ResearchontheDegreeofCouplingbetweentheUrbanPublic ...downloads.hindawi.com/journals/mpe/2019/8206902.pdf · e research framework of SOSM combines top-down infrastructure supply management

Research ArticleResearch on the Degree of Coupling between the Urban PublicInfrastructure System and the Urban Economic Social andEnvironmental System A Case Study in Beijing China

ZhiMei Tao 12

1College of Management and Economics Tianjin University Tianjin 300072 China2School of Public Administration Tianjin University of Commerce Tianjin 300134 China

Correspondence should be addressed to ZhiMei Tao 499626452qqcom

Received 25 January 2019 Revised 26 August 2019 Accepted 31 August 2019 Published 25 September 2019

Academic Editor Konstantinos Karamanos

Copyright copy 2019 ZhiMei Tao +is 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 isproperly cited

+e coordinated development of urban public infrastructure system and urban economic social and environmental system is animportant goal for the integrated management and sustainable development of urban public infrastructure system +is paperconstructs a research model of the degree of coupling coordination between urban public infrastructure system and urbaneconomic social and environmental system using the analytic network process (ANP) the analytic hierarchy process (AHP) acombination evaluation method based on game theory and a coupling coordination degree model Using Beijing data from 2000to 2016 the degree of coupling coordination between the Beijing urban public infrastructure system and the urban economicsocial and environmental system is empirically analyzed +is study finds that (1) the supply level of Beijingrsquos urban publicinfrastructure system has an obvious impact on the degree of coupling coordination between the two systems (2) +e globalfinancial crisis reduced the supply speed of the urban public infrastructure system in Beijing and put the dynamic coupling state ofthe two systems in the low-level symbiosis stage Beijing needs to improve the supply of urban public infrastructure to support thedevelopment of the urban economic social and environmental system (3) Improving the supply level of the urban environmentalinfrastructure in Beijing especially improving sewage disposal capacity and increasing the number of special vehicles for urbansanitation and the amount of domestic waste clearance will positively affect the degree of coupling coordination between twosystems (4) An increase in the GDP of Beijing has a direct positive impact on the degree of coupling coordination In addition theincrease in the social development level of the employees in three industries in Beijing has a significant impact on the degree ofcoupling coordination

1 Introduction

An infrastructure system consisting of subsystems such asenergy transportation water resources postal service andtelecommunication and environmental facilities is animportant basis for economic productivity and populationwelfare [1] As a supporting system and carrier of urbaneconomic and social activities urban infrastructure supplyfaces a series of pressures and challenges under globalurbanization Due to a wide range of economic socialtechnological and other factors the demand for urbaninfrastructure is gradually increasing and many

investments have been made to meet the needs of urbanpublic infrastructure Since 1981 Chinarsquos fixed asset in-vestment in urban public infrastructure has continued toincrease and its supply and service levels have continued toimprove over the long term [2] Nevertheless the supplylevel of urban infrastructure still fails to meet social de-mand in China After summer rainstorms the drainage incities is not adequate and in the summer ldquogoing to the cityto see the seardquo has become a phenomenon in many citiesSome cities are besieged by garbage in some places gar-bage is blown by the wind and sewage is evaporated andother problems such as road zippers traffic congestion air

HindawiMathematical Problems in EngineeringVolume 2019 Article ID 8206902 19 pageshttpsdoiorg10115520198206902

and water pollution still exist Improving the supply effi-ciency of urban infrastructure systems is an importantproblem for urban managers

+e urban public infrastructure system is a multibodycomplex and composite system of energy transportationpostal services and telecommunications the environmentwater resources and other subsystems +ese subsystemsare interdependent and interrelated and form the wholeurban public infrastructure system together providing thebasic products and services needed for urban development[3 4] Infrastructure supply is affected by the human re-search view and the specialized division of urban publicinfrastructure supply and traditionally which is providedby each department alone there is a lack of communicationand contact between departments [3 5 6] Over timepeople have become increasingly aware that the varioussubsystems of urban public infrastructure are interrelatedand interact forming a system of urban public in-frastructure Only by including supply management in thesystem as a whole can we improve the overall supply level ofurban public infrastructure in an orderly manner so thatthe urban public infrastructure system can meet the needsof urban economic and social development +e UnitedKingdom proposed studying the relationship between thenational infrastructure system and economic and socialdevelopment and managing the future development plan ofthe national infrastructure system as a whole [7] In 2017Chinarsquos ldquo13th Five-Year Plan for Urban Public In-frastructure Constructionrdquo propose for the first time tochange the way in which previous departments compiledindustry plans separately to consider the overall planningof urban infrastructure in a systematic way and to co-ordinate the supply of products and services in all sectors tomeet the requirements of urban economic and socialdevelopment

Understanding the interdependence of the varioussubsystems of urban public infrastructure is a prerequisitefor studying the overall supply of urban public in-frastructure systems Different scholars define and classifythe interdependence among subsystems of urban publicinfrastructure Rinaldi believes that thee physical in-formation spatial and logical interdependence existsamong the subsystems of urban public infrastructure [3]Many scholars have summarized classified and simulatedthe interdependence of urban public infrastructure [8ndash10]Jaime presents a System Safety Management System(SSMS) model to interdependency modelling for the case ofthe Mexico City Metro transport network which highlightsthat interdependency in the Metro transportation networkoccurs vertically and horizontally [11] +e study of theinterdependence of urban public infrastructure mainlyfocuses on the impact of urban public infrastructure in-terdependence when a sudden event occurs [12] Howeverthe interdependence of urban public infrastructure existsnot only when an emergency arises but also in peoplersquosdaily lives and the impact on the supply of urban publicinfrastructure products and services is equally important[13] +e research on the interdependence of the varioussubsystems of urban public infrastructure has been

deepening Tao proposes that the indispensability com-pleteness and irreplaceability of the subsystems of urbanpublic infrastructure are the essence and fundamentalreasons for the interdependence of the subsystems of urbanpublic infrastructure and an important basis for the for-mation of the overall supply management system of urbaninfrastructure +e interdependence of the various sub-systems of urban public infrastructure is of great signifi-cance to the normal operation of urban publicinfrastructure and the integrated supply management ofthe system [4] Due to the complexity of the in-terdependence of urban infrastructure systems and theirsubsystems studying the role of interdependence of in-frastructure systems and the supply management of in-frastructure systems is challenging [14]

+e urban public infrastructure system should promotethe cityrsquos economic growth social welfare and environ-mental quality development An improvement in thesupply level of urban public infrastructure systems willincrease the labor productivity of the society expand totalsocial demand increase the accumulation of fixed capitalincrease the total output of the society and guarantee theeconomic growth of the city [15 16] In addition an in-crease in the supply level of urban public infrastructure willpromote the convenience of urban production and livingactivities attract foreign populations increase employmentopportunities and improve the social welfare level of cities[17 18] +e advancement of urbanization has put pressureon the urban environment to a certain extent Urban publicinfrastructure can deal with urban garbage and sewagereduce air pollution slow the heat island effect improveurban climate conditions etc and have a positive impacton the urban environment [19ndash21] On the one hand animprovement in the urban public infrastructure supplylevel will increase the level of urban development and thegrowth of urban social wealth so that the city governmentwill be stronger and have more funds to invest in theconstruction and operation of urban infrastructure On theother hand due to the advancement of urbanization urbanpopulation concentration economic growth and envi-ronmental quality have put pressure on urban public in-frastructure Urban public infrastructure is interdependentand mutually influential An urban public infrastructuresystem based on interdependence is a collection of humanactivities that actively arrange and integrate the physicalfacilities and activities of the subsystems of urban publicinfrastructure and ensure that the subsystems of the urbanpublic infrastructure interact to improve the overall effi-ciency of the urban public infrastructure system +roughinfrastructure management control the collection of in-formation regarding system infrastructure demand aconsideration of the interdependence between the sub-systems of infrastructure expert opinion and governmentdecision-making city governments engage in urban in-frastructure supply management and make decisions toensure the supply of urban public infrastructure system canmeet to support the development of urban economicsocial and environmental system +e interaction thatoccurs between urban public infrastructure systems and

2 Mathematical Problems in Engineering

urban economic and social environmental systems isshown in Figure 1 +e direct goal of coordinated devel-opment between urban public infrastructure system andurban economic social and environmental system is torealize the integrated management of the supply benefits ofurban public infrastructure systems to improve the eco-nomic growth social welfare and environmental quality ofcities +e long-term goal of the coordinated developmentof urban public infrastructure systems and urban eco-nomic social and environmental systems is to achieve therational allocation of resources to urban public in-frastructure systems and realize the long-term sustainabledevelopment of cities

+ere is no research on the coordinated development ofinfrastructure and the economic environment in foreigncountries In the UK the Infrastructure TransformationResearch Consortium (ITRC) which consists of researchersfrom seven universities including Oxford CambridgeNewcastle and Leeds proposes that urban infrastructuresystems are complex applied systems [22] +rough the useof system-of-system modeling (SOSM) this consortiumsimulates and studies the relationship between nationalinfrastructure and economic and social development andconducts cross-sectoral performance evaluations of in-frastructure systems that face an uncertain future [7] Wecompare research on the coordinated development of in-frastructure and social development with SOSM researchand find the following

+e similarities between the two types of studies are asfollows

(1) Both have comprehensive strategic objectives +eultimate goal of both studies is to achieve sustainableregional or urban development through an orderlyallocation of resources

(2) Both have received considerable attention at thenational level In the UK the national infrastructuresystem is highly regarded while the national fi-nance department proposes using an integratedapproach to the development of national in-frastructure plans [7] Chinarsquos Ministry of Con-struction proposes systematically studying theconstruction and management planning of urbanpublic infrastructure and promoting solutions forurban problems

(3) Both have a similar research objective ITRC focuseson the long-term supply management of energytransportation water resources solid waste andwastewater clean-up and recycling and data andinformation communication services +e main re-search objective related to Chinarsquos infrastructure andurban coordinated development is the relationshipbetween the supply level of urban infrastructuresystems and the level of urban development

+e differences between the two studies are as follows

(1) +eir research focus is different SOSM proposesmanaging the infrastructure system across departments

as a whole for the purpose of transforming storing andtransmitting infrastructure traffic by managing phys-ical infrastructure entities and the corresponding hu-man system behaviors to allow for the long-termperformance evaluation of the various departmentsinvolved in infrastructure Research on the coordinateddevelopment of urban infrastructure and urban eco-nomic social and environmental systems considers theoverall supply of urban public infrastructure and thegiven resources and their ability to support sustainableurban development mainly by considering the overallmanagement of the interaction between the supplylevel of infrastructure systems and the level of urbandevelopment

(2) +e scope of each type of research is different +escope of research conducted using SOSM is limitedto the UKrsquos national infrastructure because the UKrsquosinfrastructure supply policy is made at the nationallevel and data on infrastructure supply inputs andoutputs throughout the Commonwealth are avail-able Considering Chinarsquos vast geographical scopeand regional differences Chinarsquos research on thecoordination of infrastructure and urban develop-ment mainly considers the synergistic relationshipbetween the infrastructure provided by cities orregions and their jurisdiction and the developmentlevel of the cities or regions Generally coordinateddevelopment studies are not conducted at the na-tional level

(3) +e perspective of each type of research is different+e research framework of SOSM combines top-down infrastructure supply management withbottom-up infrastructure providers and the be-havioral performance of service objects based onthe quality of service of the infrastructure (such asreliability cost security and environmental im-pact) and focuses on the long-term management ofnational infrastructure through the linkage andmanagement of a large number of infrastructureservice departments Coordinated developmentresearch generally does not consider subjectivedemand and differences in infrastructure service

Benefit

Effect

Demandfeedback

ControlSupply

Urban infrastructuremanagement control

decision system

Urban publicinfrastructure

system

Urban economic socialand environmental

systems

Figure 1 Interaction between urban public infrastructure supplyand urban economic and social environment

Mathematical Problems in Engineering 3

objects +is research mainly examines the level ofurban public infrastructure supply by consideringthe number of services provided by urban in-frastructure (eg electricity supply and garbageremoval) and explores the interaction betweeninfrastructure supply levels and the level of urbandevelopment

(4) Each type of research has a different understandingof the interdependence of the infrastructure sub-systems SOSM is based on the premise that theinterdependence of infrastructure subsystems is thebasis for national infrastructure system integrationmodeling It has been proposed that infrastructureinvolves more than the operation of a single spe-cialized department It is necessary to present theinterdependence of various departments of the in-frastructure using a cross-sectoral integration modeland evaluate the cross-department performance ofeach subsystem of infrastructure Existing researchon urban coordinated development of infrastructureand the level of urban development does not rec-ognize the interdependence of infrastructure sub-systems and proposes that the urban publicinfrastructure system should support the level ofurban development but not enforce an excessive levelof urban development which would waste socialresources

+e earliest research on urban infrastructure andurban coordinated development was conducted by ZhangJunyong who believes that urban infrastructure con-struction investment and economic development have amutually reinforcing relationship [23] At present Chi-nese scholarsrsquo research on the coordinated developmentof infrastructure and cities is divided into two categoriesqualitative research and quantitative research Qualitativeresearch focus on the sharing co-construction and co-ordinated development of environmental infrastructure[24] interact with each other on transportation in-frastructure and urbanization [25] Scholars who conductquantitative research mainly include the following Yuet al [26] construct an index system to evaluate economicand social development and analyze the coordinateddevelopment of Qingdaorsquos urban resources in-frastructure and economic society Wu et al [27]con-struct evaluation indicators for regional economicsystems and calculate the coordination degree of theeconomic system and infrastructure system in variousprovinces and cities in China Ying et al [28] analyze thecoordination of Hangzhou infrastructure and climatebased on the coupling relationship between climate andgreen infrastructure

In short there is still a wide range of research fields thatconsider the coordinated development of domestic andforeign urban infrastructure supply and the level of urbandevelopment (1) In terms of the evaluation index systemexisting research is more focused on the coordinated de-velopment of the level of infrastructure supply and the levelof urban development+is study incorporates indicators for

the level of urban development measuring the environ-mental pressures in cities and constructs indicators for theurban economic social and environmental system by fo-cusing on the three aspects of urban economic developmentsocial welfare and environmental pressure +is is a newbreakthrough in the construction of an index system (2) Interms of research methods the methods used to generate theweights of the evaluation indicators are mainly limited tousing the coupling coordination degree model +e dynamiccoupling and coordination model has not been used (3) Interms of the research design this study focuses on the in-frastructure system and the interdependence of the in-frastructure subsystems +is study applies the networkanalytic hierarchy process (AHP) and considers the in-frastructure of the interdependence of the subsystems toevaluate the supply level of the urban public infrastructuresystem

+is paper constructs a model of the coupling co-ordination degree of an urban infrastructure system andan urban economic social and environmental systemusing Beijing as an example In addition this paperprovides a theoretical basis and discusses methods forensuring the long-term and sustainable supply manage-ment of urban public infrastructure systems +e researchdesign used in this paper is shown in Figure 2 +e secondpart describes the research model used in this study whichinvolves AHP ANP the entropy method a combinationweight method based game theory a coupling co-ordination degree model and a dynamic coupling co-ordination degree model +e research model is used toevaluate the coordination of the urban public in-frastructure system and the urban economic social andenvironmental system +e last part of this paper describesthe empirical analysis of data on Beijing from 2000 to 2016using the research model

2 Research Materials Research Methods andModel Construction

21 Research Materials

211 Research Object Beijing is the capital of China It is thepolitical economic and cultural center of the country andhas advanced and comprehensive urban public in-frastructure In addition data on Beijingrsquos urban publicinfrastructure are abundant typical and representativeResearch on the system integration supply management ofBeijingrsquos urban public infrastructure shows that it can beused as a model for other cities

212 Evaluation Index System To measure the relation-ship between the urban infrastructure system and theurban economic social and environmental system thispaper initially develops an index framework based onrelevant references [26ndash30] +en according to the spe-cific situation of Beijing and the principles of appropri-ateness comparability and availability a final evaluationof the index system is conducted +e urban infrastructure


system consists of five subsystems energy transportationenvironment water resources postal services and tele-communications as well as 20 evaluation indicators +eurban economic social and environmental system in-cludes three subsystems the urban economic social andenvironmental subsystems as well as 12 evaluation in-dicators +e final evaluation indicators are shown inTables 1 and 2

22 Research Method

221 Preliminary Processing of Data +e relevant data onthe supply level of various subsystems of Beijingrsquos in-frastructure and on the development level of Beijingrsquos urbaneconomic social and environmental system (2000ndash2016)were acquired from the Beijing Statistical Yearbook (BeijingBureau of Statistics 2000ndash2016) through simple processingAll per capita indicators (including I11 I12 I14 I22 I41 I43and I51) represent the corresponding statistical data dividedby the number of permanent residents in that year Alldensity indicators (including I21 I42 and I44) represent thecorresponding statistical data divided by the area of Beijing+e indicator I21 is the sum of railway mileage and highwaymileage divided by the area of Beijing +e data are stan-dardized using formulas (1) and (2) (as shown in Tables 3and 4)

Positive indicator

Yij Xij minus min Xj1113966 1113967

max Xj1113966 1113967 minus min Xj1113966 1113967 (1)

Negative indicator

Yij max Xj1113966 1113967 minus Xij


where Xij represents the observed value of the jth index inthe ith year max Xj1113966 1113967 represents the maximum observationmin Xj1113966 1113967 represents the minimum observation and Yij is astandardized value

222 e ANP Is Used to Evaluate the Interdependence of theSubsystems of Urban Public Infrastructure +e ANP is amultiobjective decision-making method developed by Pro-fessor Saaty TL and is based on the AHP which is especiallyapplicable to complex system decision-making problems withinternal interdependence and feedback from indicator ele-ments [31]+e ANPmethod is used to evaluate the decision-making of the interdependence subsystem in the network toobtain weights of subsystem in the paper

Related literature review

Selection research object main method andevaluation index

ANPEntropy weighting

combination evaluation

Evaluation of urban public infrastructure

supply level

AHPEntropy weighting


Urban economic socialand environmental system evaluation

Evaluation and analysis of coupling coordination degree model

Evaluation and analysis of dynamic coupling coordination degree model

Research conclusions and policy recommendations

Figure 2 Research design flow chart


223 e Weight of the Evaluation Index of Each SubsystemIs Obtained by Using a Combination Weighting MethodBased on Game eory Game theory is an important part ofoperations research and is used for studying competitive el-ements Drawing on game theory relevant experts have de-veloped a game theory combination weighting method[32 33] that uses comprehensive subjective and objective

weighting to overcome the limitations of subjective weightingand objective weighting +e paper uses a combined weightmethod based on game theory to calculate the weight of theevaluation indicators of the urban public infrastructure systemand the urban economic social and environmental system

+e calculation process of combination weightingmethod based on game theory is as follows

Table 1 Evaluation indicators of the supply levels of the various subsystems of urban public infrastructure

Criteria layer System layer Indicator layer Unit uIEW uANP ulowastcw

Economicbenefit I1 energy facilities system

I11 per capita social electricityconsumption

Kilowatt-hoursperson 00307 00294 00298

I12 per capita energy consumption tons of standardcoalperson 00421 00664 00593

I13 natural gas ratio 00206 00157 00171I14 per capita heating area m2person 00265 00114 00158

Social benefit I2 road traffic system

I21 railway and highway facilitiesdensity kmkm2 00586 01575 01287

I22 per capita urban road area m2person 00277 00241 00251I23 number of publictransportation lines Number 00491 00442 00456

I24 bus operation passengervolume 10000 persons 00571 01011 00883

Environmentbenefit

I3 environmental protection system

I31 per capita park green area m2person 00436 00580 00538I32 sewage treatment capacity 10000m3day 00404 00302 00332I33 total number of urban

sanitation special vehicle andequipment

unit 00335 00217 00251

I34 household garbage clearancevolume 10000 tons 00519 00941 00818

I4 water resources and water supplyand drainage system

I41 per capita annual water supply m3person 01020 00957 00975I42 density of piped water supply kmkm2 00458 00590 00552I43 per capita comprehensivewater production capacity

10 thousand m3day person 00400 00307 00334

I44 sewage pipe density kmkm2 00542 00221 00314

I5 postal and telecommunicationfacilities system

I51 per capita postal andtelecommunications volume CNYperson 00709 00864 00819

I52 mobile phone penetration rate Household100people 00349 00151 00209

I53 mainline penetration rate 00466 00088 00198I54 bureau number of post and

telecommunications Unit 01238 00028 00380

Note +e relevant data are from the Beijing Statistical Yearbook 2000ndash2016

Table 2 Urban economic social and environmental system evaluation indicators

Dimension layer Indicator layer Unit uIEW uAHP ulowastcw

S1 economic aspect

S11 the actual value of gross domestic product 100 million CNY 00728 03365 02560S12 the proportion of the tertiary industry 00646 00586 00604

S13 actual utilization of foreign direct investment 10000 USD 01349 00342 00649S14 fixed assets investment ratio 00634 01103 00960

S2 social aspect

S21 per capita household disposable income CNY 01194 00580 00767S22 per capita consumption expenditure CNY 01197 00941 01019

S23 number of employees in three industries Person 00757 00302 00441S24 urbanization rate 00725 00217 00372

S3 environmental aspects

S31 annual average of inhalable particles mgm3 00670 00078 00259S32 total wastewater discharge 10 thousand tons 01234 00766 00909

S33 general industrial solid waste production 10 thousand tons 00375 00251 00289S34 sulfur dioxide emissions 10 thousand tons 00492 00133 00243



Tabl

e3

+estandardized

data

ofurbanpu

blic

infrastructure

system

year

Percapita

social

electricity

consum

ption

I 11

Percapita

energy

consum

ption

I 12

Natural

gasratio

I 13

Per

capita

heating

area

I 14

Railw

ayand

high

way

facilities

density

I 21

Per

capita

urban

road

area I 22

Num

berof

public

transportatio

nlin

esI 23

Bus

operation

passenger

traffi

cI 24

Per

capita

park

green

area I 31

Sewage

treatm

ent

capacity

I 32

Total

numberof

urban

vehicle

sanitatio

nspecial

equipm

ent

I 33

Dom

estic

garbage

removal

volume

I 34

Per

capita

annu

alwater

supp

lyI 41

Tap

water

supp

lypipe

density

I 42

Percapita

tap

water

comprehensiv

eprod

uctio

ncapacity

I 43

Sewage

pipe

density

I 44

Percapita

postaland

telecommun

ications

volumeI 51

Mob

ileph

one

penetration

rate

I 52

Fixedlin

emainline

penetration

rate

I 53

Bureau

numberof

post

and

telecommun

ications

I 54

2000

00000

00000

00000

00000

00000

00000

03735

00000

00000

00000

00000

00000

10000

00000

06906

00000

00000

00000

00375

00000

2001

00364

00355

04163

01323

00329

04355

00000

01052

00637

00310

01859

00238

08757

00573

06780

00515

00002

01214

02048

00047

2002

02486

01929

04871

02382

00878

10000

01088

02088

01398

01078

02048

00447

05718

01010

10000

01335

00405

02386

03106

00177

2003

03754

03775

04421

04598

00961

00347

01912

00487

02748

01789

02572

01140

05935

01783

09396

01741

00989

03087

05085

00250

2004

05346

10000

04167

05401

01169

03915

01941

02276

02780

02616

03969

01911

04806

02535

06726

01751

01406

03923

08464

00213

2005

06168

06046

05918

06281

01248

06958

02088

02715

03634

04043

03861

02756

04204

02375

02708

01108

02142

04234

10000

00273

2006

07935

08251

06777

06882

08050

05245

02029

01504

03634

04188

04271

04224

03393

04586

03365

02561

03042

04430

08362

00278

2007

08480

09660

08351

07056

08344

05360

02765

01991

04565

04540

04337

05292

02861

05905

03396

04149

04704

04265

07713

01077

2008

09348

05646

09242

07949

07852

08167

03647

04542

06118

04155

05139

06257

02100

06958

02889

04317

05685

04015

06143

01062

2009

06154

04736

09181

07843

08338

07522

04294

06161

07516

04705

05081

06248

01509

07678

02873

04378

06478

04430

05461

01202

2010

06977

05010

09482

07856

08759

06693

05059

06919

08292

04891

05768

05847

00588

09124

02762

04351

07866

05070

04471

01949

2011

06670

03221

09069

08526

09162

05281

06147

07720

08758

04982

06396

05871

00501

10000

03496

04825

01624

06229

04027

02003

2012

07493

03294

09535

08643

09388

04847

06000

08674

09068

05377

08046

06113

00110

06863

00000

06432

02056

07785

03652

03074

2013

07987

03475

09351

08849

09602

05308

08088

09729

09379

05471

08536

06518

00000

07361

01110

07472

02914

08176

03072

04034

2014

08186

03363

09293

09136

09817

05898

10000

10000

09689

06132

09078

07595

00175

07895

03443

07759

03696

10000

02253

04405

2015

08369

02923

09769

09405

09859

05739

09971

08107

09845

06432

09661

08574

00312

08351

03379

08787

05771

09835

01433

06948

2016

10000

04077

10000

10000

10000

06353

10000

08023

10000

10000

10000

10000

00519

08695

03264

10000

10000

09304

00000

08269


Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482


(1) Obtain n weights according to the n-type weightingmethod and then construct a basic weight vector setU u1 u2 un1113864 1113865 +ese n vectors are arbitrarilylinearly combined to form a possible set of weights

U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)

where u is a possible weight vector of a possible set of weightvectors and Wk is the weight coefficient

We use game theory to find the most satisfactory ulowast inthe possible vector set +e most satisfactory weight vectorcan be transformed by optimizing the linear combinationweight coefficient Wk +e goal of optimization is to min-imize the dispersion of u from each uk +at is

min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)

Based on the differential properties of the matrix thefirst derivative condition of the optimization of equation (4)is

1113944

n

j1Wj times uj times u

Tj ui times u

Tj (i 1 2 n) (5)

Equation (5) corresponds to a linear system of equationsu1 middot uT

1 u1 middot uT2 middot middot middot u1 middot uT

n

u2 middot uT1 u2 middot uT

2 middot middot middot u2 middot uTn

middot middot middot middot middot middot middot middot middot middot middot middot

un middot uT1 un middot uT

2 middot middot middot un middot uTn

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2

middot middot middot

wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)

After obtaining (w1 w2 wn) using formula (6) wenormalize it

Wlowastk

wk

1113936nk1wk

(7)

Finally the combined weight is

ulowast

1113944n

k1wku

Tk (8)

23 Research Model Construction

231 Model Used to Evaluate the Supply Level of the UrbanPublic Infrastructure System +emodel used to evaluate thesupply level of the urban public infrastructure system (seeFigure 3) is divided into three levels +e first level is the rulelayer which includes three aspects economic growth socialwelfare and environmental pressure on urban public in-frastructure systems +e second layer of the model is thenetwork layer Considering the purpose of the research fivesubsystems of the public infrastructure system are includedin the model namely water resources and water supply anddrainage system (I1) transportation system (I2) postalpower system (I3) environmental facilities system (I4) and

energy facilities system (I5) which are consistent with Ta-ble 1 +e third layer of the model is the system indicatorlayer which consists of the evaluation indicators for thesupply level of each subsystem

+e main process used to evaluate the supply level of theurban public infrastructure system is described below

Step 1 According to the urban development orientation theestablished stock of the urban public infrastructure and theinterdependence of the public infrastructure determine thestructural relationship of the urban public infrastructuresystem and act as the basis for constructing the structure ofthe urban public infrastructure system ANP managementactivities +is process needs to be conducted by experts

Step 2 +e ANP super matrix and the weighted supermatrix are calculated +e evaluation criteria used for theANP act as the basis for evaluating the relationships in thesystem and reflect the overall goal of the evaluation Let theevaluation criteria in the ANP structure beCi i 1 2 m +e systemrsquos network layer has sub-systems Ij j 1 2 n For evaluating the supply level ofurban public infrastructure systems and interdependence Ciis used as a criterion to judge the interdependence of urbanpublic infrastructure subsystems On this basis the judg-ment matrix is constructed to form the feature vector(W1j W2j Wij) When the feature vector passes theconsistency test it is expressed as a matrix form and a localweight vector matrix Wij is generated m supermatrices W

are formed under the influence of the control criterion indexCi however W is not a normalized matrix To ensure thecalculation results are objective and comparable thesupermatrix columns are normalized +e correspondingweighting factor Yij i j 1 2 3 n is set and thesuperweighted matrix is Wij yijwij

To accurately reflect the interaction between the sub-systems the stability of the supermatrix must be processedStability processing is performed on the superweightingmatrix Wij generating an ANP limit matrix Winfin +eprocessing method is as follows

Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)

Equation (9) is convergent and unique and the value ofthe corresponding column in the original matrix is theweight of the stability of the urban public infrastructuresubsystem

Step 3 After the subsystem weights are obtained theweights of the internal indicators of each subsystem areobtained using AHP

Step 4 +e entropy method is used to obtain the evaluationindex weight of each subsystem [34 35]

Step 5 Using a combination weighting method based ongame theory the weights of the evaluation indexes of eachsubsystem are obtained


Step 6 +e supply level of each subsystem and the overallsystem are obtained

+e supply level of each subsystem and the system supplylevel are obtained by using index weights are calculatedusing a combination weighting method based on gametheory

Ssubsystemir 1113944

n

j1ulowastjrYij (10)

where Ssubsystemir represents the supply level of each sub-system 1 2 5 represent 5 different subsystems i rep-resents the year and ulowastjr represents the weight of thecombination index (which is based on game theory) for eachsubsystem

+e supply level of the urban public infrastructuresystem is obtained by using the following formula

Ssystemi 1113944n

j1ulowastj Yij (11)

where ulowastjr represents the supply level of the urban publicinfrastructure system and ulowast represents the weight of thecombination index (which is based on game theory) of theurban public infrastructure system

232 Coupling Coordination Analysis

(1) Coupling Coordination Model (CCM) Coupling is a termused in physics to indicate the degree to which two or moresystems interact and affect each other to reach a degree ofsynergy Coupling is used to measure the degree of agree-ment in terms of the level of system development Liao wasthe first to develop a model to evaluate the degree of cou-pling coordination within a system or between differentsystems and further differentiated the levels of couplingcoordination degree [36] +is paper constructs a CCM ofthe urban public infrastructure system and the urban eco-nomic social and environmental system to analyze the de-gree of coordinated development between the urban publicinfrastructure system and the level of urban development+e calculation process of the CCM is as follows

(1) +e evaluation value of the urban public in-frastructure system and the urban economic socialand environmental system is calculated which arerepresented by f(x) and g(y) respectively +eseare shown in Table 5

(2) +e coupling degree of the urban public in-frastructure system and the urban economic socialand environmental system is calculated

Evaluation of the management of the urban infrastructure system

Economic growth C1 Social development C2 Environment pressure C3

I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2

Figure 3 Model used to evaluate the management of the supply level of the urban public infrastructure system


C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)

where D represents the degree of the coupling between thetwo systems D isin (0 1) C represents the degree of co-ordination between the two systems C isin (0 1) T representsthe comprehensive coordination index of the two systemsand a and b represent the contribution of the two systemsLet f(x)

(2) Dynamic Coupling Coordination Model (DCCM) +eDCCM is used to determine the coupling degree of thecomposite system [37] Li and Ding was the first to propose aDCCM and used it to evaluate the coordination of resourceenvironment systems and social economic systems and thencalculated the coordination degree of the composite system[38]

To clarify the relationship between the urban publicinfrastructure system and the urban economic social andenvironmental system this paper assumes that both ofthese systems and their relationship form a compositesystem Based on theory of the evolution of subsystems in ageneral system we construct a DCCM to analyze theevolution state and coupling state of the composite systems+e changes between the urban public infrastructure sys-tem and the urban economic social and environmentalsystem are nonlinear so the evolution equation can beexpressed as

dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)

where f is a nonlinear function of xi +e motion stability ofa nonlinear system depends on the characteristic rootproperty of the first approximation system +e high-orderterm can guarantee the stability of motion and be used toobtain an approximate linear system

dx(t)

dt

1113944n

i1aixi i 1 2 n (14)

Using the above method we establish the generalfunction of the urban public infrastructure system and theurban economic social and environmental system

f(x) 1113944n

i1aixlowasti i 1 2 n

g(y) 1113944n

i1biylowasti i 1 2 n

(15)

We assume that the urban public infrastructure systemand the urban economic social and environmental systemand their relationship are in the same system which has twoelements F(x) and F(y) According to Beta Langfirsquos generalsystem theory the evolution equation of a composite systemis expressed as

F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)

Table 5 Evaluation of the supply level of urban infrastructure system and the demand level of the urban economic social and envi-ronmental system

Years Urban infrastructure system supply level (f(x)) Urban economic social and environmental systemevaluation value (g(y))

2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097


F(x) and G(y) are the evolutionary states of the urbanpublic infrastructure system and the urban economic socialand environmental system under their own interaction andexternal conditions VF(x) and VG(y) are the respectiveevolutionary speeds of the urban public infrastructuresystem and the urban economic social and environmentalsystem In a composite system because the entire systemcontains only two elements F(x) and G(y) any changes inthe subsystem that occur when F(x) and G(y) interact willcause the entire system to change +e evolution rate V of acomposite system can be seen as a function of VF(x) andVG(y) so VG(y) +erefore VF(x) and VG(y) are used ascontrol variables the coupling relationship between thecomposite system and the two subsystems can be obtainedby studying the variation in V Because the evolution of theentire system satisfies the S-type development mechanismwe assume that the dynamic coupling and coordinationrelationship between the urban public infrastructure systemand the urban economic social and environmental system iscyclical Since a change in V is caused by VF(x) and VG(y) weanalyze V on the two-dimensional coordinate plane (VF(x)VG(y))+e change in V is an ellipse in the coordinate system(the change in the urban economic social and environ-mental system is not as rapid as that of the urban publicinfrastructure system and the amplitude is relatively small)as shown in Figure 4

In this case the variable V is an ellipse +e variable βrepresents the angle between VF(x) and VG(y) According tothe value of β we can determine the value of the dynamiccoupling coordination degree of the composite systemBased on relevant research [38] this paper proposes thedevelopment stage and state of the dynamic coupling co-ordination degree of the composite system as shown inTable 6

β arctanVF(x)

VG(y)

1113888 1113889 (18)

3 Empirical Research

31 Calculation of the Evaluation Value of the Supply Level ofthe Urban Public Infrastructure System

311 ANP Analysis of the SupplyWeights of the Urban PublicInfrastructure Subsystem Under the constraints of thecomprehensive development level of the economic socialand environmental subsystems in cities this paper usesSuper Decisions software to evaluate the supply level of theurban public infrastructure Taking into account the strongprofessionalism of the research questions this paper selectseight experts including senior management personnel andsenior engineers who have 10ndash20 years of experience in theurban public infrastructure field to score the judgmentmatrix reflecting the supply structure management of theurban public infrastructure system +e experts evaluatedbased on a comparison of contribution rates the principle ofthe universality rate and the principle of irreplaceability +eresults are shown in Tables 7ndash14

In the ANPmodel of the overall supply level of the urbanpublic infrastructure system evaluation criteria for eco-nomic growth (C1) social welfare (C2) and environmentalpressure (C3) evaluation criteria are used to identify theinteractions among the subsystems of urban public in-frastructure in the network layer and the correspondingjudgment matrix is established as shown in the table below+e relationship between the judgment indicators in thetable is based on a 9-point method 1ndash9 indicates that theinfluence of one subsystem on the other subsystem hasgradually increased +e score of the judgment matrix istaken as the mean of the expert score +e consistency testresult of the judgment matrix is 0056 (lt01) indicating thatthe judgment matrix passes the consistency test

When all the judgment matrices pass the consistencytest the ANP supermatrix the weighted supermatrix andthe limit matrix of the urban public infrastructure systemsupply level evaluation model are generated using SuperDecisions software Since the limits in the limit matrixconverge and are unique the weights of the interdependentsubsystems in the model of the supply level of urban publicinfrastructure are obtained which is Wi (05396 0297001634) +e weights of the subsystems in the network layerare (02075 03270 01386 02040 and 01229)

312 Entropy Method +rough the collection processingand standardization of the statistical yearbook data used inthe evaluation indexes of the five subsystems in Beijing theentropy weight of the evaluation index is calculated using theentropy method (see Table 1)

313 e Weights in Each Indicator System Are CalculatedUsing a Combined Weight Method Based on Game eory+e weight of the evaluation index of each subsystem ob-tained by the entropy method is uIEW +e weight of theevaluation index obtained by the ANP method is uANPUsing the combined weight method based on game theorycombined with the objective evaluation of the entropymethod and the subjective evaluation of ANP the weight of

β

VF(x)

VG(y)

IIV

IIIII

Figure 4 Dynamic coupling degree between urban public in-frastructure and the urban economic social and environmentalsystem (created by author based on Li Chongmingrsquos study [38])


the optimal urban public infrastructure evaluation index isexpressed as ulowastcw (as shown in Table 1)

314 e Evaluation Value of the Supply Level of the TypicalUrban Public Infrastructure System Is Obtained +e eval-uation value of the urban infrastructure system supply levelis obtained by using equation (11) (Table 5) +e evaluationvalue of the urban infrastructure system from 2000 to2016 gradually increased the supply level of the urban

infrastructure systems from 01383 to 06372 with a growthrate of 783

32 Calculation of the Evaluation Value of the Urban Eco-nomic Social and Environmental System Using the entropymethod and the AHPmethod on the urban economic socialand environmental system indicators shown in Table 2 theindex weights are obtained by using a combined weightmethod based on game theory +en the evaluation value ofthe demand level of the economic social and environmental

Table 6 Dynamic coupling and coordination of the composite system

Range of β Stage System development stage System status

minus 90∘≺ βle 0∘ I Low-level symbiosis

At this stage of development the development speedof urban public infrastructure systems is very lowand the impact of urban public infrastructure systems

on urban economic social and environmentalsystems is almost 0

0∘ ≺ β≺ 45∘ II Primary coordinated development stage

VF(x) ltVG(y) +e development speed of urban publicinfrastructure system is lower than that of urban

economic social and environmental system Urbanpublic infrastructure system can not promote the

development of urban economic social andenvironmental system showing that urban

infrastructure system can not carry the developmentof urban economic social and environmental

system

β 45∘ Coordinated development stage

VF(x) VG(y) +e speed of urban publicinfrastructure system is equal to the urban economicsocial and environmental system and the urban

public infrastructure system and the urban economicsocial and environmental system are coordinated

45∘≺ βle 90∘ Coordinated development stage

VF(x) gtVG(y) With the development of the urbanpublic infrastructure system the two systems beganto interact with each other +e restrictions of theurban economic social and environmental systemon the urban public infrastructure system began to

appear but it was not obvious

90∘ ≺ βle 180∘ III Extreme development stage

With the accelerated development of urbaneconomic social and environmental systems urbanpublic infrastructure systems have increased the

demand for urban development and thecontradiction between infrastructure systems andurban systems has emerged and began to limit the

improvement of urban development level

minus 180∘ ≺ βle minus 90∘ IV High-level coordinated development stage

+e composite system gradually transforms into acommon development stage and finally reaches thehigh-level coordinated development of the urban

public infrastructure system and the urban economicsocial and environmental system

+e authors edited the table by themselves according to Li Chongmingrsquos literature [38]

Table 7 ANP judgment matrix of the system (based on C1)

I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


system in Beijing is obtained (Table 5) +e demand level ofthe urban economic social and environmental system hasgradually increased from 2000 to 2016 from 01590 to07097 with a growth rate of 776

+e time series of the evaluation values of the supplylevel of the urban public infrastructure system and the de-mand level of the urban economic social and environmentalsystem from 2000 to 2016 can be divided into four stages +eevaluation value of the urban public infrastructure systemfrom 2000 to 2005 is very close to the demand level of theurban economic social and environmental system From2006 to 2011 the supply level of the urban infrastructure

system is greater than the demand level of the urban eco-nomic social and environmental system From 2011 to 2015the supply level of the urban public infrastructure system isclose to the evaluation level of the demand level of the urbaneconomic social and environmental system In 2016 thedemand level of the urban economic social and environ-mental system is greater than the supply level of the urbanpublic infrastructure system During the 11th Five-Year Planperiod the average annual growth rate of urban infrastructurefixed asset investment reached 27 which is much higherthan 729 in the 15th period and 735 in the 12th Five-YearPlan period As a result of the global financial crisis BeijingrsquosGDP had negative growth in 2009 which explains why thesupply of the urban public infrastructure system from 2006 to2010 is higher than the demand for the urban economicsocial and environmental system

33Analysis of theCouplingDegree of the Level of Supply of theUrban Public Infrastructure System and the Urban EconomicSocial and Environmental System Table 15 shows that thedegree of coordination between the urban public in-frastructure system and the urban economic social andenvironmental system increases from 09976 to 09986 from2000 to 2016 and the change is relatively stable Howeverthe coupling coordination degree D increases from 03851 to08200 and a significant change occurs +e third column ofTable 15 shows that the coupling and coordination degreehas gone through three stages from 2000 to 2016 namely theunbalanced development stage from 2000 to 2003 themicrobalance stage from 2004 to 2005 and the balanceddevelopment stage from 2006 to 2016

To determine the influence of the evaluation values oftwo systems on the coupling coordination degree D thispaper establishes a multivariate linear regression model thatuses the coupling coordination degree D as the explainedvariable and the evaluation values of the urban public in-frastructure system and the urban economic social andenvironmental system as explanatory variables +e modelfitting results shown in Tables 16 and 17 are obtained by SPSSsoftware+e fitting results show that the R2 fit of the model is0995 which is very close to 1 indicating that the model has ahigh degree of fit +e model is shown in Table 17 When thesupply level of the urban infrastructure system increases byone unit the coupling coordination degree D increases by0555 When the demand for the urban economic social andenvironmental system increases by one unit the couplingcoordination degree D increases by 0244

34 Analysis of the Dynamic Coupling Coordination Degreebetween theUrbanPublic Infrastructure Systemand theUrbanEconomic Social and Environmental System According tothe evaluation value of the supply level of the urban in-frastructure system (f(x)) and the urban economic socialand environmental system (g(y)) shown in Table 5 we canobtain the evaluation curves and fitting functions of thesupply level of the urban infrastructure system (f(x)) andthe evaluation value of the urban economic social andenvironmental system (g(y)) All of these are presented in


I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1

Table 10 ANP judgment matrix of the system (based on I1)

I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


Figure 5 +e dynamic degree of coupling coordinationbetween the urban public infrastructure system and theurban economic social and environmental system is ob-tained by using equation (16)ndash18 (Figure 6)

Figure 6 shows that the degree of the dynamic couplingcoordination between the urban public infrastructure sys-tem and the urban economic social and environmentalsystem in Beijing can be divided into three stages +e firstphase in 2000 shows that the degree of the dynamic couplingcoordination between the two systems is 3215deg and that thetwo systems are in the primary coordinated developmentstage From 2001 to 2009 the degree of the dynamic cou-pling coordination between the two systems ranges from4896deg to 8355deg this is the second stage At this stage the twosystems are in a symbiotic and coordinated developmentstage +e two systems begin to interact with each other andthe supply level of the urban public infrastructure systemincreases the demand level of the urban economic socialand environmental system Because of the influence of theglobal financial crisis in 2008 from 2010 to 2016 the degreeof the dynamic coupling coordination of two systemschanged from 8177deg to 5626deg which represents a low level ofcoexistence and the state of low interaction between the twosystems

35 Analysis of the Influencing Factors of the Degree ofCoupling between the Urban Public Infrastructure System andthe Urban Economic Social and Environmental System+e degree of the coupling between the urban public in-frastructure system and the urban economic social andenvironmental system is affected by many factors+is papermainly examines the impact of 20 evaluation indicators ofthe urban public infrastructure system and 12 evaluationindicators of the urban economic social and environmentalsystem Using SPSS software a linear regression analysis wasperformed between coupling degree D and 36 evaluationindicators of the two systems

As shown in Table 18 the degree of the coupling co-ordination between the urban infrastructure system and theurban economic social and environmental system is mostaffected by urban sewage treatment capacity In Table 18 it canbe seen that in the 20 indicators in the urban public in-frastructure system the top five influencing factors on thedegree of the coupling coordination between two systems aresewage treatment capacity natural gas ratio and per capitaheating area total number of urban sanitation special vehiclesand equipment household garbage clearance volume andbureau number of post and telecommunications +e urbaninfrastructure system indicators that have a weaker impact on

Table 15 Degree of coordination between the urban public infrastructure system and urban economic social and environmental system

Years Coordination degree C Coupling coordination degree D Coordination level2000 09976 03851 Mild imbalance development2001 09983 04214 Slightly unbalanced development2002 09999 04773 Slightly unbalanced development2003 09999 04943 Slightly unbalanced development2004 09961 05413 Slightly unbalanced development2005 09998 05721 Slightly unbalanced development2006 09986 06478 Mild imbalance development2007 09950 06757 Mild imbalance development2008 09922 06850 Mild imbalance development2009 09965 07128 Moderately balanced development2010 09958 07315 Moderately balanced development2011 10000 07394 Moderately balanced development2012 10000 07458 Moderately balanced development2013 09999 07728 Moderately balanced development2014 09995 08003 Highly balanced development2015 10000 08302 Highly balanced development2016 09986 08200 Highly balanced development

Table 16 Summary of multiple linear regression models

Model R R Side Adjust the R side Standard estimated error1 0997a 0995 0994 00111601aPredictor (constant) g(y) f(x)

Table 17 Multiple linear regression coefficientsa

Model Nonstandardized coefficient Standard coefficientt Sig

B Standard error Trial version1 (constant) 0293 0008 38834 0000f(x) 0555 0054 0707 10224 0000g(y) 0244 0057 0299 4322 0001aDependent variable D


the degree of coupling coordination between the two systemsaremainly railway density and highway facilities the amount ofpostal and telecommunications services per capita and thenumber of public transportation lines and passenger traffic onpublic transportation per capita annual water supply Table 19shows that in the urban economic social and environmental

system the most influential indicator of the degree of couplingcoordination are the regional GDP actual value +e nextindicators are three social development indicators the numberof employees in the industry the per capita household dis-posable income and per capita consumption expenditures+elast indicator is actual utilization of foreign direct investment

y = 4E ndash 05x4 ndash 00014x3 + 00153x2 ndash 00112x + 01372R2 = 09753

y = 1E ndash 05x4 ndash 00005x3 + 00049x2 + 00161x + 0139R2 = 09931

0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17

Urban infrastructure system supply level f(x)Urban economic social and environmental system evaluation value g(y)Poly (urban infrastructure system supply level f(x)

Figure 5 Trend function of the Beijing urban infrastructure system and the urban economic social and environmental system

ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Degree of the dynamic coupling coordination

Figure 6 Degree of the dynamic coupling coordination between the urban infrastructure system and the urban economic social andenvironmental system in Beijing


4 Conclusion

Research on the relationship between the urban publicinfrastructure system and the urban economic social andenvironmental system is important for the effective man-agement of integrated urban public infrastructure systemsand the long-term sustainable development of the cityTaking Beijing as an example this paper empirically studiesthe degree of coupling coordination between two systemusing data from 2000 to 2016 +is study finds thefollowing

(1) From 2000 to 2016 the comprehensive evaluationvalue of Beijingrsquos urban public infrastructure systemand the urban economic social and environmentalsystem gradually increased and the two values are

relatively close From 2006 to 2011 due to the impactof the financial crisis on Beijingrsquos economic devel-opment level and the increase of urban infrastructureinvestment during the Eleventh Five-Year Plan inBeijing the supply level of Beijingrsquos infrastructuresystem was higher than that of the urban economicsocial and environmental system+e supply level ofurban public infrastructure system was slightly lowerthan the level of urban economic and social envi-ronment development in 2016

(2) +e analysis of the degree of coupling coordinationbetween the Beijing infrastructure system and theurban economic social and environmental systemshows that it is gradually increasing the supply levelof the urban public infrastructure system has a

Table 18 Impact of the 20 indicators of the urban public infrastructure system on the degree of coupling coordination

Indicator layer Linear regression equation R2 Sort

Urban public infrastructure system

I11 per capita social electricity consumption Y 0382 + 0432x 0807 8I12 per capita energy consumption Y 0604 + 0103x 0042

I13 natural gas ratio Y 0310 + 0468x 0896 2I14 per capita heating area Y 0341 + 0468x 0942 2

I21 railway road facility density Y 0449 + 0329x 0911 13I22 per capita urban road area Y 0524 + 0233x 0163

I23 number of public transportation lines Y 0483 + 0361x 0686 11I24 bus operation passenger volume Y 0476 + 0361x 0789 11

I31 per capita park green area Y 0425 + 0390x 0941 10I32 sewage treatment capacity Y 0428 + 0534x 0862 1

I33 total number of urban sanitation special vehicleand equipment Y 0406 + 0457x 0898 3

I34 household garbage clearance volume Y 0439 + 0454x 0951 4I41 per capita annual water supply Y 0784 minus 0441x 0943 14I42 density of water supply pipe Y 0432 + 0404x 0898 9

I43 per capita comprehensive water productioncapacity Y 0821 minus 0401x 0597

I44 sewage pipe density Y 0468 + 0434x 0858 7I51 per capita total postal and telecommunications

volume Y 0527 + 0358x 0532 12

I52 mobile phone penetration rate Y 0421 + 0442x 0841 6I53 mailine penetration rate Y 0677 minus 0060x 0015

I54 bureau number of post and telecommunications Y 0558 + 0444x 0612 5Y represents the coupling coordination degree D and x represents the corresponding evaluation indicator of urban public infrastructure system in the table

Table 19 Influence of 12 indicators of urban economic social and environmental system on coupling coordination degree

Indicator layer Linear regression equation R2 SortS11 regional GDP actual value Y 0425 + 0434x 0950 1S12 the proportion of the tertiary industry Y 0538 + 0288x 0241S13 actual utilization of foreign direct investment Y 0511 + 0402x 0779 5S14 fixed assets investment ratio Y 0854 minus 0365x 0669 8S21 per capita household disposable income Y 0498 + 0416x 0818 3S22 per capita consumption expenditure Y 0504 + 0413x 0785 4S23 number of employees in three industries Y 0416 + 0429x 0978 2S24 urbanization rate Y 0411 + 0361x 0934 7S31 annual average of inhalable particles Y 0858 minus 0387x 0783 9S32 total wastewater discharge Y 0488 + 0388x 0860 6S33 general industrial solid waste production Y 0808 minus 0236x 0195S34 sulfur dioxide emissions Y 0846 minus 0349x 0476Y represents the coupling coordination degree D and x represents the corresponding evaluation indicator of the urban economic social and environmentalsystem in the table


significant impact on the coupling coordinationdegree of the two systems

(3) +e analysis of the degree of dynamic couplingcoordination between the Beijing urban publicinfrastructure system and the urban economicsocial and environmental system shows that thesetwo systems were in dynamic coupling co-ordination states from 2000 to 2009 +e globalfinancial crisis affected the degree of dynamiccoupling coordination between the two systemsand the two systems entered a low-level symbioticcoupling stage from 2010 to 2016 mainly becausethe growth rate of urban public infrastructuresystem supply is negative +is indicates that thedynamic coupling coordination development be-tween two systems can be realized only by accel-erating the improvement of urban infrastructuresupply in Beijing

(4) To promote the coupling degree of the two systemsin Beijing the government should give priority toan improvement in the supply level of urban en-vironmental infrastructure especially an im-provement in sewage treatment capacity thenumber of urban sanitation special vehicles andequipment and household garbage clearance vol-ume Furthermore improving Beijingrsquos GDP andthe social development level such as the number ofemployees in three industries in Beijing has asignificant impact on the coupling coordinationdegree

On the basis of previous studies this paper activelydiscusses the integration and management of urban publicinfrastructure systems and the coordinated development ofurban public infrastructure systems and urban economicsocial and environmental systems We hope that this re-search has a positive effect on urban public infrastructuresystems by helping them meet their development needsHowever restrictions regarding the availability of relevantstatistical data on Beijing affected the evaluation of thesupply level of the urban public infrastructure system inBeijing to some extent +is is a problem that should beemphasized in future research

Data Availability

+e data of this research are from Beijing statistical yearbook2000ndash2016 and the data are reliable and available

Conflicts of Interest

+e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

+e research was supported by the Philosophical SocialScience Fund Project in Tianjin (project approval noTJGL18-034)

References

[1] OECD (Organisation for Economic Co-Operation and De-velopment) Infrastructure to 2030 Telecom Land TransportWater and Electricity OECD Parise France 2006

[2] China statistical yearbook 2017 httpwwwstatsgovcntjsjndsj2017indexchhtm

[3] S M Rinalidi J P Peerenboom and T Kelly ldquoIdentifyingunderstanding and analyzing critical infrastructure in-terdependenciesrdquo IEEE Control System Magazine vol 21no 6 pp 11ndash25 2001

[4] Z M Tao and Y Sun ldquoDynamic analysis on influencingfactors of urban infrastructure system supply effectivenesscase study of Beijing Chinardquo Research on Financial andEconomic Issues vol 415 no 6 pp 131ndash137 2018

[5] J W Hall R J Nicholls A J Hickford et al IntroductionNational Infrastructure assessmentthe Future of NationalInfrastructure a System-of-System Approach CambridgeUniversity Press Cambridge UK 2016

[6] J W Hall A Otto A J Hickford et al A framework foranalysing the long-term performance of interdependent in-frastructure system e Future of National Infrastructure aSystem-of-System Approach Cambridge University PressCambridge UK 2016

[7] A Otto J W Hall A J Hickford et al ldquoA quantified system-of-systems modeling framework for robust national in-frastructure planningrdquo IEEE Systems Journal vol 10 no 2pp 385ndash396 2016

[8] R Zimmerman and C E Restrepo ldquo+e next step quanti-fying infrastructure interdependencies to improve securityrdquoInternational Journal of Critical Infrastructures vol 2 no 23pp 215ndash230 2006

[9] C-N Huang J J H Liou and Y-C Chuang ldquoA method forexploring the interdependencies and importance of criticalinfrastructuresrdquo Knowledge-Based Systems vol 55 no 5pp 66ndash74 2014

[10] P Zhang and S Peeta ldquoDynamic and disequilibrium analysisof interdependent infrastructure systemsrdquo TransportationResearch Part B Methodological vol 67 no 8 pp 357ndash3812014

[11] J Santos-Reyes D Padilla-Perez and A N Beard ldquoModelingcritical infrastructure interdependency the case of the Mexicocity Metro transport systemrdquo Human and Ecological RiskAssessment An International Journal vol 21 no 5pp 1428ndash1444 2015

[12] P Pederson D Dudenhoeffer S Hartley et al Critical In-frastructure Interdependency Modeling A Survey of US AndInternational Research Idaho National Laboratory IdahoFalls ID USA 2006

[13] C-L Chai X Liu W J Zhang and Z Baber ldquoApplication ofsocial network theory to prioritizing oil amp gas industriesprotection in a networked critical infrastructure systemrdquoJournal of Loss Prevention in the Process Industries vol 24no 5 pp 688ndash694 2011

[14] S Saeid L Kattana P Jayasinghea et al ldquoIntegrated in-frastructure systemsmdasha reviewrdquo Sustainable Cities and So-ciety vol 36 pp 1ndash11 2018

[15] A Pereira and J Andraz ldquoOn the economic effects of publicinfrastructure investment a survey of the international evi-dencerdquo Journal of Economic Development vol 38 no 4pp 1ndash37 2013

[16] Z Elburz P Nijkamp and E Pels ldquoPublic infrastructure andregional growth lessons from meta-analysisrdquo Journal ofTransport Geography vol 58 no 5 pp 1ndash8 2017


[17] I Yakubu M A Akaateba and B A A Akanbang ldquoA studyof housing conditions and characteristics in the TamaleMetropolitan Area Ghanardquo Habitat International vol 44no 8 pp 394ndash402 2014

[18] L A Sierra E Pellicer and V Yepes ldquoMethod for estimatingthe social sustainability of infrastructure projectsrdquo Environ-mental Impact Assessment Review vol 65 no 7 pp 41ndash532017

[19] A Schafer and M Swilling ldquoValuing green infrastructure inan urban environment under pressure the Johannesburgcaserdquo Ecological Economics vol 86 no 9 pp 246ndash257 2013

[20] E Andersson S Barthel S Borgstrom et al ldquoReconnectingcities to the Biosphere stewardship of green infrastructureand urban ecosystem servicesrdquo AMBIO vol 43 no 4pp 445ndash453 2014

[21] W Y Chen ldquo+e role of urban green infrastructure in off-setting carbon emissions in 35 major Chinese cities a na-tionwide estimaterdquo Cities vol 44 no 6 pp 112ndash120 2015

[22] H Hall and N Hickford ldquoSystems-of-systems analysis ofnational infrastructurerdquo Engineering Sustainability vol 166no 5 pp 249ndash257 2016

[23] J Y Zhang ldquoResearch on coordinated development of in-frastructure construction investment in Wuhanrdquo Journal ofHuazhong University of Science and Technology (Urban Sci-ence Edition) vol 1 pp 1ndash5 2015

[24] Q Zhang ldquoStudy on the coordinated development of envi-ronmental infrastructure in urban intensive areas inChinamdashmdasha case study of environmental infrastructure in thepearl river delta urban agglomerationrdquo City Planning vol 10pp 41ndash43 2004

[25] Y B Ji and Y D Dou ldquoNew urbanization and coordinateddevelopment of transportation infrastructurerdquo AcademicExchange vol 268 no 7 pp 127ndash132 2016

[26] B Yu X M Liu and X I Zheng ldquoQuantitative evaluationand analysis of the coordinated development of urban re-sources infrastructure and economic and social developmentin Qingdaordquo China Population Resources and Environmentvol 4 pp 149ndash153 2007

[27] J N Wu Y H Cao S M Yao et al ldquoAnalysis of the co-ordinated development of infrastructure and regional eco-nomic systemsrdquo Economic Geography vol 29 no 10pp 1624ndash1628 2009

[28] J Ying X Q Yao Y Cheng et al ldquoQuantitative analysis ofcoordination relationship between climate and green in-frastructure in Hangzhou city based on coupling modelrdquoChinese Garden vol 33 no 12 pp 53ndash57 2017

[29] Y Sun Z M Tao and P Yao ldquoStudy on the coordinateddevelopment degree of urban public infrastructure compositesystemrdquo Urban Development Research vol 22 no 5pp 24ndash28 2015

[30] Z M Tao and Y Sun ldquoStudy on the utility improvement ofurban public infrastructure system from the perspective ofsupply and demand coordinationrdquo Journal of ShenzhenUniversity (Humanities and Social Sciences) vol 33 no 3pp 100ndash105 2016

[31] L F Wang ldquo+eories and algorithms of network analysisprogress (ANP)rdquo System Engineering eory and Practicevol 3 pp 44ndash50 2001

[32] X Z Wu Nonparametric Statistical Method ChongqingHigher Education Press Chongqing China 1996

[33] D P Hou Introduction to Game eory Hefei University ofScience and Technology of China Press Hefei China 2004

[34] J H Yan C H Feng and L Li ldquoSustainability assessment ofmachining process based on extension theory and entropy

weight approachrdquo Advance Manufacture Technology vol 71pp 1419ndash14312014

[35] F K Jesmin and M B Sharif ldquoWeighted entropy for seg-mentation evaluationrdquo Optics amp Laser Technology vol 57pp 236ndash242 2014

[36] C B Liao ldquoQuantitative evaluation and classification systemof coordinated development of environment and econo-mymdashtaking the pearl river delta urban agglomeration as anexamplerdquo Tropical Geography vol 2 pp 76ndash82 1999

[37] X J Li and J G Tao ldquo+e dynamic coupling analysis forcoordinated development of the environment and economybased on cloud model case study of Henanrdquo in Proceedings ofthe 2014 International Conference on Management Science ampEngineering pp 726ndash735 IEEE Helsinki Finland August2014

[38] C M Li and L Y Ding ldquoEvaluation model and application ofcoordinated development of resource environment and socialeconomy in small townsrdquo Systems Engineering eory andPractice vol 11 pp 134ndash139 2004


Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


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


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

and water pollution still exist Improving the supply effi-ciency of urban infrastructure systems is an importantproblem for urban managers

+e urban public infrastructure system is a multibodycomplex and composite system of energy transportationpostal services and telecommunications the environmentwater resources and other subsystems +ese subsystemsare interdependent and interrelated and form the wholeurban public infrastructure system together providing thebasic products and services needed for urban development[3 4] Infrastructure supply is affected by the human re-search view and the specialized division of urban publicinfrastructure supply and traditionally which is providedby each department alone there is a lack of communicationand contact between departments [3 5 6] Over timepeople have become increasingly aware that the varioussubsystems of urban public infrastructure are interrelatedand interact forming a system of urban public in-frastructure Only by including supply management in thesystem as a whole can we improve the overall supply level ofurban public infrastructure in an orderly manner so thatthe urban public infrastructure system can meet the needsof urban economic and social development +e UnitedKingdom proposed studying the relationship between thenational infrastructure system and economic and socialdevelopment and managing the future development plan ofthe national infrastructure system as a whole [7] In 2017Chinarsquos ldquo13th Five-Year Plan for Urban Public In-frastructure Constructionrdquo propose for the first time tochange the way in which previous departments compiledindustry plans separately to consider the overall planningof urban infrastructure in a systematic way and to co-ordinate the supply of products and services in all sectors tomeet the requirements of urban economic and socialdevelopment

Understanding the interdependence of the varioussubsystems of urban public infrastructure is a prerequisitefor studying the overall supply of urban public in-frastructure systems Different scholars define and classifythe interdependence among subsystems of urban publicinfrastructure Rinaldi believes that thee physical in-formation spatial and logical interdependence existsamong the subsystems of urban public infrastructure [3]Many scholars have summarized classified and simulatedthe interdependence of urban public infrastructure [8ndash10]Jaime presents a System Safety Management System(SSMS) model to interdependency modelling for the case ofthe Mexico City Metro transport network which highlightsthat interdependency in the Metro transportation networkoccurs vertically and horizontally [11] +e study of theinterdependence of urban public infrastructure mainlyfocuses on the impact of urban public infrastructure in-terdependence when a sudden event occurs [12] Howeverthe interdependence of urban public infrastructure existsnot only when an emergency arises but also in peoplersquosdaily lives and the impact on the supply of urban publicinfrastructure products and services is equally important[13] +e research on the interdependence of the varioussubsystems of urban public infrastructure has been

deepening Tao proposes that the indispensability com-pleteness and irreplaceability of the subsystems of urbanpublic infrastructure are the essence and fundamentalreasons for the interdependence of the subsystems of urbanpublic infrastructure and an important basis for the for-mation of the overall supply management system of urbaninfrastructure +e interdependence of the various sub-systems of urban public infrastructure is of great signifi-cance to the normal operation of urban publicinfrastructure and the integrated supply management ofthe system [4] Due to the complexity of the in-terdependence of urban infrastructure systems and theirsubsystems studying the role of interdependence of in-frastructure systems and the supply management of in-frastructure systems is challenging [14]

+e urban public infrastructure system should promotethe cityrsquos economic growth social welfare and environ-mental quality development An improvement in thesupply level of urban public infrastructure systems willincrease the labor productivity of the society expand totalsocial demand increase the accumulation of fixed capitalincrease the total output of the society and guarantee theeconomic growth of the city [15 16] In addition an in-crease in the supply level of urban public infrastructure willpromote the convenience of urban production and livingactivities attract foreign populations increase employmentopportunities and improve the social welfare level of cities[17 18] +e advancement of urbanization has put pressureon the urban environment to a certain extent Urban publicinfrastructure can deal with urban garbage and sewagereduce air pollution slow the heat island effect improveurban climate conditions etc and have a positive impacton the urban environment [19ndash21] On the one hand animprovement in the urban public infrastructure supplylevel will increase the level of urban development and thegrowth of urban social wealth so that the city governmentwill be stronger and have more funds to invest in theconstruction and operation of urban infrastructure On theother hand due to the advancement of urbanization urbanpopulation concentration economic growth and envi-ronmental quality have put pressure on urban public in-frastructure Urban public infrastructure is interdependentand mutually influential An urban public infrastructuresystem based on interdependence is a collection of humanactivities that actively arrange and integrate the physicalfacilities and activities of the subsystems of urban publicinfrastructure and ensure that the subsystems of the urbanpublic infrastructure interact to improve the overall effi-ciency of the urban public infrastructure system +roughinfrastructure management control the collection of in-formation regarding system infrastructure demand aconsideration of the interdependence between the sub-systems of infrastructure expert opinion and governmentdecision-making city governments engage in urban in-frastructure supply management and make decisions toensure the supply of urban public infrastructure system canmeet to support the development of urban economicsocial and environmental system +e interaction thatoccurs between urban public infrastructure systems and













Benefit

Effect

Demandfeedback

ControlSupply


decision system


system


systems















22 Research Method


Positive indicator



Negative indicator










supply level























Environmentbenefit




unit 00335 00217 00251














S1 economic aspect



S2 social aspect








Tabl

e3

+estandardized

data

ofurbanpu

blic

infrastructure

system

year

Percapita

social

electricity

consum

ption

I 11

Percapita

energy

consum

ption

I 12

Natural

gasratio

I 13

Per

capita

heating

area

I 14

Railw

ayand

high

way

facilities

density

I 21

Per

capita

urban

road

area I 22

Num

berof

public

transportatio

nlin

esI 23

Bus

operation

passenger

traffi

cI 24

Per

capita

park

green

area I 31

Sewage

treatm

ent

capacity

I 32

Total

numberof

urban

vehicle

sanitatio

nspecial

equipm

ent

I 33

Dom

estic

garbage

removal

volume

I 34

Per

capita

annu

alwater

supp

lyI 41

Tap

water

supp

lypipe

density

I 42

Percapita

tap

water

comprehensiv

eprod

uctio

ncapacity

I 43

Sewage

pipe

density

I 44

Percapita

postaland

telecommun

ications

volumeI 51

Mob

ileph

one

penetration

rate

I 52

Fixedlin

emainline

penetration

rate

I 53

Bureau

numberof

post

and

telecommun

ications

I 54

2000

00000

00000

00000

00000

00000

00000

03735

00000

00000

00000

00000

00000

10000

00000

06906

00000

00000

00000

00375

00000

2001

00364

00355

04163

01323

00329

04355

00000

01052

00637

00310

01859

00238

08757

00573

06780

00515

00002

01214

02048

00047

2002

02486

01929

04871

02382

00878

10000

01088

02088

01398

01078

02048

00447

05718

01010

10000

01335

00405

02386

03106

00177

2003

03754

03775

04421

04598

00961

00347

01912

00487

02748

01789

02572

01140

05935

01783

09396

01741

00989

03087

05085

00250

2004

05346

10000

04167

05401

01169

03915

01941

02276

02780

02616

03969

01911

04806

02535

06726

01751

01406

03923

08464

00213

2005

06168

06046

05918

06281

01248

06958

02088

02715

03634

04043

03861

02756

04204

02375

02708

01108

02142

04234

10000

00273

2006

07935

08251

06777

06882

08050

05245

02029

01504

03634

04188

04271

04224

03393

04586

03365

02561

03042

04430

08362

00278

2007

08480

09660

08351

07056

08344

05360

02765

01991

04565

04540

04337

05292

02861

05905

03396

04149

04704

04265

07713

01077

2008

09348

05646

09242

07949

07852

08167

03647

04542

06118

04155

05139

06257

02100

06958

02889

04317

05685

04015

06143

01062

2009

06154

04736

09181

07843

08338

07522

04294

06161

07516

04705

05081

06248

01509

07678

02873

04378

06478

04430

05461

01202

2010

06977

05010

09482

07856

08759

06693

05059

06919

08292

04891

05768

05847

00588

09124

02762

04351

07866

05070

04471

01949

2011

06670

03221

09069

08526

09162

05281

06147

07720

08758

04982

06396

05871

00501

10000

03496

04825

01624

06229

04027

02003

2012

07493

03294

09535

08643

09388

04847

06000

08674

09068

05377

08046

06113

00110

06863

00000

06432

02056

07785

03652

03074

2013

07987

03475

09351

08849

09602

05308

08088

09729

09379

05471

08536

06518

00000

07361

01110

07472

02914

08176

03072

04034

2014

08186

03363

09293

09136

09817

05898

10000

10000

09689

06132

09078

07595

00175

07895

03443

07759

03696

10000

02253

04405

2015

08369

02923

09769

09405

09859

05739

09971

08107

09845

06432

09661

08574

00312

08351

03379

08787

05771

09835

01433

06948

2016

10000

04077

10000

10000

10000

06353

10000

08023

10000

10000

10000

10000

00519

08695

03264

10000

10000

09304

00000

08269


Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482



U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018



















Benefit

Effect

Demandfeedback

ControlSupply


decision system


system


systems















22 Research Method


Positive indicator



Negative indicator










supply level























Environmentbenefit




unit 00335 00217 00251














S1 economic aspect



S2 social aspect








Tabl

e3

+estandardized

data

ofurbanpu

blic

infrastructure

system

year

Percapita

social

electricity

consum

ption

I 11

Percapita

energy

consum

ption

I 12

Natural

gasratio

I 13

Per

capita

heating

area

I 14

Railw

ayand

high

way

facilities

density

I 21

Per

capita

urban

road

area I 22

Num

berof

public

transportatio

nlin

esI 23

Bus

operation

passenger

traffi

cI 24

Per

capita

park

green

area I 31

Sewage

treatm

ent

capacity

I 32

Total

numberof

urban

vehicle

sanitatio

nspecial

equipm

ent

I 33

Dom

estic

garbage

removal

volume

I 34

Per

capita

annu

alwater

supp

lyI 41

Tap

water

supp

lypipe

density

I 42

Percapita

tap

water

comprehensiv

eprod

uctio

ncapacity

I 43

Sewage

pipe

density

I 44

Percapita

postaland

telecommun

ications

volumeI 51

Mob

ileph

one

penetration

rate

I 52

Fixedlin

emainline

penetration

rate

I 53

Bureau

numberof

post

and

telecommun

ications

I 54

2000

00000

00000

00000

00000

00000

00000

03735

00000

00000

00000

00000

00000

10000

00000

06906

00000

00000

00000

00375

00000

2001

00364

00355

04163

01323

00329

04355

00000

01052

00637

00310

01859

00238

08757

00573

06780

00515

00002

01214

02048

00047

2002

02486

01929

04871

02382

00878

10000

01088

02088

01398

01078

02048

00447

05718

01010

10000

01335

00405

02386

03106

00177

2003

03754

03775

04421

04598

00961

00347

01912

00487

02748

01789

02572

01140

05935

01783

09396

01741

00989

03087

05085

00250

2004

05346

10000

04167

05401

01169

03915

01941

02276

02780

02616

03969

01911

04806

02535

06726

01751

01406

03923

08464

00213

2005

06168

06046

05918

06281

01248

06958

02088

02715

03634

04043

03861

02756

04204

02375

02708

01108

02142

04234

10000

00273

2006

07935

08251

06777

06882

08050

05245

02029

01504

03634

04188

04271

04224

03393

04586

03365

02561

03042

04430

08362

00278

2007

08480

09660

08351

07056

08344

05360

02765

01991

04565

04540

04337

05292

02861

05905

03396

04149

04704

04265

07713

01077

2008

09348

05646

09242

07949

07852

08167

03647

04542

06118

04155

05139

06257

02100

06958

02889

04317

05685

04015

06143

01062

2009

06154

04736

09181

07843

08338

07522

04294

06161

07516

04705

05081

06248

01509

07678

02873

04378

06478

04430

05461

01202

2010

06977

05010

09482

07856

08759

06693

05059

06919

08292

04891

05768

05847

00588

09124

02762

04351

07866

05070

04471

01949

2011

06670

03221

09069

08526

09162

05281

06147

07720

08758

04982

06396

05871

00501

10000

03496

04825

01624

06229

04027

02003

2012

07493

03294

09535

08643

09388

04847

06000

08674

09068

05377

08046

06113

00110

06863

00000

06432

02056

07785

03652

03074

2013

07987

03475

09351

08849

09602

05308

08088

09729

09379

05471

08536

06518

00000

07361

01110

07472

02914

08176

03072

04034

2014

08186

03363

09293

09136

09817

05898

10000

10000

09689

06132

09078

07595

00175

07895

03443

07759

03696

10000

02253

04405

2015

08369

02923

09769

09405

09859

05739

09971

08107

09845

06432

09661

08574

00312

08351

03379

08787

05771

09835

01433

06948

2016

10000

04077

10000

10000

10000

06353

10000

08023

10000

10000

10000

10000

00519

08695

03264

10000

10000

09304

00000

08269


Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482



U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018




















22 Research Method


Positive indicator



Negative indicator










supply level























Environmentbenefit




unit 00335 00217 00251














S1 economic aspect



S2 social aspect








Tabl

e3

+estandardized

data

ofurbanpu

blic

infrastructure

system

year

Percapita

social

electricity

consum

ption

I 11

Percapita

energy

consum

ption

I 12

Natural

gasratio

I 13

Per

capita

heating

area

I 14

Railw

ayand

high

way

facilities

density

I 21

Per

capita

urban

road

area I 22

Num

berof

public

transportatio

nlin

esI 23

Bus

operation

passenger

traffi

cI 24

Per

capita

park

green

area I 31

Sewage

treatm

ent

capacity

I 32

Total

numberof

urban

vehicle

sanitatio

nspecial

equipm

ent

I 33

Dom

estic

garbage

removal

volume

I 34

Per

capita

annu

alwater

supp

lyI 41

Tap

water

supp

lypipe

density

I 42

Percapita

tap

water

comprehensiv

eprod

uctio

ncapacity

I 43

Sewage

pipe

density

I 44

Percapita

postaland

telecommun

ications

volumeI 51

Mob

ileph

one

penetration

rate

I 52

Fixedlin

emainline

penetration

rate

I 53

Bureau

numberof

post

and

telecommun

ications

I 54

2000

00000

00000

00000

00000

00000

00000

03735

00000

00000

00000

00000

00000

10000

00000

06906

00000

00000

00000

00375

00000

2001

00364

00355

04163

01323

00329

04355

00000

01052

00637

00310

01859

00238

08757

00573

06780

00515

00002

01214

02048

00047

2002

02486

01929

04871

02382

00878

10000

01088

02088

01398

01078

02048

00447

05718

01010

10000

01335

00405

02386

03106

00177

2003

03754

03775

04421

04598

00961

00347

01912

00487

02748

01789

02572

01140

05935

01783

09396

01741

00989

03087

05085

00250

2004

05346

10000

04167

05401

01169

03915

01941

02276

02780

02616

03969

01911

04806

02535

06726

01751

01406

03923

08464

00213

2005

06168

06046

05918

06281

01248

06958

02088

02715

03634

04043

03861

02756

04204

02375

02708

01108

02142

04234

10000

00273

2006

07935

08251

06777

06882

08050

05245

02029

01504

03634

04188

04271

04224

03393

04586

03365

02561

03042

04430

08362

00278

2007

08480

09660

08351

07056

08344

05360

02765

01991

04565

04540

04337

05292

02861

05905

03396

04149

04704

04265

07713

01077

2008

09348

05646

09242

07949

07852

08167

03647

04542

06118

04155

05139

06257

02100

06958

02889

04317

05685

04015

06143

01062

2009

06154

04736

09181

07843

08338

07522

04294

06161

07516

04705

05081

06248

01509

07678

02873

04378

06478

04430

05461

01202

2010

06977

05010

09482

07856

08759

06693

05059

06919

08292

04891

05768

05847

00588

09124

02762

04351

07866

05070

04471

01949

2011

06670

03221

09069

08526

09162

05281

06147

07720

08758

04982

06396

05871

00501

10000

03496

04825

01624

06229

04027

02003

2012

07493

03294

09535

08643

09388

04847

06000

08674

09068

05377

08046

06113

00110

06863

00000

06432

02056

07785

03652

03074

2013

07987

03475

09351

08849

09602

05308

08088

09729

09379

05471

08536

06518

00000

07361

01110

07472

02914

08176

03072

04034

2014

08186

03363

09293

09136

09817

05898

10000

10000

09689

06132

09078

07595

00175

07895

03443

07759

03696

10000

02253

04405

2015

08369

02923

09769

09405

09859

05739

09971

08107

09845

06432

09661

08574

00312

08351

03379

08787

05771

09835

01433

06948

2016

10000

04077

10000

10000

10000

06353

10000

08023

10000

10000

10000

10000

00519

08695

03264

10000

10000

09304

00000

08269


Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482



U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018









22 Research Method


Positive indicator



Negative indicator










supply level























Environmentbenefit




unit 00335 00217 00251














S1 economic aspect



S2 social aspect








Tabl

e3

+estandardized

data

ofurbanpu

blic

infrastructure

system

year

Percapita

social

electricity

consum

ption

I 11

Percapita

energy

consum

ption

I 12

Natural

gasratio

I 13

Per

capita

heating

area

I 14

Railw

ayand

high

way

facilities

density

I 21

Per

capita

urban

road

area I 22

Num

berof

public

transportatio

nlin

esI 23

Bus

operation

passenger

traffi

cI 24

Per

capita

park

green

area I 31

Sewage

treatm

ent

capacity

I 32

Total

numberof

urban

vehicle

sanitatio

nspecial

equipm

ent

I 33

Dom

estic

garbage

removal

volume

I 34

Per

capita

annu

alwater

supp

lyI 41

Tap

water

supp

lypipe

density

I 42

Percapita

tap

water

comprehensiv

eprod

uctio

ncapacity

I 43

Sewage

pipe

density

I 44

Percapita

postaland

telecommun

ications

volumeI 51

Mob

ileph

one

penetration

rate

I 52

Fixedlin

emainline

penetration

rate

I 53

Bureau

numberof

post

and

telecommun

ications

I 54

2000

00000

00000

00000

00000

00000

00000

03735

00000

00000

00000

00000

00000

10000

00000

06906

00000

00000

00000

00375

00000

2001

00364

00355

04163

01323

00329

04355

00000

01052

00637

00310

01859

00238

08757

00573

06780

00515

00002

01214

02048

00047

2002

02486

01929

04871

02382

00878

10000

01088

02088

01398

01078

02048

00447

05718

01010

10000

01335

00405

02386

03106

00177

2003

03754

03775

04421

04598

00961

00347

01912

00487

02748

01789

02572

01140

05935

01783

09396

01741

00989

03087

05085

00250

2004

05346

10000

04167

05401

01169

03915

01941

02276

02780

02616

03969

01911

04806

02535

06726

01751

01406

03923

08464

00213

2005

06168

06046

05918

06281

01248

06958

02088

02715

03634

04043

03861

02756

04204

02375

02708

01108

02142

04234

10000

00273

2006

07935

08251

06777

06882

08050

05245

02029

01504

03634

04188

04271

04224

03393

04586

03365

02561

03042

04430

08362

00278

2007

08480

09660

08351

07056

08344

05360

02765

01991

04565

04540

04337

05292

02861

05905

03396

04149

04704

04265

07713

01077

2008

09348

05646

09242

07949

07852

08167

03647

04542

06118

04155

05139

06257

02100

06958

02889

04317

05685

04015

06143

01062

2009

06154

04736

09181

07843

08338

07522

04294

06161

07516

04705

05081

06248

01509

07678

02873

04378

06478

04430

05461

01202

2010

06977

05010

09482

07856

08759

06693

05059

06919

08292

04891

05768

05847

00588

09124

02762

04351

07866

05070

04471

01949

2011

06670

03221

09069

08526

09162

05281

06147

07720

08758

04982

06396

05871

00501

10000

03496

04825

01624

06229

04027

02003

2012

07493

03294

09535

08643

09388

04847

06000

08674

09068

05377

08046

06113

00110

06863

00000

06432

02056

07785

03652

03074

2013

07987

03475

09351

08849

09602

05308

08088

09729

09379

05471

08536

06518

00000

07361

01110

07472

02914

08176

03072

04034

2014

08186

03363

09293

09136

09817

05898

10000

10000

09689

06132

09078

07595

00175

07895

03443

07759

03696

10000

02253

04405

2015

08369

02923

09769

09405

09859

05739

09971

08107

09845

06432

09661

08574

00312

08351

03379

08787

05771

09835

01433

06948

2016

10000

04077

10000

10000

10000

06353

10000

08023

10000

10000

10000

10000

00519

08695

03264

10000

10000

09304

00000

08269


Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482



U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018






















Environmentbenefit




unit 00335 00217 00251














S1 economic aspect



S2 social aspect








Tabl

e3

+estandardized

data

ofurbanpu

blic

infrastructure

system

year

Percapita

social

electricity

consum

ption

I 11

Percapita

energy

consum

ption

I 12

Natural

gasratio

I 13

Per

capita

heating

area

I 14

Railw

ayand

high

way

facilities

density

I 21

Per

capita

urban

road

area I 22

Num

berof

public

transportatio

nlin

esI 23

Bus

operation

passenger

traffi

cI 24

Per

capita

park

green

area I 31

Sewage

treatm

ent

capacity

I 32

Total

numberof

urban

vehicle

sanitatio

nspecial

equipm

ent

I 33

Dom

estic

garbage

removal

volume

I 34

Per

capita

annu

alwater

supp

lyI 41

Tap

water

supp

lypipe

density

I 42

Percapita

tap

water

comprehensiv

eprod

uctio

ncapacity

I 43

Sewage

pipe

density

I 44

Percapita

postaland

telecommun

ications

volumeI 51

Mob

ileph

one

penetration

rate

I 52

Fixedlin

emainline

penetration

rate

I 53

Bureau

numberof

post

and

telecommun

ications

I 54

2000

00000

00000

00000

00000

00000

00000

03735

00000

00000

00000

00000

00000

10000

00000

06906

00000

00000

00000

00375

00000

2001

00364

00355

04163

01323

00329

04355

00000

01052

00637

00310

01859

00238

08757

00573

06780

00515

00002

01214

02048

00047

2002

02486

01929

04871

02382

00878

10000

01088

02088

01398

01078

02048

00447

05718

01010

10000

01335

00405

02386

03106

00177

2003

03754

03775

04421

04598

00961

00347

01912

00487

02748

01789

02572

01140

05935

01783

09396

01741

00989

03087

05085

00250

2004

05346

10000

04167

05401

01169

03915

01941

02276

02780

02616

03969

01911

04806

02535

06726

01751

01406

03923

08464

00213

2005

06168

06046

05918

06281

01248

06958

02088

02715

03634

04043

03861

02756

04204

02375

02708

01108

02142

04234

10000

00273

2006

07935

08251

06777

06882

08050

05245

02029

01504

03634

04188

04271

04224

03393

04586

03365

02561

03042

04430

08362

00278

2007

08480

09660

08351

07056

08344

05360

02765

01991

04565

04540

04337

05292

02861

05905

03396

04149

04704

04265

07713

01077

2008

09348

05646

09242

07949

07852

08167

03647

04542

06118

04155

05139

06257

02100

06958

02889

04317

05685

04015

06143

01062

2009

06154

04736

09181

07843

08338

07522

04294

06161

07516

04705

05081

06248

01509

07678

02873

04378

06478

04430

05461

01202

2010

06977

05010

09482

07856

08759

06693

05059

06919

08292

04891

05768

05847

00588

09124

02762

04351

07866

05070

04471

01949

2011

06670

03221

09069

08526

09162

05281

06147

07720

08758

04982

06396

05871

00501

10000

03496

04825

01624

06229

04027

02003

2012

07493

03294

09535

08643

09388

04847

06000

08674

09068

05377

08046

06113

00110

06863

00000

06432

02056

07785

03652

03074

2013

07987

03475

09351

08849

09602

05308

08088

09729

09379

05471

08536

06518

00000

07361

01110

07472

02914

08176

03072

04034

2014

08186

03363

09293

09136

09817

05898

10000

10000

09689

06132

09078

07595

00175

07895

03443

07759

03696

10000

02253

04405

2015

08369

02923

09769

09405

09859

05739

09971

08107

09845

06432

09661

08574

00312

08351

03379

08787

05771

09835

01433

06948

2016

10000

04077

10000

10000

10000

06353

10000

08023

10000

10000

10000

10000

00519

08695

03264

10000

10000

09304

00000

08269


Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482



U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018








Tabl

e3

+estandardized

data

ofurbanpu

blic

infrastructure

system

year

Percapita

social

electricity

consum

ption

I 11

Percapita

energy

consum

ption

I 12

Natural

gasratio

I 13

Per

capita

heating

area

I 14

Railw

ayand

high

way

facilities

density

I 21

Per

capita

urban

road

area I 22

Num

berof

public

transportatio

nlin

esI 23

Bus

operation

passenger

traffi

cI 24

Per

capita

park

green

area I 31

Sewage

treatm

ent

capacity

I 32

Total

numberof

urban

vehicle

sanitatio

nspecial

equipm

ent

I 33

Dom

estic

garbage

removal

volume

I 34

Per

capita

annu

alwater

supp

lyI 41

Tap

water

supp

lypipe

density

I 42

Percapita

tap

water

comprehensiv

eprod

uctio

ncapacity

I 43

Sewage

pipe

density

I 44

Percapita

postaland

telecommun

ications

volumeI 51

Mob

ileph

one

penetration

rate

I 52

Fixedlin

emainline

penetration

rate

I 53

Bureau

numberof

post

and

telecommun

ications

I 54

2000

00000

00000

00000

00000

00000

00000

03735

00000

00000

00000

00000

00000

10000

00000

06906

00000

00000

00000

00375

00000

2001

00364

00355

04163

01323

00329

04355

00000

01052

00637

00310

01859

00238

08757

00573

06780

00515

00002

01214

02048

00047

2002

02486

01929

04871

02382

00878

10000

01088

02088

01398

01078

02048

00447

05718

01010

10000

01335

00405

02386

03106

00177

2003

03754

03775

04421

04598

00961

00347

01912

00487

02748

01789

02572

01140

05935

01783

09396

01741

00989

03087

05085

00250

2004

05346

10000

04167

05401

01169

03915

01941

02276

02780

02616

03969

01911

04806

02535

06726

01751

01406

03923

08464

00213

2005

06168

06046

05918

06281

01248

06958

02088

02715

03634

04043

03861

02756

04204

02375

02708

01108

02142

04234

10000

00273

2006

07935

08251

06777

06882

08050

05245

02029

01504

03634

04188

04271

04224

03393

04586

03365

02561

03042

04430

08362

00278

2007

08480

09660

08351

07056

08344

05360

02765

01991

04565

04540

04337

05292

02861

05905

03396

04149

04704

04265

07713

01077

2008

09348

05646

09242

07949

07852

08167

03647

04542

06118

04155

05139

06257

02100

06958

02889

04317

05685

04015

06143

01062

2009

06154

04736

09181

07843

08338

07522

04294

06161

07516

04705

05081

06248

01509

07678

02873

04378

06478

04430

05461

01202

2010

06977

05010

09482

07856

08759

06693

05059

06919

08292

04891

05768

05847

00588

09124

02762

04351

07866

05070

04471

01949

2011

06670

03221

09069

08526

09162

05281

06147

07720

08758

04982

06396

05871

00501

10000

03496

04825

01624

06229

04027

02003

2012

07493

03294

09535

08643

09388

04847

06000

08674

09068

05377

08046

06113

00110

06863

00000

06432

02056

07785

03652

03074

2013

07987

03475

09351

08849

09602

05308

08088

09729

09379

05471

08536

06518

00000

07361

01110

07472

02914

08176

03072

04034

2014

08186

03363

09293

09136

09817

05898

10000

10000

09689

06132

09078

07595

00175

07895

03443

07759

03696

10000

02253

04405

2015

08369

02923

09769

09405

09859

05739

09971

08107

09845

06432

09661

08574

00312

08351

03379

08787

05771

09835

01433

06948

2016

10000

04077

10000

10000

10000

06353

10000

08023

10000

10000

10000

10000

00519

08695

03264

10000

10000

09304

00000

08269


Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482



U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018








Tabl

e4

+estandardized

data

ofurbanecon

omic

social

andenvironm

entalsystem

Year

Gross

region

alprod

uct

actual

value

S 11

+e

prop

ortio

nof

thetertiary

indu

stries

S 12

Actualu

seof

foreign

investment

amou

ntS 1

3

Fixedassets

investment

ratio

S 14

Percapita

household

disposable

incomeS 2

1

Percapita

consum

ption

expend

iture

S 22

Num

berof

employeesin

three

indu

stries

S 23

Urbanization

rate

S 24

Ann

ual

average

inhalable

particlesS 3

1

Total

wastewater

discharge

S 32

General

indu

strial

solid

waste

prod

uctio

nvolumeS 3

3

Sulfu

rdioxide

emiss

ions

S 34

2000

00000

02210

00000

07978

00000

00000

00000

00000

09459

00000

07017

10000

2001

00674

02918

00035

08216

00262

00144

00160

00574

09865

00044

06976

08959

2002

01294

03938

00195

08978

00451

00602

00997

01127

10000

00532

05834

08572

2003

01952

01303

00343

10000

00753

00884

01398

01680

06622

00555

07664

08161

2004

02817

00000

01175

08840

01127

01245

03908

02219

07703

01116

09274

00000

2005

03315

03173

01567

07514

01556

01596

04306

06778

06757

01498

08256

08511

2006

03833

04023

02482

08470

02052

02127

05000

07574

09324

02016

10000

07837

2007

04862

03598

02934

07235

02480

02297

05383

07757

07568

02383

08886

06771

2008

05498

10000

02478

01641

03063

02677

06019

08205

04054

03091

07260

05501

2009

05350

03088

02934

06932

03492

03158

06308

08322

03919

06672

08442

05303

2010

06347

00992

03835

05891

03990

03844

06863

09384

03919

06100

08805

05136

2011

07641

05099

04086

03365

04806

04533

07497

09691

02973

07277

06832

04370

2012

08096

04136

04698

03146

05566

05226

08123

09652

02297

06602

06536

04190

2013

08707

03739

05575

02521

06387

05974

08683

09767

02162

07161

05711

03884

2014

08795

04561

06461

02460

07152

06557

08945

09878

03243

07959

05390

03519

2015

09002

07932

09971

01736

09059

09458

09434

10000

01351

08091

01111

03175

2016

10000

05694

10000

00000

10000

10000

10000

09991

00000

10000

00000

01482



U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018









U 1113944n

k1Wku

Tk wk ge 0( 1113857 (3)



min11138681113868111386811138681113868111386811138681113868 1113944

n

j1wj times u

Tj minus u

Tj

111386811138681113868111386811138681113868111386811138682 (i 1 2 n) (4)


1113944

n


Tj ui times u

Tj (i 1 2 n) (5)



n






⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

w1

w2


wn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

u1 middot uT1

u1 middot uT2


un middot uTn

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(6)


Wlowastk

wk

1113936nk1wk

(7)


ulowast

1113944n

k1wku

Tk (8)









Winfin

limk⟶infin

1m

1113874 1113875 1113944

m

i1W

k (9)









n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018











n

j1ulowastjrYij (10)



Ssystemi 1113944n

j1ulowastj Yij (11)








I11

I12

I13

I1

I14

I51

I5

I52I53

I54

I4

I44

I43I42

I41

I34 I33

I32

I31

I3

I24

I23

I22

I21

I2



C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018








C f(x)lowastg(y)

((f(x) + g(y))2)21113896 1113897

12

T af(x) + bg(y)

D(x y) C middot T

radic

(12)




dx(t)

dt

f x1 x2 xn( 1113857 i 1 2 n (13)


dx(t)

dt

1113944n

i1aixi i 1 2 n (14)


f(x) 1113944n


g(y) 1113944n


(15)


F(x) df(x)

dt

T1f(x) + T2g(y)

VF(x) dF(x)

dt

(16)

G(y) dg(x)

dt

U1f(x) + U2g(y)

VG(y) dG(y)

dt

(17)



2000 01383 015902001 01675 018822002 02247 023102003 02413 024742004 03200 026832005 03204 033442006 04425 039792007 05045 041312008 05320 041382009 05528 046702010 05862 048842011 05519 054162012 05568 055562013 06076 058702014 06606 062102015 06860 069242016 06372 07097




β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018










β arctanVF(x)

VG(y)

1113888 1113889 (18)








β

VF(x)

VG(y)

IIV

IIIII

















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018






















system
















I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1


I1 I2 I3 I4 I5I1 1 12 2 5 3I2 2 1 3 6 4I3 12 13 1 4 2I4 15 16 14 1 13I5 13 14 12 3 1









I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018















I1 I2 I3 I4 I51 2 12 3 512 1 13 2 42 3 1 4 713 12 14 1 315 14 17 13 1


I2 I3 I4 I5I2 1 4 2 6I3 14 1 12 3I4 12 2 1 5I5 16 13 15 1


I1 I3 I4 I5I1 1 3 2 5I3 13 1 12 3I4 12 2 1 4I5 15 13 14 1


I1 I2 I4 I5I1 1 12 1 3I2 2 1 2 4I4 1 12 1 3I5 13 14 13 1


I1 I2 I3 I5I1 1 12 3 5I2 2 1 4 6I3 13 14 1 3I5 15 16 13 1


I1 I2 I3 I4I1 1 12 3 5I2 2 1 4 7I3 13 14 1 3I4 15 17 13 1


















0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018
























0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018












0

01

02

03

04

05

06

07

08

1 3 5 7 9 11 13 15 17



ndash100

ndash80

ndash60

ndash40

ndash20

0

20

40

60

80

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17




4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018








4 Conclusion

















volume Y 0527 + 0358x 0532 12










Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018












Data Availability




Acknowledgments


References

















































Journal of












Journal of







Volume 2018






Volume 2018







































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

ResearchontheDegreeofCouplingbetweentheUrbanPublic ...downloads.hindawi.com/journals/mpe/2019/8206902.pdf · e research framework of SOSM combines top-down infrastructure supply management