PredictionoftheStrengthofRubberizedConcretebyanEvolved ...downloads.hindawi.com/journals/ace/2019/5198583.pdf · overﬁtting problems. e ﬂowchart of hyperparameter tuning of RF

Research ArticlePrediction of the Strength of Rubberized Concrete by an EvolvedRandom Forest Model

Yuantian Sun 1 Guichen Li 1 Junfei Zhang 2 and Deyu Qian 1

1School of Mines Key Laboratory of Deep Coal Resource Mining Ministry of Education of ChinaChina University of Mining and Technology Xuzhou 221116 China2Department of Civil Environmental and Mining Engineering ampe University of Western Australia Perth 6009 Australia

Correspondence should be addressed to Guichen Li liguichencumteducn and Junfei Zhangjunfeizhang2010163com

Received 8 November 2019 Accepted 5 December 2019 Published 28 December 2019

Guest Editor Binh -ai Pham

Copyright copy 2019 Yuantian Sun et al -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 is properly cited

Rubberized concrete (RC) has attracted more attention these years as it is an economical and environmental-friendly constructionmaterial Normally the uniaxial compressive strength (UCS) of RC needs to be evaluated before application In this study anevolutionary random forest model (BRF) combining random forest (RF) and beetle antennae search (BAS) algorithms was proposedwhich can be used for establishing the relationship between UCS of RC and its key variables A total number of 138 cases werecollected from the literature to develop and validate the BRF model -e results showed that the BAS can tune the RF effectively andtherefore the hyperparameters of RF were obtained -e proposed BRF model can accurately predict the UCS of RC with a highcorrelation coefficient (096) Furthermore the variable importance was determined and the results showed that the age of RC is themost significant variable followed by water-cement ratio fine rubber aggregate coarse rubber aggregate and coarse aggregate -isstudy provides a new method to access the strength of RC and can efficiently guide the design of RC in practice

1 Introduction

Concrete has been themost widely used constructionmaterialin civil engineering and its demand still increases quickly dueto the rapid growth in urbanization and industrializationReducing costs and maximizing the strength and durability ofconcrete are quite challenging issues [1] Hence recycledaggregate concrete (RAC) containing some recycling mate-rials such as plastic materials [2 3] construction and de-molition (CampD) wastes [4 5] and waste tire rubber [6] hasbeen a hot research area Given the rapid growth of tire rubberwaste and its harmful effect on the environment using rubberas a substitute in concrete not only contributes to economicgrowth but also benefits the environment [7] Considering itsductility and strain behavior rubber is normally utilized asfine aggregates (FAs) and coarse aggregates (CAs) in concreteand therefore the new cementitious composites namelyrubberized concrete (RC) can be applied in civil engineering

RC has some special advantages such as reducing CO2emissions and decreasing construction costs and therefore it

attracts many concerns of scholars recently [8ndash11] To evaluatethe applicability of RC some mechanical properties includingcompressive strength and elastic modulus have been studied[12ndash15] Moreover the uniaxial compressive strength (UCS) isthe key indicator that has been commonly used for assessingthe strength property of RC Normally with the increase in thecontent of rubber in RC the compressive strength decreasesSome models considering the laboratory tests or compileddatabases of previous studies have been proposed to predictthe UCS of RC [16ndash18] However due to the limitations ofinput parameters and the small number of obtained resultsthese models are not generalizable and not convenient forapplication Consequently systematical investigations arenecessary to evaluate the compressive strength of RC by moreeconomic and efficient techniques as per a compressive da-tabase including various input parameters

Nowadays machine learning methods are considerablyused for the prediction of the mechanical properties ofcementitious materials [19ndash21] -e estimation of the me-chanical strength of RAC has also been considered For

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 5198583 7 pageshttpsdoiorg10115520195198583

example the multilinear and nonlinear regression modelswere proposed and used for evaluating the UCS of RAC [22]-e artificial neural network (ANN) methods were appliedto assess the strength of RAC [23ndash25] Genetic programming(GA) methods were also introduced for nonlinear regressionin predicting mechanical properties of RAC [26 27]However to the authorsrsquo knowledge there were no reportsof the prediction of RC by artificial intelligence approachesIn addition though the mentioned machine learning al-gorithms (ANN GA etc) were used for prediction inconcrete they still had some limitations such as lower ef-ficiency time-consuming and indefinite structures -ere-fore more robust and simple machine learning models needto be proposed and utilized in predicting the compressivestrength of RC Nowadays the random forest (RF) approachhas been employed in predicting the mechanical parametersof concrete due to its excellent performance on nonlinearregression and classification [28 29] However no relativestudies to date used RF to predict the strength of RC Itshould be pointed out that some hyperparameters still needto be optimized to reach its best predictive ability In thispaper a high-efficiency global optimization algorithm calledthe beetle antennae search (BAS) algorithm was applied toobtain the best parameters of RF [30]

-erefore a robust machine learning technique (evolvedrandom forest namely BRF) was proposed for the evalu-ation of the UCS of RC Several contributions to the liter-ature are as follows

(1) -e random forest (RF) and beetle antennae search(BAS) algorithms were combined to form the BRFmodel

(2) -e strength of rubberized concrete (RC) was for thefirst time predicted and analyzed considering 9 keyinfluencing variables

(3) -e variable importance that affected the UCS of RCwas first revealed

-e proposed method can be a fast tool for estimatingthe strength of RC and efficiently guide the design andapplication of RC in practice

2 Materials and Methods

21 Model of Evolved Random Forest (BRF) As mentionedabove the BRF is the combination of RF and BAS in whichthe RF was applied to obtain the nonlinear relationship indatasets while the BAS was used for hyperparameter tuningof RF In this part the RF and BASwere introduced as follows

211 Random Forest (RF) Random forest is a classificationalgorithm that employs an ensemble of classification treeseach of which is established by applying a bootstrap sampleof the data [31] For tree building the variables are selectedrandomly as the candidate set of variables at each split -eother way is to use bagging which can combine unstablelearners successfully -e random forest has outstandingperformance in classification tasks such as strong robustnessin terms of large feature sets incorporation of interactions

among predictor variables and high quality and freeimplementations [32] -e diagram of the structure of RF isshown in Figure 1 -is method has been widely used fordealing with the questions of classification and regression incivil engineering

212 Beetle Antennae Search (BAS) BAS algorithm isproposed recently which can be efficiently used for opti-mizing the global problems and has been used for selectingthe optimum parameters of algorithms such as BPNN andSVM [33 34] It simulates the behavior of beetles that utilizetwo antennae to explore nearby areas randomly and turn to ahigher concentration of odor -e flowchart of beetle an-tennae search algorithms is depicted in Figure 2

22 Performance Validation and Evaluation Methods Inthis paper the proposed model was trained and validated onthe 70 dataset and tested on the other 30 dataset [21]During the training and testing processes all data were splitrandomly In addition the predictive effect on the datasetwas assessed by the correlation coefficient (R) and root-mean-square error (RMSE) which were widely used in theprevious literature -e relevant equations are as follows

R 1113936

Ni1 ylowasti minus ylowast( 1113857 yi minus y( 1113857

1113936Ni1 ylowasti minus ylowast( 1113857

21113969

1113936Ni1 yi minus y( 1113857

21113969

RMSE

1N

1113944

N

i1ylowasti minus yi( 1113857

2

11139741113972

(1)

where N denotes the numbers in the collected dataset ylowastiand yi are the expected values and real values respectivelyand y and ylowast indicate the mean predicted values and meanactual values respectively

Furthermore to minimalize the bias a 10-fold cross-validation method was introduced [35] Specifically thesamples in the training dataset were divided into 10 subsets-en one of the 10 subsets was selected for validating theoverall performance of the proposed model while the other9 subsets were applied to train -is process would be re-peated for 10 times

23Procedures ofHyperparameterTuning To obtain the beststructure of RF the hyperparameter tuning is necessary Inthis paper two key parameters (ie the number of the trees(tree_num) and the minimum required samples at a leafnode (min_sample_leaf) in RF) were tuned by BAS By thedescribed 10-folder cross-validationmethod the 9 subsets astraining sets were used for searching the ideal hyper-parameters of RF by BAS for 50 times-e smallest RMSE interms of the validation set can be chosen after 50 iterationswhich represents the best RF model in this fold -ereforethe best RF model and its corresponding optimum hyper-parameters (tree_num and min_sample_leaf) were chosenafter 10-folds -e performance of the RF model should beverified by evaluating the test set due to the possibility of

2 Advances in Civil Engineering

overfitting problems -e flowchart of hyperparametertuning of RF by BAS in training and testing is shown inFigure 3

24 Dataset Description -e dataset of RC was collectedfrom the literature [13 15 18 36ndash38] which was used forestablishing and validating the BRF model for strengthprediction A total number of 138 valid samples with 9 keyinfluencing variables were assembled in this studyGenerally depending on the different sizes of rubber thecrumb rubber is used for replacing the fine aggregate (FA)in concrete while the tire chips are used for replacing

coarse aggregate (CA) -e compressive strength nor-mally decreased with different rates by replacing variouscontents of rubber and different rubber types -erefore itis necessary to distinguish the rubber into two types in RCie fine rubber aggregate (FRA) and coarse rubber ag-gregate (CRA) Moreover the influencing variables andtheir description in statistics are given in Table 1 -emain objectives are to predict the UCS of RC that isdetermined by its influencing variables -e relative im-portance of variables is to be further analyzed To improvethe efficiency of the model the collected data were nor-malized into [0 1] According to the percentage split ofthe dataset 97 samples were randomly chosen as the

Input

Prediction 1 Prediction 2 Prediction n

Average all predictions

Random forest prediction

Tree 1 Tree 2 Tree n

Figure 1 General structure of the RF model

Initialize the position ofbeetle

Fitness function ofbeetle

Is the current fitnessbetter than thebest position

Update the bestposition

Unchange

Set beetle direction andcalculate fitness of antennae

Fitness of left antennae gtfitness of right antennae

A step to right

Stopping criterionBest solution

Yes

No

No

Yes

No

Yes

A step to left

Figure 2 -e flowchart of beetle antennae search algorithm

Advances in Civil Engineering 3

training set and the remaining 41 samples were set as thetest set

3 Results and Discussion

31 Results of Hyperparameter Tuning In this studyaccording to the RMSE obtained from 10-fold cross-valida-tion the hyperparameters were tuned on the testing set -eRMSE versus iterations during BAS tuning is shown Figure 4As can be seen the RMSE decreased considerably revealingthat the BAS can tune the RF effectively -en the RMSEbecame stable at 15 iterations Here only 20 iterations wereshown -e final hyperparameters of RF are given in Table 2

32 Assessment of the EstablishedModel -e comparison ofthe predicted UCS of RC by the BRF model and actualUCS of RC in datasets is depicted in Figure 5 As can beseen the predicted UCS values of RC were rather close tothe actual UCS indicating that the BRF can establish thenonlinear relationship between UCS of RC and inputvariables successfully and therefore the model canpredict the strength accurately In addition the high Rvalues for the training set and test set were 0985 and0959 respectively -e low RMSE values of 224 in thetraining set and 390 in the testing set were observedOverall the above results showed that there is nounderfitting or overfitting phenomena by the proposedBRF model

33 Variable Importance of RC Furthermore the relativeimportance of the input variables is shown in Figure 6 Ascan be seen the age of RC was the most important variablewith an important score of 142 and this result was con-sistent with the strength development of cementitiousmaterials reported in the previous studies [12 39] -ewater-cement ratio also played a crucial role in the strengthof RC and the superposition effect of water and cement inthis study was similar to the age -is agrees well with somestudies that the water-cement ratio affects the strengthconsiderably [40 41] As can be seen the FA ranked thirdwith an importance score of 123 which was more sensitivethan CA (importance score of 049) in RC Correspondinglythe FRA had a relatively larger influence on the UCS of RCthan CRA It should be pointed out that both the FRA andCRA affect the strength of RC obviously and therefore moreattention should be paid when adding rubber materials toRC in practice -e admixture of SP and SCMs had the leastinfluence on the strength of RC with the importance score of027 and 024 respectively -e obtained results can guidethe design of RC effectively and select the proper parameters

Table 1 -e input influencing variables in the BRF model

No Influencingvariables Min Max Average Standard

deviation1 Cement (kgm3) 131 550 3681 7392 Water (kgm3) 150 225 1876 2433 aSCMs (kgm3) 0 3575 710 1253

4 Superplasticizer() 0 78 176 29

5 bCA (kgm3) 0 12028 9998 23836 cCRA (kgm3) 0 1160 631 18677 dFA (kgm3) 0 942 6194 16518 eFRA (kgm3) 0 630 499 9839 Ages (d) 1 91 266 257aSupplementary cementitious materials bcoarse aggregate cfine aggregatedcoarse rubber aggregate efine rubber aggregate

Dataset

Training set (70)

Testing set (30)

10-fold CV BAS

RF

R RMSE

R RMSE

Trainingresults

Testingresults

Figure 3 -e flowchart of hyperparameter tuning of RF by BAS

1

2

3

4

5

6

RMSE

5 10 15 200Iteration

Figure 4 RMSE versus iterations

Table 2 -e obtained hyperparameters of RF

Parameters Empirical scope Initial Resultstree_num [1 10] 6 8min_sample_leaf [1 10] 6 1


for optimizing RC -e results can guide the accurate designof RC and boost the application of RC

4 Conclusions

-is paper presented an evolved random forest algorithmnamely BRF for evaluating the UCS of RC Based on the 138samples collected from the previous literature and 9 keyinfluencing variables the compressive strength of RC can bedetermined by the independent variables by BRF -ehyperparameters of RF were tuned by using the BAS al-gorithm and validated by 10-fold cross-validation In ad-dition the performance of optimized BRF was examined byR and RMSE -e variable importance was first revealed anddiscussed-emain results are as follows BAS can efficientlytune the hyperparameters of RF and can be used in evolvedRF to establish the BRF prediction model the proposed BRFmodel can accurately predict the strength of RC which canguide the design of RC on the testing set R and RMSE were096 and 39 respectively meaning that the proposed BRFmodel has a good prediction on the collected RC data theage of RC is the most significant variable for the strength

followed by the cement ratio FRA CRA and CA the SP andSCMs have the least influence on the strength of RC

It should be pointed out that the results were limited bythe amount of the samples If the larger dataset was obtainedthe more accurate results would be derived In the future wewould collect more samples and design a bigger dataset foranalysis by machine learning methods which can signifi-cantly promote the application of RC in the field

Data Availability

-e Microsoft Excel Worksheet data used to support thefindings of this study are available from the correspondingauthor upon request

Conflicts of Interest

-e authors declare that there are no conflicts of interest

Acknowledgments

-is study was financially supported by the National KeyResearch and Development Program (Grant no2016YFC0600901) National Natural Science Foundation ofChina (Grant nos 51574224 and 51704277) and NaturalScience Fundamental Research Program Enterprise UnitedFund of Shaanxi Province of China (Grant no 2019JLZ-04)-e authors are grateful to Huaibei Mining (Group) Co LtdSpecial thanks are due to Dr Zuqi Wang for her encour-agement and help

References

[1] T Xie A Gholampour and T Ozbakkaloglu ldquoToward thedevelopment of sustainable concretes with recycled concreteaggregates comprehensive review of studies on mechanicalpropertiesrdquo Journal of Materials in Civil Engineering vol 30no 9 Article ID 04018211 2018

[2] R Siddique J Khatib and I Kaur ldquoUse of recycled plastic inconcrete a reviewrdquo Waste Management vol 28 no 10pp 1835ndash1852 2008

RMSE = 22401R = 09854

10

20

30

40

50

60

70

80

Pred

icte

d U

CS

40 60 8020Actual UCS

(a)

RMSE = 39032R = 09596

10

20

30

40

50

60

70

Pred

icte

d U

CS

20 30 40 50 60 7010Actual UCS

(b)

Figure 5 Comparison of UCS values (a) Training dataset (b) Testing dataset

0 05 1 15Importance score

SCM

SP

CA

Cement

CRA

FRA

Water

FA

Age

Influ

entia

l var

iabl

e

02403

02771

04952

05231

07660

08288

09194

12680

14170

Figure 6 Variable importance of RC based on the BRF


[3] Z Z Ismail and E A Al-Hashmi ldquoUse of waste plastic inconcrete mixture as aggregate replacementrdquo Waste Man-agement vol 28 no 11 pp 2041ndash2047 2008

[4] G Dimitriou P Savva and M F Petrou ldquoEnhancing me-chanical and durability properties of recycled aggregateconcreterdquo Construction and Building Materials vol 158pp 228ndash235 2018

[5] S-C Kou C-S Poon and H-W Wan ldquoProperties of con-crete prepared with low-grade recycled aggregatesrdquo Con-struction and Building Materials vol 36 pp 881ndash889 2012

[6] F Azevedo F Pacheco-Torgal C Jesus J L Barroso deAguiar and A F Camotildees ldquoProperties and durability of HPCwith tyre rubber wastesrdquoConstruction and BuildingMaterialsvol 34 pp 186ndash191 2012

[7] Z Zhang H Ma and S Qian ldquoInvestigation on properties ofECC incorporating crumb rubber of different sizesrdquo Journalof Advanced Concrete Technology vol 13 no 5 pp 241ndash2512015

[8] A S Hameed and A P Shashikala ldquoSuitability of rubberconcrete for railway sleepersrdquo Perspectives in Science vol 8pp 32ndash35 2016

[9] R Pacheco-Torres E Cerro-Prada F Escolano and F VarelaldquoFatigue performance of waste rubber concrete for rigid roadpavementsrdquo Construction and Building Materials vol 176pp 539ndash548 2018

[10] P Asutkar S B Shinde and R Patel ldquoStudy on the behaviourof rubber aggregates concrete beams using analytical ap-proachrdquo Engineering Science and Technology an InternationalJournal vol 20 no 1 pp 151ndash159 2017

[11] A Grinys H Sivilevicius and M Dauksys ldquoTyre rubberadditive effect on concrete mixture strengthrdquo Journal of CivilEngineering and Management vol 18 no 3 pp 393ndash4012012

[12] I B Topccedilu ldquo-e properties of rubberized concretesrdquo Cementand Concrete Research vol 25 no 2 pp 304ndash310 1995

[13] B S -omas R C Gupta P Kalla and L CseteneyildquoStrength abrasion and permeation characteristics of cementconcrete containing discarded rubber fine aggregatesrdquo Con-struction and Building Materials vol 59 pp 204ndash212 2014

[14] Z K Khatib and F M Bayomy ldquoRubberized portland cementconcreterdquo Journal of Materials in Civil Engineering vol 11no 3 pp 206ndash213 1999

[15] L Zheng X S Huo and Y Yuan ldquoStrength modulus ofelasticity and brittleness index of rubberized concreterdquoJournal of Materials in Civil Engineering vol 20 no 11pp 692ndash699 2008

[16] F Aslani ldquoMechanical properties of waste tire rubber con-creterdquo Journal of Materials in Civil Engineering vol 28 no 3Article ID 4015152 2015

[17] T-C Ling ldquoPrediction of density and compressive strengthfor rubberized concrete blocksrdquo Construction and BuildingMaterials vol 25 no 11 pp 4303ndash4306 2011

[18] W H Yung L C Yung and L H Hua ldquoA study of thedurability properties of waste tire rubber applied to self-compacting concreterdquo Construction and Building Materialsvol 41 pp 665ndash672 2013

[19] C Qi A Fourie Q Chen and Q Zhang ldquoA strength pre-diction model using artificial intelligence for recycling wastetailings as cemented paste backfillrdquo Journal of Cleaner Pro-duction vol 183 pp 566ndash578 2018

[20] C Qi A Fourie and Q Chen ldquoNeural network and particleswarm optimization for predicting the unconfined com-pressive strength of cemented paste backfillrdquo Constructionand Building Materials vol 159 pp 473ndash478 2018

[21] J Zhang G Ma Y Huang J Sun F Aslani and B NenerldquoModelling uniaxial compressive strength of lightweight self-compacting concrete using random forest regressionrdquo Con-struction and Building Materials vol 210 pp 713ndash719 2019

[22] K H Younis and K Pilakoutas ldquoStrength prediction modeland methods for improving recycled aggregate concreterdquoConstruction and Building Materials vol 49 pp 688ndash7012013

[23] Z H Duan S C Kou and C S Poon ldquoPrediction ofcompressive strength of recycled aggregate concrete usingartificial neural networksrdquo Construction and Building Mate-rials vol 40 pp 1200ndash1206 2013

[24] N Deshpande S Londhe and S Kulkarni ldquoModelingcompressive strength of recycled aggregate concrete by ar-tificial neural network model tree and non-linear regressionrdquoInternational Journal of Sustainable Built Environment vol 3no 2 pp 187ndash198 2014

[25] K Sahoo P Sarkar and P Robin Davis ldquoArtificial NeuralNetworks for Prediction of Compressive Strength of RecycledAggregate Concreterdquo International Journal of Research inChemical Metallurgical and Civil Engineering vol 3 no 12016

[26] I Gonzalez-Taboada B Gonzalez-Fonteboa F Martınez-Abella and J L Perez-Ordontildeez ldquoPrediction of the me-chanical properties of structural recycled concrete usingmultivariable regression and genetic programmingrdquo Con-struction and Building Materials vol 106 pp 480ndash499 2016

[27] A Gholampour A H Gandomi and T Ozbakkaloglu ldquoNewformulations for mechanical properties of recycled aggregateconcrete using gene expression programmingrdquo Constructionand Building Materials vol 130 pp 122ndash145 2017

[28] L Breiman ldquoRandom forestsrdquo Machine Learning vol 45no 1 pp 5ndash32 2001

[29] E Scornet ldquoOn the asymptotics of random forestsrdquo Journal ofMultivariate Analysis vol 146 pp 72ndash83 2016

[30] X Jiang and S Li ldquoBAS beetle antennae search algorithm foroptimization problemsrdquo International Journal of Robotics andControl vol 1 no 1 pp 1ndash3 2018

[31] A Liaw and M Wiener ldquoClassification and regression byrandom forestrdquo R News vol 2 no 3 pp 18ndash22 2002

[32] S Janitza G Tutz and A-L Boulesteix ldquoRandom forest forordinal responses prediction and variable selectionrdquo Com-putational Statistics amp Data Analysis vol 96 pp 57ndash73 2016

[33] Y Sun J Zhang G Li Y Wang J Sun and C JiangldquoOptimized neural network using beetle antennae search forpredicting the unconfined compressive strength of jetgrouting coalcretesrdquo International Journal for Numerical andAnalytical Methods in Geomechanics vol 43 no 4 pp 801ndash813 2019

[34] Y Sun J Zhang G Li et al ldquoDetermination of Youngrsquosmodulus of jet grouted coalcretes using an intelligent modelrdquoEngineering Geology vol 252 pp 43ndash53 2019

[35] J Sun J Zhang Y Gu Y Huang Y Sun and G MaldquoPrediction of permeability and unconfined compressivestrength of pervious concrete using evolved support vectorregressionrdquo Construction and Building Materials vol 207pp 440ndash449 2019

[36] M M Reda Taha A S El-Dieb M A Abd El-Wahab andM E Abdel-Hameed ldquoMechanical fracture and microstruc-tural investigations of rubber concreterdquo Journal of Materials inCivil Engineering vol 20 no 10 pp 640ndash649 2008

[37] S-F Wong and S-K Ting ldquoUse of recycled rubber tires innormal-and high-strength concretesrdquo ACI Materials Journalvol 106 no 4 p 325 2009


[38] Q Dong B Huang and X Shu ldquoRubber modified concreteimproved by chemically active coating and silane couplingagentrdquo Construction and Building Materials vol 48pp 116ndash123 2013

[39] F Valadares M Bravo and J de Brito ldquoConcrete with usedtire rubber aggregates mechanical performancerdquo ACI Ma-terials Journal vol 109 no 3 p 283 2012

[40] Z Chen Y Zhang J Chen and J Fan ldquoSensitivity factorsanalysis on the compressive strength and flexural strength ofrecycled aggregate infill wall materialsrdquo Applied Sciencesvol 8 no 7 p 1090 2018

[41] J Tinoco A Gomes Correia and P Cortez ldquoApplication ofdata mining techniques in the estimation of the uniaxialcompressive strength of jet grouting columns over timerdquoConstruction and Building Materials vol 25 no 3pp 1257ndash1262 2011


International Journal of

AerospaceEngineeringHindawiwwwhindawicom Volume 2018

RoboticsJournal of

Hindawiwwwhindawicom Volume 2018


Active and Passive Electronic Components

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawiwwwhindawicom

Volume 2018

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Control Scienceand Engineering

Journal of



Journal ofEngineeringVolume 2018

SensorsJournal of



RotatingMachinery


Modelling ampSimulationin EngineeringHindawiwwwhindawicom Volume 2018


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation


Hindawi

wwwhindawicom Volume 2018

Advances in

Multimedia

Submit your manuscripts atwwwhindawicom

example the multilinear and nonlinear regression modelswere proposed and used for evaluating the UCS of RAC [22]-e artificial neural network (ANN) methods were appliedto assess the strength of RAC [23ndash25] Genetic programming(GA) methods were also introduced for nonlinear regressionin predicting mechanical properties of RAC [26 27]However to the authorsrsquo knowledge there were no reportsof the prediction of RC by artificial intelligence approachesIn addition though the mentioned machine learning al-gorithms (ANN GA etc) were used for prediction inconcrete they still had some limitations such as lower ef-ficiency time-consuming and indefinite structures -ere-fore more robust and simple machine learning models needto be proposed and utilized in predicting the compressivestrength of RC Nowadays the random forest (RF) approachhas been employed in predicting the mechanical parametersof concrete due to its excellent performance on nonlinearregression and classification [28 29] However no relativestudies to date used RF to predict the strength of RC Itshould be pointed out that some hyperparameters still needto be optimized to reach its best predictive ability In thispaper a high-efficiency global optimization algorithm calledthe beetle antennae search (BAS) algorithm was applied toobtain the best parameters of RF [30]

-erefore a robust machine learning technique (evolvedrandom forest namely BRF) was proposed for the evalu-ation of the UCS of RC Several contributions to the liter-ature are as follows

(1) -e random forest (RF) and beetle antennae search(BAS) algorithms were combined to form the BRFmodel

(2) -e strength of rubberized concrete (RC) was for thefirst time predicted and analyzed considering 9 keyinfluencing variables

(3) -e variable importance that affected the UCS of RCwas first revealed

-e proposed method can be a fast tool for estimatingthe strength of RC and efficiently guide the design andapplication of RC in practice

2 Materials and Methods

21 Model of Evolved Random Forest (BRF) As mentionedabove the BRF is the combination of RF and BAS in whichthe RF was applied to obtain the nonlinear relationship indatasets while the BAS was used for hyperparameter tuningof RF In this part the RF and BASwere introduced as follows

211 Random Forest (RF) Random forest is a classificationalgorithm that employs an ensemble of classification treeseach of which is established by applying a bootstrap sampleof the data [31] For tree building the variables are selectedrandomly as the candidate set of variables at each split -eother way is to use bagging which can combine unstablelearners successfully -e random forest has outstandingperformance in classification tasks such as strong robustnessin terms of large feature sets incorporation of interactions

among predictor variables and high quality and freeimplementations [32] -e diagram of the structure of RF isshown in Figure 1 -is method has been widely used fordealing with the questions of classification and regression incivil engineering

212 Beetle Antennae Search (BAS) BAS algorithm isproposed recently which can be efficiently used for opti-mizing the global problems and has been used for selectingthe optimum parameters of algorithms such as BPNN andSVM [33 34] It simulates the behavior of beetles that utilizetwo antennae to explore nearby areas randomly and turn to ahigher concentration of odor -e flowchart of beetle an-tennae search algorithms is depicted in Figure 2

22 Performance Validation and Evaluation Methods Inthis paper the proposed model was trained and validated onthe 70 dataset and tested on the other 30 dataset [21]During the training and testing processes all data were splitrandomly In addition the predictive effect on the datasetwas assessed by the correlation coefficient (R) and root-mean-square error (RMSE) which were widely used in theprevious literature -e relevant equations are as follows

R 1113936

Ni1 ylowasti minus ylowast( 1113857 yi minus y( 1113857

1113936Ni1 ylowasti minus ylowast( 1113857

21113969

1113936Ni1 yi minus y( 1113857

21113969

RMSE

1N

1113944

N

i1ylowasti minus yi( 1113857

2

11139741113972

(1)

where N denotes the numbers in the collected dataset ylowastiand yi are the expected values and real values respectivelyand y and ylowast indicate the mean predicted values and meanactual values respectively

Furthermore to minimalize the bias a 10-fold cross-validation method was introduced [35] Specifically thesamples in the training dataset were divided into 10 subsets-en one of the 10 subsets was selected for validating theoverall performance of the proposed model while the other9 subsets were applied to train -is process would be re-peated for 10 times

23Procedures ofHyperparameterTuning To obtain the beststructure of RF the hyperparameter tuning is necessary Inthis paper two key parameters (ie the number of the trees(tree_num) and the minimum required samples at a leafnode (min_sample_leaf) in RF) were tuned by BAS By thedescribed 10-folder cross-validationmethod the 9 subsets astraining sets were used for searching the ideal hyper-parameters of RF by BAS for 50 times-e smallest RMSE interms of the validation set can be chosen after 50 iterationswhich represents the best RF model in this fold -ereforethe best RF model and its corresponding optimum hyper-parameters (tree_num and min_sample_leaf) were chosenafter 10-folds -e performance of the RF model should beverified by evaluating the test set due to the possibility of





Input










Unchange



A step to right


Yes

No

No

Yes

No

Yes

A step to left













Dataset

Training set (70)

Testing set (30)

10-fold CV BAS

RF

R RMSE

R RMSE

Trainingresults

Testingresults


1

2

3

4

5

6

RMSE







4 Conclusions




Data Availability




Acknowledgments


References



RMSE = 22401R = 09854

10

20

30

40

50

60

70

80

Pred

icte

d U

CS


(a)

RMSE = 39032R = 09596

10

20

30

40

50

60

70

Pred

icte

d U

CS

20 30 40 50 60 7010Actual UCS

(b)



SCM

SP

CA

Cement

CRA

FRA

Water

FA

Age

Influ

entia

l var

iabl

e

02403

02771

04952

05231

07660

08288

09194

12680

14170














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





Input










Unchange



A step to right


Yes

No

No

Yes

No

Yes

A step to left













Dataset

Training set (70)

Testing set (30)

10-fold CV BAS

RF

R RMSE

R RMSE

Trainingresults

Testingresults


1

2

3

4

5

6

RMSE







4 Conclusions




Data Availability




Acknowledgments


References



RMSE = 22401R = 09854

10

20

30

40

50

60

70

80

Pred

icte

d U

CS


(a)

RMSE = 39032R = 09596

10

20

30

40

50

60

70

Pred

icte

d U

CS

20 30 40 50 60 7010Actual UCS

(b)



SCM

SP

CA

Cement

CRA

FRA

Water

FA

Age

Influ

entia

l var

iabl

e

02403

02771

04952

05231

07660

08288

09194

12680

14170














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












Dataset

Training set (70)

Testing set (30)

10-fold CV BAS

RF

R RMSE

R RMSE

Trainingresults

Testingresults


1

2

3

4

5

6

RMSE







4 Conclusions




Data Availability




Acknowledgments


References



RMSE = 22401R = 09854

10

20

30

40

50

60

70

80

Pred

icte

d U

CS


(a)

RMSE = 39032R = 09596

10

20

30

40

50

60

70

Pred

icte

d U

CS

20 30 40 50 60 7010Actual UCS

(b)



SCM

SP

CA

Cement

CRA

FRA

Water

FA

Age

Influ

entia

l var

iabl

e

02403

02771

04952

05231

07660

08288

09194

12680

14170














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



4 Conclusions




Data Availability




Acknowledgments


References



RMSE = 22401R = 09854

10

20

30

40

50

60

70

80

Pred

icte

d U

CS


(a)

RMSE = 39032R = 09596

10

20

30

40

50

60

70

Pred

icte

d U

CS

20 30 40 50 60 7010Actual UCS

(b)



SCM

SP

CA

Cement

CRA

FRA

Water

FA

Age

Influ

entia

l var

iabl

e

02403

02771

04952

05231

07660

08288

09194

12680

14170














































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

PredictionoftheStrengthofRubberizedConcretebyanEvolved ...downloads.hindawi.com/journals/ace/2019/5198583.pdf · overﬁtting problems. e ﬂowchart of hyperparameter tuning of RF