure 1 Format of block

(5) 119863119886119905119886119867119886119904ℎ = Hash(1198611198681198721198891198861199051198861 1198611198681198721198891198861199051198862 sdot sdot sdot 119861119868119872119889119886119905119886119899) Suppose the number of BIM in thistime-span is 119899 That is it is the numbers of BIMdata that will be packaged in blockchain during ablock generation period 119863119886119905119886119867119886119904ℎ guarantees theintegrity of block contents consisting ofmodifiedBIMdata

The purpose of blockchain is to record the historical pro-cess of BIM record modification A blockhead is composedof multiple BIM data which can speed up the uplink of BIMrecord modification The necessary BIM data need to recordthe history of modification but the ordinary BIM can notimplement it The method of calculating block hash valuescan get hash values of all uplink BIM data more quickly andefficiently than calculating Merkle tree roots We propose aBIM via blockchain to storage data which solve the problemof tracing proving and preventing tampering with BIMhistorical data At the same time it can generate a unifiedformat to support future open sharing This method uses thehash structure of blockhead to ensure the integrity of all blockdata In addition block integrity is guaranteed by hash valueand the signature guarantees blockheadrsquos integrity The valueof hash andnonce in blockhead guarantees fair consensus andnontampering

43 Example Public Blockchain bcBIM In this scene theblockchain-based BIM data organization method is based ona decentralized measure also known as a public blockchainmethod which includes the following steps

(1) Each node of the public blockchain denoted as B isusually a node with its own independent BIM data Itis necessary to establish the openness and sharing ofBIM data among all nodes and maintain irreparabledata modification and traceability of time

(2) The central node of the public blockchain records theBIM data which need to be saved in the local storagemedium and uniformly packs it into the blockhead atevery P time

(3) Assume that the BIM data recorded in P time are11986111986811987211198611198681198722 119861119868119872119899 The method of uniformlypacking blocks into blockheads is as follows Blocksare recorded asBIMDATA and the components of theblocks include 11986111986811987211198611198681198722 119861119868119872119899 each BIMiincludes metadata modified BIM data and accessaddress ofmodifiedBIMdata calculate119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899)

(4) The blockhead is named BIMHEAD its compo-sition includes PreviousHash BIMHASH LinkOf-DATA Timestamp and NonceandRequirement Pre-viousHash is the hash value of the previous block-head LinkofDATA is the access address of cur-rent block BIMDATA Timestamp is a time stampfor building blockheads Nonce is a random num-ber Requirement is a requirement for hash valuethat is 119867119886119904ℎ(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119874119891119863119860119879119860 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890 119868119863) meetsthe Requirement

8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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2 Mathematical Problems in Engineering

provides new impetus for transformation and innovationof the information industry itself but also provides greatopportunities for the upgrading of traditional industries andthe development of new industries

With the rapid development of society more and moredifficulties appear in current models The main difficultyis that they cannot safely track revisions For example thedesign may be modified due to budget or host requirementsThe revision of BIM data is usually updated rather thanretaining the revision history Even if the update records arestored it is difficult to guarantee the integrity of historicaldata In addition record updates depend on the full trust ofthe central operator Once the internal operators misbehavethe data will lead to construction rework or even disas-ter

However the marriage of them with BIM has beenexplored by few related work The BIM cloud will signif-icantly reduce the latency of information access makingBIM information available to all users It provides a high-capacity storage fast retrieval and on-demand calculationsfor building information As a result mobile cloud archi-tectures can make BIM information popular and availableto a large number of users Although the mobile cloud forBIM provides conveniences of information accessing it alsoraises several security issues [3ndash5] In this paper we mainlysolve the following problem the audit of BIM modificationThe current challenges are as follows (1) Keep only thelast modification record (2) The source of the modifieditem cannot be traced (3) Attacks from the central operatorcannot be recorded and tracked In order to solve the abovechallenges we combine BIM with blockchain to providea BIM data organization method which can track proveand prevent the tampering of BIM historical data At thesame time a unified format is generated to support theopen sharing of future data In addition BIM models andparameters may be modified during smart construction Ifthe chain of revision history is stored for later audit theprovenance and accountability will be possible Howevercurrent BIM architecture pays insufficient concerns for thedata audit In this paper we propose a bcBIM modelcustomized for BIM data audit and mobile cloud BIMarchitecture The contributions of the paper are listed asfollows

(1) We make the first attempt to propose a bcBIMmodel enhanced by blockchain for BIM data auditprovenance and accountability

(2) We propose traceable and authenticated bcBIMmodel via blockchain that can satisfy traceability bytimestamp for recording BIMmodification history

The rest of the paper is organized as follows Section 2summarizes the related preliminary work In Section 3 weanalyze the audit problem and propose a bcBIM modelvia blockchain In Section 4 we propose a further ICTparadigm for mobile cloud BIM architecture and describethe proposed model bcBIM in detail In Section 5 we analyzebcBIMmodelrsquos security and performance extensively FinallySection 6 concludes the full paper

2 Related Work

In view of the combination of architecture with BIM Nassiriet al [6] combined BIM with decision method (entropy-TOPSIS) to scientifically optimize the choice of sustainablebuilding materials during the conceptual design phase of abuilding project Oti and Tizani et al [7] provided a BIMintegrated system that combined three green metrics lifecycle costs ecological footprint and carbon footprint to helpstructural engineers conduct sustainability assessments ofalternative designs Inyim et al [8] introduced an optimiza-tion tool combining BIM with construction environmentalimpact simulation to help designers achieve multiple sus-tainable goals in the decision-making process such as thoserelated to construction time initial construction costs andCO2 emissions Wang et al [9] discussed and investigatedhowBIM can be extended to the site via the ldquopractical armrdquo ofAR Kokorus et al [10] used Building Information Modeling(BIM) technology to design innovative approach to the sub-station Dawood et al [11] combined Building InformationModeling (BIM) with genetic algorithm (GA) to find theoptimal design with minimum life cycle cost in the servicelife of buildings Pasini et al [12] built information modelingframework for management of cognitive buildings to explorehow BIM practices and technologies could improve a data-driven asset management Zhu et al [13] combined withBIM construction and other building technologies greatlyshortened the time of modeling development and signifi-cantly improved the efficiency of modeling Isikdag et al[14] proposed a BIM-oriented service-oriented architecturedesign pattern Yoon and Park et al [15] put forward a designmethod of energy-saving building based on BIM On thespecific practice of BIM the practical implementation of BIMframework is proposed by Jung and Joo et al [16] Linderothet al [17] understood adoption and used BIM as the creationof actor networks Lu and Li et al [18] established informationmodeling and changed construction practice Desogus et al[19] presented preliminary performance monitoring plan forenergy retrofit The ldquoMandolesi Pavillonrdquo at the University ofCagliari

Considering the combination of big data and BIMArslanet al [20] developed a prototype system using Hadoop fordata storage and processing The results of processing BIMand sensor data in a Hadoop architecture have demonstratedthat the system can effectively provide data visualizationsto facility managers Building life cycle assessment (BLCA)of energy consumption is an important issue in the fieldof sustainable development and green building Yuan et al[21] summarized the features of building life cycle energyconsumption (BLCEC) data proposed the method of infor-mation exchange and integration management by BIM andutilized cloud computing technology to achieve wide-areaBLC energy data management Ferguson et al [22] presentedan application of linked data views (or semantic views) as partof a larger modular and extensible framework that provideda method to automatically query understand and translateBIM instances into linked data for better supporting moreaccurate decision Bottaccioli et al [23] proposed buildingenergy modeling and monitoring through the integration

Mathematical Problems in Engineering 3

Table 1 A comparison of three kinds of blockchain

Application ofDecentralized

DegreeAccess Mechanism Transaction

SpeedTransaction

CostExecutionEfficiency

Applicationexample

private Centralize Specific individualsor entities fast low high Acrblock

consortium Partialdecentralization

Authorizedorganizations orinstitutions

mid mid mid R3 Hyperledger

public Completedecentralization All slow high low BTC ETH NEO

of Internet of Things equipment and building informationmodel Razavi et al [24] proposed using BIM to realize mul-tisensor data fusion of material tracking in construction site

Themobile cloud or blockchain marries with BIMmodelare a new topic and the literatures are very limited Park andASCE et al [25] presented a framework for this safety moni-toring system as a cloud-based real-time on-site applicationThe system integrates Bluetooth low-energy- (BLE-) basedlocation detection technology BIM-based hazard identifica-tion and a cloud-based communication platform Garcia-Fernandez et al [26] discussed the different approaches todate on the BIM generation chain from 3D point cloud datacollection to semantically enriched parametric models Inthis paper we proposed a bcBIMmodel via blockchain whichcan not only satisfy traceability by timestamp for recordingBIM modification history but also enhanced for BIM dataaudit provenance and accountability

3 Problem Formulation

31 System Model In this section we briefly describe howthe bcBIM model implements our proposed scheme beforediscussing the adversary model

BIM can collect a large amount of information through-out the lifecycle of a project by creating a database Throughthe adjustment addition and modification of the data infor-mation the overall status of the project can be accuratelyreflected Through the association with the data fasterdecision-making progress can be achieved and the quality ofdecision-making can be improved thereby improving projectquality and increasing project profit However the mainweaknesses of BIM in terms of security are as follows

The audit and provenance of revised BIM data somerevision for BIM data may not be avoided in constructionfor example design may be revised due to budgets orrequirements of hostsThemajor difficulties in current modelare that the revision can not be traced securely The revisionof BIM data is usually updating not remaining the revisionhistory Even the updating record is stored the integrity forhistorical data is difficult to be guaranteed Furthermorethe updating of record relies on the fully trust of centraloperators Once internal operators conduct misbehavior thedata will lead to construction rework or even disaster

To solve the overcome weakness we consider usingblockchain technology to improve BIM Blockchain can be

roughly divided into three categories public blockchainprivate blockchain and consortium blockchain Publicblockchain is open to all whichmeans anyone can participateit private blockchain is open to individual or entity andconsortium blockchain is open to specific organizations andgroups Although the above three blockchains are all based onconsensus mechanisms to ensure the security and reliabilityof blockchain technology operations satisfying traceableand nontamperable they also have significant differencesFrom private blockchain consortium blockchain to publicblockchain the degree of decentralization has graduallyincreased and the scope of authority has been expandingDifferent levels of information disclosure and central controlhelp blockchain meet different types of application require-ments Table 1 makes comparison of three blockchain

In the basic model we discuss our proposal with privateblockchain which can be signed by a trusted center Howeverif applying in consortium blockchain it can be signed bythe federation node Private blockchain refers to the writerights which are entirely in the hands of an organizationand all the nodes involved in the chain are strictly con-trolled In some cases some rules in the private blockchaincan be modified by the organization such as restoringthe transaction process Compared with public blockchainprivate blockchain have the greatest advantage of encryptingaudit and public identity information That is no one cantamper with data once some errors occur it is possible totrack the source of errors Therefore private blockchain iscommon in internal system or network Due to its privacysome private chains also omit the function of ldquominingrdquowhich greatly improves the efficiency of implementationPrivate blockchain can not only prevent a single node inan organization from deliberately concealing or tamper-ing with data but also quickly identify sources wheneverthere are occurs some errors Different from the open andsemiopen characteristics of public blockchain or consortiumblockchain private blockchain emphasizes privacy which islimited to user access and transactions within an enterprisebetween two organizations such as Acrblock For examplesome financial and auditing institutions are used to storebooks and databases only users with relevant authority canaccess and modify data The advantages of private blockchainare as follows(1) Private blockchain has fast transaction speed Its

transaction progress only requires a few generally recognized

4 Mathematical Problems in Engineering

high-power nodes and rather requires the confirmation of allnetwork nodes(2) Transaction costs are very low compared with public

and consortium blockchain(3) Since the privacy of receipts is limited it is difficult for

participants to obtain data on private blockchain that is theprivacy protection is better than others

The disadvantage of private blockchain is as followsthe risk of receiving attacks is higher because it can bemanipulated price or modified code

Unlike private blockchain consortium blockchain hasseveral organizations or institutions which participating inthe management Each organization or institution controlsone or more nodes and they record transaction data togetherOnly organizations and institutions which have relevantauthorities can read write or send transaction data onconsortium blockchain Since it only opens parts of func-tions to members the permissions and accounting rules onconsortium blockchain are ldquocustomizedrdquo according to theconsortium The consensus process is controlled by prese-lected nodes on consortium blockchain It is suitable for B2Bscenarios such as interagency transactions settlement andliquidation For example many financial institutions connecttheir blockchain networks together to form a consortiumnet-work which facilitates data docking and collaboration Forexample R3 Hyperledger and Golden Chain Consortiumeach node has its corresponding entity or organization onconsortium blockchain Only authorized to join or exit thenetwork which is aiming at reducing costs and improvingefficiency In addition it is also suitable for scenarios suchas transaction and settlement between different entitiesConsortium blockchain is maintained by the participatingmember organizations and provides a complete set of safetymanagement functions such as management certificationauthorization monitoring and auditing of the participatingmembers For example the R3 consortium is a consortiumblockchain of banking industry which was established in2015 At present it has joined more than 40 membersincluding world famous banks such as JPMorgan ChaseHSBC and Goldman Sachs Each bank can become a nodebut the transfer behavior of one bank must be confirmed byother bank nodes (23 number) in order to make the blockeffective Nowadays BIM is usually used internally such asa bridge design institute architectural design institute and alarge group company In addition almost no POWconsensusmechanism is used in consortium blockchain but consensusalgorithms such as proof of rights or PBTF are used Theadvantages of consortium blockchain are as follows(1) Due to the fact that the number of nodes has been

streamlined consortium blockchain has faster transactionspeed and lower cost(2) Compared with public blockchain consortium

blockchain requires more transactions to be confirmed perunit time

The disadvantage of consortium blockchain is as followsthe safety and performance requirements are relatively high

Considering that contemporary green construction isassembled building we discuss how to establish a BIMshared component library One of the applications of public

blockchain is recording BIM database which can be addedby anyone that is it can form BIM shared componentlibrary We propose this scheme as an advanced model withPOWmechanism In addition public blockchain is a kind ofnontampering account book and it is the most widely usedblockchain at present In addition public blockchain estab-lishes a centralized autonomous organization which can bebooks electricity transactions big data transactions or BIMdatabase Bitcoin and Ethernet are the most popular publicblockchain which means the behavior of public blockchainis open However it is not controlled by anyone nor ownedby anyone it is a ldquocompletely decentralizedrdquo blockchain Theadvantages of public blockchain are as follows(1)The access threshold is so low that any user with an

Internet-connected computer can access it(2) Open and transparent since the whole system is

ldquocompletely decentralizedrdquo the process of running the systemis open and transparent(3) Anonymity since nodes do not need to trust each

other all operations can be performed anonymously that isthe privacy is well protected(4) Free from the influence of the developer reading

and writing public blockchain data are not controlled by anyorganization or individual so it can also protect users fromprogrammers

The disadvantages of public blockchain are as follows lowefficiency large power consumption and long time requiredto validate and complete transactions

32 AdversaryModel In this section we identify four poten-tial vulnerabilities that can be exploited by our opponents toundermine our solutions (1) the modified content cannot betraced to its source (2) the integrity of the historical data istampered with the last modification record (3) attacks fromthe central operator cannot be recorded and tracking Somemodifications of BIM data may be unavoidable in construc-tion for example design modifications due to budget or hostrequirements The revision of BIM data is usually updatedrather than retaining the revision historyTherefore attackersmay be able to modify the source of BIM data In our schemewe combine BIMwith blockchain to ensure that the source ofBIM data is not modified

As mentioned above the traditional BIM model onlyretains the last modification record In the process of revisingBIM data even if the update record is stored the historicaldata can be modified by attackers and the integrity of thehistorical data is difficult to guarantee In our model theintegrity of historical data can be guaranteed by using thetraceability of blockchain and the nontampering character-istics of information In traditional BIM model recordingupdates depend on the full trust of the central operatoronce improper behavior of internal operators occurs thedata will lead to construction rework or even disaster Inour scheme we combine BIM with blockchain and takeadvantage of the decentralization of blockchain Since theuse of distributed billing and storage there is no centralizedhardware or management organization that is the rightsand obligations of any node are the same In addition the

Mathematical Problems in Engineering 5

data blocks in BIM system are maintained by the nodes withmaintenance function in the whole system

4 Proposed Scheme

Our solution is briefly described in the above section and thedetails of our solution are detailed in this section

41 Proposed Basic Architecture In this section we pro-pose the mobile cloud BIM architecture for further ICTparadigms

411 BIM as a Service BIMaaS BIMaaS is a cloud service forproviding outsourced BIM data storage and computation Itcan be looked as a united virtual central server by harvestingmultiple computing resources which provides an on-demandstorage and computation service BIMaaS is managed bydedicated cloud computing software It can smoothly respondto any storage and computation requests by migrating orredistributing the tasks to a resource pool which is trans-parent to users Thus users do not need to care about theimplementation details on BIMaaS and just look it as a virtualserver

The BIMaaS can be further classified into two folders(1) BIM data are outsourced to a public cloud that is

provided by cloud service companies such as AWS AzureandAliYun Such public cloud service is paid according to theresource requirements The initial investment for hardwareand software is avoided as both of them are rented from thepublic BIMaaS It can obviously decrease the startup budgetfor small business in AEC industry Besides the managementof BIMaaS can also be outsourced to public BIMaaS thepersonnel enrollments and cost for human resourcesmay alsobe alleviated(2) For some giant companies in AEC industry it may

be possible to integrate private BIMaaS by themselves Suchcompanies have already deployed an information infrastruc-ture such as data center before They usually have their ICTdivision and have a large number of human resources for ICTsupports Thus they construct their private BIMaaS servicesvia some publicly available software tools such as OpenStack

412 Big Data Sharing among BIMaaS With the develop-ment of BIMaaS BIM data is accumulated with time elapsingand project conducting Even for one building a large volumeof BIM data is aggregated Once revision occurs during aconstruction life time all historical data may also be snapshotand stored for further audit For example once a designfor a model is modified all legacy versions may also bestored respectively for tracing revised model locations andparameters When such traceability is required for criticalstructures or components an additive data organization withprovenance capability will be required In addition BIMdata sharing should be a trend once the data is accumulatedsufficiently large For example for different buildings in thesame category BIM data can be mutually accessed or refer-enced among them Some validated best practices and designexperiences can be migrated from one project (building)

to another Some common characteristics in design can beabstracted by data mining or machine learning Informationexchanges between BIM data will let users form a global viewof specific design in multiple projects

413 Pervasively Accessing by Mobile Terminals Anyone canaccess BIM data and revoke the BIM computation servicesuch as model visualization from BIMaaS or big data poolMobile terminal is a convenient tool for mobile usersespecially field engineers in smart construction It is a hand-held device that can access the BIM information any timeanywhere by wireless It can be divided into two folders asfollows(1) Mobile terminals can be hand-held devices such as

smart phones tablets laptops and so on Currently suchdevices are largely used as personal computing tools By themdesigners can verify the conformation of engineering regu-lation the monitors can check the schedules of engineeringprocedures the suppliers can consult the future requirementsfor material resources(2) Mobile terminals can be wearable devices such as

smart watches smart glasses and smart helmets Those areequipped with sensors for instant information collectionor displayers for smooth human-machine interaction Forexample wireless sensors for environmental monitors 3Dinformation presentation such as Virtual Reality (VR) orAugmented Reality (AR) It can improve operational effi-ciency especially for field engineers in a limited space Itcan support smart and automatic construction scenarios Forexample smart helmet for engineers on constructing fieldsmay access BIM data remotely and reconstruct VR by thelatest data Construction robots may access BIM data andcollect sensing information from sensors in constructingfields to evaluate sustainable design parameters for greenhouses

414 Automatically Exchanging by Internet of Things Inter-net of Things (IoTs) is a network with wireless sensors Insmart construction those sensors may deploy with facilitiesin operational fields with Internet accessing via wirelesscommunications such as 4G or NB-IOT Those sensors cancollect the construction environmental data and upload theminto BIMaaS server once those data can help the revisionor improvement of the design in BIM For example windand sunshine design evaluation for green construction canbe justified or amended after analysis from the field sensingdata during the construction This feedback will enhancethe initial design in BIM that only relies on simulationor emulation but also is manipulated from realistic on-site parameters Moreover the construction engineeringmachines (eg crane) that are equipped wireless devicescan also access BIM data in BIMaaS They may access theBIM information automatically and display the result tooperators to guide the future instructions Some equipmentsuch as surveillance video cameras can automatically set upthe direction of lens by fetch specific installation data fromBIMaaS

6 Mathematical Problems in Engineering

In summary BIMaaS provides a storage and computationservice for BIM data including data retrieval data updat-ing and data computation BIM big data is accumulativelymerged and shared to form a unified resource pool forresponding on-demanded requests from traditional desktopPCs or especially mobile terminals in construction fieldsSome special wearable devices such as helmets may providemore enhancement for BIM information presentation BIMdata can be accessed any time anywhere not only by mobiledevices but also by wireless sensors Those sensors createIoTs to collect critical data about on-site construction ontime The analysis on those data can help reevaluate thequality of design or construction and provide amendingfeedback Moreover IoT devices on construction machinecan access and display BIM data to empower the intelligenceof construction machines This architecture not only enablesthe pervasive retrievals of BIM information but also supportsthe ubiquitous information exchanging or cooperativelyconstructing It provides a promising framework for theexchanging and sharing of BIM data in smart construction

415 Structure of Blockchain Blockchain is a distributedledger a technical solution to collectively maintain a reliabledatabase throughdecentralized trustedways and blockchainis a distributed database that is almost impossible to changeldquoDistributedrdquo here is not only a distributed storage of databut also a distributed record of data (ie shared by thesystem participants) blockchain is not a single technologybut a result of a variety of technology integration thesetechnologies are in a new structure together to form a newway of data recording storage and expression Combinedwith these technologies the contents of the scheme afteradopting the present inventionwill be difficult to bemodifiedand the security can be improved

Data stored using blockchain technology is also timeseries tamper-proof forged and privacy-pending which isproven in many documents bcBIM also inherits these fea-tures and guarantees the absolute security of the informationdata from two aspects one is to ensure that the pseudo-blockdoes not appear on the blockchain

Each node in the receipt of the new block will be the blockvalidation pseudo-block because it can not be verified will bediscarded and will not be written into the blockchain if themalicious node would like to use pseudo-branched chain toreplace the correct blockchain which is the computing powerof todayrsquos computer which is almost impossible to achieve thetask the other is to ensure that the data in the chain will notbe modified Because each chunk contains the hash value ofthe previous chunk if the malicious node changes a chunk ofdata you must change the chunk behind all the blocks whichare changed but also in the future with their own pseudo-branched chain to cover the correct blockchain in terms ofmodern computer capabilities this is also an impossible task

The basic processing unit of blockchain technology is adata block that stores all transaction data and related verifica-tion information for a certain period of time The blockchainis combined into a specific data structure in chronologicalorder which forms the nontamper and nonfalsification data

sharing information guaranteed by cryptography and usesthe SHA 256 algorithm and theMerkle tree to realize the datamanagement system with simple and safe storage successiverelation efficient and fast verification [27]

Block is the basic unit of block chain which is composedof blocks and blocks The block header contains blockID version number previous block hash value timestampMerkle root the block target hash value and so onThemainbody of the block contains the main data information ofthe block including identity certificate transaction contentamount of breach of contract and so on (Figure 1)

The characteristic of BIM data organization methodbased on blockchain is that each newly generated block savesthe hash value of the previous block Therefore we combineBIM with blockchain to provide BIM data organizationmethod which can track prove and prevent tampering ofBIM historical data At the same time it can generate unifiedformat to support open sharing of future data

42 Blockchain-Based Model for Audit and Provenance Inthis section we propose to use blockchain to facilitate theaudit and provenance of historical BIM data

Blockchain consists of a data structurewith cryptographichash value to guarantee the integrity of a serial data Themajor items in proposed blockchain-based model are asfollows (= denotes that ldquois defined asrdquo)

(1) Block = ⟨119861119897119900119888119896119867119890119886119889119863119886119905119886⟩ 119861119897119900119888119896119867119890119886119889 guaran-tees the integrity (nonmodification) of 119863119886119905119886 andmodifying history of 119863119886119905119886

(2) BlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎNonce Difficulty Timestamp⟩ The 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ is the hash value of the intermediate previousblock head 119863119886119905119886119867119886119904ℎ is the hash value of 119863119886119905119886 inthis block 119873119900119899119888119890 is a value to be determined byrandomly checking whetherZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 119885119890119903119900(sdot) is afunction that returns the number of left consecutivezeros in an inputting string in bytes 119863119894119891119891119894119888119906119897119905119910 isan integer to tell the requirement on how manyconsecutive zeros in the head of hash result Forexample 119863119894119891119891119894119888119906119897119905119910 = 2 means the first 2 bytes oftarget hash outputting is 0 That is the first 2 bytesof 119867119886119904ℎ(sdot) is 0 119879119894119898119890119904119905119886119898119901 is the time snapshot ofcurrent packaging block

(3) Data = ⟨119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886⟩ 119872119890119905119886119889119886119905119886 is anoptional tuple for data description on 119861119868119872119889119886119905119886which can be empty The 119861119868119872119889119886119905119886 is a mandatorytuple for concrete BIM data Once BIM data ismodified 119863119886119905119886 will be created and wait for beingappended into blockchain in a batch

(4) 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) where119861119897119900119888119896119867119890119886119889 is the previous blockhead where119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ tuple is located That is the hashvalue of previous blockhead is embedded into nextblock head It can also be looked as a link of twoadjacent block heads

Mathematical Problems in Engineering 7

Block Header

Field Description

Version Block Version Number

Previous Block HashHash of the previous block

in the chain

Merkle Tree RootHash of the Merkle tree root

Timestamp Creation time of this block

Targeted Difficultye Proof-Of-Work

difficulty target

Nonce

2IIN-

A counter for the Proof-Of-Work

Figure 1 Format of block

(5) 119863119886119905119886119867119886119904ℎ = Hash(1198611198681198721198891198861199051198861 1198611198681198721198891198861199051198862 sdot sdot sdot 119861119868119872119889119886119905119886119899) Suppose the number of BIM in thistime-span is 119899 That is it is the numbers of BIMdata that will be packaged in blockchain during ablock generation period 119863119886119905119886119867119886119904ℎ guarantees theintegrity of block contents consisting ofmodifiedBIMdata

The purpose of blockchain is to record the historical pro-cess of BIM record modification A blockhead is composedof multiple BIM data which can speed up the uplink of BIMrecord modification The necessary BIM data need to recordthe history of modification but the ordinary BIM can notimplement it The method of calculating block hash valuescan get hash values of all uplink BIM data more quickly andefficiently than calculating Merkle tree roots We propose aBIM via blockchain to storage data which solve the problemof tracing proving and preventing tampering with BIMhistorical data At the same time it can generate a unifiedformat to support future open sharing This method uses thehash structure of blockhead to ensure the integrity of all blockdata In addition block integrity is guaranteed by hash valueand the signature guarantees blockheadrsquos integrity The valueof hash andnonce in blockhead guarantees fair consensus andnontampering

43 Example Public Blockchain bcBIM In this scene theblockchain-based BIM data organization method is based ona decentralized measure also known as a public blockchainmethod which includes the following steps

(1) Each node of the public blockchain denoted as B isusually a node with its own independent BIM data Itis necessary to establish the openness and sharing ofBIM data among all nodes and maintain irreparabledata modification and traceability of time

(2) The central node of the public blockchain records theBIM data which need to be saved in the local storagemedium and uniformly packs it into the blockhead atevery P time

(3) Assume that the BIM data recorded in P time are11986111986811987211198611198681198722 119861119868119872119899 The method of uniformlypacking blocks into blockheads is as follows Blocksare recorded asBIMDATA and the components of theblocks include 11986111986811987211198611198681198722 119861119868119872119899 each BIMiincludes metadata modified BIM data and accessaddress ofmodifiedBIMdata calculate119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899)

(4) The blockhead is named BIMHEAD its compo-sition includes PreviousHash BIMHASH LinkOf-DATA Timestamp and NonceandRequirement Pre-viousHash is the hash value of the previous block-head LinkofDATA is the access address of cur-rent block BIMDATA Timestamp is a time stampfor building blockheads Nonce is a random num-ber Requirement is a requirement for hash valuethat is 119867119886119904ℎ(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119874119891119863119860119879119860 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890 119868119863) meetsthe Requirement

8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

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Hindawiwwwhindawicom Volume 2018

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Mathematical Problems in Engineering 3

Table 1 A comparison of three kinds of blockchain

Application ofDecentralized

DegreeAccess Mechanism Transaction

SpeedTransaction

CostExecutionEfficiency

Applicationexample

private Centralize Specific individualsor entities fast low high Acrblock

consortium Partialdecentralization

Authorizedorganizations orinstitutions

mid mid mid R3 Hyperledger

public Completedecentralization All slow high low BTC ETH NEO

of Internet of Things equipment and building informationmodel Razavi et al [24] proposed using BIM to realize mul-tisensor data fusion of material tracking in construction site

Themobile cloud or blockchain marries with BIMmodelare a new topic and the literatures are very limited Park andASCE et al [25] presented a framework for this safety moni-toring system as a cloud-based real-time on-site applicationThe system integrates Bluetooth low-energy- (BLE-) basedlocation detection technology BIM-based hazard identifica-tion and a cloud-based communication platform Garcia-Fernandez et al [26] discussed the different approaches todate on the BIM generation chain from 3D point cloud datacollection to semantically enriched parametric models Inthis paper we proposed a bcBIMmodel via blockchain whichcan not only satisfy traceability by timestamp for recordingBIM modification history but also enhanced for BIM dataaudit provenance and accountability

3 Problem Formulation

31 System Model In this section we briefly describe howthe bcBIM model implements our proposed scheme beforediscussing the adversary model

BIM can collect a large amount of information through-out the lifecycle of a project by creating a database Throughthe adjustment addition and modification of the data infor-mation the overall status of the project can be accuratelyreflected Through the association with the data fasterdecision-making progress can be achieved and the quality ofdecision-making can be improved thereby improving projectquality and increasing project profit However the mainweaknesses of BIM in terms of security are as follows

The audit and provenance of revised BIM data somerevision for BIM data may not be avoided in constructionfor example design may be revised due to budgets orrequirements of hostsThemajor difficulties in current modelare that the revision can not be traced securely The revisionof BIM data is usually updating not remaining the revisionhistory Even the updating record is stored the integrity forhistorical data is difficult to be guaranteed Furthermorethe updating of record relies on the fully trust of centraloperators Once internal operators conduct misbehavior thedata will lead to construction rework or even disaster

To solve the overcome weakness we consider usingblockchain technology to improve BIM Blockchain can be

roughly divided into three categories public blockchainprivate blockchain and consortium blockchain Publicblockchain is open to all whichmeans anyone can participateit private blockchain is open to individual or entity andconsortium blockchain is open to specific organizations andgroups Although the above three blockchains are all based onconsensus mechanisms to ensure the security and reliabilityof blockchain technology operations satisfying traceableand nontamperable they also have significant differencesFrom private blockchain consortium blockchain to publicblockchain the degree of decentralization has graduallyincreased and the scope of authority has been expandingDifferent levels of information disclosure and central controlhelp blockchain meet different types of application require-ments Table 1 makes comparison of three blockchain

In the basic model we discuss our proposal with privateblockchain which can be signed by a trusted center Howeverif applying in consortium blockchain it can be signed bythe federation node Private blockchain refers to the writerights which are entirely in the hands of an organizationand all the nodes involved in the chain are strictly con-trolled In some cases some rules in the private blockchaincan be modified by the organization such as restoringthe transaction process Compared with public blockchainprivate blockchain have the greatest advantage of encryptingaudit and public identity information That is no one cantamper with data once some errors occur it is possible totrack the source of errors Therefore private blockchain iscommon in internal system or network Due to its privacysome private chains also omit the function of ldquominingrdquowhich greatly improves the efficiency of implementationPrivate blockchain can not only prevent a single node inan organization from deliberately concealing or tamper-ing with data but also quickly identify sources wheneverthere are occurs some errors Different from the open andsemiopen characteristics of public blockchain or consortiumblockchain private blockchain emphasizes privacy which islimited to user access and transactions within an enterprisebetween two organizations such as Acrblock For examplesome financial and auditing institutions are used to storebooks and databases only users with relevant authority canaccess and modify data The advantages of private blockchainare as follows(1) Private blockchain has fast transaction speed Its

transaction progress only requires a few generally recognized

4 Mathematical Problems in Engineering

high-power nodes and rather requires the confirmation of allnetwork nodes(2) Transaction costs are very low compared with public

and consortium blockchain(3) Since the privacy of receipts is limited it is difficult for

participants to obtain data on private blockchain that is theprivacy protection is better than others

The disadvantage of private blockchain is as followsthe risk of receiving attacks is higher because it can bemanipulated price or modified code

Unlike private blockchain consortium blockchain hasseveral organizations or institutions which participating inthe management Each organization or institution controlsone or more nodes and they record transaction data togetherOnly organizations and institutions which have relevantauthorities can read write or send transaction data onconsortium blockchain Since it only opens parts of func-tions to members the permissions and accounting rules onconsortium blockchain are ldquocustomizedrdquo according to theconsortium The consensus process is controlled by prese-lected nodes on consortium blockchain It is suitable for B2Bscenarios such as interagency transactions settlement andliquidation For example many financial institutions connecttheir blockchain networks together to form a consortiumnet-work which facilitates data docking and collaboration Forexample R3 Hyperledger and Golden Chain Consortiumeach node has its corresponding entity or organization onconsortium blockchain Only authorized to join or exit thenetwork which is aiming at reducing costs and improvingefficiency In addition it is also suitable for scenarios suchas transaction and settlement between different entitiesConsortium blockchain is maintained by the participatingmember organizations and provides a complete set of safetymanagement functions such as management certificationauthorization monitoring and auditing of the participatingmembers For example the R3 consortium is a consortiumblockchain of banking industry which was established in2015 At present it has joined more than 40 membersincluding world famous banks such as JPMorgan ChaseHSBC and Goldman Sachs Each bank can become a nodebut the transfer behavior of one bank must be confirmed byother bank nodes (23 number) in order to make the blockeffective Nowadays BIM is usually used internally such asa bridge design institute architectural design institute and alarge group company In addition almost no POWconsensusmechanism is used in consortium blockchain but consensusalgorithms such as proof of rights or PBTF are used Theadvantages of consortium blockchain are as follows(1) Due to the fact that the number of nodes has been

streamlined consortium blockchain has faster transactionspeed and lower cost(2) Compared with public blockchain consortium

blockchain requires more transactions to be confirmed perunit time

The disadvantage of consortium blockchain is as followsthe safety and performance requirements are relatively high

Considering that contemporary green construction isassembled building we discuss how to establish a BIMshared component library One of the applications of public

blockchain is recording BIM database which can be addedby anyone that is it can form BIM shared componentlibrary We propose this scheme as an advanced model withPOWmechanism In addition public blockchain is a kind ofnontampering account book and it is the most widely usedblockchain at present In addition public blockchain estab-lishes a centralized autonomous organization which can bebooks electricity transactions big data transactions or BIMdatabase Bitcoin and Ethernet are the most popular publicblockchain which means the behavior of public blockchainis open However it is not controlled by anyone nor ownedby anyone it is a ldquocompletely decentralizedrdquo blockchain Theadvantages of public blockchain are as follows(1)The access threshold is so low that any user with an

Internet-connected computer can access it(2) Open and transparent since the whole system is

ldquocompletely decentralizedrdquo the process of running the systemis open and transparent(3) Anonymity since nodes do not need to trust each

other all operations can be performed anonymously that isthe privacy is well protected(4) Free from the influence of the developer reading

and writing public blockchain data are not controlled by anyorganization or individual so it can also protect users fromprogrammers

The disadvantages of public blockchain are as follows lowefficiency large power consumption and long time requiredto validate and complete transactions

32 AdversaryModel In this section we identify four poten-tial vulnerabilities that can be exploited by our opponents toundermine our solutions (1) the modified content cannot betraced to its source (2) the integrity of the historical data istampered with the last modification record (3) attacks fromthe central operator cannot be recorded and tracking Somemodifications of BIM data may be unavoidable in construc-tion for example design modifications due to budget or hostrequirements The revision of BIM data is usually updatedrather than retaining the revision historyTherefore attackersmay be able to modify the source of BIM data In our schemewe combine BIMwith blockchain to ensure that the source ofBIM data is not modified

As mentioned above the traditional BIM model onlyretains the last modification record In the process of revisingBIM data even if the update record is stored the historicaldata can be modified by attackers and the integrity of thehistorical data is difficult to guarantee In our model theintegrity of historical data can be guaranteed by using thetraceability of blockchain and the nontampering character-istics of information In traditional BIM model recordingupdates depend on the full trust of the central operatoronce improper behavior of internal operators occurs thedata will lead to construction rework or even disaster Inour scheme we combine BIM with blockchain and takeadvantage of the decentralization of blockchain Since theuse of distributed billing and storage there is no centralizedhardware or management organization that is the rightsand obligations of any node are the same In addition the

Mathematical Problems in Engineering 5

data blocks in BIM system are maintained by the nodes withmaintenance function in the whole system

4 Proposed Scheme

Our solution is briefly described in the above section and thedetails of our solution are detailed in this section

41 Proposed Basic Architecture In this section we pro-pose the mobile cloud BIM architecture for further ICTparadigms

411 BIM as a Service BIMaaS BIMaaS is a cloud service forproviding outsourced BIM data storage and computation Itcan be looked as a united virtual central server by harvestingmultiple computing resources which provides an on-demandstorage and computation service BIMaaS is managed bydedicated cloud computing software It can smoothly respondto any storage and computation requests by migrating orredistributing the tasks to a resource pool which is trans-parent to users Thus users do not need to care about theimplementation details on BIMaaS and just look it as a virtualserver

The BIMaaS can be further classified into two folders(1) BIM data are outsourced to a public cloud that is

provided by cloud service companies such as AWS AzureandAliYun Such public cloud service is paid according to theresource requirements The initial investment for hardwareand software is avoided as both of them are rented from thepublic BIMaaS It can obviously decrease the startup budgetfor small business in AEC industry Besides the managementof BIMaaS can also be outsourced to public BIMaaS thepersonnel enrollments and cost for human resourcesmay alsobe alleviated(2) For some giant companies in AEC industry it may

be possible to integrate private BIMaaS by themselves Suchcompanies have already deployed an information infrastruc-ture such as data center before They usually have their ICTdivision and have a large number of human resources for ICTsupports Thus they construct their private BIMaaS servicesvia some publicly available software tools such as OpenStack

412 Big Data Sharing among BIMaaS With the develop-ment of BIMaaS BIM data is accumulated with time elapsingand project conducting Even for one building a large volumeof BIM data is aggregated Once revision occurs during aconstruction life time all historical data may also be snapshotand stored for further audit For example once a designfor a model is modified all legacy versions may also bestored respectively for tracing revised model locations andparameters When such traceability is required for criticalstructures or components an additive data organization withprovenance capability will be required In addition BIMdata sharing should be a trend once the data is accumulatedsufficiently large For example for different buildings in thesame category BIM data can be mutually accessed or refer-enced among them Some validated best practices and designexperiences can be migrated from one project (building)

to another Some common characteristics in design can beabstracted by data mining or machine learning Informationexchanges between BIM data will let users form a global viewof specific design in multiple projects

413 Pervasively Accessing by Mobile Terminals Anyone canaccess BIM data and revoke the BIM computation servicesuch as model visualization from BIMaaS or big data poolMobile terminal is a convenient tool for mobile usersespecially field engineers in smart construction It is a hand-held device that can access the BIM information any timeanywhere by wireless It can be divided into two folders asfollows(1) Mobile terminals can be hand-held devices such as

smart phones tablets laptops and so on Currently suchdevices are largely used as personal computing tools By themdesigners can verify the conformation of engineering regu-lation the monitors can check the schedules of engineeringprocedures the suppliers can consult the future requirementsfor material resources(2) Mobile terminals can be wearable devices such as

smart watches smart glasses and smart helmets Those areequipped with sensors for instant information collectionor displayers for smooth human-machine interaction Forexample wireless sensors for environmental monitors 3Dinformation presentation such as Virtual Reality (VR) orAugmented Reality (AR) It can improve operational effi-ciency especially for field engineers in a limited space Itcan support smart and automatic construction scenarios Forexample smart helmet for engineers on constructing fieldsmay access BIM data remotely and reconstruct VR by thelatest data Construction robots may access BIM data andcollect sensing information from sensors in constructingfields to evaluate sustainable design parameters for greenhouses

414 Automatically Exchanging by Internet of Things Inter-net of Things (IoTs) is a network with wireless sensors Insmart construction those sensors may deploy with facilitiesin operational fields with Internet accessing via wirelesscommunications such as 4G or NB-IOT Those sensors cancollect the construction environmental data and upload theminto BIMaaS server once those data can help the revisionor improvement of the design in BIM For example windand sunshine design evaluation for green construction canbe justified or amended after analysis from the field sensingdata during the construction This feedback will enhancethe initial design in BIM that only relies on simulationor emulation but also is manipulated from realistic on-site parameters Moreover the construction engineeringmachines (eg crane) that are equipped wireless devicescan also access BIM data in BIMaaS They may access theBIM information automatically and display the result tooperators to guide the future instructions Some equipmentsuch as surveillance video cameras can automatically set upthe direction of lens by fetch specific installation data fromBIMaaS

6 Mathematical Problems in Engineering

In summary BIMaaS provides a storage and computationservice for BIM data including data retrieval data updat-ing and data computation BIM big data is accumulativelymerged and shared to form a unified resource pool forresponding on-demanded requests from traditional desktopPCs or especially mobile terminals in construction fieldsSome special wearable devices such as helmets may providemore enhancement for BIM information presentation BIMdata can be accessed any time anywhere not only by mobiledevices but also by wireless sensors Those sensors createIoTs to collect critical data about on-site construction ontime The analysis on those data can help reevaluate thequality of design or construction and provide amendingfeedback Moreover IoT devices on construction machinecan access and display BIM data to empower the intelligenceof construction machines This architecture not only enablesthe pervasive retrievals of BIM information but also supportsthe ubiquitous information exchanging or cooperativelyconstructing It provides a promising framework for theexchanging and sharing of BIM data in smart construction

415 Structure of Blockchain Blockchain is a distributedledger a technical solution to collectively maintain a reliabledatabase throughdecentralized trustedways and blockchainis a distributed database that is almost impossible to changeldquoDistributedrdquo here is not only a distributed storage of databut also a distributed record of data (ie shared by thesystem participants) blockchain is not a single technologybut a result of a variety of technology integration thesetechnologies are in a new structure together to form a newway of data recording storage and expression Combinedwith these technologies the contents of the scheme afteradopting the present inventionwill be difficult to bemodifiedand the security can be improved

Data stored using blockchain technology is also timeseries tamper-proof forged and privacy-pending which isproven in many documents bcBIM also inherits these fea-tures and guarantees the absolute security of the informationdata from two aspects one is to ensure that the pseudo-blockdoes not appear on the blockchain

Each node in the receipt of the new block will be the blockvalidation pseudo-block because it can not be verified will bediscarded and will not be written into the blockchain if themalicious node would like to use pseudo-branched chain toreplace the correct blockchain which is the computing powerof todayrsquos computer which is almost impossible to achieve thetask the other is to ensure that the data in the chain will notbe modified Because each chunk contains the hash value ofthe previous chunk if the malicious node changes a chunk ofdata you must change the chunk behind all the blocks whichare changed but also in the future with their own pseudo-branched chain to cover the correct blockchain in terms ofmodern computer capabilities this is also an impossible task

The basic processing unit of blockchain technology is adata block that stores all transaction data and related verifica-tion information for a certain period of time The blockchainis combined into a specific data structure in chronologicalorder which forms the nontamper and nonfalsification data

sharing information guaranteed by cryptography and usesthe SHA 256 algorithm and theMerkle tree to realize the datamanagement system with simple and safe storage successiverelation efficient and fast verification [27]

Block is the basic unit of block chain which is composedof blocks and blocks The block header contains blockID version number previous block hash value timestampMerkle root the block target hash value and so onThemainbody of the block contains the main data information ofthe block including identity certificate transaction contentamount of breach of contract and so on (Figure 1)

The characteristic of BIM data organization methodbased on blockchain is that each newly generated block savesthe hash value of the previous block Therefore we combineBIM with blockchain to provide BIM data organizationmethod which can track prove and prevent tampering ofBIM historical data At the same time it can generate unifiedformat to support open sharing of future data

42 Blockchain-Based Model for Audit and Provenance Inthis section we propose to use blockchain to facilitate theaudit and provenance of historical BIM data

Blockchain consists of a data structurewith cryptographichash value to guarantee the integrity of a serial data Themajor items in proposed blockchain-based model are asfollows (= denotes that ldquois defined asrdquo)

(1) Block = ⟨119861119897119900119888119896119867119890119886119889119863119886119905119886⟩ 119861119897119900119888119896119867119890119886119889 guaran-tees the integrity (nonmodification) of 119863119886119905119886 andmodifying history of 119863119886119905119886

(2) BlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎNonce Difficulty Timestamp⟩ The 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ is the hash value of the intermediate previousblock head 119863119886119905119886119867119886119904ℎ is the hash value of 119863119886119905119886 inthis block 119873119900119899119888119890 is a value to be determined byrandomly checking whetherZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 119885119890119903119900(sdot) is afunction that returns the number of left consecutivezeros in an inputting string in bytes 119863119894119891119891119894119888119906119897119905119910 isan integer to tell the requirement on how manyconsecutive zeros in the head of hash result Forexample 119863119894119891119891119894119888119906119897119905119910 = 2 means the first 2 bytes oftarget hash outputting is 0 That is the first 2 bytesof 119867119886119904ℎ(sdot) is 0 119879119894119898119890119904119905119886119898119901 is the time snapshot ofcurrent packaging block

(3) Data = ⟨119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886⟩ 119872119890119905119886119889119886119905119886 is anoptional tuple for data description on 119861119868119872119889119886119905119886which can be empty The 119861119868119872119889119886119905119886 is a mandatorytuple for concrete BIM data Once BIM data ismodified 119863119886119905119886 will be created and wait for beingappended into blockchain in a batch

(4) 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) where119861119897119900119888119896119867119890119886119889 is the previous blockhead where119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ tuple is located That is the hashvalue of previous blockhead is embedded into nextblock head It can also be looked as a link of twoadjacent block heads

Mathematical Problems in Engineering 7

Block Header

Field Description

Version Block Version Number

Previous Block HashHash of the previous block

in the chain

Merkle Tree RootHash of the Merkle tree root

Timestamp Creation time of this block

Targeted Difficultye Proof-Of-Work

difficulty target

Nonce

2IIN-

A counter for the Proof-Of-Work

Figure 1 Format of block

(5) 119863119886119905119886119867119886119904ℎ = Hash(1198611198681198721198891198861199051198861 1198611198681198721198891198861199051198862 sdot sdot sdot 119861119868119872119889119886119905119886119899) Suppose the number of BIM in thistime-span is 119899 That is it is the numbers of BIMdata that will be packaged in blockchain during ablock generation period 119863119886119905119886119867119886119904ℎ guarantees theintegrity of block contents consisting ofmodifiedBIMdata

The purpose of blockchain is to record the historical pro-cess of BIM record modification A blockhead is composedof multiple BIM data which can speed up the uplink of BIMrecord modification The necessary BIM data need to recordthe history of modification but the ordinary BIM can notimplement it The method of calculating block hash valuescan get hash values of all uplink BIM data more quickly andefficiently than calculating Merkle tree roots We propose aBIM via blockchain to storage data which solve the problemof tracing proving and preventing tampering with BIMhistorical data At the same time it can generate a unifiedformat to support future open sharing This method uses thehash structure of blockhead to ensure the integrity of all blockdata In addition block integrity is guaranteed by hash valueand the signature guarantees blockheadrsquos integrity The valueof hash andnonce in blockhead guarantees fair consensus andnontampering

43 Example Public Blockchain bcBIM In this scene theblockchain-based BIM data organization method is based ona decentralized measure also known as a public blockchainmethod which includes the following steps

(1) Each node of the public blockchain denoted as B isusually a node with its own independent BIM data Itis necessary to establish the openness and sharing ofBIM data among all nodes and maintain irreparabledata modification and traceability of time

(2) The central node of the public blockchain records theBIM data which need to be saved in the local storagemedium and uniformly packs it into the blockhead atevery P time

(3) Assume that the BIM data recorded in P time are11986111986811987211198611198681198722 119861119868119872119899 The method of uniformlypacking blocks into blockheads is as follows Blocksare recorded asBIMDATA and the components of theblocks include 11986111986811987211198611198681198722 119861119868119872119899 each BIMiincludes metadata modified BIM data and accessaddress ofmodifiedBIMdata calculate119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899)

(4) The blockhead is named BIMHEAD its compo-sition includes PreviousHash BIMHASH LinkOf-DATA Timestamp and NonceandRequirement Pre-viousHash is the hash value of the previous block-head LinkofDATA is the access address of cur-rent block BIMDATA Timestamp is a time stampfor building blockheads Nonce is a random num-ber Requirement is a requirement for hash valuethat is 119867119886119904ℎ(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119874119891119863119860119879119860 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890 119868119863) meetsthe Requirement

8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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4 Mathematical Problems in Engineering

high-power nodes and rather requires the confirmation of allnetwork nodes(2) Transaction costs are very low compared with public

and consortium blockchain(3) Since the privacy of receipts is limited it is difficult for

participants to obtain data on private blockchain that is theprivacy protection is better than others

The disadvantage of private blockchain is as followsthe risk of receiving attacks is higher because it can bemanipulated price or modified code

Unlike private blockchain consortium blockchain hasseveral organizations or institutions which participating inthe management Each organization or institution controlsone or more nodes and they record transaction data togetherOnly organizations and institutions which have relevantauthorities can read write or send transaction data onconsortium blockchain Since it only opens parts of func-tions to members the permissions and accounting rules onconsortium blockchain are ldquocustomizedrdquo according to theconsortium The consensus process is controlled by prese-lected nodes on consortium blockchain It is suitable for B2Bscenarios such as interagency transactions settlement andliquidation For example many financial institutions connecttheir blockchain networks together to form a consortiumnet-work which facilitates data docking and collaboration Forexample R3 Hyperledger and Golden Chain Consortiumeach node has its corresponding entity or organization onconsortium blockchain Only authorized to join or exit thenetwork which is aiming at reducing costs and improvingefficiency In addition it is also suitable for scenarios suchas transaction and settlement between different entitiesConsortium blockchain is maintained by the participatingmember organizations and provides a complete set of safetymanagement functions such as management certificationauthorization monitoring and auditing of the participatingmembers For example the R3 consortium is a consortiumblockchain of banking industry which was established in2015 At present it has joined more than 40 membersincluding world famous banks such as JPMorgan ChaseHSBC and Goldman Sachs Each bank can become a nodebut the transfer behavior of one bank must be confirmed byother bank nodes (23 number) in order to make the blockeffective Nowadays BIM is usually used internally such asa bridge design institute architectural design institute and alarge group company In addition almost no POWconsensusmechanism is used in consortium blockchain but consensusalgorithms such as proof of rights or PBTF are used Theadvantages of consortium blockchain are as follows(1) Due to the fact that the number of nodes has been

streamlined consortium blockchain has faster transactionspeed and lower cost(2) Compared with public blockchain consortium

blockchain requires more transactions to be confirmed perunit time

The disadvantage of consortium blockchain is as followsthe safety and performance requirements are relatively high

Considering that contemporary green construction isassembled building we discuss how to establish a BIMshared component library One of the applications of public

blockchain is recording BIM database which can be addedby anyone that is it can form BIM shared componentlibrary We propose this scheme as an advanced model withPOWmechanism In addition public blockchain is a kind ofnontampering account book and it is the most widely usedblockchain at present In addition public blockchain estab-lishes a centralized autonomous organization which can bebooks electricity transactions big data transactions or BIMdatabase Bitcoin and Ethernet are the most popular publicblockchain which means the behavior of public blockchainis open However it is not controlled by anyone nor ownedby anyone it is a ldquocompletely decentralizedrdquo blockchain Theadvantages of public blockchain are as follows(1)The access threshold is so low that any user with an

Internet-connected computer can access it(2) Open and transparent since the whole system is

ldquocompletely decentralizedrdquo the process of running the systemis open and transparent(3) Anonymity since nodes do not need to trust each

other all operations can be performed anonymously that isthe privacy is well protected(4) Free from the influence of the developer reading

and writing public blockchain data are not controlled by anyorganization or individual so it can also protect users fromprogrammers

The disadvantages of public blockchain are as follows lowefficiency large power consumption and long time requiredto validate and complete transactions

32 AdversaryModel In this section we identify four poten-tial vulnerabilities that can be exploited by our opponents toundermine our solutions (1) the modified content cannot betraced to its source (2) the integrity of the historical data istampered with the last modification record (3) attacks fromthe central operator cannot be recorded and tracking Somemodifications of BIM data may be unavoidable in construc-tion for example design modifications due to budget or hostrequirements The revision of BIM data is usually updatedrather than retaining the revision historyTherefore attackersmay be able to modify the source of BIM data In our schemewe combine BIMwith blockchain to ensure that the source ofBIM data is not modified

As mentioned above the traditional BIM model onlyretains the last modification record In the process of revisingBIM data even if the update record is stored the historicaldata can be modified by attackers and the integrity of thehistorical data is difficult to guarantee In our model theintegrity of historical data can be guaranteed by using thetraceability of blockchain and the nontampering character-istics of information In traditional BIM model recordingupdates depend on the full trust of the central operatoronce improper behavior of internal operators occurs thedata will lead to construction rework or even disaster Inour scheme we combine BIM with blockchain and takeadvantage of the decentralization of blockchain Since theuse of distributed billing and storage there is no centralizedhardware or management organization that is the rightsand obligations of any node are the same In addition the

Mathematical Problems in Engineering 5

data blocks in BIM system are maintained by the nodes withmaintenance function in the whole system

4 Proposed Scheme

Our solution is briefly described in the above section and thedetails of our solution are detailed in this section

41 Proposed Basic Architecture In this section we pro-pose the mobile cloud BIM architecture for further ICTparadigms

411 BIM as a Service BIMaaS BIMaaS is a cloud service forproviding outsourced BIM data storage and computation Itcan be looked as a united virtual central server by harvestingmultiple computing resources which provides an on-demandstorage and computation service BIMaaS is managed bydedicated cloud computing software It can smoothly respondto any storage and computation requests by migrating orredistributing the tasks to a resource pool which is trans-parent to users Thus users do not need to care about theimplementation details on BIMaaS and just look it as a virtualserver

The BIMaaS can be further classified into two folders(1) BIM data are outsourced to a public cloud that is

provided by cloud service companies such as AWS AzureandAliYun Such public cloud service is paid according to theresource requirements The initial investment for hardwareand software is avoided as both of them are rented from thepublic BIMaaS It can obviously decrease the startup budgetfor small business in AEC industry Besides the managementof BIMaaS can also be outsourced to public BIMaaS thepersonnel enrollments and cost for human resourcesmay alsobe alleviated(2) For some giant companies in AEC industry it may

be possible to integrate private BIMaaS by themselves Suchcompanies have already deployed an information infrastruc-ture such as data center before They usually have their ICTdivision and have a large number of human resources for ICTsupports Thus they construct their private BIMaaS servicesvia some publicly available software tools such as OpenStack

412 Big Data Sharing among BIMaaS With the develop-ment of BIMaaS BIM data is accumulated with time elapsingand project conducting Even for one building a large volumeof BIM data is aggregated Once revision occurs during aconstruction life time all historical data may also be snapshotand stored for further audit For example once a designfor a model is modified all legacy versions may also bestored respectively for tracing revised model locations andparameters When such traceability is required for criticalstructures or components an additive data organization withprovenance capability will be required In addition BIMdata sharing should be a trend once the data is accumulatedsufficiently large For example for different buildings in thesame category BIM data can be mutually accessed or refer-enced among them Some validated best practices and designexperiences can be migrated from one project (building)

to another Some common characteristics in design can beabstracted by data mining or machine learning Informationexchanges between BIM data will let users form a global viewof specific design in multiple projects

413 Pervasively Accessing by Mobile Terminals Anyone canaccess BIM data and revoke the BIM computation servicesuch as model visualization from BIMaaS or big data poolMobile terminal is a convenient tool for mobile usersespecially field engineers in smart construction It is a hand-held device that can access the BIM information any timeanywhere by wireless It can be divided into two folders asfollows(1) Mobile terminals can be hand-held devices such as

smart phones tablets laptops and so on Currently suchdevices are largely used as personal computing tools By themdesigners can verify the conformation of engineering regu-lation the monitors can check the schedules of engineeringprocedures the suppliers can consult the future requirementsfor material resources(2) Mobile terminals can be wearable devices such as

smart watches smart glasses and smart helmets Those areequipped with sensors for instant information collectionor displayers for smooth human-machine interaction Forexample wireless sensors for environmental monitors 3Dinformation presentation such as Virtual Reality (VR) orAugmented Reality (AR) It can improve operational effi-ciency especially for field engineers in a limited space Itcan support smart and automatic construction scenarios Forexample smart helmet for engineers on constructing fieldsmay access BIM data remotely and reconstruct VR by thelatest data Construction robots may access BIM data andcollect sensing information from sensors in constructingfields to evaluate sustainable design parameters for greenhouses

414 Automatically Exchanging by Internet of Things Inter-net of Things (IoTs) is a network with wireless sensors Insmart construction those sensors may deploy with facilitiesin operational fields with Internet accessing via wirelesscommunications such as 4G or NB-IOT Those sensors cancollect the construction environmental data and upload theminto BIMaaS server once those data can help the revisionor improvement of the design in BIM For example windand sunshine design evaluation for green construction canbe justified or amended after analysis from the field sensingdata during the construction This feedback will enhancethe initial design in BIM that only relies on simulationor emulation but also is manipulated from realistic on-site parameters Moreover the construction engineeringmachines (eg crane) that are equipped wireless devicescan also access BIM data in BIMaaS They may access theBIM information automatically and display the result tooperators to guide the future instructions Some equipmentsuch as surveillance video cameras can automatically set upthe direction of lens by fetch specific installation data fromBIMaaS

6 Mathematical Problems in Engineering

In summary BIMaaS provides a storage and computationservice for BIM data including data retrieval data updat-ing and data computation BIM big data is accumulativelymerged and shared to form a unified resource pool forresponding on-demanded requests from traditional desktopPCs or especially mobile terminals in construction fieldsSome special wearable devices such as helmets may providemore enhancement for BIM information presentation BIMdata can be accessed any time anywhere not only by mobiledevices but also by wireless sensors Those sensors createIoTs to collect critical data about on-site construction ontime The analysis on those data can help reevaluate thequality of design or construction and provide amendingfeedback Moreover IoT devices on construction machinecan access and display BIM data to empower the intelligenceof construction machines This architecture not only enablesthe pervasive retrievals of BIM information but also supportsthe ubiquitous information exchanging or cooperativelyconstructing It provides a promising framework for theexchanging and sharing of BIM data in smart construction

415 Structure of Blockchain Blockchain is a distributedledger a technical solution to collectively maintain a reliabledatabase throughdecentralized trustedways and blockchainis a distributed database that is almost impossible to changeldquoDistributedrdquo here is not only a distributed storage of databut also a distributed record of data (ie shared by thesystem participants) blockchain is not a single technologybut a result of a variety of technology integration thesetechnologies are in a new structure together to form a newway of data recording storage and expression Combinedwith these technologies the contents of the scheme afteradopting the present inventionwill be difficult to bemodifiedand the security can be improved

Data stored using blockchain technology is also timeseries tamper-proof forged and privacy-pending which isproven in many documents bcBIM also inherits these fea-tures and guarantees the absolute security of the informationdata from two aspects one is to ensure that the pseudo-blockdoes not appear on the blockchain

Each node in the receipt of the new block will be the blockvalidation pseudo-block because it can not be verified will bediscarded and will not be written into the blockchain if themalicious node would like to use pseudo-branched chain toreplace the correct blockchain which is the computing powerof todayrsquos computer which is almost impossible to achieve thetask the other is to ensure that the data in the chain will notbe modified Because each chunk contains the hash value ofthe previous chunk if the malicious node changes a chunk ofdata you must change the chunk behind all the blocks whichare changed but also in the future with their own pseudo-branched chain to cover the correct blockchain in terms ofmodern computer capabilities this is also an impossible task

The basic processing unit of blockchain technology is adata block that stores all transaction data and related verifica-tion information for a certain period of time The blockchainis combined into a specific data structure in chronologicalorder which forms the nontamper and nonfalsification data

sharing information guaranteed by cryptography and usesthe SHA 256 algorithm and theMerkle tree to realize the datamanagement system with simple and safe storage successiverelation efficient and fast verification [27]

Block is the basic unit of block chain which is composedof blocks and blocks The block header contains blockID version number previous block hash value timestampMerkle root the block target hash value and so onThemainbody of the block contains the main data information ofthe block including identity certificate transaction contentamount of breach of contract and so on (Figure 1)

The characteristic of BIM data organization methodbased on blockchain is that each newly generated block savesthe hash value of the previous block Therefore we combineBIM with blockchain to provide BIM data organizationmethod which can track prove and prevent tampering ofBIM historical data At the same time it can generate unifiedformat to support open sharing of future data

42 Blockchain-Based Model for Audit and Provenance Inthis section we propose to use blockchain to facilitate theaudit and provenance of historical BIM data

Blockchain consists of a data structurewith cryptographichash value to guarantee the integrity of a serial data Themajor items in proposed blockchain-based model are asfollows (= denotes that ldquois defined asrdquo)

(1) Block = ⟨119861119897119900119888119896119867119890119886119889119863119886119905119886⟩ 119861119897119900119888119896119867119890119886119889 guaran-tees the integrity (nonmodification) of 119863119886119905119886 andmodifying history of 119863119886119905119886

(2) BlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎNonce Difficulty Timestamp⟩ The 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ is the hash value of the intermediate previousblock head 119863119886119905119886119867119886119904ℎ is the hash value of 119863119886119905119886 inthis block 119873119900119899119888119890 is a value to be determined byrandomly checking whetherZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 119885119890119903119900(sdot) is afunction that returns the number of left consecutivezeros in an inputting string in bytes 119863119894119891119891119894119888119906119897119905119910 isan integer to tell the requirement on how manyconsecutive zeros in the head of hash result Forexample 119863119894119891119891119894119888119906119897119905119910 = 2 means the first 2 bytes oftarget hash outputting is 0 That is the first 2 bytesof 119867119886119904ℎ(sdot) is 0 119879119894119898119890119904119905119886119898119901 is the time snapshot ofcurrent packaging block

(3) Data = ⟨119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886⟩ 119872119890119905119886119889119886119905119886 is anoptional tuple for data description on 119861119868119872119889119886119905119886which can be empty The 119861119868119872119889119886119905119886 is a mandatorytuple for concrete BIM data Once BIM data ismodified 119863119886119905119886 will be created and wait for beingappended into blockchain in a batch

(4) 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) where119861119897119900119888119896119867119890119886119889 is the previous blockhead where119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ tuple is located That is the hashvalue of previous blockhead is embedded into nextblock head It can also be looked as a link of twoadjacent block heads

Mathematical Problems in Engineering 7

Block Header

Field Description

Version Block Version Number

Previous Block HashHash of the previous block

in the chain

Merkle Tree RootHash of the Merkle tree root

Timestamp Creation time of this block

Targeted Difficultye Proof-Of-Work

difficulty target

Nonce

2IIN-

A counter for the Proof-Of-Work

Figure 1 Format of block

(5) 119863119886119905119886119867119886119904ℎ = Hash(1198611198681198721198891198861199051198861 1198611198681198721198891198861199051198862 sdot sdot sdot 119861119868119872119889119886119905119886119899) Suppose the number of BIM in thistime-span is 119899 That is it is the numbers of BIMdata that will be packaged in blockchain during ablock generation period 119863119886119905119886119867119886119904ℎ guarantees theintegrity of block contents consisting ofmodifiedBIMdata

The purpose of blockchain is to record the historical pro-cess of BIM record modification A blockhead is composedof multiple BIM data which can speed up the uplink of BIMrecord modification The necessary BIM data need to recordthe history of modification but the ordinary BIM can notimplement it The method of calculating block hash valuescan get hash values of all uplink BIM data more quickly andefficiently than calculating Merkle tree roots We propose aBIM via blockchain to storage data which solve the problemof tracing proving and preventing tampering with BIMhistorical data At the same time it can generate a unifiedformat to support future open sharing This method uses thehash structure of blockhead to ensure the integrity of all blockdata In addition block integrity is guaranteed by hash valueand the signature guarantees blockheadrsquos integrity The valueof hash andnonce in blockhead guarantees fair consensus andnontampering

43 Example Public Blockchain bcBIM In this scene theblockchain-based BIM data organization method is based ona decentralized measure also known as a public blockchainmethod which includes the following steps

(1) Each node of the public blockchain denoted as B isusually a node with its own independent BIM data Itis necessary to establish the openness and sharing ofBIM data among all nodes and maintain irreparabledata modification and traceability of time

(2) The central node of the public blockchain records theBIM data which need to be saved in the local storagemedium and uniformly packs it into the blockhead atevery P time

(3) Assume that the BIM data recorded in P time are11986111986811987211198611198681198722 119861119868119872119899 The method of uniformlypacking blocks into blockheads is as follows Blocksare recorded asBIMDATA and the components of theblocks include 11986111986811987211198611198681198722 119861119868119872119899 each BIMiincludes metadata modified BIM data and accessaddress ofmodifiedBIMdata calculate119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899)

(4) The blockhead is named BIMHEAD its compo-sition includes PreviousHash BIMHASH LinkOf-DATA Timestamp and NonceandRequirement Pre-viousHash is the hash value of the previous block-head LinkofDATA is the access address of cur-rent block BIMDATA Timestamp is a time stampfor building blockheads Nonce is a random num-ber Requirement is a requirement for hash valuethat is 119867119886119904ℎ(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119874119891119863119860119879119860 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890 119868119863) meetsthe Requirement

8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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Mathematical Problems in Engineering 5

data blocks in BIM system are maintained by the nodes withmaintenance function in the whole system

4 Proposed Scheme

Our solution is briefly described in the above section and thedetails of our solution are detailed in this section

41 Proposed Basic Architecture In this section we pro-pose the mobile cloud BIM architecture for further ICTparadigms

411 BIM as a Service BIMaaS BIMaaS is a cloud service forproviding outsourced BIM data storage and computation Itcan be looked as a united virtual central server by harvestingmultiple computing resources which provides an on-demandstorage and computation service BIMaaS is managed bydedicated cloud computing software It can smoothly respondto any storage and computation requests by migrating orredistributing the tasks to a resource pool which is trans-parent to users Thus users do not need to care about theimplementation details on BIMaaS and just look it as a virtualserver

The BIMaaS can be further classified into two folders(1) BIM data are outsourced to a public cloud that is

provided by cloud service companies such as AWS AzureandAliYun Such public cloud service is paid according to theresource requirements The initial investment for hardwareand software is avoided as both of them are rented from thepublic BIMaaS It can obviously decrease the startup budgetfor small business in AEC industry Besides the managementof BIMaaS can also be outsourced to public BIMaaS thepersonnel enrollments and cost for human resourcesmay alsobe alleviated(2) For some giant companies in AEC industry it may

be possible to integrate private BIMaaS by themselves Suchcompanies have already deployed an information infrastruc-ture such as data center before They usually have their ICTdivision and have a large number of human resources for ICTsupports Thus they construct their private BIMaaS servicesvia some publicly available software tools such as OpenStack

412 Big Data Sharing among BIMaaS With the develop-ment of BIMaaS BIM data is accumulated with time elapsingand project conducting Even for one building a large volumeof BIM data is aggregated Once revision occurs during aconstruction life time all historical data may also be snapshotand stored for further audit For example once a designfor a model is modified all legacy versions may also bestored respectively for tracing revised model locations andparameters When such traceability is required for criticalstructures or components an additive data organization withprovenance capability will be required In addition BIMdata sharing should be a trend once the data is accumulatedsufficiently large For example for different buildings in thesame category BIM data can be mutually accessed or refer-enced among them Some validated best practices and designexperiences can be migrated from one project (building)

to another Some common characteristics in design can beabstracted by data mining or machine learning Informationexchanges between BIM data will let users form a global viewof specific design in multiple projects

413 Pervasively Accessing by Mobile Terminals Anyone canaccess BIM data and revoke the BIM computation servicesuch as model visualization from BIMaaS or big data poolMobile terminal is a convenient tool for mobile usersespecially field engineers in smart construction It is a hand-held device that can access the BIM information any timeanywhere by wireless It can be divided into two folders asfollows(1) Mobile terminals can be hand-held devices such as

smart phones tablets laptops and so on Currently suchdevices are largely used as personal computing tools By themdesigners can verify the conformation of engineering regu-lation the monitors can check the schedules of engineeringprocedures the suppliers can consult the future requirementsfor material resources(2) Mobile terminals can be wearable devices such as

smart watches smart glasses and smart helmets Those areequipped with sensors for instant information collectionor displayers for smooth human-machine interaction Forexample wireless sensors for environmental monitors 3Dinformation presentation such as Virtual Reality (VR) orAugmented Reality (AR) It can improve operational effi-ciency especially for field engineers in a limited space Itcan support smart and automatic construction scenarios Forexample smart helmet for engineers on constructing fieldsmay access BIM data remotely and reconstruct VR by thelatest data Construction robots may access BIM data andcollect sensing information from sensors in constructingfields to evaluate sustainable design parameters for greenhouses

414 Automatically Exchanging by Internet of Things Inter-net of Things (IoTs) is a network with wireless sensors Insmart construction those sensors may deploy with facilitiesin operational fields with Internet accessing via wirelesscommunications such as 4G or NB-IOT Those sensors cancollect the construction environmental data and upload theminto BIMaaS server once those data can help the revisionor improvement of the design in BIM For example windand sunshine design evaluation for green construction canbe justified or amended after analysis from the field sensingdata during the construction This feedback will enhancethe initial design in BIM that only relies on simulationor emulation but also is manipulated from realistic on-site parameters Moreover the construction engineeringmachines (eg crane) that are equipped wireless devicescan also access BIM data in BIMaaS They may access theBIM information automatically and display the result tooperators to guide the future instructions Some equipmentsuch as surveillance video cameras can automatically set upthe direction of lens by fetch specific installation data fromBIMaaS

6 Mathematical Problems in Engineering

In summary BIMaaS provides a storage and computationservice for BIM data including data retrieval data updat-ing and data computation BIM big data is accumulativelymerged and shared to form a unified resource pool forresponding on-demanded requests from traditional desktopPCs or especially mobile terminals in construction fieldsSome special wearable devices such as helmets may providemore enhancement for BIM information presentation BIMdata can be accessed any time anywhere not only by mobiledevices but also by wireless sensors Those sensors createIoTs to collect critical data about on-site construction ontime The analysis on those data can help reevaluate thequality of design or construction and provide amendingfeedback Moreover IoT devices on construction machinecan access and display BIM data to empower the intelligenceof construction machines This architecture not only enablesthe pervasive retrievals of BIM information but also supportsthe ubiquitous information exchanging or cooperativelyconstructing It provides a promising framework for theexchanging and sharing of BIM data in smart construction

415 Structure of Blockchain Blockchain is a distributedledger a technical solution to collectively maintain a reliabledatabase throughdecentralized trustedways and blockchainis a distributed database that is almost impossible to changeldquoDistributedrdquo here is not only a distributed storage of databut also a distributed record of data (ie shared by thesystem participants) blockchain is not a single technologybut a result of a variety of technology integration thesetechnologies are in a new structure together to form a newway of data recording storage and expression Combinedwith these technologies the contents of the scheme afteradopting the present inventionwill be difficult to bemodifiedand the security can be improved

Data stored using blockchain technology is also timeseries tamper-proof forged and privacy-pending which isproven in many documents bcBIM also inherits these fea-tures and guarantees the absolute security of the informationdata from two aspects one is to ensure that the pseudo-blockdoes not appear on the blockchain

Each node in the receipt of the new block will be the blockvalidation pseudo-block because it can not be verified will bediscarded and will not be written into the blockchain if themalicious node would like to use pseudo-branched chain toreplace the correct blockchain which is the computing powerof todayrsquos computer which is almost impossible to achieve thetask the other is to ensure that the data in the chain will notbe modified Because each chunk contains the hash value ofthe previous chunk if the malicious node changes a chunk ofdata you must change the chunk behind all the blocks whichare changed but also in the future with their own pseudo-branched chain to cover the correct blockchain in terms ofmodern computer capabilities this is also an impossible task

The basic processing unit of blockchain technology is adata block that stores all transaction data and related verifica-tion information for a certain period of time The blockchainis combined into a specific data structure in chronologicalorder which forms the nontamper and nonfalsification data

sharing information guaranteed by cryptography and usesthe SHA 256 algorithm and theMerkle tree to realize the datamanagement system with simple and safe storage successiverelation efficient and fast verification [27]

Block is the basic unit of block chain which is composedof blocks and blocks The block header contains blockID version number previous block hash value timestampMerkle root the block target hash value and so onThemainbody of the block contains the main data information ofthe block including identity certificate transaction contentamount of breach of contract and so on (Figure 1)

The characteristic of BIM data organization methodbased on blockchain is that each newly generated block savesthe hash value of the previous block Therefore we combineBIM with blockchain to provide BIM data organizationmethod which can track prove and prevent tampering ofBIM historical data At the same time it can generate unifiedformat to support open sharing of future data

42 Blockchain-Based Model for Audit and Provenance Inthis section we propose to use blockchain to facilitate theaudit and provenance of historical BIM data

Blockchain consists of a data structurewith cryptographichash value to guarantee the integrity of a serial data Themajor items in proposed blockchain-based model are asfollows (= denotes that ldquois defined asrdquo)

(1) Block = ⟨119861119897119900119888119896119867119890119886119889119863119886119905119886⟩ 119861119897119900119888119896119867119890119886119889 guaran-tees the integrity (nonmodification) of 119863119886119905119886 andmodifying history of 119863119886119905119886

(2) BlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎNonce Difficulty Timestamp⟩ The 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ is the hash value of the intermediate previousblock head 119863119886119905119886119867119886119904ℎ is the hash value of 119863119886119905119886 inthis block 119873119900119899119888119890 is a value to be determined byrandomly checking whetherZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 119885119890119903119900(sdot) is afunction that returns the number of left consecutivezeros in an inputting string in bytes 119863119894119891119891119894119888119906119897119905119910 isan integer to tell the requirement on how manyconsecutive zeros in the head of hash result Forexample 119863119894119891119891119894119888119906119897119905119910 = 2 means the first 2 bytes oftarget hash outputting is 0 That is the first 2 bytesof 119867119886119904ℎ(sdot) is 0 119879119894119898119890119904119905119886119898119901 is the time snapshot ofcurrent packaging block

(3) Data = ⟨119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886⟩ 119872119890119905119886119889119886119905119886 is anoptional tuple for data description on 119861119868119872119889119886119905119886which can be empty The 119861119868119872119889119886119905119886 is a mandatorytuple for concrete BIM data Once BIM data ismodified 119863119886119905119886 will be created and wait for beingappended into blockchain in a batch

(4) 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) where119861119897119900119888119896119867119890119886119889 is the previous blockhead where119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ tuple is located That is the hashvalue of previous blockhead is embedded into nextblock head It can also be looked as a link of twoadjacent block heads

Mathematical Problems in Engineering 7

Block Header

Field Description

Version Block Version Number

Previous Block HashHash of the previous block

in the chain

Merkle Tree RootHash of the Merkle tree root

Timestamp Creation time of this block

Targeted Difficultye Proof-Of-Work

difficulty target

Nonce

2IIN-

A counter for the Proof-Of-Work

Figure 1 Format of block

(5) 119863119886119905119886119867119886119904ℎ = Hash(1198611198681198721198891198861199051198861 1198611198681198721198891198861199051198862 sdot sdot sdot 119861119868119872119889119886119905119886119899) Suppose the number of BIM in thistime-span is 119899 That is it is the numbers of BIMdata that will be packaged in blockchain during ablock generation period 119863119886119905119886119867119886119904ℎ guarantees theintegrity of block contents consisting ofmodifiedBIMdata

The purpose of blockchain is to record the historical pro-cess of BIM record modification A blockhead is composedof multiple BIM data which can speed up the uplink of BIMrecord modification The necessary BIM data need to recordthe history of modification but the ordinary BIM can notimplement it The method of calculating block hash valuescan get hash values of all uplink BIM data more quickly andefficiently than calculating Merkle tree roots We propose aBIM via blockchain to storage data which solve the problemof tracing proving and preventing tampering with BIMhistorical data At the same time it can generate a unifiedformat to support future open sharing This method uses thehash structure of blockhead to ensure the integrity of all blockdata In addition block integrity is guaranteed by hash valueand the signature guarantees blockheadrsquos integrity The valueof hash andnonce in blockhead guarantees fair consensus andnontampering

43 Example Public Blockchain bcBIM In this scene theblockchain-based BIM data organization method is based ona decentralized measure also known as a public blockchainmethod which includes the following steps

(1) Each node of the public blockchain denoted as B isusually a node with its own independent BIM data Itis necessary to establish the openness and sharing ofBIM data among all nodes and maintain irreparabledata modification and traceability of time

(2) The central node of the public blockchain records theBIM data which need to be saved in the local storagemedium and uniformly packs it into the blockhead atevery P time

(3) Assume that the BIM data recorded in P time are11986111986811987211198611198681198722 119861119868119872119899 The method of uniformlypacking blocks into blockheads is as follows Blocksare recorded asBIMDATA and the components of theblocks include 11986111986811987211198611198681198722 119861119868119872119899 each BIMiincludes metadata modified BIM data and accessaddress ofmodifiedBIMdata calculate119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899)

(4) The blockhead is named BIMHEAD its compo-sition includes PreviousHash BIMHASH LinkOf-DATA Timestamp and NonceandRequirement Pre-viousHash is the hash value of the previous block-head LinkofDATA is the access address of cur-rent block BIMDATA Timestamp is a time stampfor building blockheads Nonce is a random num-ber Requirement is a requirement for hash valuethat is 119867119886119904ℎ(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119874119891119863119860119879119860 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890 119868119863) meetsthe Requirement

8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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6 Mathematical Problems in Engineering

In summary BIMaaS provides a storage and computationservice for BIM data including data retrieval data updat-ing and data computation BIM big data is accumulativelymerged and shared to form a unified resource pool forresponding on-demanded requests from traditional desktopPCs or especially mobile terminals in construction fieldsSome special wearable devices such as helmets may providemore enhancement for BIM information presentation BIMdata can be accessed any time anywhere not only by mobiledevices but also by wireless sensors Those sensors createIoTs to collect critical data about on-site construction ontime The analysis on those data can help reevaluate thequality of design or construction and provide amendingfeedback Moreover IoT devices on construction machinecan access and display BIM data to empower the intelligenceof construction machines This architecture not only enablesthe pervasive retrievals of BIM information but also supportsthe ubiquitous information exchanging or cooperativelyconstructing It provides a promising framework for theexchanging and sharing of BIM data in smart construction

415 Structure of Blockchain Blockchain is a distributedledger a technical solution to collectively maintain a reliabledatabase throughdecentralized trustedways and blockchainis a distributed database that is almost impossible to changeldquoDistributedrdquo here is not only a distributed storage of databut also a distributed record of data (ie shared by thesystem participants) blockchain is not a single technologybut a result of a variety of technology integration thesetechnologies are in a new structure together to form a newway of data recording storage and expression Combinedwith these technologies the contents of the scheme afteradopting the present inventionwill be difficult to bemodifiedand the security can be improved

Data stored using blockchain technology is also timeseries tamper-proof forged and privacy-pending which isproven in many documents bcBIM also inherits these fea-tures and guarantees the absolute security of the informationdata from two aspects one is to ensure that the pseudo-blockdoes not appear on the blockchain

Each node in the receipt of the new block will be the blockvalidation pseudo-block because it can not be verified will bediscarded and will not be written into the blockchain if themalicious node would like to use pseudo-branched chain toreplace the correct blockchain which is the computing powerof todayrsquos computer which is almost impossible to achieve thetask the other is to ensure that the data in the chain will notbe modified Because each chunk contains the hash value ofthe previous chunk if the malicious node changes a chunk ofdata you must change the chunk behind all the blocks whichare changed but also in the future with their own pseudo-branched chain to cover the correct blockchain in terms ofmodern computer capabilities this is also an impossible task

The basic processing unit of blockchain technology is adata block that stores all transaction data and related verifica-tion information for a certain period of time The blockchainis combined into a specific data structure in chronologicalorder which forms the nontamper and nonfalsification data

sharing information guaranteed by cryptography and usesthe SHA 256 algorithm and theMerkle tree to realize the datamanagement system with simple and safe storage successiverelation efficient and fast verification [27]

Block is the basic unit of block chain which is composedof blocks and blocks The block header contains blockID version number previous block hash value timestampMerkle root the block target hash value and so onThemainbody of the block contains the main data information ofthe block including identity certificate transaction contentamount of breach of contract and so on (Figure 1)

The characteristic of BIM data organization methodbased on blockchain is that each newly generated block savesthe hash value of the previous block Therefore we combineBIM with blockchain to provide BIM data organizationmethod which can track prove and prevent tampering ofBIM historical data At the same time it can generate unifiedformat to support open sharing of future data

42 Blockchain-Based Model for Audit and Provenance Inthis section we propose to use blockchain to facilitate theaudit and provenance of historical BIM data

Blockchain consists of a data structurewith cryptographichash value to guarantee the integrity of a serial data Themajor items in proposed blockchain-based model are asfollows (= denotes that ldquois defined asrdquo)

(1) Block = ⟨119861119897119900119888119896119867119890119886119889119863119886119905119886⟩ 119861119897119900119888119896119867119890119886119889 guaran-tees the integrity (nonmodification) of 119863119886119905119886 andmodifying history of 119863119886119905119886

(2) BlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎNonce Difficulty Timestamp⟩ The 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ is the hash value of the intermediate previousblock head 119863119886119905119886119867119886119904ℎ is the hash value of 119863119886119905119886 inthis block 119873119900119899119888119890 is a value to be determined byrandomly checking whetherZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 119885119890119903119900(sdot) is afunction that returns the number of left consecutivezeros in an inputting string in bytes 119863119894119891119891119894119888119906119897119905119910 isan integer to tell the requirement on how manyconsecutive zeros in the head of hash result Forexample 119863119894119891119891119894119888119906119897119905119910 = 2 means the first 2 bytes oftarget hash outputting is 0 That is the first 2 bytesof 119867119886119904ℎ(sdot) is 0 119879119894119898119890119904119905119886119898119901 is the time snapshot ofcurrent packaging block

(3) Data = ⟨119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886⟩ 119872119890119905119886119889119886119905119886 is anoptional tuple for data description on 119861119868119872119889119886119905119886which can be empty The 119861119868119872119889119886119905119886 is a mandatorytuple for concrete BIM data Once BIM data ismodified 119863119886119905119886 will be created and wait for beingappended into blockchain in a batch

(4) 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) where119861119897119900119888119896119867119890119886119889 is the previous blockhead where119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ tuple is located That is the hashvalue of previous blockhead is embedded into nextblock head It can also be looked as a link of twoadjacent block heads

Mathematical Problems in Engineering 7

Block Header

Field Description

Version Block Version Number

Previous Block HashHash of the previous block

in the chain

Merkle Tree RootHash of the Merkle tree root

Timestamp Creation time of this block

Targeted Difficultye Proof-Of-Work

difficulty target

Nonce

2IIN-

A counter for the Proof-Of-Work

Figure 1 Format of block

(5) 119863119886119905119886119867119886119904ℎ = Hash(1198611198681198721198891198861199051198861 1198611198681198721198891198861199051198862 sdot sdot sdot 119861119868119872119889119886119905119886119899) Suppose the number of BIM in thistime-span is 119899 That is it is the numbers of BIMdata that will be packaged in blockchain during ablock generation period 119863119886119905119886119867119886119904ℎ guarantees theintegrity of block contents consisting ofmodifiedBIMdata

The purpose of blockchain is to record the historical pro-cess of BIM record modification A blockhead is composedof multiple BIM data which can speed up the uplink of BIMrecord modification The necessary BIM data need to recordthe history of modification but the ordinary BIM can notimplement it The method of calculating block hash valuescan get hash values of all uplink BIM data more quickly andefficiently than calculating Merkle tree roots We propose aBIM via blockchain to storage data which solve the problemof tracing proving and preventing tampering with BIMhistorical data At the same time it can generate a unifiedformat to support future open sharing This method uses thehash structure of blockhead to ensure the integrity of all blockdata In addition block integrity is guaranteed by hash valueand the signature guarantees blockheadrsquos integrity The valueof hash andnonce in blockhead guarantees fair consensus andnontampering

43 Example Public Blockchain bcBIM In this scene theblockchain-based BIM data organization method is based ona decentralized measure also known as a public blockchainmethod which includes the following steps

(1) Each node of the public blockchain denoted as B isusually a node with its own independent BIM data Itis necessary to establish the openness and sharing ofBIM data among all nodes and maintain irreparabledata modification and traceability of time

(2) The central node of the public blockchain records theBIM data which need to be saved in the local storagemedium and uniformly packs it into the blockhead atevery P time

(3) Assume that the BIM data recorded in P time are11986111986811987211198611198681198722 119861119868119872119899 The method of uniformlypacking blocks into blockheads is as follows Blocksare recorded asBIMDATA and the components of theblocks include 11986111986811987211198611198681198722 119861119868119872119899 each BIMiincludes metadata modified BIM data and accessaddress ofmodifiedBIMdata calculate119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899)

(4) The blockhead is named BIMHEAD its compo-sition includes PreviousHash BIMHASH LinkOf-DATA Timestamp and NonceandRequirement Pre-viousHash is the hash value of the previous block-head LinkofDATA is the access address of cur-rent block BIMDATA Timestamp is a time stampfor building blockheads Nonce is a random num-ber Requirement is a requirement for hash valuethat is 119867119886119904ℎ(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119874119891119863119860119879119860 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890 119868119863) meetsthe Requirement

8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 7

Block Header

Field Description

Version Block Version Number

Previous Block HashHash of the previous block

in the chain

Merkle Tree RootHash of the Merkle tree root

Timestamp Creation time of this block

Targeted Difficultye Proof-Of-Work

difficulty target

Nonce

2IIN-

A counter for the Proof-Of-Work

Figure 1 Format of block

(5) 119863119886119905119886119867119886119904ℎ = Hash(1198611198681198721198891198861199051198861 1198611198681198721198891198861199051198862 sdot sdot sdot 119861119868119872119889119886119905119886119899) Suppose the number of BIM in thistime-span is 119899 That is it is the numbers of BIMdata that will be packaged in blockchain during ablock generation period 119863119886119905119886119867119886119904ℎ guarantees theintegrity of block contents consisting ofmodifiedBIMdata

The purpose of blockchain is to record the historical pro-cess of BIM record modification A blockhead is composedof multiple BIM data which can speed up the uplink of BIMrecord modification The necessary BIM data need to recordthe history of modification but the ordinary BIM can notimplement it The method of calculating block hash valuescan get hash values of all uplink BIM data more quickly andefficiently than calculating Merkle tree roots We propose aBIM via blockchain to storage data which solve the problemof tracing proving and preventing tampering with BIMhistorical data At the same time it can generate a unifiedformat to support future open sharing This method uses thehash structure of blockhead to ensure the integrity of all blockdata In addition block integrity is guaranteed by hash valueand the signature guarantees blockheadrsquos integrity The valueof hash andnonce in blockhead guarantees fair consensus andnontampering

43 Example Public Blockchain bcBIM In this scene theblockchain-based BIM data organization method is based ona decentralized measure also known as a public blockchainmethod which includes the following steps

(1) Each node of the public blockchain denoted as B isusually a node with its own independent BIM data Itis necessary to establish the openness and sharing ofBIM data among all nodes and maintain irreparabledata modification and traceability of time

(2) The central node of the public blockchain records theBIM data which need to be saved in the local storagemedium and uniformly packs it into the blockhead atevery P time

(3) Assume that the BIM data recorded in P time are11986111986811987211198611198681198722 119861119868119872119899 The method of uniformlypacking blocks into blockheads is as follows Blocksare recorded asBIMDATA and the components of theblocks include 11986111986811987211198611198681198722 119861119868119872119899 each BIMiincludes metadata modified BIM data and accessaddress ofmodifiedBIMdata calculate119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899)

(4) The blockhead is named BIMHEAD its compo-sition includes PreviousHash BIMHASH LinkOf-DATA Timestamp and NonceandRequirement Pre-viousHash is the hash value of the previous block-head LinkofDATA is the access address of cur-rent block BIMDATA Timestamp is a time stampfor building blockheads Nonce is a random num-ber Requirement is a requirement for hash valuethat is 119867119886119904ℎ(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119874119891119863119860119879119860 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890 119868119863) meetsthe Requirement

8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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8 Mathematical Problems in Engineering

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

Nonce

ID

Requirement

Figure 2 Public blockchain block data structure diagram

(5) Each center node adds data to the entire publicblockchain Each central node needs to calculate theNonce value that meets theRequirement According tothe nature of the hash function Noncersquos calculationscan only rely on random attempt Next the centralnode broadcasts the calculated block and if everyonepasses the verification it is deemed to be correct Inaddition recording block work will be rewarded tothe recorder and the reward will be completed offlineaccording to the statistics of ID

(6) Password-safe hash functions include 11987811986711986025611987811986711986011198861198991198891198721198635

The block data structure is shown in Figure 2Each newly generated block holds the hash value of

the previous block Due to the characteristics of the hashfunction whatever small modifications will lead to greatchanges in the results Therefore the data uploaded by userscannot be tampered Besides Nonce is a random numberwhich causes the block hash value having a number of 0before it and the number of 0 is determined by the value ofRequirement such as Requirement = 5

44 Example Private Blockchain bcBIM bcBIM on thepublic blockchain is primarily used for autonomous orga-nizations but private blockchain may be easier to build forcompanies

In this scene the BIM data organization method basedon blockchain is based on a central method also knownas a private blockchain or consortium blockchain method

Recording BIM data in P time is BIM1 BIM2 BIMn

Blocks are marked as BIMDATA which consists of

Calculating HASH values of blocks BIMHASH=Hash(BIM1

||BIM2 || BIMn)

Packing data into block head BIMHEAD

BIM1 BIM2 BIMn

Figure 3 Flowchart of BIM data organization method based onblockchain

As shown in Figure 3 the following steps are specificallyincluded

(1) The center node records the BIM data which needs tobe saved on the local storage media and packages ituniformly into the blockhead every P time

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 9

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

PreviousBlock

Hash

BIMHASH

LinkofDATA

Timestamp

BIMINDEX

Signature

Figure 4 Private blockchain block data structure diagram

(2) Assuming that the BIM data recorded during P timeare 11986111986811987211198611198681198722 119861119868119872119899 The method of unifyingthe packet into the blockheads is as follows theblock is recorded as BIMDATA and the compositionof the block includes 11986111986811987211198611198681198722 119861119868119872119899 eachBIMi includes metadata-META modified BIM data-BIMNEW and access address of modified BIM data-BIMLOCATION where 119868 isin [1 119899] and the method ofrecording the blockhead can knowwhere the BIMhasbeen changed and what it is after changing

(3) Calculate the hash value of the block 119861119868119872119867119860119878119867 =119867119886119904ℎ(1198611198681198721 1198611198681198722 sdot sdot sdot 119861119868119872119899) the func-tions that calculate the hash value include 11987811986711986025611987811986711986011198861198991198891198721198635

(4) The area is recorded as BIMHEAD and the com-position of the blockhead includes PreviousHashBIMHASH LinkofDATA Timestamp and BIMIN-DEXandSignature PreviousHash can ensure that theprevious block has not been modified BINHASH canensure the BIMDATA is not modified Linkofdata canfind the location ofBIMDATA and Timestamp Times-tamp is the time stamp that establishes the blockheadwhich marks the time series of the block BIMINDEXis a global index information about the BIM mod-ule including keywords object number and modelnumber and Signature ensures the authority of theblock which is generated by the central node of theprivate blockchain In this paper PreviousHash is thehash value of the previous block head LinkofDATAis the access address of block BIMDATA Timestampis a time stamp for building blocks and Signature

is the signature of PreviousHash BIMHASH Linkof-DATAandTimestamp by the central node using its pri-vate key namely 119878119894g119899(119875119903119890V119894119900119906119904119867119886119904ℎ 119861119868119872119867119860119878119867 119871119894119899119896119900119891119863119860119879119860 119879119894119898119890119904119905119886119898119901)

The resulting block data structure is shown in Figure 4

45 Discussion Next we discuss the proposed novel bcBIMmodel implementation in the process of developing BIMarchitectural projects

Application of bcBIM model in design using bcBIMmodel in design stage the architectural design can beanalyzed and optimized to ensure the constructibility ofdesign First of all we should establish 3D design modelsof related construction projects including constructionsstructures and construction equipment Secondly based onthe established 3D design model design detection and col-laborative modification can be carried out Design detectioncan set relevant parameters according to the requirement anddetermine the detection range so as to detect design conflictsand constructibility problems Next with the help of bcBIMit is possible to analyze and communicate the above problemsin time so as to solve the problems in an effective way andobtain a reasonable construction drawing In addition the3D design of projects will be realized through the establishedmodels bcBIMhas the ability to generate a variety of graphicsand documents automatically from 3D models which arealways related to modelsrsquo logics When a model changesthe graphics and documents which are associated with itare automatically updated Compared to the traditional BIMmodel it is worth noting that the modified records can betracked in bcBIM

Application of bcBIM model in construction bcBIMmodel is used to carry out the virtual construction of projects

10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

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10 Mathematical Problems in Engineering

through simulating analyzing and optimizing the projectconstruction plan so as to discover the possible problemsduring the construction and take precaution measures beforebeginning construction With the help of bcBIM it isgreatly reducing the cost of rework the waste of resourcesand safety issues when guiding actual construction As thecomplexity of the project increases such as the increase insize or the complexity of building coefficients traditional2D cannot express buildings intuitively and accurately Inthis paper the application of bcBIM technology changesthe building from 2D to nD so as to solve the problemof shortening the construction period and controlling thecost

In addition bcBIM can provide additional advantages infurther expansion as shown below(1) Financial services in the construction industry a large

amount of capital is exchanged for equipment materialsand services bcBIM provides strong support for supplychain financing In addition since blockchain is nontam-pered safe and reliable it can provide reliable guaranteefor financial activities in supply chain finance At the sametime financial audit during operation can also providetransparent notarized and untouchable records throughblockchain so as to guarantee operational share and assettransfers(2) Credit reporting and ownership management the

certification of the relevant qualification of building materialsproducts can only be carried out by the previous central-ized organization thus there will inevitably be counterfeitand shoddy products Since data on blockchain cannot betampered bcBIM can comply with the relevant evaluationstandards and certification productsThe preservation of rel-evant authentication and qualification in blockchain not onlyensures fairness but also guarantees objectivity eliminatingthe occurrence of fake and inferior commodities In additionownership management of digital assets such as designdrawings BIMmodels andBIMcomponentsmay be anotherapplication point With the help of blockchain architects andbuilders of buildings can store information in a nontamper-ing and nonrepudiation manner Once occurrence qualitysafety accident may follow up the related responsible personaccording to the chart and once blockchain identifies digitalassets online transactions can take place creating a healthyecosystem(3) Resource sharing the decentralized application of

blockchain can reduce the cost of management in leasingmanagement of large equipment such as shield machineand tower crane In addition to physical devices resourcesharing of digital assets based on blockchain may be realizedfaster(4) Trade management blockchain technology can help

automate cumbersome procedures and processes in buildingmaterials trade and logistics supply chains Moreover bcBIMwill bring great convenience to participating multipartyenterprises Therefore the digitization of sales contractsand legal contracts in terms of trade goods monitoringand detection and real-time payment can enable bcBIM todisplay its skills

5 Security Analysis and Performance Analysis

In this section we will analyze the security and performanceof bcBIM

51 Security Analysis If a blockhead is changed the hashvalue of the block head denoted as Hash(119861119897119900119888119896119867119890119886119889) willbe changed too It is computationally intractable to computea block that is distinct with the original block but has thesame hash value That is given Hash(119861119897119900119888119896119867119890119886119889) = 119886 itis computationally intractable to compute 1198611198971199001198881198961198671198901198861198891015840 suchthat Hash(1198611198971199001198881198961198671198901198861198891015840) = 119886 In cryptography it is calledsecond preimage resistance

Similarly if a block data is changed the hash valueof block data will be changed That is if 119863119886119905119886 is altered119863119886119905119886119867119886119904ℎ will be altered too It will consequently alterrelated 119861119897119900119888119896119867119890119886119889 and corresponding 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎas well as all later influenced blocks in whole blockchainIn other words once one 119863119886119905119886 is changed some items inblockchain must be changed for consistence Otherwise itis very likely to detect such changes and inconsistence inblockchain

The blockchain cannot be modified by any attackers Ifany modification of any tuple in blockchain occurs 119873119900119899119888119890will be fault with high probability (that will be explained later)because anyone can detect the inconsistence by verifyingwhether Zero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 If attackers try tofind corresponding119873119900119899119888119890 to maintain the consistence it willcost a large amount of computation and almost impossibleto recreate a fake blockchain that is longer than originalblockchain

The separation of blockhead and block data will let theblockhead maintain the same size The size of block data isvaried and related to the number of modified BIM data It canalso make the computation of 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ be moreefficient because the fix length of block head The searchingof119873119900119899119888119890will be energy and time saving

The details of BIM data depends on the context such asspecific storage modes in underlying BIM systems whosesemantics is independent with our design For example ifa model or parameter is changed the location of modifiedvalue in terms of specific table column or tuple will bealso recorded depending on the specific selection of under-lying database system in concrete BIM systems waiting forblochchain enhancement119863119886119905119886119867119886119904ℎ is generated by concatenation instead of

Merkel tree root Concatenation can reduce the hash compu-tation from 119874(1198992) to 1 which will be analyzed in detail later119863119886119905119886 and 119863119886119905119886119867119886119904ℎ have an implicit linkage between

them Given 119863119886119905119886119867119886119904ℎ there exists one and only one119863119886119905119886 such that 119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) Inversely given119863119886119905119886 there exists one and only one 119863119886119905119886119867119886119904ℎ such that119863119886119905119886119867119886119904ℎ = Hash(119863119886119905119886) In implementation an explicitlinkage can be added for fast jumping such as a variable withpoint type in C programming language

Similarly 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ and previous 119887119897119900119888119896 havean implicit linkage between them Given 119875119903119890V119894119900119906119904119861119897119900119888119896-119867119886119904ℎ there exists one and only one 119861119897119900119888119896 such that

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 11

119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) Inversely given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ there exists one and only one119861119897119900119888119896 suchthat119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ = Hash(119861119897119900119888119896119867119890119886119889) In implemen-

tation an explicit linkage can be added for fast fetching suchas a variable with point type in C programming language

Proposition 1 If any item in blockhead is changedZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863a119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890))119863119894119891119891119894119888119906119897119905119910 is maintained with theprobability 12119863119894119891119891119894119888119906119897119905119910lowast8

Proof The computation of hash function is assumed to becomputationally indistinguishable with a random selection ofa range [0 2119871] where 119871 is the length of hash function outputEach bit is a coin tossing with probability 12 with 0 and 1The number of consecutive zeros in front of hash value is atleast 119863119894119891119891119894119888119906119897119905119910 lowast 8 thus the probability is 12119863119894119891119891119894119888119906119897119905119910lowast8 If119863119894119891119891119894119888119906119897119905119910 is sufficiently large the probability will be smallenough to negligible

Proposition 2 Our proposed model reduces the hash compu-tation from 119874(1198992) to 1 by concatenation

Proof If the number of BIM data is 119899 For computing Merkeltree root the number of hash function computation is 119899 +1198992+ 1198994 + sdot sdot sdot + 1 1+ 1 + sdot sdot sdot 1 = 119899 lt 119899 + 1198992+ 1198994 + sdot sdot sdot + 1 lt119899+119899+ = 119899lowast119899 = 1198992Thus the computation cost is119874(1198992) Butin our proposed model the number of hash computation is 1as desired

Proposition 3 If the size of BIM data is 119904 the number of BIMdata during the period of locking data into blockchain is 119899 thatis the size of one block is about 119887 = 119904 lowast 119899

Proof Straightforward 119904 = |119872119890119905119886119889119886119905119886 119861119868119872119889119886119905119886| 119887 =|119861119897119900119888119896| 119887 = 119904 lowast 119899 + |119861119897119900119888119896ℎ119890119886119889| asymp 119904 lowast 119899 when 119904 lowast 119899 gtgt|119861119897o119888119896ℎ119890119886119889|

The block size can be tuned by setting different period ofpackaging blocks into blockchain The period influences thetimestamp gap between adjacent revision

Proposition 4 In 119861119897119900119888119896119867119890119886119889 the119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 and only by randomtrials

Proof 119873119900119899119888119890 is computed byZero(Hash(119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ

119879119894119898119890119904119905119886119898119901 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910 after given119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886119904ℎ 119879119894119898119890119904119905119886119898119901 Asthe value of Hash(sdot) is unpredictable and almost random(normal distribution in outputting range) Hash(sdot 119873119900119899119888119890) is almost random It can only be achievedby brute force trials to find satisfying 119873119900119899119888119890 such thatZero(Hash(sdot 119873119900119899119888119890)) ge 119863119894119891119891119894119888119906119897119905119910

119863119894119891119891119894119888119906119897119905119910 can be tuned by default regulation such as let-ting the searching period for119873119900119899119888119890 to 119901where 119901 depends on

the requirements onmodification audit or revision frequency(eg 24 hours)

Proposition 5 Suppose the computing throughput of hashfunction on average computing devices is 119888 (in terms of119872119867119875119878denoting MillionHash Per Second) the time cost 119905 (in terms of119904) for searching of119873119900119899119888119890 can be estimated by119905 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 = 2119863119894119891119891119894119888119906119897119905119910lowast8106 lowast 119888 where

119863119894119891119891119894119888119906119897119905119910 specifies the number of consecutive zeros in theleftmost of hash value

Proof The probability of one time success for required hashvalue is 12119863119894119891119891119894119888119906119897119905119910lowast8 Thus the number of times for hashcomputation is 2119863119894119891119891119894119888119906119897119905119910lowast8The computation throughput ofhash function is 119888MHPS or 106 lowast119888 times of hash per secondTherefore the time for one successful searching of 119873119900119899119888119890 is2119863119894119891119891119894119888119906119897119905119910lowast8(106 lowast 119888) on average or in expectation

Proposition 6 In private blockchain blockhead could beBlockHead = ⟨119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ119863119886119905119886119867119886119904ℎ 119878119894119892

119879119894119898119890119904119905119886119898119901⟩ where 119878119894119892 is the signature of blockchain gener-ator and119878119894119892 = Sign(119875119903119894119870119890119910 119875119903119890V119894119900119906119904119861119897119900119888119896119867119886119904ℎ 119863119886119905119886119867119886sℎ

119879119894119898119890119904119905119886119898119901) where Sign(sdot) is a signing function of an asym-metric cryptography

Proof Straightforward In private blockchain that all blocksare packaging by generators blockchain generators are trust-worthy It signs the blockhead with its signature to guaranteethe integrity of blockchain All other users can check theintegrity of blockchain by verifying the signature

In general the blockhead is composed of multiple BIMdata which can speed up the updating speed of BIM recordmodification In addition the important BIM data needsto record the history of modifications However ordinaryBIM cannot record the history of modifications The schemeproposed in this paper can improve the security of BIM Themethod of calculating block hash values can obtain all thehash values of upstream BIM data faster and more effectivelythan that of Merkle tree roots In this paper a method of BIMdata storage based on blockchain is proposed which solvesthe problem of tracking proving and preventing tamperingof BIM historical data At the same time it can also generatea unified format to support future open sharing This methoduses the chain hash structure of block heads to ensure theintegrity of all block data In addition block integrity isguaranteed by block hash value block signature guaranteesblock integrity block hash and Nonce guarantees fairnessconsistency and nontampering

52 PerformanceAnalysis In this section wemainly performperformance analysis on transaction throughput and uplinkdelay

On the one hand transaction throughputmainly tests oneindicator call contract TPS For blockchain systems TPS isa new transaction record generated every second In theoryBitcoin can only handle seven transactions per second oneblock per 10 minutes which is equivalent to 7 transaction

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

12 Mathematical Problems in Engineering

throughput Bitcoinrsquos transaction processing speed is 6 to7 transactions per second for public chains However thistransaction throughput can not meet the business needs ofenterprises For consortium chains thousands of transactionscan be processed per second Miners pack blocks and submitthem to the network and each blockchain contains a certainnumber of transaction records Thus in the bcBIM systemwe can also calculate TPS TPS = the number of transactionscontained in a block block generation time Take Bitcoinas an example one block size is 1 mb and the average sizeof each transaction record is 495 bytes The average numberof transactions per block = 1 lowast 1024 lowast 1024 bytes495 = 2118Block generation time is about 10 minutes that is TPS = 2118(10 lowast 60) = 353

On the other hand in terms of uplink delay time theinherent property of blockchain leads to transaction delayThe time of public chain is fixed and the transaction delayis 10 minutes In order to be safe it is necessary to waitfor at least six blocks to confirm the validity of paymentThe generation of a block takes about 10 minutes andthe confirmation time is at least 1 hour Besides privateblockchain is faster the main delay is one signing time

6 Conclusions

In this paper we proposed a novel BIMmodel for enhancingcurrent BIM ICT architecture called bcBIM by a componenta blockchain-based BIM data audit mechanism for BIM dataaggregation in time serials bcBIM model can guarantee theBIM data integrity and provenance by adding blockchainin current BIM database and facilitate mobile computingand pervasive accessing for BIM information bcBIM is verylikely an inevitable trend because of the development ofmobile devices such as smart phones and tablets cloudcomputing Internet ofThings and BIM big data sharingTheproposed bcBIMmodel can guide the design for further BIMinformation system and foster more interesting applicationsin BIM ICT systems for example accessing BIM cloudsecurely by engineering machines construction robots andwearable helmets in constriction area

We designed a blockchain-based method for BIM dataaggregation including data structure and basic computationfor consensus We analyzed its system parameters such assecurity strength block size packaging period and hashingtime cost This method uses blockchain record BIM tomodify history to ensure the integrity and unverifiabilityof messages Blockchain technology can greatly improvethe security and quality of BIM data and solve the hiddensecurity risks of modifying BIM model and parameters inintelligent structure Therefore the use of blockchain willgreatly promote the development of BIM technology

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The research was financially supported by the National KeyRampD Program of China with no 2016YFC0702107

References

[1] B Succar ldquoBuilding information modelling framework aresearch and delivery foundation for industry stakeholdersrdquoAutomation in Construction vol 18 no 3 pp 357ndash375 2009

[2] Y Lu Z Wu R Chang and Y Li ldquoBuilding InformationModeling (BIM) for green buildings A critical review andfuture directionsrdquo Automation in Construction vol 83 pp 134ndash148 2017

[3] C Perera R Ranjan L Wang S U Khan and A Y ZomayaldquoBig data privacy in the internet of things erardquo IT Professionalvol 17 no 3 pp 32ndash39 2015

[4] C Perera R Ranjan and L Wang ldquoEnd-to-end privacy foropen big data marketsrdquo IEEE Cloud Computing vol 2 no 4pp 44ndash53 2015

[5] J Zhao L Wang J Tao et al ldquoA security framework in G-Hadoop for big data computing across distributed cloud datacentresrdquo Journal of Computer and System Sciences vol 80 no 5pp 994ndash1007 2014

[6] F Jalaei A Jrade andM Nassiri ldquoIntegrating decision supportsystem (DSS) and building information modeling (BIM) tooptimize the selection of sustainable building componentsrdquoJournal of Information Technology in Construction vol 20 no25 pp 399ndash420 2015

[7] A H Oti and W Tizani ldquoBIM extension for the sustainabilityappraisal of conceptual steel designrdquo Advanced EngineeringInformatics vol 29 no 1 pp 28ndash46 2015

[8] P Inyim J Rivera and Y Zhu ldquoIntegration of building infor-mation modeling and economic and environmental impactanalysis to support sustainable building designrdquo Journal ofManagement in Engineering vol 31 no 1 2015

[9] X Wang and P E D Love ldquoBIM + AR Onsite informationsharing and communication via advanced visualizationrdquo inPro-ceedings of the IEEE 16th International Conference on ComputerSupported Cooperative Work in Design (CSCWDrsquo12) pp 850ndash855 Wuhan China 2012

[10] M Kokorus W Eyrich and R Zacharias ldquoInnovative approachto the substation design using building information modeling(BIM) technologyrdquo in Proceedings of the IEEEPES Transmissionand Distribution Conference and Exposition (TD16) pp 1ndash5Dallas Tex USA 2016

[11] MHDawood ldquoBIMbased optimal life cycle cost of sustainablehouse frameworkrdquo in Proceedings of the 3rd MEC InternationalConference on Big Data and Smart City (ICBDSCrsquo16) pp 1ndash5Muscat Oman 2016

[12] D Pasini S M Ventura S Rinaldi P Bellagente A Flamminiand A L Ciribini ldquoExploiting Internet of Things and buildinginformationmodeling framework for management of cognitivebuildingsrdquo in Proceedings of the IEEE International Smart CitiesConference (ISC2rsquo16) pp 1ndash6 Trento Italy September 2016

[13] W Zhu B Eynard M Bricogne S Remy andWWan ldquoFrame-work for information modeling of an integrated buildingrdquoin Proceedings of the International Conference on Smart andSustainable City andBigData (ICSSCrsquo15) pp 139ndash144 ShanghaiChina 2015

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Mathematical Problems in Engineering 13

[14] U Isikdag ldquoDesign patterns for BIM-based service-orientedarchitecturesrdquo Automation in Construction vol 25 pp 59ndash712012

[15] S Yoon N Park and J Choi ldquoA BIM-based design methodfor energy-efficient buildingrdquo in Proceedings of the Fifth Inter-national Joint Conference on INC IMS and IDC (NCMrsquo09) pp376ndash381 August 2009

[16] Y Jung and M Joo ldquoBuilding information modelling (BIM)framework for practical implementationrdquo Automation in Con-struction vol 20 no 2 pp 126ndash133 2011

[17] H C J Linderoth ldquoUnderstanding adoption and use of BIMas the creation of actor networksrdquo Automation in Constructionvol 19 no 1 pp 66ndash72 2010

[18] H Li and W W S Lu ldquoBuilding information modeling andchanging construction practicesrdquo Automation in Constructionvol 20 no 2 pp 99-100 2011

[19] G Desogus E Quaquero A Sanna et al ldquoPreliminary perfor-mancemonitoring plan for energy retrofit a cognitive buildingthe ldquoMandolesi Pavillonrdquo at the University of Cagliarirdquo inProceedings of the AEIT International Annual Conference pp 1ndash6 Cagliari Italy 2017

[20] M Arslan Z Riaz and S Munawar ldquoBuilding informationmodeling (BIM) enabled facilities management using hadooparchitecturerdquo in Proceedings of the Portland InternationalConference on Management of Engineering and Technology(PICMET17) pp 1ndash7 Portland Ore USA 2017

[21] Y Yuan and Z Jin ldquoLife cycle assessment of building energyin big-data era theory and frameworkrdquo in Proceedings of theInternational Conference on Network and Information Systemsfor Computers pp 601ndash605 Wuhan China 2015

[22] H Ferguson C Vardeman and J Nabrzyski ldquoLinked data viewmethodology and application to BIM alignment and interoper-abilityrdquo in Proceedings of the IEEE International Conference onBig Data (Big Data rsquo16) pp 2626ndash2635 Washington DC WashUSA 2016

[23] L Bottaccioli A Aliberti F Ugliotti et al ldquoBuilding energymodelling and monitoring by integration of IoT devices andbuilding information modelsrdquo in Proceedings of the IEEE41st Annual Computer Software and Applications Conference(COMPSAC17) pp 914ndash922 Turin Italy 2017

[24] S N Razavi and C T Haas ldquoMultisensor data fusion foron-site materials tracking in constructionrdquo Automation inConstruction vol 19 no 8 pp 1037ndash1046 2010

[25] J Park K Kim and Y K Cho ldquoFramework of automatedconstruction-safety monitoring using cloud-enabled BIM andBLEmobile tracking sensorsrdquo Journal of Construction Engineer-ing and Management vol 143 no 2 Article ID 05016019 2017

[26] J Garcia-Fernandez J Anssi Y Ahn and J J FernandezldquoQuantitative + qualitative information for heritage conserva-tion an open science research for paving rsquocollaborativelyrsquo theway to historical-BIMrdquo in Proceedings of the Digital Heritagepp 207-208 Granada Spain 2015

[27] Y Yuan and FWang ldquoBlockchain the state of the art and futuretrendsrdquoActaAutomatica Sinica vol 42 no 4 pp 481ndash494 2016

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawiwwwhindawicom Volume 2018

OptimizationJournal of

Hindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom Volume 2018

Engineering Mathematics

International Journal of

Hindawiwwwhindawicom Volume 2018

Operations ResearchAdvances in

Journal of

Hindawiwwwhindawicom Volume 2018

Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences

Hindawiwwwhindawicom Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018

Hindawiwwwhindawicom Volume 2018

Decision SciencesAdvances in

Hindawiwwwhindawicom Volume 2018

AnalysisInternational Journal of

Hindawiwwwhindawicom Volume 2018

Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom