An alternative method using Artificial Intelligence (AI) to predict the 28-day strength of concrete from its primary ingredients is presented in this research. A series of 424 data samples collected from a previous study were employed for developing, testing, and validation of Adaptive Neuro-Fuzzy Inference System (ANFIS) models. Seven mix parameters, namely Cement, Blast Furnace Slag, Fly Ash, Water, Superplasticizer, Coarse Aggregate, and Fine Aggregate were used as the inputs of the models while the output was the 28-day compressive strength of concrete. In the first step, different models with various input membership functions were explored and compared to obtain an optimal ANFIS model. In the second step, that model was utilized to predict the compressive strength value for each concrete sample, and to compare with those obtained from the compressive test in laboratory.
Journal of Science and Technology in Civil Engineering NUCE 2020 14 (2): 40–52 AN ARTIFICIAL INTELLIGENCE APPROACH FOR CONCRETE HARDENED PROPERTY ESTIMATION Tu Trung Nguyena,∗, Kien Dinhb a Department of Civil, Construction, and Environmental Engineering, University of Alabama, Tuscaloosa, AL 35487, USA b NDT Concrete LLC, 1082 Algoma St, Deltona, FL 32725, USA Article history: Received 12/12/2019, Revised 03/01/2020, Accepted 06/01/2020 Abstract An alternative method using Artificial Intelligence (AI) to predict the 28-day strength of concrete from its primary ingredients is presented in this research A series of 424 data samples collected from a previous study were employed for developing, testing, and validation of Adaptive Neuro-Fuzzy Inference System (ANFIS) models Seven mix parameters, namely Cement, Blast Furnace Slag, Fly Ash, Water, Superplasticizer, Coarse Aggregate, and Fine Aggregate were used as the inputs of the models while the output was the 28-day compressive strength of concrete In the first step, different models with various input membership functions were explored and compared to obtain an optimal ANFIS model In the second step, that model was utilized to predict the compressive strength value for each concrete sample, and to compare with those obtained from the compressive test in laboratory The results showed that the selected ANFIS model can be used as a reliable tool for predicting the compressive strength of concrete with Root Mean Squared Error values of 5.97 MPa and 7.73 MPa, respectively, for the training and test sets In addition, the sensitivity analysis results revealed that the accuracy of the proposed model improved with an increase in the number of input parameters/variables Keywords: artificial intelligence; adaptive neuro-fuzzy inference system; concrete strength; sensitivity analysis https://doi.org/10.31814/stce.nuce2020-14(2)-04 c 2020 National University of Civil Engineering Introduction Concrete and reinforced concrete are commonly used as building construction materials all over the world In the United States, reinforced concrete is a dominant structural material in engineered construction [1] The reinforced concrete is widely used for many structures such as skyscrapers, as well as for the large infrastructures, including bridges, superhighways, and dams Concrete is a mixture of cement, aggregate, and water A proper concrete mixture requires workability for fresh concrete and durability and strength for the hardened stage Small coarse aggregate sizes are often used for the relatively thin buildings, and the larger aggregates, up to 15 cm in diameter, are utilized for large dam structures [2] Water is needed for the chemical reaction to form a cement paste and offers workability for fresh concrete Typical components of a concrete mixture are depicted in Fig Among many concrete characteristics, compression strength is usually considered the most valuable hardened property of concrete It is measured by breaking cylindrical concrete specimens in a compression-testing machine at 28 days of standard curing The testing procedure and standard size of ∗ Corresponding author E-mail address: nttu@crimson.ua.edu (Nguyen, T T.) 40 Water is needed for the chemical reaction to form a cement paste and offers workability for fresh concrete Typical ofofaScience concrete mixture areEngineering depicted in Figure Nguyen, T.components T., Dinh, K / Journal and Technology in Civil FigureFigure Components ofconcrete concrete Components of [2] [2] Among many concrete characteristics, compression strength is usually considered testvaluable specimens hardened are in accordance with American Society It foris Testing and Materials (ASTM) C39 [3] the most property of concrete measured by breaking cylindrical To obtain the average strength of concrete, the strength test results of at least two specimens are often concreterequired specimens in a compression-testing machine at 28 days of standard curing The [4] Several factors might affect the concrete compressive strength such as age, ingredients, testing water procedure and standard size ofetc testTypically, specimens are in accordance with American to cement ratio, curing conditions, the compression test result of concrete at 28 Societydays forisTesting and Materials (ASTM) C39 [3] To obtain the average strength of considered as a standard to determine the quality of concrete If the compression result of does meettwo the specimens required strength, mix required design needs to Several be concrete, the strength testtest results atnot least are the often [4] replaced, which might be labor-intensive and time-consuming To minimize the risk of a specific factors might affect the concrete compressive strength such as age, ingredients, water to concrete mix design falling short of compression strength requirement at the age of 28 days, a method cement toratio, curing conditions, etc Typically, the compression test result of concrete at predict the 28-day strength from its primary ingredients is essential Traditionally, the experimental 28 daysmethod is considered a to standard determine the quality concrete is broadly as used study theto properties of materials [5–8] of In recent years, the application of the artificial intelligence-based models such as ANFIS and Artificial Neural Networks (ANN) to If the compression test result does not meet the required strength, the mix design predict the concrete mechanical properties has increased significantly Those models have an ability needs toto be which mightthebe labor-intensive time-consuming Toforminimize learnreplaced, from the data to establish non-linear relationship and between the inputs and outputs the the riskcomplex of a specific concrete engineering issues mix design falling short of compression strength requirement Many have used to ANFIS modelthe to predict thestrength 28-day compressive of different at the age of 28researchers days, a method predict 28-day from itsstrength primary ingredients concrete types In their research, the number of the inputs, the number of membership functions, and is essential Traditionally, the experimental method is broadly used to study the properties the input ingredients were varied from one to another depending on the available experimental data of materials [5-8] In recent years, the application of the artificial intelligence-based models For example, Khademi et al [9] used 173 concrete mix designs to develop, train, and test ANFIS such asmodels ANFISSeven andinput Artificial Neural Networks (ANN) the concrete mechanical parameters and one output were selectedtoinpredict such models The coefficient of properties has increased significantly models an ability to learn the data determination was used to evaluate the Those performance of thehave proposed model The resultsfrom from that study indicated that the ANFIS model could be used forthe predicting 28-day concretefor compressive to establish the non-linear relationship between inputstheand outputs the complex strength The application of the ANFIS model was also presented in the work for high-performance engineering issues concrete [10–12], no-slump concrete [13], and for determining the Bridge Deck Corrosiveness Index [14] Many researchers have used ANFIS model to predict the 28-day compressive Another AI-based model,types ANN model, is also popular the among researchers to estimate strength of different concrete In their research, number of the inputs,the thecomnumber pressive strength of concrete For instance, Duan et al., [15] applied the ANN method for recycled of membership functions, and the input ingredients were varied from one to another aggregate concrete In that study, an ANN model with 14 input parameters was trained and tested depending data Khademi al [9] used 173 with on 146 the data available points Threeexperimental indicators, namely Root For Meanexample, Squared Error, Absolute et Fraction of Variconcrete mix designs to develop, train, and test ANFIS models Seven input parameters and one output were selected in such models.41 The coefficient of determination was used to evaluate the performance of the proposed model The results from that study indicated that Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering ation, and Mean Absolute Percentage Error, were used for the ANN model evaluation The study concluded that the ANN had a fair accuracy in predicting the strength of recycled aggregate concrete Additionally, the ANN model was employed for the prediction of compressive strength of other concrete types, including light-weight concrete [16, 17], and self-compacting concrete [18–20] Besides the applications for estimating the compressive strength of various types of concrete material, the ANFIS and ANN approach have also been utilized by many researchers to deal with the various engineering problems As an example, Bingăol et al., [21] applied the ANN approach to study the effects of the high temperature on the light-weight compression strength The results from Bingăols study revealed that the ANN model successfully predicted the nonlinear behavior of the concrete compressive strength after high-temperature effects Other researchers applied the ANN model to estimate the slump of concrete [22, 23], to determine the ultimate load factor of nonlinear inelastic steel truss [24], to forecast the air quality [25], to predict the bridge desk rating [26], or to optimize the performance in the wastewater treatment plant [27] In this study, a supervised learning ANFIS model was developed to predict the compressive strength of concrete at 28 days Data used in training and testing model were collected from a previous study [28] The ANFIS structure was developed in MATLAB R2019a Runtime Environment with seven input parameters and one output The performance of various ANFIS models using different membership functions was evaluated to determine the optimal model for the experimental data In addition, the proposed ANFIS model was used to study the sensitivity of the number of inputs to the model performance Data preparation The original data contained the compressive strength of concrete at different ages Since the current study aimed to predict the 28-day compressive strength concrete using the data-driven method, only the concrete test samples with 28-day compressive strength were extracted from the original dataset The data after refinements were stored in a table format of 424 rows and columns Each row in the table included both input and output information of each test sample The input parameters were stored from column one to column seven, and the output parameter was archived in the last column Table Characteristics of input and output Input Output No CEM (kg/m3 ) BFS (kg/m3 ) FLA (kg/m3 ) WTR (kg/m3 ) SPP (kg/m3 ) COA (kg/m3 ) FIA (kg/m3 ) F28 (MPa) 422 423 424 Min Max 540 380 266 148.5 159.1 260.9 102 540 95 114 139.4 186.7 100.5 359 0 108.6 78.3 200 162 228 228 192.7 175.6 200.6 122 247 2.5 0 6.1 11.3 8.6 32 1055 932 932 892.4 989.6 864.5 801 1145 676 594 670 780 788.9 761.5 594 993 62 36 46 24 33 32 82 42 Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering Table Number of samples in each specific range of 28 days compressive strength No 28-day compressive strength (MPa) Number of samples Total - 15 15 - 30 30 - 45 45 - 60 60 - 75 75 - 90 17 129 181 61 33 424 Seven concrete ingredients namely Cement (CEM), Blast Furnace Slag (BFS), Fly Ash (FLA), Water (WTR), Superplasticizer (SPP), Coarse Aggregate (COA), and Fine Aggregate (FIA) were used as the inputs of the model The model output was the 28-day compressive strength of concrete (F28) The range of the input and output parameters is shown in Table The classification of the 28-day compression strength of concrete in each specific interval is presented in Table Adaptive Neuro-Fuzzy Inference System The Adaptive Neuro-Fuzzy Inference System uses Neural Network learning method to fine-tune The Adaptive Neuro-Fuzzy Inference System uses Neural Network learning method to the Fuzzy Inference System parameters The basic ANFIS architecture with two input variables is fine-tune System parameters The basic ANFIS with two illustratedthe in Fuzzy Fig Inference In this architecture, two fuzzy IF-THEN rules based architecture on a first-order Sugeno input variables is illustrated in Figure In this architecture, two fuzzy IF-THEN rules model are presented based on a first-order Sugeno model are presented Rule x isAND A1 AND f1 = p1 x + q1 y + r1 , THENf = Rule 1: IF1:x IF is A y isy Bis1,BTHEN 1 p x + q y + r1 Rule 2: IF x is A2 AND y is B2 , THEN f2 = p2 x + q2 y + r2 Rule 2: IF x is A2 AND y is B2, THEN f2= p2x + q2y + r2 where xx and B are the fuzzy sets; fi are the outputs within the fuzzy region where: and yy are arethe theinputs; inputs;AiAand fi are the outputs within the fuzzy i andi Bi are the fuzzy sets; specified by the fuzzy rule; p , q , and r are the design parameters that are determined during the i i i region specified by the fuzzy rule; pi, qi, and ri are the design parameters that are determined training process during the training process Layer A1 x A2 Layer Layer p x y Layer w1 N w1 Layer w1 f f B1 y p N w2 w2 f w2 x y B2 Figure Structure ANFIS model Figure Structureof of the the ANFIS model As shown in Figure 2, the ANFIS model includes layers with the fixed nodes depicts as circles The details of each layer are identified in the following [4] 43 (i) Layer consists of all adaptive nodes and the outputs are the fuzzy membership grade of the inputs, as given by equation (1) 𝑂#,% = 𝜇() (𝑥), (1) Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering As shown in Fig 2, the ANFIS model includes layers with the fixed nodes depicts as circles The details of each layer are identified in the following [4] (i) Layer consists of all adaptive nodes and the outputs are the fuzzy membership grade of the inputs, as given by Eq (1) O1,i = µAi (x) (1) where x is the inputs to node i, and Ai is the linguistic labels associated with this node function (ii) Layer involves fuzzy operator that related to the firing strength of the rules The output of this layer is given by O2,i = wi = àAi (x) ì àBi (y), y = 1, (2) (iii) Layer is related to the normalization of the firing strength for each node in this layer using Eq (3) The output from this layer is normalized firing strengths O3,i = wl = wi , w1 + w2 y = 1, (3) (iv) Layer involves in the production between the normalized strength at each node with a firstorder polynomial For the Sugeno model, the output of this layer is calculated as O4,i = wl × fi = ωl (pi x + qi y + ri ) , y = 1, (4) where wl is the output of Layer 3, and pi , qi , and ri are the design parameters (v) Layer includes the summation of all input signals to produce a single output O5,i = w × fi = i × fi i wi i wi (5) 3.1 Model construction The ANFIS model was used to predict the compressive strength of concrete at 28 days (F28) Inputs for the model were seven parameters of concrete, namely CEM, BFS, FLA, WTR, SPP, COA, and FIA Data set used for the ANFIS model was randomly divided into two subsets in which the training data subset contains about 85% of the entire data, i.e., 360 data samples and a testing data subset accounts for 15% of the entire data, i.e., 64 data samples The structure of the ANFIS model is depicted in Fig For simplicity, only some connections are presented in the figure Both hybrid and backpropagation optimal methods with different epoch numbers were tested for optimum performance To generate the initial ANFIS model, different number and type of input membership functions were examined to obtain the optimum solution Both the linear and constant membership function was used for the output For each combination, the performance of the ANFIS model was evaluated by calculating the RMSE for both training and testing data set Table presents details of several combinations and the average performance error for both training and testing data An ANFIS model was selected based on the optimum performance and time of computing of all models in the combinations The selected ANFIS model consisted of two ‘gaussmf’ input membership functions and one ‘linearmf’ output membership function The optimal backpropagation method was chosen with an epoch number of 100 More detailed information about the selected ANFIS model is listed in Table 44 selected based on the optimum performance and time of computing of all models in the combinations The selected ANFIS model consisted of two ‘gaussmf’ input membership functions and one ‘linearmf’ output membership function The optimal backpropagation method was chosen with an epoch number of 100 More detailed information about the Nguyen, T Dinh, K Journal of4.Science and Technology in Civil Engineering selected ANFIS model isT.,listed in/ Table Input Inputmf Outputmf Rule CEM BFS FLA Output WTR F28 SPP COA FIA Figure Structure of the ANFIS model Table Average performance error of some selected combinations Input membership function trimf trapmf gbellmf gaussmf gauss2mf pimf dsigmf psigmf Output membership function Number epochs linearmf 100 RMSE Training data Testing data 5.80 6.32 6.12 5.97 6.32 6.57 6.21 6.21 7.85 7.97 7.66 7.73 7.99 8.23 7.35 7.35 Table Structure of the ANFIS model Information Value Number of nodes Number of nonlinear parameters Number of nonlinear parameters Total number of parameters Number of training data pairs Number of fuzzy rules 294 1024 42 1066 360 128 3.2 Model assessment The root mean squared error indicator (RMSE) was used to evaluate the performance of the model RMSE is the root of the average squared difference between predicted outputs and actual outputs RMSE can be calculated using Eq (6) RMSE = n n (yi − yˆ i )2 i=1 45 (6) Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering where yi is the ith actual output; yi is the ith predicted outputs; n is the total number of samples It is worth mentioning that the lower the value of RMSE is, the better the model would be The It Itisisworth worthmentioning mentioningthat thatthe thelower lowerthe thevalue valueofofRMSE RMSEis,is,the thebetter betterthe themodel model value of the error size depends on several factors, including the quantity and type of input memwould be The value of the error size depends on several factors, including the quantity and would be The value of the error size depends on several factors, including the quantity bership functions, types of output membership functions, optimization methods, and the number ofand type ofofinput functions, types ofofoutput membership optimization type inputmembership membership functions, types output membership functions, optimization epochs/iterations By adjusting these factors, the effective ANFIS model withfunctions, the minimum error size methods, and the number of epochs/iterations By adjusting these factors, the methods, and the number of epochs/iterations By adjusting these factors, theeffective effective can be achieved ANFIS ANFISmodel modelwith withthe theminimum minimumerror errorsize sizecan canbebeachieved achieved Resultsand and discussion 4.4 Results Results anddiscussion discussion Figure 4shows training the selected ANFIS model The ofofRMSE Figure theresults resultsof thetraining training the selected ANFIS model Thevalues values RMSE Fig 4shows showsthe the results ofofthe the the selected ANFIS model The values of RMSE were were decreased significantly ininthe epochs and reached the minimum decreased significantly in the first 30 epochs reached the minimum of 5.97value MPa of atof5.97 an5.97 were decreased significantly thefirst first3030and epochs and reached thevalue minimum value iteration 100, as shown in100, Fig.as 4(a) The comparison of4a the compressiveof strength of 360 MPa atatanof ofof100, ininFigure The MPa aniteration iteration asshown shown Figure 4a.concrete Thecomparison comparison ofthe theconcrete concrete samples in the testing data with the compressive strength of the test samples predicted from the ANFIS compressive compressivestrength strengthofof360 360samples samplesininthe thetesting testingdata datawith withthe thecompressive compressivestrength strengthofof model issamples shown in Fig 4(b) from the test predicted the testsamples predicted fromthe theANFIS ANFISmodel modelisisshown shownininFigure Figure4b 4b 40 40 90 90 80 80 35 35 Concrete strength, MPa Concrete strength, MPa Root Mean Squared Error Root Mean Squared Error 70 70 30 30 60 60 25 25 50 50 40 40 20 20 30 30 15 15 20 20 10 10 Training Data Training Data ANFIS Output ANFIS Output X: 100 X: 100 Y: 5.975 Y: 5.975 10 10 20 20 30 30 40 40 50 50 60 60 70 70 80 80 90 90 100100 Epoch Number Epoch Number (a) Variation of RMSE in training Variation RMSE training (a)(a)Variation ofofRMSE inintraining 10 10 0 0 50 50 100100 150150 200200 250250 300300 350350 400400 Sample number Sample number (b)(b) Original vs prediction value Original prediction value (b) Original vsvsprediction value Figure ANFIS model intraining training Figure 4.4.4 ANFIS Figure ANFIS model model inin training ordertotoevaluate evaluatethe theperformance performanceofofthe theproposed proposedANFIS ANFISmodel, model,the thetrained trained InInorder In order to evaluate the performance of the proposed ANFIS model, the trained model was tested model was tested with the unseen data in the test set It worth noting again that the testset set model wasunseen testeddata with thetest unseen data in the test worth again that the which test with the in the set It worth noting againset thatItthe test setnoting contained 64 samples, contained samples, which wererandomly randomly selectedin from theoriginal original dataand andnot not contained 6464samples, which were from the were randomly selected from the original data and notselected included the training set The data performance included the training set The performance the ANFIS modelfor forthe thedata datatest testset setare are included ininthe training set The ofofin the ANFIS model of the ANFIS model for the data testperformance set are presented Fig presented in Figure presented inbeFigure As can seen in5.Fig 5(a), the ANFIS model performed well on the data test set with the value of RMSE was 7.73 be Fig.in5(b) presents the errors the entire testwell set using thedata proposed can seen Figure 5a,the theprediction ANFISmodel modelof performed the testset set AsAscan beMPa seen in Figure 5a, ANFIS performed well ononthe data test model The prediction errors were calculated by subtracting the compression strength of concrete withthe thevalue valueofofRMSE RMSEwas was7.73 7.73MPa MPa.Figure Figure5b5bpresents presentsthe theprediction predictionerrors errorsofofthe the with samples in the experimental test data with the sample compressive strength predicted by the ANFIS entiretest test setusing using theproposed proposedmodel model.The Theprediction predictionerrors errorswere were calculated calculated by entire model For set the most testthe samples, the prediction error of the proposed model varied within an accept-by subtracting the compression strength of concrete samples in the experimental testdata data with subtracting compression strength of concrete asamples in the experimental test with able range the of ±5 MPa Some specimens experienced huge difference between the predictions and the samplecompressive compressive strength predicted theANFIS ANFIS model For themost most testsamples, samples, the sample strength predicted bybythe test experimental data The reason for the unexpected results mightmodel be due toFor thethe inherent nature of the the prediction error of the proposed model varied within an acceptable range of ± 5MPa MPa theexperimental predictiondata errorAsoflisted the inproposed model varied within an acceptable rangewith of the ± 5comTable 2, the original data contained very few test samples Some specimens experienced huge difference between the predictions and experimental pression strength lower than 15 MPa or higher than 75 between MPa Thus, insufficient general characteristics Some specimens experienced a ahuge difference the predictions and experimental data The reason for the unexpected results might be due to the inherent nature the from limited samples would result in the poor performance of the model data The reason for the unexpected results might be due to the inherent nature ofofthe experimentaldata data.AsAslisted listedininTable Table2,2,the theoriginal originaldata datacontained containedvery veryfew fewtest testsamples samples experimental withthe thecompression compressionstrength strengthlower lowerthan than151546 MPaororhigher higherthan than7575MPa MPa.Thus, Thus,insufficient insufficient with MPa general characteristics characteristics from fromlimited limitedsamples sampleswould wouldresult resultininthe thepoor poorperformance performanceofofthe the general generalcharacteristics characteristicsfrom fromlimited limitedsamples sampleswould wouldresult resultininthe thepoor poorperformance performance of the general of the model model model model Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering 40 40 4040 25 25 25 25 20 20 20 20 15 15 15 15 10 10 10 10 5 5 0 0 -5 -5 -5 -5 -10 -10 -10-10 -15 -15 -15-15 -20 -20 -20-20 -25 -25 -25-25 Prediction erorrs, MPa Prediction erorrs, MPa Prediction erorrs, MPa Prediction erorrs, MPa Root Mean Squared Error Root Mean Squared Error Root Mean Squared Error Root Mean Squared Error 35 35 3535 30 30 3030 25 25 2525 20 20 2020 15 15 1515 X: 100 X: 100 Y: 7.739 X: 100 Y:X:7.739 100 Y: 7.739 Y: 7.739 10 10 1010 55 10 100 05 10 2020 3030 4040 5050 6060 7070 8080 9090 100 50 6060 70 70 80 80 90 90 100100 00 1010 2020 3030 Epoch 4040 50 Number Mean value Mean value Mean value Mean value 1010 10 10 Epoch Number EpochNumber Number Epoch (a)Variation Variation ofRMSE RMSE in testing (a) of in Variation of in testing (a) Variation ofRMSE inintesting testing (a)(a) Variation ofRMSE RMSE testing 3030 40 40 40 30 30number Sample Sample number40 Sample number Sample number 50 50 50 50 60 60 60 60 (b)Prediction Prediction errors (b)(b) Prediction errors errors (b) errors (b)Prediction Prediction errors 8080 80 80 70 70 7070 7070 70 70 60 60 6060 6060 60 60 Prediction,MPa MPa(y) (y) Prediction, Prediction, MPa (y) Prediction, MPa (y) Concrete strength, MPa Concrete strength, MPa Concrete strength, MPa Concrete strength, MPa 80 80 8080 50 50 5050 5050 50 50 40 40 4040 4040 40 40 30 30 3030 3030 30 30 20 20 2020 2020 20 20 10 10 1010 00 000 2020 20 20 1010 10 10 2020 20 20 3030 30 4040 40 30 number 40 Sample number Sample Sample Samplenumber number 1010 10 10 TestData Data Test Test Data ANFIS Output Test Data ANFIS Output ANFIS Output ANFIS Output 5050 6060 7070 50 60 70 50 60 70 00 00 00 (c) Originalvs vs prediction valuevalue (c)Original Original vs prediction value (c) prediction 1010 10 10 Compression Strength Compression Strength Compression Linear fittingStrength Compression Strength Linear fitting yfitting fitting xLinear =x y=Linear x = yx = y 2020 3030 4040 50 50 60 60 70 70 80 80 20 30 40 50 60 70 80 20 30 40 50 70 80 Experimental results, MPa Experimental results, MPa (x)(x) 60 Experimental results, MPa (x) (x) Experimental results, MPa (d)Linear Linearregression regression (d) (c) (d) (c)Original Originalvsvsprediction predictionvalue value (d)Linear Linearregression regression Figure Performance of ANFIS model Figure Performance of ANFIS model Figure Performance of ANFIS model Figure Figure5.5.Performance PerformanceofofANFIS ANFISmodel model Figure 5c and 5d show the visualization of the performance ofthe theANFIS ANFISmodel modelfor for Figure 5c and 5d show the visualization of the performance of Figure 5c and 5d show the visualization ofofthe performance of the ANFIS model for Figure 5c and 5d show the visualization the performance of the ANFIS model for Figs 5(c) and 5(d) show the visualization of the performance of the ANFIS model for the test the test data While in 5c, the concrete from data the test data While inFigure Figure 5c, thecompressive compressive concretestrength strength fromexperimental experimental data the test data While in Figure 5c, the compressive concrete strength from experimental data the testWhile data.inWhile in Figure 5c, the compressive concrete strength from experimental data data Fig 5(c), thethe compressive concrete strength from experimental data and the value and the value predicted by model comparable for sample, plot and the value predicted by the modelwere were comparable foreach each sample,the theregression regression plot and the value predicted by the model were comparable for each sample, the regression plot and the value bycomparable the modelforwere comparable for each sample, the provided regression plot predicted byprovided thepredicted model were each sample, the regression plot in Fig 5(d) the in 5d the of proposed ANFIS performance In in Figure 5d provided thevisualization visualization ofthe the proposed ANFISmodel model performance Inthe the ininFigure Figure 5d provided the visualization of the proposed ANFIS model performance In the Figure 5d provided the visualization of the proposed ANFIS model performance In the visualization of the proposed ANFIS modelthe performance In thedata figure, the horizontal axis represents figure, the horizontal axis experimental the test and figure, the horizontal axis represents represents the experimental dataof of the testsamples, samples, andthe the figure, the horizontal axis represents the experimental data of the test samples, and the figure, the horizontal axistest represents thetheexperimental data ofthethe thepredictions test samples, and the the experimental data of the samples, and vertical axis represents The data vertical axis represents the vertical axis represents the predictions predictions.The Thedata datasamples sampleswith with the thecompression compressionstrength strength vertical axis represents the predictions The data samples with compression strength samples with compression values positioned the diagonal linethe presented the coincident vertical axis the represents thestrength predictions The dataoncoincident samples with compression strength values positioned on the line values positioned on thediagonal diagonal linepresented presentedthe the coincident coincidentbetween betweenexperimental experimentaldata data values positioned on the diagonal line presented the between experimental data between experimental data and prediction values values positioned on the diagonal line presented the coincident between experimental data and prediction values and prediction values and and prediction values 4.1 Inputsand andoutput output relationship 4.1 Inputs relationship 4.1 Inputs and output relationship 4.1 4.1 Inputs and outputrelationship relationship (d) Linear regression The ANFIS model was also used to establish the relationship between the inputs and the output Fig shows the three-dimensional (3D) surface diagram of the relationship between different input parameters and the 28-day concrete compression strength The relationships between some major selected input ingredients and the output of the ANFIS model are presented in Fig As can be seen from Fig 6, the connection between cement and other inputs such as Blast Furnace 47 The ANFIS modelwas wasalso alsoused usedtotoestablish establish thesurface relationship between therelationship The ANFIS the relationship between the inputs and the output Figure 6model shows the (3D) diagram of the The ANFIS model was also three-dimensional used to establish the relationship between the inputs and the output Figure shows the three-dimensional (3D) surface diagram of the output Figure shows three-dimensional surface diagram the relationship between different input parameters and the 28-day concrete compression The output Figure shows the the three-dimensional (3D)(3D) surface diagram of theofstrength relationship between different input parameters and the 28-day concrete compression strength The between different input parameters and the 28-day concrete compression strength relationships between some major selected ingredients the outputstrength of the ANFIS between different input parameters and theinput 28-day concreteand compression The The relationships between some major selected input ingredients and the output of the ANFIS relationships between some selected ingredients andoutput the output the ANFIS model are presented in some Figure major relationships between major selected inputinput ingredients and the of theofANFIS model are presented inFigure Figure7.7 model are presented in Nguyen, T., Dinh,7.K / Journal of Science and Technology in Civil Engineering model are presented inT.Figure Concrete Strength, MPa Concrete Strength, MPa 40 50 50 30 40 40 20 30 30 50 40 30 20 10 20 20 400 10 Bla 10 300 10 400 st F 400 urn Bla400 st F 200 300 Bla Balce st F astSFla 300urna300 ce S 100 200 urn ugrn, k la 200 ace acg/m 200 100 Sla e Sl g, kg100 /m 3100 100 g, k ag, g/m k3g/ 1000 m 400 500 600 60 60 50 60 50 50 50 40 40 40 40 30 30 20 200 20 600200 600500 600 500 400 500 200 400300 400 /m 300200 t, kg t, kg/m 0200100 Cermen300 n 200 e rm e g/m 100 ent, k C nt, kg/m 300 70 70 60 70 Concrete Strength, MPa Concrete Strength, MPa 60 60 50 60 Concrete Strength, MPa MPa Concrete Strength, 70 Concrete Strength, MPa Concrete Strength, MPa 60 30 30 20 200 20 150 200 100150 Fly 150 Ash Fl 150 yA , kg 100 s Fly Ash , Cerm Cerme 100 50 Fly/m h, k 100 g/m 50 As kg/ h, kg m /m (a) BFS and CEM vs F28vs F28 BFS and CEM (a)(a) BFS andCEM CEM vs (a) (a) BFS and vsF28 F28 BFS and CEM vs F28 70 40 20 20 250 250 60 60 40 40 20 20 250 200 250 200 200 500 600 600500 400 500400 Wa W 150 150 300 200 ate 400300 ter, 5003 W r, k 150 200 300200 atkeg/ g 400 /m150 r,W g/m 100 100 100 200100 kmga/ t, kgg/m ent, k en300 /m m rm 100 100 r tm e e er, k C rment, C 200 kg/ Ce m 100 100 g/m ent, k Cerm 70 60 60 50 50 40 40 30 30 20 40 20 40 600 Sup Su erp (c) WTR and CEM vs F28 45 40 35 30 40 50 45 40 35 30 40 10 800 70 70 60 60 50 50 40 40 30 3020 40 20 Sup30 30e40 rp 30 500 600 500 600 20 last 20 400 500 400 i20 ci30 300 400300 zer 10 sticpeerr, 10 3 500 , k / 20 ize plkag/ 200 300200 400 g/m r, k stim g10 m 100 0200 /m 100 g/mcize3 t,gk/mgrm ent, k enk300 m 010 100 r e e r, k Crment, C 200 g/m 100 Ce g/m ent, k Cerm 600 600 50 50 55 30 Sup30 Sup erp erp 20 last 20 last iciz iciz er, 10 er, kg/ kg/ m m e Cerm (d) SPP and CEM vs F28 Concrete Strength, MPa Concrete Strength, MPa Concrete Strength, MPa 50 600 600 (d)and SPPCEM and CEM vs F28 (d) SPP SPP and CEM vsF28 F28 (d) vs (d) SPP and CEM vs F28 60 55 Cerm p la 600 erpla sStiuciz (c) WTR and CEM vs F28 (c) and vs (c)WTR WTR andCEM CEM vs F28 F28 (c) WTR and CEM vs F28 60 600 Concrete Strength, MPa Concrete Strength, MPa 40 80 Concrete Strength, MPa 60 Concrete Strength, MPa Concrete Strength, MPa Concrete Strength, MPa 60 500 (b) FLA and CEM vs F28 (b)FLA FLA and CEM (b) CEM F28vs F28 (b) FLA andand CEM vsvs F28 (b) FLA and CEM vs F28 80 80 Concrete Strength, MPa Concrete Strength, MPa Concrete Strength, MPa 80 400 600 500 5003400 500 200 300 50 400 400 100 t, kg/m 300 200men300 /m 50 0200100 r g e k C t, n 200 e rm 100 100 g/me /m ent, k C nt, kg 300 45 40 35 45 40 35 30 1000 30 1000 1200 1200 1200 Fi800 800 Fin ne 1100 eA Ag 1100 gre gg 1000 600 reg 1000 g 600 ate, ate, 900 900 900 kg/ , kg/m , kg/m g/m g/m kg/ m 3400 800 400 800 gate, kAggregate gate, k Aggregate 800 re re m g g g g e A Coarse e A Coarse Coars Coars 1000 900 1100 1000 1200 1100 (e) SPP and COA vs F28 (f) FIA and COA vs F28 (e) and SPPCOA and COA (e) SPP vs F28vs F28 FIACOA and vs COA (f) FIA(f)and F28vs F28 Figure Surface diagram for the relationship between different inputs and output Figure Surface diagram the relationship between different and output Figure Surface diagram for thefor relationship between different inputsinputs and output Asbecan be seen from Figure the andinputs other inputs such As can seen from Figure 6,Water the 6, connection cementcement and other such Slag (Fig 6(a)), Fly Ash (Fig 6(b)), (Fig.connection 6(c)),between and between Superplasticizer (Fig 6(d)) to the 28as Furnace Slag Slag (Figure 6a), almost Fly (Figure 6b),theWater (Figure 6c), and as Blast Furnace (Figure 6a), Ash Fly Ash (Figure 6b), Water (Figure 6c), and dayBlast concrete compression strength was linear However, strong non-linear relationship Superplasticizer (Figure 6d) to the 28-day concrete compression strength was almost linear Superplasticizer (Figure 6d) to the 28-day concrete compression strength was almost linear was found between the Coarse Aggregate and other inputs to the output, as presented in Figs.6(e) However, the strong non-linear relationship found between Aggregate andin the However, the strong non-linear relationship was found between the Coarse Aggregate and and 6(f) This non-linear relationship was alsowas observed clearly in the the Coarse two-dimensional plot other inputs to thetooutput, as presented in Figure 6e and6e6f.and This relationship other inputs the output, as presented in Figure 6f.non-linear This non-linear relationship following section was also clearly in theintwo-dimensional plot inplot the in following section was observed also observed clearly the two-dimensional the following section 60 55 55 55 55 50 50 50 MPa 60 MPa 60 MPa MPa 48 60 50 Superplasticizer(Figure (Figure6d) 6d)totothe the28-day 28-dayconcrete concretecompression compressionstrength strengthwas wasalmost almostlinear linear Superplasticizer However,the thestrong strongnon-linear non-linearrelationship relationshipwas wasfound foundbetween betweenthe theCoarse CoarseAggregate Aggregateand and However, other otherinputs inputstotothe theoutput, output,asaspresented presentedininFigure Figure6e6eand and6f.6f.This Thisnon-linear non-linearrelationship relationship was clearly in the two-dimensional plot in the following section wasalso alsoobserved observed clearly in the two-dimensional plot in the following section Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering 55 55 55 55 Concrete Strength, MPa Concrete Strength, MPa 60 60 Concrete Strength, MPa Concrete Strength, MPa 60 60 50 50 50 50 45 45 45 45 40 40 40 40 35 35 35 35 30 30 30 30 25 25 100100 150150 200200 250250 300300 350350 400400 450450 500500 550550 25 25 120120 140140 160160 180180 200200 220220 240240 260260 3 Cerment, kg/m Cerment, kg/m Water, kg/m Water, kg/m (a)F28 F28 vs CEM (a) CEM (a) F28vsvs CEM F28vs vs WTR (b) F28 (b)(b) F28 vsWTR WTR 48 48 46 46 45 45 Concrete Strength, MPa Concrete Strength, MPa Concrete Strength, MPa Concrete Strength, MPa 46 46 44 44 44 44 43 43 42 42 42 42 40 40 41 41 38 38 40 40 36 36 800800 850850 900900 950950 1000 1000 1050 1050 3 Coarse Aggregate, kg/m Coarse Aggregate, kg/m (c) vs vs COA (c)F28 F28 vsCOA COA (c) F28 1100 1100 1150 1150 39 39 550550 600600 650650 700700 750750 800800 850 850 900 900 950 950 1000 1000 3 Fine Aggregate, kg/m Fine Aggregate, kg/m (d) F28 vs vsvs FIA (d) F28 FIA (d) F28 FIA Figure Two-dimensional plot forthe therelationship relationship between different inputs andinputs output Figure7.7.Two-dimensional Two-dimensional plot for the relationship between different inputsand andoutput output Figure plot for between different Withinthe thecontext contextofofthis thisstudy, study,data datafrom fromthe thetwo-dimensional two-dimensionalplot plotininFigure Figure7a 7a Within Within thethe context of this compressive study, data fromstrength the two-dimensional plot in Fig 7(a)along indicated thataathe indicated that theconcrete concrete compressive strength 28days days increased along with riseinin indicated that atat28 increased with rise concrete compressive strength at 28 days increased along with a rise in the amount of cement in the theamount amountofofcement cementininthe themixture mixture.The Thereversed reversedtrend trendwas wasfound foundtrue truefor forthe theamount amountofof the mixture The reversed trend was found true for the amount of water in the concrete mixture, as shown water theconcrete concretemixture, mixture,asasshown shownininFigure Figure7b 7b.With Withrespect respecttotothe theamount amountofofcoarse coarse water ininthe in Fig 7(b) With respect to the amount of coarse and fine aggregate, the 28-day compressive strength and fineconcrete aggregate, the28-day 28-day compressive strength the concrete specimens decreased and aggregate, the compressive strength ofofthe concrete specimens decreased offine the specimens decreased when the amount of coarse and fine aggregate increased, as when the amount of coarse and fine aggregate increased, as presented in Figure 7c and 7d when the amount of coarse and fine aggregate increased, as presented in Figure 7c and presented in Figs 7(c) and 7(d) The 28-day concrete compressive strength was reached the maximum 7d 3 The 28-day concrete compressive strengthwas was reached the670 maximum when the concrete The 28-day concrete compressive reached maximum when the concrete mixture contained strength approximately 830 kg/m the and kg/m forwhen coarsethe andconcrete fine 3 3 mixture contained approximately830 830kg/m kg/m and and670 670kg/m kg/m for forcoarse coarseand andfine fineaggregate, aggregate, aggregate, respectively mixture contained approximately respectively respectively 4.2 Number of input analysis 4.2.Number Numberofofinput inputanalysis analysis 4.2 The number of input analysis was also evaluated in this study using the ANFIS model To that, a number basic ANFIS0 modelanalysis was constructed using four mandatory concrete input ingredients, namely (i) To The number input analysis wasalso also evaluated this studyusing using theANFIS ANFIS model To The ofofinput was evaluated ininthis study the model Cement (CEM), (ii), Water (WTR), (iii) Coarse Aggregate (COA), and (iv) Fine Aggregate (FIA) In that,a abasic basicANFIS0 ANFIS0model modelwas wasconstructed constructedusing usingfour fourmandatory mandatoryconcrete concreteinput input dodothat, order to conduct the sensitivity analysis on the number of inputs, different models were developed by ingredients,namely namely(i)(i)Cement Cement(CEM), (CEM),(ii), (ii),Water Water(WTR), (WTR),(iii) (iii)Coarse CoarseAggregate Aggregate(COA), (COA), ingredients, and (iv) Fine Aggregate (FIA) In order to conduct the sensitivity analysis on the number 49 and (iv) Fine Aggregate (FIA) In order to conduct the sensitivity analysis on the number inputs,different differentmodels modelswere weredeveloped developedby byadding addingthe theinput inputparameter parameterinto intothe thebasic basic ofofinputs, model.AAvariable variableofofBSF BSFwas wasadded addedinto intothe theANFIS0 ANFIS0totocreate createan anANFIS1 ANFIS1model model model Similarly,ananANFIS2 ANFIS2model modelwas wascreated createdby byadding addingFLA FLAtotothe theANFIS1 ANFIS1model, model,and andaa Similarly, Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering adding the input parameter into the basic model A variable of BSF was added into the ANFIS0 to create an ANFIS1 model Similarly, an ANFIS2 model was created by adding FLA to the ANFIS1 ANFIS3 CEM, WTR, COA, FIA, BFS, ANFIS3 CEM, BFS,FLA, FLA, model, and a parameter SPP was added to theWTR, ANFIS2COA, model FIA, to construct an ANFIS3 model It is SPP worth noting that the new results variable was added sensitivity to the ANFIS analysis model without considering the order of The ofSPP Theperformance performance results ofthe the sensitivity analysisforforthe thenumber numberofofinput input the parameters Detailed of these models are listed in Table parameters are listed in Table The analysis was started at the ANFIS0 model with four parameters are listed in Table The analysis was started at the ANFIS0 model with four inputs The lastlast analysis performed thethe ANFIS3 Table was ANFIS models forfor sensitivity analysis ofmodel the inputwith numbers inputs The analysis was performed for ANFIS3 model withthe theentire entireseven seveninput input variables The output of these models was the compressive strength of concrete at 28 days variables The output of these models was the compressive strength of concrete at 28 days Model calculated for the data test set was parameter The RMSE indication used totoevaluate The RMSE indication calculated for the data test set Input was used evaluatethe theperformance performance of of each model The final value of RMSE was evaluated without considering the ANFIS0 CEM, WTR, COA, FIA each model The final value of RMSE was evaluated without considering thereducing reducing ANFIS1 CEM, WTR, COA, FIA, BFS rate rate ANFIS2 CEM, WTR, COA, FIA, BFS, FLA Table 6 Performance results forfor sensitivity analysis number ofofinputs Table Performance results sensitivity analysis ofthethe number inputs ANFIS3 CEM, WTR, COA,of FIA, BFS, FLA, SPP Model RMSE forfor testing Model RMSE testing Number Numberofofinputs inputs Table Performance results for sensitivity analysis of the number of inputs ANFIS0 10.01 44 ANFIS0 10.01 Model ANFIS1 RMSE for testing 8.28 ANFIS1 ANFIS0 ANFIS2 ANFIS2 ANFIS1 of inputs 5Number 8.28 10.01 7.74 7.74 8.28 ANFIS2 ANFIS3 ANFIS3 ANFIS3 66 7.74 7.73 7.73 7.73 77 80 80 80 70 70 70 70 60 60 60 60 50 50 40 40 30 30 20 20 10 10 0 Concrete strength, MPa Concrete strength, MPa Concrete strength, MPa 80 Concrete strength, MPa AsAs presented in in Table 6, 6, thethe RMSE value decreased with ananincrease the number presented Table RMSE value increaseinin number The performance results of the sensitivity analysis fordecreased the numberwith of input parameters arethe listed of of input parameters in the model That means, the prediction accuracy of the ANFIS model input parameters in the That prediction ANFIS in Table The analysis wasmodel started at the means, ANFIS0 the model with four accuracy inputs Theof lastthe analysis wasmodel increased along with the rise in the number of input parameters In other words, the increased along the rise inwith the the number input parameters Inoutput otherofwords, thegreater greater performed for thewith ANFIS3 model entire of seven input variables The these models thethe number of of inputs is,is,thethe more ofofthe ANFIS model would ToTo have was the compressive strength of concrete at 28 days The indication calculated for data number inputs moreaccuracy accuracy theRMSE ANFIS model wouldbe be.the havea a test set wason used toperformance evaluate the performance of each model The final value of RMSE was evaluated visualization thethe ofof thethe model inin analyzing thethe number ofofinputs, the visualization on performance model analyzing number inputs, theresults results without considering the reducing rate from thethe data testtest setset of of two selected ANFIS models were presented from data two selected ANFIS models were presentedininFigure Figure8.8 50 50 40 40 30 30 20 20 10 10 Test Test DataData ANFIS Output ANFIS Output 10 10 20 20 30 30 40 40 50 50 60 60 70 70 Sample number Sample number 0 TestTest DataData ANFIS Output ANFIS Output 10 10 20 20 30 30 40 40 50 50 60 60 70 70 Sample number Sample number (a) ANFIS0 (a)(a) ANFIS0 ANFIS0 (b)(b)ANFIS2 ANFIS2 (b) ANFIS2 Performance two ANFIS models for testfor set Figure 8.Figure Performance ofof two ANFIS models Figure Performance of two ANFIS models fortest testsetset 5 Conclusion Conclusion 50 paper,thethe28-day 28-dayconcrete concretecompression compressionstrength strengthwas waspredicted predictedfrom fromthe thefresh fresh In In thisthis paper, properties concrete with ANFIS model Various model configurationswith withdifferent different properties of of concrete with thethe ANFIS model Various model configurations Nguyen, T T., Dinh, K / Journal of Science and Technology in Civil Engineering As presented in Table 6, the RMSE value decreased with an increase in the number of input parameters in the model That means, the prediction accuracy of the ANFIS model increased along with the rise in the number of input parameters In other words, the greater the number of inputs is, the more accuracy of the ANFIS model would be To have a visualization on the performance of the model in analyzing the number of inputs, the results from the data test set of two selected ANFIS models were presented in Fig to control sequence Conclusions In this paper, the 28-day concrete compression strength was predicted from the fresh properties of concrete with the ANFIS model Various model configurations with different features such as type of input and output membership function, number of input membership functions and epochs, type of optimal methods were thoroughly examined In addition, different ANFIS models with varying number of input parameters were evaluated to study the effects of the number of input parameters The ANFIS model performed well with the RMSE values of 5.97 MPa and 7.73 MPa for the training set and test set, respectively Among the popular input membership functions, the application of the ‘gaussmf’ function in the ANFIS model produced the best prediction of the 28-day concrete compression strength Furthermore, the ANFIS model can be used as an effective tool for analyzing the relationship between one or more inputs to the output via the two-dimensional plots and the surface diagrams Finally, based on the results from the sensitivity input analysis, it was concluded that the prediction accuracy of the ANFIS model was proportional to the increase in the number of input parameters References [1] Wight, J K., MacGregor, J G (2012) Reinforced concrete: mechanics and design 6th edition, Pearson Education, Inc., Upper 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