Prediction Of Mechanical Strength Of Fiber Admixed .

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HindawiAdvances in Materials Science and EngineeringVolume 2019, Article ID 4654070, 7 pageshttps://doi.org/10.1155/2019/4654070Research ArticlePrediction of Mechanical Strength of Fiber Admixed ConcreteUsing Multiple Regression Analysis and Artificial Neural NetworkS. Karthiyaini ,1 K. Senthamaraikannan ,2 J. Priyadarshini,3 Kamal Gupta,1and M. Shanmugasundaram 11School of Mechanical and Building Sciences, Vellore Institute of Technology-Chennai Campus, Chennai-600127, Tamilnadu,India2Department of Civil and Architectural Engineering, Al Musanna College of Technology, Muladdah Musanna, Oman3School of Computing Science and Engineering, Vellore Institute of Technology-Chennai Campus, Chennai-600127, Tamilnadu,IndiaCorrespondence should be addressed to M. Shanmugasundaram; shanmugaresearch@gmail.comReceived 28 September 2018; Accepted 21 March 2019; Published 7 May 2019Guest Editor: Kazunori FujikakeCopyright 2019 S. Karthiyaini et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The present study is to compare the multiple regression analysis (MRA) model and artificial neural network (ANN) modeldesigned to predict the mechanical strength of fiber-reinforced concrete on 28 days. The model uses the data from early literatures;the data consist of tensile strength of fiber, percentage of fiber, water/cement ratio, cross-sectional area of test specimen, Young’smodulus of fiber, and mechanical strength of control specimen, and these were used as the input parameters; the respectivestrength attained was used as the target parameter. The models are created and are used to predict compressive, split tensile, andflexural strength of fiber admixed concrete. These models are evaluated through the statistical test such as coefficient of determination (R2) and root mean squared error (RMSE). The results show that these parameters produce a valid model throughboth MRA and ANN, and this model gives more precise prediction for the fiber admixed concrete.1. IntroductionConcrete is considered to be the fundamental and an important material in construction industry. Maintaining andtesting the quality and behavior of concrete is the challengefaced by the industries in recent times. Also, the modeling ofmaterials through regression tools and AI tools is recentlyincreasing due to its accurate prediction and evaluation. Theconcrete as generally known for its good compressive behavior is made to behave well under tension and flexurethrough addition of fiber additives. The general tensile andflexural strength enhancements are made through additionof fibers made up of various materials with different physicaland chemical properties. The addition of fibers made up ofvarious materials changes the behavior of cement-basedcomposites and enhances the toughness, tension resistance, and flexural resistance [1–9]. These fibers act atvarious levels in altering the mechanical behavior of concreteand thus defy the rules framed for its tensile and flexuralperformance, making it hard to predict. The major factorsthat act in enhancing the tensile and flexural strength arefiber distribution and its physical parameters. In recentyears, analyzing the concrete properties through predictionmodeling is gaining importance due to its accuracy andeffectiveness in real-time application. These concrete modelswere presumed to predict the strength development throughcertain factors which are used as input parameters. Thisprediction facilitates in making decision on concrete mixand material selection [10–15]. But there is a challenge whencreating a model of concrete for predicting tensile strengthand flexural strength, as an effective prediction model is notcreated through parameters which were used for predictingthe compressive strength [16–18]. The challenge on accuracyin prediction increases in fiber admixed concrete whilepredicting tensile strength and flexural strength; this is dueto the fiber properties and its distribution.In this study, the predictive model was created throughmultiple regression analysis (MRA) and artificial neural

2Advances in Materials Science and Engineeringnetwork (ANN). The fiber properties were used as parameters along with basic concrete and fiber parameters withsingle target system, and the model is tested through statistical tools for its performance.2. Prediction Modeling and TestingThe model created here is for fiber-reinforced concrete; thedata set was collected for steel fiber, polypropylene fiber,hybrid fiber, glass fiber, and basalt fiber from early studies.The actual compressive strength, split tensile strength, andflexural strength are taken as the target values based on thefollowing parameters which are used as input parameters:(1)(2)(3)(4)(5)(6)Tensile strength of fiber (F)Percentage of fiber (P)Water/cement ratio (R)Cross-sectional area of test specimen (A)Young’s modulus of fiber (Y)Mechanical strength of control specimen (S)Based on the input parameter and target values, theoutput was generated through ANN and MRA, and theseoutput values were compared with target (actual) values. Thetypes of fibers and its respective literature source are presented in Table 1. The active compressive strength data set has5 columns and 252 rows (5 252) of input data and 1 columnand 252 rows (1 252) of target data. The active split tensilestrength data set has 5 columns and 119 rows (5 119) ofinput data and 1 column and 119 rows (1 119) of target data.The active flexural strength data set has 5 columns and 150rows (5 150) of input data and 1 column and 150 rows(1 150) of target data. The target data for compressivestrength, split tensile strength, and flexural strength were usedin both the MRA and ANN model as separate target in thisstudy. This single target system was used due to the usage ofcross-sectional area of test specimens as one of the parameters, and it was known that the shape of the specimens varieswith different mechanical strengths.2.1. Prediction Model and Its Statistical Test. Two predictionmodels, artificial neural network (ANN) and multiple regression analysis (MRA), are used in this study to predict thecompressive strength, split tensile strength, and flexuralstrength of fiber-reinforced concrete (FRC).2.2. Artificial Neural Network (ANN). The ANN predictionmodel is programmed through MATLAB with two hiddenlayers, 15 neurons in each hidden layer and one output layerwith dependent variable as compressive strength, split tensile strength, and flexural strength. Among all the data, approximately 70%, 15%, and 15% has been considered fortraining, testing, and validation, respectively. The Levenberg–Marquardt (LM) algorithm is used for training due to itsrobustness and speed. Layered feed-forward networks havebeen used in this algorithm, in which the neurons are arrangedin layers. Here, signals are sent forward, and errors arepropagated backwards.2.3. Multiple Regression Analysis (MRA). In this study, thelinear-type multiple regression analysis modeling is carriedout using MS excel. The coefficients of regression are calculated by considering 95% confidence level; hence, the errortolerance level is limited to maximum of 5%. For a giveninput variable, the calculated probability value (p value)is considered to be significant, if and only if its value is lessthan 0.05. Through the regression analysis, the followingcoefficients presented in Table 2 were found and substitutedin linear multiple regression equation (equation (1)):output I C1 F C2 P C3 R C4 A C5 Y C6 S.(1)2.4. Statistical Test. The performance of the ANN and MRAprediction for the mechanical behavior was tested throughthe statistical methods. The tests involved are coefficient ofdetermination (R2) and root mean squared error (RMSE).The coefficient of determination is presented in equation (2).This can be obtained from the comparative chart of predicted compressive strength vs. experimental compressivestrength. The accuracy of the predictions of a network wasquantified by the root of the mean squared error difference(RMSE), between the experimented and the predictedvalues, and the procedure of finding RMSE is presented inequation (3):sum of squares of residualsR2 1 ,(2)sum of sqaures of predicted values 1 nRMSE (ACST PCST)2 .n i 1(3)3. Results and DiscussionThe effectiveness and the acceptance of prediction modelsare based upon the ability of the model to predict the output.In this study, the models were designed to predict themechanical behavior (mechanical strength) of FRC based oninput parameters, and two methods of predictions, ANNand MRA, are used. The prediction models are validatedthrough coefficient of determination (R2) and root meansquared error (RMSE) and are consolidated in Table 3.The MRA and ANN prediction of the compressivestrength value is plotted with respect to the actual compressivestrength and presented in Figures 1 and 2, respectively. TheMRA prediction has the coefficient of determination R2 as0.93 which is almost an acceptable value, whereas the ANNhas an R2 value of 1 which indicates that the ANN model isaccurate. The RMSE of the MRA model is 7.23 MPa, and theANN model is 0.14 MPa which demonstrates that error in theMRA model is large and cannot be relied upon for predictingthe compressive strength.The MRA and ANN prediction model plot for splittensile strength with respect to its actual value is presented inFigures 3 and 4, respectively. The R2 value for the MRAmodel is 0.87 and ANN model is 0.94. The RMSE for the

Steel fiber [19–27]Polypropylene fiber[18, 24, 28–34]Hybrid fiber [35, 36]Glass fiber [15, 37–48]Basalt fiber [23, 49–52]Type of 37503400–4600Percentageadditionof fiber1000–2800Tensilestrengthof fiberin ��141371600–22500Area ofspecimentested forcompressionin 812.7–97.5Data range for prediction modelArea ofArea ofspecimenspecimenCompressiontested fortested forstrengthtensionflexurein MPain mm2in mm222500–6283225200–9000038.2–146.3Table 1: Range of parameters in data base for prediction 95Splittensilestrengthin 20.2Flexuralstrengthin of fiberin MPaAdvances in Materials Science and Engineering3

4Advances in Materials Science and EngineeringTable 2: Multiple regression analysis coefficients.Coefficients forCoefficientssplit tensilefor 726 10 05 4.23499 10 050.816445710.513456489 6.912788644 13.368827138.71841 10 06 1.9284 10 054.70901 10 05 2.60556 10 050.4752578980.551752286Table 3: Statistical test conducted on prediction models.Predicted parametersR20.930.870.92Compression strengthSplit tensile strengthFlexural strengthMRARMSE7.230.700.99R21.000.940.94MRA predicted compressivestrength in MPa160.00ANNRMSE0.140.420.79R2 003.002.001.000.000.002.004.006.008.0010.00Actual split tensile strength in MPaFigure 3: Actual vs. MRA predicted value for split tensile strength.10.00R2 .0020.000.000.00MRA predicted split tensilestrength in MPaIC1C2C3C4C5C6Coefficients forcompressivestrength 2.0839447950.0006692271.097340646 31.43416778 5.56151 10 050.0011548440.569536979ANN predicted split tensile strength in MPaMRAcoefficientsR2 0.879.002.004.006.008.0010.00Actual split tensile strength in MPa20.0040.0060.0080.00 100.00 120.00 140.00 160.00Figure 4: Actual vs. ANN predicted value for split tensile strength.Actual compressive strength in MPaFigure 1: Actual vs. MRA predicted value for compressivestrength.ANN predicted compressivestrength in MPa160.00R2 0040.00 60.00 80.00 100.00 120.00 140.00 160.00Actual compressive strength in MPaFigure 2: Actual vs. ANN predicted value for compressivestrength.MRA model is 0.70 MPa and ANN is 0.42 MPA. The statistical validation of the split tensile strength model showsthat both the MRA model and ANN model are in acceptablelimit; even though ANN shows more accuracy than MRA,the mathematical model is also predicting the split tensilestrength in par with the ANN model. From Figure 3, it isobserved that the MRA model predicts to a high accuracyuntil actual split tensile strength is 4 MPa, after which thescatter plots were deviating from the actual trend line. FromFigure 4, it is observed that the ANN prediction is accurateuntil the actual strength is 7.5 MPa, after which the scatteredplot almost does not fit the trend line.The MRA and ANN prediction model plot for flexuralstrength with respect to its actual value is presented inFigures 5 and 6, respectively. The R2 value for MRA andANN was 0.92 and 0.94, respectively, which has similarvalidation value. The RMSE value of the MRA model is0.99 MPa and ANN model is 0.79 MPa. Both the MRA andANN were having similar model behavior in terms of statistical validation and graphical representation throughFigures 5 and 6. The prediction is accurate in both MRA andANN models until the actual flexural strength is 9 MPa afterwhich the scattered plot is observed for both models. Butthere were fitted plots for the MRA model at higher actualflexural strength which lies between 13 MPa and 14 MPa.This higher-order flexural strength fitness towards the trendline was not observed in the ANN model. The observationindicates that flexural strength prediction using MRA andANN model has effectiveness, and more accurate predictionis rendered in both models. Through the three strengthaspects, it was observed that the MRA gains its accuratenessin predicting split tensile and flexural strength. The ANNpredicts compressive strength to the maximum possibleaccuracy, and the prediction of split tensile strength and

MRA predicted flexural strengthin MPaAdvances in Materials Science and Engineering25.005R2 l flexural strength in MPa20.00ANN predicted flexural strengthin MPaFigure 5: Actual vs. MRA predicted value for flexural strength.split tensile and flexural strength has similar statisticalvaluation. The MRA model shows more robustness whilepredicting the flexural strength, than the split tensilestrength. Also, it is noted that the MRA model performs wellin split tensile and flexural strength prediction and is validated through the R2 and RMSE values. The MRA performswell similar to that of ANN and achieves half its effectiveness, except in compressive strength prediction. The studyconcludes that the fiber properties contribute high to theprediction model, thus increasing the models’ performance.Data Availability15.00The data supporting this work are available from previouslyreported studies and datasets, which have been cited. Theprocessed data used to support the findings of this study areavailable from the corresponding author upon request.10.00Conflicts of Interest25.00R2 0.9420.00The authors declare no conflicts of l flexural strength in MPaFigure 6: Actual vs. ANN predicted value for flexural strength.flexural strength was also of higher accuracy. Though thefibers have various factors on influencing the strength development in concrete, the prediction models MRA andANN are accurate by its output values. The ANN eventhough has its advantage of higher accuracy over MRAmodel; the performance of the MRA model is also efficient.The contribution of fiber properties in the prediction modelproved to be effective and also gives more preciseness to themodel. Earlier models that uses other parameters such asquantity of cement, admixtures, coarse aggregate, fine aggregate, and water were not able to perform well in prediction of tensile and flexural properties [53]; this limitationwas overcome by the current model, where both the MRAand ANN model performs well with the given factors. Thus,both current models can predict the complete mechanicalbehavior of fiber admixed concrete with high precision.4. ConclusionThis study investigated the feasibility of modeling a predictive analysis through earlier study data, converting theunstructured factors to possible structured parameters andusing those in creating the MRA model and ANN model.Also, the effectiveness of these models is tested using statistical tools such as R2 and RMSE. The compressive strengthmodel shows that ANN has efficient prediction model withR2 value in unity. The MRA model has R2 value of 0.93, butthe error difference is 7.23 MPa which is very high for apredictive model. The MRA model of split tensile strengthand flexural strength shows high efficiency; even though theR2 values are lesser than the compressive model, the performance of models is relatively strong. The ANN model forReferences[1] X. Lu and C.-T. T. Hsu, “Behavior of high strength concretewith and without steel fiber reinforcement in triaxial compression,” Cement and Concrete Research, vol. 36, no. 9,pp. 1679–1685, 2006.[2] V. F. P. Dutra, S. Maghous, and A. C. Filho, “A homogenization approach to macroscopic strength criterion of steelfiber reinforced concrete,” Cement and Concrete Research,vol. 44, pp. 34–45, 2013.[3] P. S. Song and S. Hwang, “Mechanical properties of highstrength steel fiber-reinforced concrete,” Construction andBuilding Materials, vol. 18, no. 9, pp. 669–673, 2004.[4] M. L. Allan and L. E. Kukacka, “Strength and durability ofpolypropylene fibre reinforced grouts,” Cement and ConcreteResearch, vol. 25, no. 3, 1995.[5] B. Chen and J. Liu, “Residual strength of hybrid-fiberreinforced high-strength concrete after exposure to hightemperatures,” Cement and Concrete Research, vol. 34, no. 6,pp. 1065–1069, 2004.[6] C. S. Poon, Z. H. Shui, and L. Lam, “Compressive behavior offiber reinforced high-performance concrete subjected to elevated temperatures,” Cement and Concrete Research, vol. 34,no. 12, pp. 2215–2222, 2004.[7] Y. Ding, C. Azevedo, J. B. Aguiar, and S. Jalali, “Study onresidual behaviour and flexural toughness of fibre cocktailreinforced self compacting high performance concrete afterexposure to high temperature,” Construction and BuildingMaterials, vol. 26, no. 1, 2011.[8] A. Avci, H. Arikan, and A. Akdemir, “Fracture behavior ofglass fiber reinforced polymer composite,” Cement andConcrete Research, vol. 34, no. 3, pp. 429–434, 2004.[9] I. Curosu, V. Mechtcherine, and O. Millon, “Effect of fiberproperties and matrix composition on the tensile behavior ofstrain-hardening cement-based composites (SHCCs) subjectto impact loading,” Cement and Concrete Research, vol. 82,pp. 23–35, 2016.[10] İ. B. Topçu and M. Sarıdemir, “Prediction of compressivestrength of concrete containing fly ash using artificial neuralnetworks and fuzzy logic,” Computational Materials Science,vol. 41, no. 3, pp. 305–311, 2008.

6[11] N. Al-Mutairi, M. Terro, and A.-L. Al-Khaleefi, “Effect ofrecycling hospital ash on the compressive properties ofconcrete: statistical assessment and predicting model,”Building and Environment, vol. 39, no. 5, pp. 557–566, 2004.[12] M. A. Kewalramani and R. Gupta, “Concrete compressivestrength prediction using ultrasonic pulse velocity throughartificial neural networks,” Automation in Construction,vol. 15, no. 3, pp. 374–379, 2006.[13] R. Siddique, P. Aggarwal, and Y. Aggarwal, “Prediction ofcompressive strength of self-compacting concrete containingbottom ash using artificial neural networks,” Advances inEngineering Software, vol. 42, no. 10, pp. 780–786, 2011.[14] Z. H. Duan, S. C. Kou, and C. S. Poon, “Prediction ofcompress

MRA predicted split tensile strength in MPa Actual split tensile strength in MPa Figure 3: Actual vs. MRA predictedvalue for splittensile strength. R2 0.94 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 0.00 2.00 4.00 6.00 8.00 10.00 ANN predicted split tensile strength in MPa Actual split tensile strength in MPa Figure 4: Actual vs .

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