Research Article Prediction of Concrete Compressive Strength by Evolutionary ... · 2019. 7....

Research ArticlePrediction of Concrete Compressive Strength byEvolutionary Artificial Neural Networks

Mehdi Nikoo1 Farshid Torabian Moghadam2 and Aukasz Sadowski3

1Young Researchers and Elite Club Ahvaz Branch Islamic Azad University Ahvaz Iran2Young Researchers and Elite Club khorasgan (Isfahan) Branch Islamic Azad University Isfahan Iran3Faculty of Civil Engineering Wrocław University of Technology Wybrzeze Wyspianskiego 27 50-370 Wrocław Poland

Correspondence should be addressed to Mehdi Nikoo sazeh84yahoocom

Received 12 October 2014 Accepted 2 January 2015

Academic Editor Chao Tao

Copyright copy 2015 Mehdi Nikoo et al This 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

Compressive strength of concrete has been predicted using evolutionary artificial neural networks (EANNs) as a combination ofartificial neural network (ANN) and evolutionary search procedures such as genetic algorithms (GA) In this paper for purposeof constructing models samples of cylindrical concrete parts with different characteristics have been used with 173 experimentaldata patterns Water-cement ratio maximum sand size amount of gravel cement 34 sand 38 sand and coefficient of soft sandparameters were considered as inputs and using the ANN models the compressive strength of concrete is calculated MoreoverusingGA the number of layers and nodes andweights are optimized inANNmodels In order to evaluate the accuracy of themodelthe optimized ANN model is compared with the multiple linear regression (MLR) model The results of simulation verify that therecommended ANNmodel enjoys more flexibility capability and accuracy in predicting the compressive strength of concrete

1 Introduction

In the last decade a lot of attention has been paid to the appli-cation of artificial neural networks (ANNs) in determiningthe compressive strength of concrete [1ndash9] It is proper to notethat thereweremostly conventional applications ofANNsnotdisrupted in facing inaccurate data and information for thispurposeThat is why many researchers used the combinatorymodels [10ndash12] such of ANN and fuzzy logic [13] whichdemonstrated strong potential for prediction of long-termeffects of ground granulated blast furnace slag on compressivestrength of concrete In reducing the cost and saving time inthe class of compressive strengthrsquos determination problemscascade correlation type of ANN offered quick learning withslightly accurate performance for capturing the intrinsicallynonlinear nature of patterns in the concrete properties [14]Presenting substantial results in performance combinatorialformations of ANN and meta-heuristic search algorithmshave been increasing in utilization for encountering complexstructural engineering problems For instance hybrid multi-layer perceptron (HMLP) network with centre-unified par-ticle swarm optimization was assigned for determination of

the compressive strength of concrete related to the deepbeams connected to the sheared walls and provided news-worthy results involved in significant efficiency [15] In asimilar area compressive strength of self-compacting con-crete which encompassed polypropylene fiber and mineraladditives impressed by high temperature was estimated byANN [16] According to [17] evolutionary artificial neuralnetworks (EANNs) can be considered as a combination ofartificial neural network (ANN) and evolutionary searchprocedures such as genetic algorithms (GA) Basic principlesof EANN were explained in [18] The identification of defectin the structure and compressive strength of concrete isintrinsically a pattern-study issue and for this purpose theEANNs have acted very powerfully [19 20]

The main objective of this study is to determine thecompressive strength of concrete using EANN as a replace-ment method for mathematical models and destructive testsso that more accurate results are obtained with the mini-mum cost Similar data were previously analysed by usingSelf-Organization Feature Map (SOFM) systems and Koho-nen training network and the 1198772 coefficients in training

Hindawi Publishing CorporationAdvances in Materials Science and EngineeringVolume 2015 Article ID 849126 8 pageshttpdxdoiorg1011552015849126

2 Advances in Materials Science and Engineering

Table 1 Characteristics of cylindrical samples

Number Parameters Unit Maximum Minimum Standard deviation Mean1 Compressive strength of concrete kgcm2 39400 17300 5498 279272 Water-cement ratio mdash 050 024 019 0433 Maximum size of sand mm 5000 512 1425 23894 Gravel kg 105000 55900 9571 779135 Cement kg 54900 24300 7270 385556 Sand 38 kg 52300 30300 6445 427057 Sand 34 kg 69300 36500 9006 563318 Coefficient of soft sand mdash 920 240 130 327

Table 2 Number of patterns used in ANN

Number Number of patterns Compressive strength of concrete1 2 150ndash1752 11 175ndash2003 25 201ndash2254 24 226ndash2505 20 251ndash2756 22 276ndash3007 34 301ndash3258 15 326ndash3509 17 351ndash37510 3 376ndash400Total of the number of patterns 173

validation and testing phases were equal to 0880 0993 and0946 respectively [21]

2 Materials and Methods

21 Database Compressive strength of concrete (1198911015840119862) is in

fact the 28-day strength of cylindrical concrete sample Inthis study cylindrical samples with a diameter of 15 cm anda height of 30 cm are used In addition parameters such asthe amount of 34 sand 38 sand cement silt in kilogramsmaximumsand size inmillimeter coefficient of fine sand andwater-cement ratio are used to determine the compressivestrength of concrete In the lab using a hydraulic jack 25blows are pounded on each sample of the concrete and datarelated to the intended parameters towards determinationof compressive strength are recorded The characteristics ofused data have been illustrated in Table 1 based on the datapresented in the literature [22 23]

Moreover in Table 2 the number of patterns used inANN has been shown based on compressive strength ofconcrete separately

22 Research Methodology The data were collected from theliterature [22 23] and have not been previously used innumerical modelling presented [21] In the first step severaldifferent mix designs are used to determine the compressivestrength Then Multi Layer (MLP) Feed Forward (FF)Radial Basis Function (RBF) andTime Lag RecarentNetwork

WC

Maximum size of sand

Gravel

Cement

Sand 34

Sand 38

Coefficient of soft sand

f998400C

Figure 1 Structure of EANN

(TLRN) were selected and the estimation of the compressivestrength parameter have been carried out Then the optimalgeometric structure of the intended ANN along with optimalweights is tentatively determined by genetic algorithm (GA)In the next step a multiple linear regression (MLR) modelis employed in determining the compressive strength ofconcrete Finally the performance of the MLR model andthe proposed EANN structure in predicting the compressivestrength of concrete is studied and comparison betweenobtained models has been performed In ANN models thenumber of inputs is seven parameters and the number ofoutputs is one which has been shown in Figure 1 Out of 173data patterns 80 (139 patterns) have been used for training10 (17 patterns) for cross validation and 10 (17 pat-terns) for network test Various transfer functions consistingof LinearSigmoidAxon BiasAxon TanhAxon LinearAxonSigmoidAxon LinearTanhAxon and various training algo-rithms consisting of Momentum Levenberg Marquat DeltaBar Delta Quickprop and Step were considered to determinethe best structure in the ANN [24] In order to determinethe number of nodes in the hidden layer in addition to thesoftware presupposition the following experimental formulawas used [25]

119873119867le 2119873119868+ 1 (1)

where 119873119867is the maximum number of nodes in the hidden

layer and 119873119868is the number of inputs With regard to the

Advances in Materials Science and Engineering 3

Table 3 Optimal structure of MLP FF RBF and TLRN models obtained from GA

GA for all models Learningalgorithm Transfer function

Number ofhiddenneuron

Number ofhiddenlayer

Numberof

output

Numberof input Model Number

Crossover One point Momentum TanhAxon 4 1

1 7

MLP 1Crossoverprobability 09 Step LinearAxon 15 1 FF 2

Mutationprobability 001 Delta Bar Delta LinearSigmoidAxon 4 4 2 RBF 4

Generation 100 Momentum TanhAxon 5 10 2 TLRN 3

fact that the number of obtained effective inputs is equalto 7 maximum number of nodes in the hidden layer is 15(119873119867le 15) To determine the optimal structure of each ANN

model togetherwith the number of hidden layers the numberof nodes in the hidden layers the network-learning algorithmand transfer function the in Neuro Solutions ver50 softwarehas been used Table 3 shows the optimal structure of eachof the models and their various characteristics obtained fromGA In addition Table 4 illustrates the results obtained fromtraining validation concurrent with training and test of eachmodel with the optimal structure obtained in Table 3 Forthe performance of the models and to determine the bestmodel NMSE criterion and the coefficient of determination(119903) resulting from test of models are compared with oneanother As seen in Table 4 MLP model has the highestcorrelation (119903) for the data regarding compressive strength ofthe concrete in all stages compared to the other three models

In Figure 2 the comparison of observed compressivestrength of concrete calculated by EANN models in thetraining stage has been presented From Figure 2 it can beconcluded that MLP and FF models in the training stage arecloser to real data than other models It can be also seenthat TLRN model is the worst one during training stage Aspresented in Figure 3 there is similar situation for testing andvalidation The values predicted by MLP and FF seem to bethe optimum As it has been presented in Table 4 in MLPmodel coefficients 1198772 for compressive strength of concreteparameter in the training validation and test stages are equalto 0910 0935 and 0899 respectively In addition the slopeof the straight line for this parameter is 09061 09043 and09039 These values are similar to the ones achieved in [21]Therefore MLP model has a higher correlation comparedto the other three models As a result MLP model with atopology of (7-4-1) is the best EANNmodel with the structurepresented in Figure 1

23 Analysis of Sensitivity of Outputs of EANN Model in rela-tion to Input Parameters As you are training a network youmay want to know the effect that each of the network inputsis having on the network outputThis provides feedback as towhich input channels are the most significant From thereyou may decide to prune the input space by removing theinsignificant channels This will reduce the size of the net-work which in turn reduces the complexity and the trainingtimes Sensitivity analysis is amethod for extracting the cause

0

50

100

150

200

250

300

350

400

450

0 25 50 75 100 125 150Pattern number

Real dataMLPFF

RBFTLRN

Con

cret

e com

pres

sive s

treng

th(k

gm

2 )

Figure 2 Comparison of observed compressive strength of concretecalculated by EANNmodels in the training stage

and effect relationship between the inputs and outputs ofthe network The network learning is disabled during thisoperation such that the network weights are not affectedThebasic idea is that the inputs to the network are shifted slightlyand the corresponding change in the output is reportedas either a percentage or a raw difference The activationcontrol component generates the input data for the sensitivityanalysis by temporarily increasing the input by a small value(dither)The corresponding change in output is the sensitivitydata which is reported by the ErrorCriteria componentand displayed by an attached probe [24] To determine theamount of effect of input parameters on the output parametersensitivity analysis technique is used This technique is todetermine to which input parameters the output parameterin the intended network is more sensitive so that which indexis themost effective on the output of network is specifiedTheresults obtained from the output sensitivity analysis of MLPmodel in relation to input parameters have been mentionedin Figure 4 With regard to Figure 4 water-cement ratio and38 sandparameters have themost and the least effect onMLPmodel output respectively

24 Comparison between Selected EANN (MLP) Model andMultiple Linear Regression (MLR) The statistical model used


Table4Re

sults

obtained

from

MLPFFRB

FandTL

RNop

timalmod

elsinthetrainingvalid

ation

andteststages

forc

ompressiv

estre

ngth

ofconcrete

Test

Valid

ationconcurrent

with

training

Train

Mod

elNum

ber

Bestfittin

glin

eintesting

phase

Perfo

rmance

criteria

Bestfittin

glin

einvalid

ationph

ase

Perfo

rmance

criteria

Bestfittin

glin

eintraining

phase

Perfo

rmance

criteria

Equatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903

119910=09039119909+29657

0899

0106

0948119910=09043119909+06638

0935

0070

0967119910=09061119909+26518

0910

0090

0954

MLP

1119910=071119909+77428

0843

0179

0918119910=08937119909+40161

0916

0126

0957119910=07944119909+57761

0794

0206

0891

FF2

119910=04582119909+14853

0711

0380

0843119910=04476119909+15813

0783

0379

0885119910=0443119909+15686

0734

0381

0857

RBF

3119910=06765119909+71198

0473

0705

0688119910=07052119909+87975

0317

1180

0563119910=06851119909+77142

0411

0813

064

1TL

RN4


Table 5 Coefficients of MLR model

119875 119879 SE coef Coef Predictor Numberminus600 108 minus555 0 Constant Constant parameter 101685 01601 105 0295 119909

1Water-cement ratio 2

01762 03456 051 0611 1199092

Maximum size of sand 3020611 005862 352 0001 119909

3Gravel 4

101053 006292 1606 0 1199094

Cement 504264 02541 168 0096 119909

5Sand 38 6

02452 01705 144 0153 1199096

Sand 34 7minus0529 1756 minus03 0764 119909

7Coefficient of soft sand 8

Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(a)

Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(b)

Figure 3 Comparison of observed compressive strength of concrete calculated by EANNmodels in testing (a) and validation (b) stage

000

040

080

120

160

200

Wat

erc

emen

t

Cem

ent

Coe

ffici

ent o

fso

ft sa

nd

Gra

vel

Sand

34

Max

imum

size

of g

rave

l

Sand

38

Sens

itivi

ty

Figure 4 Sensitivity analysis of compressive strength of concrete forinput parameters in MLP model

in this research is the MLR in which two or several indepen-dent variables have major effects on the dependent variableand its equation is as follows

119910 = 119891 (1199091 1199092 ) 997888rarr 119910 = 119886

0+ 11988611199091+ 11988621199092+ sdot sdot sdot (2)

where 119910 is the dependent variable 1199091 1199092 are independent

variables and 1198861 1198862 1198863 are the equation coefficients of

the regression type In this study for input and outputvariables various MLR models have been studied usingMINITABver140 software The most suitable coefficients forthe MLR model are in Table 5 In this table the numbersin Coef column show the MLR model coefficients and thestandard error of each of the estimates has been shown inSE coef column In order to obtain the confidence interval196 is to be multiplied by 95 of these numbers and theresult is algebraically added to the coefficients In additionthe numbers in 119879 column are the division of Coef by SEcoef which is used for the calculation of 119875 probability In theassumption test this probability helps us accept or reject theanswer In principle there is the probability of type 1 errorThis type of error means if less than 119886 = 0005 that therelationship between these two parameters of independentand dependent is statistically very remarkable

The bestMLRmodel which has themost correlationwithcompressive strength of concrete has been mentioned in

119884 = minus600 + 01681199091+ 0176119909

2+ 0206119909

3+ 101119909

4

+ 04261199095+ 0245119909

6minus 053119909

7

(3)

119884 is the compressive strength of concrete with regard to(3) and using data obtained from training the amount of


0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Regression

Estim

ated

com

pres

sive s

treng

th

Observed concrete compressive strength (kgm2)

Linear (y = x)

y = 07941x + 57307

R2 = 0794

(kg

cm2 )

Figure 5 Comparison of observed compressive strength of concretethat calculated one with regression model

compressive strength of concrete can be calculated In theMLRmodel 1198772 coefficient for 119910 dependent parameter equals0794 In addition the slope of the straight line for thisparameter equals 0794 which is suitable for this model Theamount of 1198772 and the slope of the straight line for (3) havebeen illustrated in Figure 5

In order to validate the performance of MLP optimalmodel in the prediction of compressive strength of concretethe results obtained from it are comparedwith those obtainedfrom MLR model For this purpose and in order to makepredictions ten laboratory samples have been used withthe two models Among the most important advantages ofthese samples is that none of them has been used in thetraining validation and test stages Figure 6 illustrates acomparison between the amounts of observed and calculatedcompressive strength of concrete as obtained from the twomodels Moreover the prediction of compressive strengthof concrete with EANN (MLP) and MLR models has beenpresented in Figure 7

With regard to the equations of regression lines on theamounts of calculated and observed compressive strength ofconcrete in each model in Figure 6 and the determinationcoefficient it can be realized that the EANN (MLP) modeldetermines the compressive strength of concrete more pre-cisely than the MLR model does In addition with regardto the prediction of compressive strength of concrete by thetwo models in Figure 7 it can be realized that EANN (MLP)model has higher flexibility and accuracy compared to themultiple linear regressionmodelThese results originate fromthe adaptable and learning capabilities of ANN in the nonlin-ear dynamic estimation of problems and complicatedmodels

MLPRegression

MLP

Regression

0

50

100

150

200

250

300

350

400

450

Estim

ated

com

pres

sive s

treng

th

0 50 100 150 200 250 300 350 400 450Observed concrete compressive strength (kgm2)

y = 09096x + 26222R2 = 09805

y = 07282x + 9138R2 = 08873

(kg

cm2 )

Figure 6 Comparison of observed compressive strength of concreteand estimated compressive strength by EANN (MLP) and MLRregression model

MLPRegression

0 1 2 3 4 5 6 7 8 9 10Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th

f998400C kgcm2

(kg

cm2 )

Figure 7 Prediction of compressive strength of concrete withEANN (MLP) and MLR regression model

3 Conclusion

In this study in order to economize on the time and costthat laboratorymethods have in determining the compressivestrength of concrete the model suggested by the ANNwhich has special capability in nonlinear mapping was used


Various geometric structures along with various learningalgorithms were suggested for network architecture

In order to obtain the required accuracy towards deter-mining compressive strength the optimal evolutionary arti-ficial neural networks (EANNs) structures consisting ofoptimal geometry in the number of hidden neurons andlayers along with optimal learning algorithm relying on thehigh power of GA were presented In addition the linearregression statisticalmodel was used to estimate the compres-sive strength and to compare its results for the validation ofsuggested EANNperformance based onGAThe comparisonof the results whether qualitative or quantitative was madebetween the statistical model and the optimized EANN

On the basis of performance criteria like normalizedmean square error coefficient of determination and corre-lation coefficient it clearly confirms the superiority of EANNfrom the point of accuracy correctness and eye-catchingflexibility of this structure in facing multidimensional non-linear complicated problems like estimation of compressivestrength parameter These obtained values of correlationcoefficient 1198772 for compressive strength of concrete parameterin the training test and validation stages were achieved equalto 0910 0935 and 0899 respectively and are similar to theones achieved in [21] In addition the slope of the straightline for this parameter is 09061 09043 and 09039 Basedon these results which are proof of reliability of suggestedstrategy in this study the generalization property of EANNhas also been used in predicting the amounts of compressivestrength based on unused collected data

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] S-C Lee ldquoPrediction of concrete strength using artificial neuralnetworksrdquo Engineering Structures vol 25 no 7 pp 849ndash8572003

[2] U Atici ldquoPrediction of the strength of mineral admixtureconcrete usingmultivariable regression analysis and an artificialneural networkrdquo Expert Systems with Applications vol 38 no 8pp 9609ndash9618 2011

[3] I B Topcu and M Saridemir ldquoPrediction of compressivestrength of concrete containing fly ash using artificial neuralnetworks and fuzzy logicrdquoComputationalMaterials Science vol41 no 3 pp 305ndash311 2008

[4] T-K Lin C-C J Lin and K-C Chang ldquoNeural networkbased methodology for estimating bridge damage after majorearthquakesrdquo Journal of the Chinese Institute of Engineers vol25 no 5 pp 415ndash424 2002

[5] A Oztas M Pala E Ozbay E Kanca N Caglar and MA Bhatti ldquoPredicting the compressive strength and slump ofhigh strength concrete using neural networkrdquoConstruction andBuilding Materials vol 20 no 9 pp 769ndash775 2006

[6] M A Kewalramani and R Gupta ldquoConcrete compressivestrength prediction using ultrasonic pulse velocity throughartificial neural networksrdquo Automation in Construction vol 15no 3 pp 374ndash379 2006

[7] A Alexandridis D Triantis I Stavrakas and C StergiopoulosldquoA neural network approach for compressive strength predic-tion in cement-based materials through the study of pressure-stimulated electrical signalsrdquo Construction and Building Mate-rials vol 30 pp 294ndash300 2012

[8] J Hola and K Schabowicz ldquoMethodology of neural identifica-tion of strength of concreterdquoACIMaterials Journal vol 102 no6 pp 459ndash464 2005

[9] G Trtnik F Kavcic and G Turk ldquoPrediction of concretestrength using ultrasonic pulse velocity and artificial neuralnetworksrdquo Ultrasonics vol 49 no 1 pp 53ndash60 2009

[10] J-S Chou C-K Chiu M Farfoura and I Al-TaharwaldquoOptimizing the prediction accuracy of concrete compressivestrength based on a comparison of data-mining techniquesrdquoJournal of Computing in Civil Engineering vol 25 no 3 pp 242ndash253 2011

[11] Ł Sadowski M Nikoo and M Nikoo ldquoPrincipal componentanalysis combined with a self organization feature map todetermine the pull-off adhesion between concrete layersrdquo Con-struction and Building Materials vol 78 pp 386ndash396 2015

[12] L Sadowski and M Nikoo ldquoCorrosion current density pre-diction in reinforced concrete by imperialist competitive algo-rithmrdquo Neural Computing and Applications vol 25 no 7-8 pp1627ndash1638 2014

[13] M Saridemir I B Topcu F Ozcan and M H SevercanldquoPrediction of long-term effects of GGBFS on compressivestrength of concrete by artificial neural networks and fuzzylogicrdquo Construction and Building Materials vol 23 no 3 pp1279ndash1286 2009

[14] M M Alshihri A M Azmy and M S El-Bisy ldquoNeuralnetworks for predicting compressive strength of structural lightweight concreterdquo Construction and Building Materials vol 23no 6 pp 2214ndash2219 2009

[15] H-C Tsai ldquoPredicting strengths of concrete-type specimensusing hybrid multilayer perceptrons with center-unified parti-cle swarm optimizationrdquo Expert Systems with Applications vol37 no 2 pp 1104ndash1112 2010

[16] MUysal andHTanyildizi ldquoEstimation of compressive strengthof self compacting concrete containing polypropylene fiber andmineral additives exposed to high temperature using artificialneural networkrdquo Construction and Building Materials vol 27no 1 pp 404ndash414 2012

[17] X Yao ldquoEvolutionary artificial neural networksrdquo in Encyclope-dia of Computer Science and Technology vol 33 pp 137ndash1701995

[18] S Ding H Li C Su J Yu and F Jin ldquoEvolutionary artificialneural networks a reviewrdquo Artificial Intelligence Review vol 39no 3 pp 251ndash260 2013

[19] R Madandoust R Ghavidel and N Nariman-Zadeh ldquoEvo-lutionary design of generalized GMDH-type neural networkfor prediction of concrete compressive strength using UPVrdquoComputational Materials Science vol 49 no 3 pp 556ndash5672010

[20] M Nikoo P Zarfam and M Nikoo ldquoDetermining displace-ment in concrete reinforcement building with using evolution-ary artificial neural networksrdquo World Applied Sciences Journalvol 16 no 12 pp 1699ndash1708 2012

[21] M Nikoo P Zarfam and H Sayahpour ldquoDetermination ofcompressive strength of concrete using Self Organization Fea-ture Map (SOFM)rdquo Engineering with Computers vol 31 no 1pp 113ndash121 2015


[22] A Oner and S Akyuz ldquoAn experimental study on optimumusage of GGBS for the compressive strength of concreterdquoCement and Concrete Composites vol 29 no 6 pp 505ndash5142007

[23] K M Lee H K Lee S H Lee and G Y Kim ldquoAutogenousshrinkage of concrete containing granulated blast-furnace slagrdquoCement and Concrete Research vol 36 no 7 pp 1279ndash12852006

[24] NeuroSolutions Getting Started Manual Version 4 NeuralNetwork Based System Identification Toolbox NeuroSolutions2005

[25] G J Bowden G C Dandy and H R Maier ldquoInput determina-tion for neural network models in water resources applicationsPart 1mdashbackground and methodologyrdquo Journal of Hydrologyvol 301 no 1ndash4 pp 75ndash92 2005

Submit your manuscripts athttpwwwhindawicom

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Table 1 Characteristics of cylindrical samples

Number Parameters Unit Maximum Minimum Standard deviation Mean1 Compressive strength of concrete kgcm2 39400 17300 5498 279272 Water-cement ratio mdash 050 024 019 0433 Maximum size of sand mm 5000 512 1425 23894 Gravel kg 105000 55900 9571 779135 Cement kg 54900 24300 7270 385556 Sand 38 kg 52300 30300 6445 427057 Sand 34 kg 69300 36500 9006 563318 Coefficient of soft sand mdash 920 240 130 327

Table 2 Number of patterns used in ANN

Number Number of patterns Compressive strength of concrete1 2 150ndash1752 11 175ndash2003 25 201ndash2254 24 226ndash2505 20 251ndash2756 22 276ndash3007 34 301ndash3258 15 326ndash3509 17 351ndash37510 3 376ndash400Total of the number of patterns 173

validation and testing phases were equal to 0880 0993 and0946 respectively [21]

2 Materials and Methods

21 Database Compressive strength of concrete (1198911015840119862) is in

fact the 28-day strength of cylindrical concrete sample Inthis study cylindrical samples with a diameter of 15 cm anda height of 30 cm are used In addition parameters such asthe amount of 34 sand 38 sand cement silt in kilogramsmaximumsand size inmillimeter coefficient of fine sand andwater-cement ratio are used to determine the compressivestrength of concrete In the lab using a hydraulic jack 25blows are pounded on each sample of the concrete and datarelated to the intended parameters towards determinationof compressive strength are recorded The characteristics ofused data have been illustrated in Table 1 based on the datapresented in the literature [22 23]

Moreover in Table 2 the number of patterns used inANN has been shown based on compressive strength ofconcrete separately

22 Research Methodology The data were collected from theliterature [22 23] and have not been previously used innumerical modelling presented [21] In the first step severaldifferent mix designs are used to determine the compressivestrength Then Multi Layer (MLP) Feed Forward (FF)Radial Basis Function (RBF) andTime Lag RecarentNetwork

WC

Maximum size of sand

Gravel

Cement

Sand 34

Sand 38

Coefficient of soft sand

f998400C

Figure 1 Structure of EANN

(TLRN) were selected and the estimation of the compressivestrength parameter have been carried out Then the optimalgeometric structure of the intended ANN along with optimalweights is tentatively determined by genetic algorithm (GA)In the next step a multiple linear regression (MLR) modelis employed in determining the compressive strength ofconcrete Finally the performance of the MLR model andthe proposed EANN structure in predicting the compressivestrength of concrete is studied and comparison betweenobtained models has been performed In ANN models thenumber of inputs is seven parameters and the number ofoutputs is one which has been shown in Figure 1 Out of 173data patterns 80 (139 patterns) have been used for training10 (17 patterns) for cross validation and 10 (17 pat-terns) for network test Various transfer functions consistingof LinearSigmoidAxon BiasAxon TanhAxon LinearAxonSigmoidAxon LinearTanhAxon and various training algo-rithms consisting of Momentum Levenberg Marquat DeltaBar Delta Quickprop and Step were considered to determinethe best structure in the ANN [24] In order to determinethe number of nodes in the hidden layer in addition to thesoftware presupposition the following experimental formulawas used [25]

119873119867le 2119873119868+ 1 (1)

where 119873119867is the maximum number of nodes in the hidden

layer and 119873119868is the number of inputs With regard to the






Numberof

output



1 7








0

50

100

150

200

250

300

350

400

450

0 25 50 75 100 125 150Pattern number

Real dataMLPFF

RBFTLRN

Con

cret

e com

pres

sive s

treng

th(k

gm

2 )





Table4Re

sults

obtained

from

MLPFFRB

FandTL

RNop

timalmod


ation

andteststages

forc

ompressiv

estre

ngth

ofconcrete

Test

Valid

ationconcurrent

with

training

Train

Mod

elNum

ber

Bestfittin

glin

eintesting

phase

Perfo

rmance

criteria

Bestfittin

glin

einvalid

ationph

ase

Perfo

rmance

criteria

Bestfittin

glin

eintraining

phase

Perfo

rmance

criteria

Equatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903

119910=09039119909+29657

0899

0106

0948119910=09043119909+06638

0935

0070

0967119910=09061119909+26518

0910

0090

0954

MLP

1119910=071119909+77428

0843

0179

0918119910=08937119909+40161

0916

0126

0957119910=07944119909+57761

0794

0206

0891

FF2

119910=04582119909+14853

0711

0380

0843119910=04476119909+15813

0783

0379

0885119910=0443119909+15686

0734

0381

0857

RBF

3119910=06765119909+71198

0473

0705

0688119910=07052119909+87975

0317

1180

0563119910=06851119909+77142

0411

0813

064

1TL

RN4





01762 03456 051 0611 1199092


3Gravel 4

101053 006292 1606 0 1199094

Cement 504264 02541 168 0096 119909

5Sand 38 6

02452 01705 144 0153 1199096

Sand 34 7minus0529 1756 minus03 0764 119909


Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(a)

Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(b)


000

040

080

120

160

200

Wat

erc

emen

t

Cem

ent

Coe

ffici

ent o

fso

ft sa

nd

Gra

vel

Sand

34

Max

imum

size

of g

rave

l

Sand

38

Sens

itivi

ty



119910 = 119891 (1199091 1199092 ) 997888rarr 119910 = 119886

0+ 11988611199091+ 11988621199092+ sdot sdot sdot (2)





119884 = minus600 + 01681199091+ 0176119909

2+ 0206119909

3+ 101119909

4

+ 04261199095+ 0245119909

6minus 053119909

7

(3)



0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Regression

Estim

ated

com

pres

sive s

treng

th


Linear (y = x)

y = 07941x + 57307

R2 = 0794

(kg

cm2 )





MLPRegression

MLP

Regression

0

50

100

150

200

250

300

350

400

450

Estim

ated

com

pres

sive s

treng

th


y = 09096x + 26222R2 = 09805

y = 07282x + 9138R2 = 08873

(kg

cm2 )


MLPRegression

0 1 2 3 4 5 6 7 8 9 10Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th

f998400C kgcm2

(kg

cm2 )


3 Conclusion








References


































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials








Numberof

output



1 7








0

50

100

150

200

250

300

350

400

450

0 25 50 75 100 125 150Pattern number

Real dataMLPFF

RBFTLRN

Con

cret

e com

pres

sive s

treng

th(k

gm

2 )





Table4Re

sults

obtained

from

MLPFFRB

FandTL

RNop

timalmod


ation

andteststages

forc

ompressiv

estre

ngth

ofconcrete

Test

Valid

ationconcurrent

with

training

Train

Mod

elNum

ber

Bestfittin

glin

eintesting

phase

Perfo

rmance

criteria

Bestfittin

glin

einvalid

ationph

ase

Perfo

rmance

criteria

Bestfittin

glin

eintraining

phase

Perfo

rmance

criteria

Equatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903

119910=09039119909+29657

0899

0106

0948119910=09043119909+06638

0935

0070

0967119910=09061119909+26518

0910

0090

0954

MLP

1119910=071119909+77428

0843

0179

0918119910=08937119909+40161

0916

0126

0957119910=07944119909+57761

0794

0206

0891

FF2

119910=04582119909+14853

0711

0380

0843119910=04476119909+15813

0783

0379

0885119910=0443119909+15686

0734

0381

0857

RBF

3119910=06765119909+71198

0473

0705

0688119910=07052119909+87975

0317

1180

0563119910=06851119909+77142

0411

0813

064

1TL

RN4





01762 03456 051 0611 1199092


3Gravel 4

101053 006292 1606 0 1199094

Cement 504264 02541 168 0096 119909

5Sand 38 6

02452 01705 144 0153 1199096

Sand 34 7minus0529 1756 minus03 0764 119909


Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(a)

Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(b)


000

040

080

120

160

200

Wat

erc

emen

t

Cem

ent

Coe

ffici

ent o

fso

ft sa

nd

Gra

vel

Sand

34

Max

imum

size

of g

rave

l

Sand

38

Sens

itivi

ty



119910 = 119891 (1199091 1199092 ) 997888rarr 119910 = 119886

0+ 11988611199091+ 11988621199092+ sdot sdot sdot (2)





119884 = minus600 + 01681199091+ 0176119909

2+ 0206119909

3+ 101119909

4

+ 04261199095+ 0245119909

6minus 053119909

7

(3)



0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Regression

Estim

ated

com

pres

sive s

treng

th


Linear (y = x)

y = 07941x + 57307

R2 = 0794

(kg

cm2 )





MLPRegression

MLP

Regression

0

50

100

150

200

250

300

350

400

450

Estim

ated

com

pres

sive s

treng

th


y = 09096x + 26222R2 = 09805

y = 07282x + 9138R2 = 08873

(kg

cm2 )


MLPRegression

0 1 2 3 4 5 6 7 8 9 10Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th

f998400C kgcm2

(kg

cm2 )


3 Conclusion








References


































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




Table4Re

sults

obtained

from

MLPFFRB

FandTL

RNop

timalmod


ation

andteststages

forc

ompressiv

estre

ngth

ofconcrete

Test

Valid

ationconcurrent

with

training

Train

Mod

elNum

ber

Bestfittin

glin

eintesting

phase

Perfo

rmance

criteria

Bestfittin

glin

einvalid

ationph

ase

Perfo

rmance

criteria

Bestfittin

glin

eintraining

phase

Perfo

rmance

criteria

Equatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903Eq

uatio

n1198772

NMSE

119903

119910=09039119909+29657

0899

0106

0948119910=09043119909+06638

0935

0070

0967119910=09061119909+26518

0910

0090

0954

MLP

1119910=071119909+77428

0843

0179

0918119910=08937119909+40161

0916

0126

0957119910=07944119909+57761

0794

0206

0891

FF2

119910=04582119909+14853

0711

0380

0843119910=04476119909+15813

0783

0379

0885119910=0443119909+15686

0734

0381

0857

RBF

3119910=06765119909+71198

0473

0705

0688119910=07052119909+87975

0317

1180

0563119910=06851119909+77142

0411

0813

064

1TL

RN4





01762 03456 051 0611 1199092


3Gravel 4

101053 006292 1606 0 1199094

Cement 504264 02541 168 0096 119909

5Sand 38 6

02452 01705 144 0153 1199096

Sand 34 7minus0529 1756 minus03 0764 119909


Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(a)

Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(b)


000

040

080

120

160

200

Wat

erc

emen

t

Cem

ent

Coe

ffici

ent o

fso

ft sa

nd

Gra

vel

Sand

34

Max

imum

size

of g

rave

l

Sand

38

Sens

itivi

ty



119910 = 119891 (1199091 1199092 ) 997888rarr 119910 = 119886

0+ 11988611199091+ 11988621199092+ sdot sdot sdot (2)





119884 = minus600 + 01681199091+ 0176119909

2+ 0206119909

3+ 101119909

4

+ 04261199095+ 0245119909

6minus 053119909

7

(3)



0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Regression

Estim

ated

com

pres

sive s

treng

th


Linear (y = x)

y = 07941x + 57307

R2 = 0794

(kg

cm2 )





MLPRegression

MLP

Regression

0

50

100

150

200

250

300

350

400

450

Estim

ated

com

pres

sive s

treng

th


y = 09096x + 26222R2 = 09805

y = 07282x + 9138R2 = 08873

(kg

cm2 )


MLPRegression

0 1 2 3 4 5 6 7 8 9 10Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th

f998400C kgcm2

(kg

cm2 )


3 Conclusion








References


































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials







01762 03456 051 0611 1199092


3Gravel 4

101053 006292 1606 0 1199094

Cement 504264 02541 168 0096 119909

5Sand 38 6

02452 01705 144 0153 1199096

Sand 34 7minus0529 1756 minus03 0764 119909


Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(a)

Real dataMLPFF

RBFTLRN

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th(k

gcm

2 )

(b)


000

040

080

120

160

200

Wat

erc

emen

t

Cem

ent

Coe

ffici

ent o

fso

ft sa

nd

Gra

vel

Sand

34

Max

imum

size

of g

rave

l

Sand

38

Sens

itivi

ty



119910 = 119891 (1199091 1199092 ) 997888rarr 119910 = 119886

0+ 11988611199091+ 11988621199092+ sdot sdot sdot (2)





119884 = minus600 + 01681199091+ 0176119909

2+ 0206119909

3+ 101119909

4

+ 04261199095+ 0245119909

6minus 053119909

7

(3)



0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Regression

Estim

ated

com

pres

sive s

treng

th


Linear (y = x)

y = 07941x + 57307

R2 = 0794

(kg

cm2 )





MLPRegression

MLP

Regression

0

50

100

150

200

250

300

350

400

450

Estim

ated

com

pres

sive s

treng

th


y = 09096x + 26222R2 = 09805

y = 07282x + 9138R2 = 08873

(kg

cm2 )


MLPRegression

0 1 2 3 4 5 6 7 8 9 10Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th

f998400C kgcm2

(kg

cm2 )


3 Conclusion








References


































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials




0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400 450

Regression

Estim

ated

com

pres

sive s

treng

th


Linear (y = x)

y = 07941x + 57307

R2 = 0794

(kg

cm2 )





MLPRegression

MLP

Regression

0

50

100

150

200

250

300

350

400

450

Estim

ated

com

pres

sive s

treng

th


y = 09096x + 26222R2 = 09805

y = 07282x + 9138R2 = 08873

(kg

cm2 )


MLPRegression

0 1 2 3 4 5 6 7 8 9 10Pattern number

0

50

100

150

200

250

300

350

400

450

Con

cret

e com

pres

sive s

treng

th

f998400C kgcm2

(kg

cm2 )


3 Conclusion








References


































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials









References


































CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials















CeramicsJournal of







Biomaterials




Journal of


Journal of





CoatingsJournal of

Advances in








MaterialsJournal of


Nano

materials



Research Article Prediction of Concrete Compressive Strength by Evolutionary ... · 2019. 7....

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Transcript of Research Article Prediction of Concrete Compressive Strength by Evolutionary ... · 2019. 7....