Machine Learning Techniques for Evaluating Concrete Strength with Waste Marble Powder

The purpose of the research is to predict the compressive and flexural strengths of the concrete mix by using waste marble powder as a partial replacement of cement and sand, based on the experimental data that was acquired from the laboratory tests. In order to accomplish the goal, the models of Support vector machines, Support vector machines with bagging and Stochastic, Linear regression, and Gaussian processes were applied to the experimental data for predicting the compressive and flexural strength of concrete. The effectiveness of models was also evaluated by using statistical criteria. Therefore, it can be inferred that the gaussian process and support vector machine methods can be used to predict the respective outputs, i.e., flexural and compressive strength. The Gaussian process and Support vector machines Stochastic predicts better outcomes for flexural and compressive strength because it has a higher coefficient of correlation (0.8235 and 0.9462), lower mean absolute and root mean squared error values as (2.2808 and 1.8104) and (2.8527 and 2.3430), respectively. Results suggest that all applied techniques are reliable for predicting the compressive and flexural strength of concrete and are able to reduce the experimental work time. In comparison to input factors for this data set, the number of curing days followed by the CA, C, FA, w, and MP is essential in predicting the flexural and compressive strength of a concrete mix for this data set.


Introduction
The emission of CO 2 is a major environmental concern. It is important to take specific steps in order to minimize the amount of CO 2 emissions into the environment. India ranks third in the world in terms of CO 2 emissions. Concrete is a major contributor to increased CO 2 levels in the atmosphere. Concrete consists of three major ingredients such as cement, which contributes to the improvement of concrete's strength; aggregates, which provides the bulkiness to the concrete; and water, which reacts with cement, which leads to the hydration process and provides strength to concrete. Except for cement, all of the other components are readily available across the world. The only method to produce cement is to manufacture it. CO 2 is released during cement production, which pollutes the environment. Over-exploitation of materials is on the rise as a result of their widespread use.
an input parameter to aid in the prediction of the final result. The linear and non-linear regression approaches are mostly used in traditional methods for anticipating outcomes. However, in recent years, AI approaches such as ANN, LR, GMDH, RF, SVM and RT have been used to estimate the mechanical characteristics of concrete [39,40]. The majority of the study is focused on predicting the mechanical characteristics of concrete mixes. Several regressions, NNT, and ANFIS models are constructed by Sobhani [32] using concrete components as input parameters in the estimation of the hardened property of concrete. The outcome demonstrates that the NNT and ANFIs algorithms are more accurate compared to proposed standard regression algorithms for predicting the 28-day compressive strength. Madandoust [41] used GMDH, NNT, and ANFIs modelling for predicting the CS of concrete using cementitious materials. A genetic algorithm was used in the study to build the GMDH kind of neural network. In order to forecast output strength, parameters such as length to diameter ratio, core diameter, and so on were used as input. The study was directed by Ayat [42] to evaluate the affectability of the constructed model to some basic factors influencing concrete compressive strength. It was discovered that the suggested ANNs model's performance was outstanding with a highly effective tool for the simulation of the compressive strength with LF. Deepa [43] estimates the CS of concrete utilizing classification methods such as M5P Tree models, Multilayer Perceptron's, and Linear Regression. The results show that tree-based algorithms predict better results for concrete strength.
The purpose of this study was to determine whether or not machine learning could be used to make accurate predictions regarding the compressive and flexural strengths of concrete mixtures by adding waste marble powder in place of cement and sand together. To achieve the objective of the study, experimental data obtained by using waste marble powder as a partial replacement with cement and sand in the following proportions: 0-100, 25-75, 50-50, 75-25, and 100-0, respectively, was analyzed with soft computing techniques such as Support Vector Machines (SVM), Gaussian Processes (GP), and Linear Regressions (LR). The findings were than compared by using statistical parameters such as Coefficient of correlation (CC), Mean absolute error (MAE), Root mean square error (RMSE), relative absolute error (RAE), and Root relative squared error (RRSE). Further to identify the most relevant parameters (C, FA, CA, w, MP, and CD) in terms of predicting the compressive and flexural strength of concrete mixes and to ascertain the best modelling technique for predicting the compressive and flexural strength of concrete, sensitivity analysis has been carried out.

Support Vector Machine (SVM)
SVM, is a complex machine learning algorithm which is used by researchers to solve challenging engineering problems such as categorization, forecasting, and regression analysis. It is a part of artificial intelligence [44,45]. The SVM analysis approach includes training and testing sub-sets coupled with input and output. The optimal margin classifier is one of two methods used in SVM analysis to separate the linear classifier. Another alternative is to use the kernel function technique. The fixed mapping technique is used after mapping the input data with n-dimensional characteristics. There has been no change in the actual input space when the kernel mapping is applied to actual observations during a high-dimensional feature [45].

Bagging
Bagging is used to improve poor learning machine predictions [46]. Bagging factor determines how much of the original database will be recombined [47]. Each model uses bootstrap resampled observed data. Bagging algorithms have three steps: Bootstrapping uses replacements to create a new training set. Distributed voting is used to associate classifier results. This approach improves generalisation and classification variance. To use this method, the basic classifier must be imbalanced; otherwise, no classification will arise. The K-Nearest Neighbor classifier is stable, while the MLPC is not [48]. In this study, bagging is applied to check the reliability of the SVM model for predicting the strength property of concrete.

Stochastic
Stochastic meta-assembly improved the traditional techniques-based model. It is used to solve nonlinear engineering problems. In some studies, stochastic methods improve random forest models [31]. The designing process is filled with uncertainties, such as natural randomness of physical quantities, Model assumptions due to shortcomings in the computer model compared to real structural data, and statistical assumptions during the identification of a quantity due to a lack of data [49]. A stochastic process consists of arbitrary variables whose values are determined by Q's state vector. Indexing the gathering uses another set Z.

Gaussian Processes (GPs)
During the preceding years, a substantial amount of work has been carried out in subject of machine learning. GP is a machine learning method for analyzing the models' using kernels which provides a hands-on approach to learning about kernel [50]. It is a set of random variables with a mutual normal distribution for each discrete variable. The two fundamental functions used in the GP l(a) are the mean function m(a) and the kernel function n(a, a ). It states that: l(a) = GP(m(a), n(a,a )), The GP's primary goal is to find, how the input variables can be used to accomplish the objective. For every objective value, such as y, there is an arbitrary regression function l(a) and independent Gaussian noise ( determines how much of the original database will be recombined [47]. Each model uses bootstrap resampled observed data. Bagging algorithms have three steps: Bootstrapping uses replacements to create a new training set. Distributed voting is used to associate classifier results. This approach improves generalisation and classification variance. To use this method, the basic classifier must be imbalanced; otherwise, no classification will arise. The K-Nearest Neighbor classifier is stable, while the MLPC is not [48]. In this study, bagging is applied to check the reliability of the SVM model for predicting the strength property of concrete.

Stochastic
Stochastic meta-assembly improved the traditional techniques-based model. It is used to solve nonlinear engineering problems. In some studies, stochastic methods improve random forest models [31]. The designing process is filled with uncertainties, such as natural randomness of physical quantities, Model assumptions due to shortcomings in the computer model compared to real structural data, and statistical assumptions during the identification of a quantity due to a lack of data [49]. A stochastic process consists of arbitrary variables whose values are determined by Q's state vector. Indexing the gathering uses another set Z.

Gaussian Processes (GPs)
During the preceding years, a substantial amount of work has been carried out in subject of machine learning. GP is a machine learning method for analyzing the models' using kernels which provides a hands-on approach to learning about kernel [50]. It is a set of random variables with a mutual normal distribution for each discrete variable. The two fundamental functions used in the GP l(a) are the mean function m(a) and the kernel function n(a, a′). It states that: l(a) = GP(m(a), n(a,a′)), The GP's primary goal is to find, how the input variables can be used to accomplish the objective. For every objective value, such as y, there is an arbitrary regression function l(a) and independent Gaussian noise (ϧ), i.e., y = l(a) + ϧ Gaussian noise with a mean of zero and variance of (σn) 2 , i.e., ϧ~L(0, σn 2 ). Then Equation (1) The identity matrix is represented by I.

Linear Regression (LR)
Linear regression is a regression analysis model that employs linear equations to represent the relationship of the two or more dependent and independent variables [32]. The primary goal of a linear regression model is to identify the linear line that best predicts the relationship of the dependent and independent variables. It is only conceivable if the total of the squares of the vertical lines is less than the specified line. Linear regression models are made up of dependent and independent variables, such as d and z from the given dataset. To discover the optimum numerical forecast, it forms a simple mathematical equation. It also aids in determining the correlation coefficient capable of describing the variances in the dataset. The closer the value is to one, the more dependable the data. [43].

Bagging
Bagging is used to improve poor learning machine predictions [46]. Bagging factor determines how much of the original database will be recombined [47]. Each model uses bootstrap resampled observed data. Bagging algorithms have three steps: Bootstrapping uses replacements to create a new training set. Distributed voting is used to associate classifier results. This approach improves generalisation and classification variance. To use this method, the basic classifier must be imbalanced; otherwise, no classification will arise. The K-Nearest Neighbor classifier is stable, while the MLPC is not [48]. In this study, bagging is applied to check the reliability of the SVM model for predicting the strength property of concrete.

Stochastic
Stochastic meta-assembly improved the traditional techniques-based model. It is used to solve nonlinear engineering problems. In some studies, stochastic methods improve random forest models [31]. The designing process is filled with uncertainties, such as natural randomness of physical quantities, Model assumptions due to shortcomings in the computer model compared to real structural data, and statistical assumptions during the identification of a quantity due to a lack of data [49]. A stochastic process consists of arbitrary variables whose values are determined by Q's state vector. Indexing the gathering uses another set Z.

Gaussian Processes (GPs)
During the preceding years, a substantial amount of work has been carried out in subject of machine learning. GP is a machine learning method for analyzing the models' using kernels which provides a hands-on approach to learning about kernel [50]. It is a set of random variables with a mutual normal distribution for each discrete variable. The two fundamental functions used in the GP l(a) are the mean function m(a) and the kernel function n(a, a′). It states that: l(a) = GP(m(a), n(a,a′)), The GP's primary goal is to find, how the input variables can be used to accomplish the objective. For every objective value, such as y, there is an arbitrary regression function l(a) and independent Gaussian noise (ϧ), i.e., y = l(a) + ϧ Gaussian noise with a mean of zero and variance of (σn) 2 , i.e., ϧ~L(0, σn 2 ). Then Equation (1) The identity matrix is represented by I.

Linear Regression (LR)
Linear regression is a regression analysis model that employs linear equations to represent the relationship of the two or more dependent and independent variables [32]. The primary goal of a linear regression model is to identify the linear line that best predicts the relationship of the dependent and independent variables. It is only conceivable if the total of the squares of the vertical lines is less than the specified line. Linear regression models are made up of dependent and independent variables, such as d and z from the given dataset. To discover the optimum numerical forecast, it forms a simple mathematical equation. It also aids in determining the correlation coefficient capable of describing the variances in the dataset. The closer the value is to one, the more dependable the data. [43].
(2) Gaussian noise with a mean of zero and variance of (σ n ) 2 , i.e.,

Bagging
Bagging is used to improve poor learning machine predictions [46]. Bag determines how much of the original database will be recombined [47]. Each bootstrap resampled observed data. Bagging algorithms have three steps: Bo uses replacements to create a new training set. Distributed voting is used to ass sifier results. This approach improves generalisation and classification varia this method, the basic classifier must be imbalanced; otherwise, no classificatio The K-Nearest Neighbor classifier is stable, while the MLPC is not [48]. In this ging is applied to check the reliability of the SVM model for predicting the stre erty of concrete.

Stochastic
Stochastic meta-assembly improved the traditional techniques-based m used to solve nonlinear engineering problems. In some studies, stochastic m prove random forest models [31]. The designing process is filled with uncerta as natural randomness of physical quantities, Model assumptions due to shor the computer model compared to real structural data, and statistical assumpt the identification of a quantity due to a lack of data [49]. A stochastic process arbitrary variables whose values are determined by Q's state vector. Indexing ing uses another set Z.

Gaussian Processes (GPs)
During the preceding years, a substantial amount of work has been ca subject of machine learning. GP is a machine learning method for analyzing using kernels which provides a hands-on approach to learning about kernel [5 of random variables with a mutual normal distribution for each discrete variab fundamental functions used in the GP l(a) are the mean function m(a) and the k tion n(a, a′). It states that: l(a) = GP(m(a), n(a,a′)), The GP's primary goal is to find, how the input variables can be used to the objective. For every objective value, such as y, there is an arbitrary regressi l(a) and independent Gaussian noise (ϧ), i.e., y = l(a) + ϧ Gaussian noise with a mean of zero and variance of (σn) 2 , i.e., ϧ~L(0, Equation (1)  The identity matrix is represented by I.

Linear Regression (LR)
Linear regression is a regression analysis model that employs linear equat resent the relationship of the two or more dependent and independent variabl primary goal of a linear regression model is to identify the linear line that b the relationship of the dependent and independent variables. It is only concei total of the squares of the vertical lines is less than the specified line. Linear models are made up of dependent and independent variables, such as d and given dataset. To discover the optimum numerical forecast, it forms a simple cal equation. It also aids in determining the correlation coefficient capable of the variances in the dataset. The closer the value is to one, the more dependab [43].

Linear Regression (LR)
Linear regression is a regression analysis model that employs linear equations to represent the relationship of the two or more dependent and independent variables [32]. The primary goal of a linear regression model is to identify the linear line that best predicts the relationship of the dependent and independent variables. It is only conceivable if the total of the squares of the vertical lines is less than the specified line. Linear regression models are made up of dependent and independent variables, such as d and z from the given dataset. To discover the optimum numerical forecast, it forms a simple mathematical equation. It also aids in determining the correlation coefficient capable of describing the variances in the dataset. The closer the value is to one, the more dependable the data. [43]. d = c 0 + c 1 z 1 + c 2 z 2 + C 3 z 3 + C 4 z 4 + C 5 z 5 + C 6 z 6 + . . .
Objective of the Study A detailed review of the literature revealed that no study had employed these modelling techniques to predict the compressive and flexural strength of concrete mix. Considering their application in construction material, an attempt was made to evaluate their potential in predicting the compressive and flexural strength of concrete mixtures by adding waste marble powder in place of cement and sand together using laboratory data.

Methodology
The following methods must be followed in order to achieve the study's purpose of estimating concrete compressive and flexural strength.

1.
Experimental data on the compressive and flexural strength.

Collection of Data
For the prediction of the compressive and flexural strength, sufficient data was necessary, which was supplied by performing experimental research using waste marble powder in various proportion as a partial replacement of cement and sand.

Experimental Investigation
Concrete with complicated structures is comprised of multiple complex materials, making them difficult to comprehend, e.g., the problem of matrix/aggregate interactions, the region between the aggregate and the matrix, the size of aggregates, etc. The size and quantity of particles, for instance, have been found to affect the fracture energy and fracture toughness of concrete. The matrix can be composed of several materials in variable amounts, which can alter their qualities, such as the w/C and C/S, among others. The same holds true for aggregate, which may be composed of pebbles, with smooth, rounded surfaces, or crushed rock with irregular shapes, varying chemical and mineralogical compositions, and extremely rough surfaces. The aggregates appearance and texture have a big effect on how well they fit together with mortar. Further, due to the large specific surface area of the marble powder (MP), which is obtained from the processing of marble waste sludge, it has the potential to be utilized as a filler in concrete. The following materials and testing methods were used on 189 cubes and 188 beam specimens with dimensions of 150 × 150 × 150 mm and 700 × 150 × 150 mm, respectively.

Aggregate
Coarse aggregate with nominal sizes of 10 and 20 mm was used in the concrete mix. The aggregate's particle size distribution was graded [51]. According to ASTM C-128 and ASTM C-127 [52,53], specific gravity, crushing, and impact were found to be 2.61%, 23.67%, and 6.74%, respectively. Table 1 shows the characteristics of fine and coarse aggregate.

Marble Powder
A nearby marble market supplied the WMP. The physical properties of WMP obtained for fineness, and Specific Gravity were 2.01% and 2.44 g/cm 3 .

Mix Design
Batches were created according to the prescribed quantities of cement, sand and marble powder, while other elements such as coarse aggregates, and water/cement ratio were utilized in the same amounts throughout. Different sets of specimens were made, each consisting of three cubes and three beams. A total of 189 cubes and 188 beams were created. The proportion of reference specimens, as well as mixes with 5, 10, 15, and 20% replacement, is listed in Table   Additionally, modified concrete was mixed in a mixer, and the necessary substitution for ordinary cement was carried out during the mixing process. The mixes were mixed to with MP, and (150 × 150 × 150) mm cubes and (150 × 150 × 700) mm beams were created. After that, samples were given a certain number of days in curing tanks to cure (CD). The CD that was chosen for this investigation ranged from 7 to 180 days. After curing, cube and beam samples were sun-dried and tested in the institute's lab using a standard compression and flexural testing machine. The CS and FS tests were carefully performed to determine the mix proportion from the collection of casted samples suitable to achieve approximately the same or better compressive and flexural strength for a selection of percentage substitutions [60,61].

Data Collection
The dataset is critical for predicting the outcome. The observations collected from laboratory study were divided into two sub-sets at random, with 70-30 ratio for the training and testing sub-sets, respectively.
In this paper, three techniques were used, namely LR, SVM, SVM Bagging and SVM Stochastic and GP, with input parameters such as C, FA, CA, w, MP, and CD, to achieve the desired outcome, with CS and FS as the output parameter, using Weka 3.9. Tables 3 and 4 lists the characteristics of the total, training, and testing datasets for CS and FS, respectively, and user defined parameters listed in Table 5. Each model's performance was evaluated using CC, MAE, RMSE, RAE, and RRSE. These variables were beneficial in finding the best model. A greater CC value and a lower error value suggest better results. A significant number of studies resulted in these user-defined ideal settings for diverse techniques. The best settings dictated the performance of each model. The optimal settings must be carefully determined because they will have an impact on the model's performance. As a result, the parameters in these examples were ideal for both training and testing datasets.

Evaluation Parameters
Evaluating parameters must be applied to the applicable algorithms in order to verify their performance. Coefficient of correlation (CC), Mean absolute error (MAE), Root mean square error (RMSE), relative absolute error (RAE), and Root relative squared error (RRSE) were utilized as evaluating parameters in this study.
Coefficient of correlation (CC): The coefficient of correlation (R) was utilised as the primary criterion to assess the effectiveness of the created models. The following equation was used to acquire the value of CC: Root mean square error (RMSE): Mean Squared Error is the most often used method for determining a model's success. It is the square root of Mean-Squared-Error with the same dimensions as the estimated values. The root mean square error (RMSE) is computed as follows: Mean absolute error (MAE): The mean absolute error is used to assess the accuracy of numerical estimation. The mean absolute error (MAE) is calculated as follows: Materials 2022, 15, 5811 9 of 22 Relative absolute error (RAE): The relative absolute error (RAE) is a metric used to assess the performance of a predictive model. It is calculated by using following equation: Root relative squared error (RRSE): It is defined as the square root of a predictive model's sum of squared errors normalized by the sum of squared errors of a simple model. To put it another way, it is the square root of the Relative Squared Error (RSE) and calculated by using formula: Coefficient of correlation (CC) values vary from −1 to +1; the greater the CC number, the better the anticipated outcomes. Lower the values better will be the outcomes, i.e., if computed error is low, it predicts better output results [62].

SVM Based Assessment
PUK base function is used in this model, along with certain user-defined parameters such as C and omega (O), and sigma (S) A large number of trials were conducted in order to arrive at the best result, which was the greatest CC value with the least errors. The dataset utilized in this study produced the best results with a c value of 1.5 and O = 4, S = 1. Table 6 lists the performance metrics of SVM for both the training and testing datasets. For the training and testing phases, the CC values were 0.9110 and 0.8153, the RMSE values were 2.2287 and 3.0367, the MAE values were 1.5123 and 2.3456, the RAE values were 33.28% and 67.87%, and the RRSE values were 41.79% and 74.13%, respectively. The agreement plot between actual and predicted flexural strength of concrete mix is shown in Figure 1. 1.    The radial basis function kernel (RBF kernel) is used in this model, along with certain user-defined parameters such as C and gamma (G). A large number of trials were conducted in order to arrive at the best result for compressive strength of concrete, which was the greatest CC value with the least errors. The dataset utilized in this study produced the best results with a c value of 5 and a Gvalue of 10. Table 7 lists the performance metrics of SVM for both the training and testing datasets. For the training and testing phases, the CC values were 0.9545 and 0.945, the RMSE values were 2.3289 and 2.2908, the MAE values were 1.2472 and 1.7305, the RAE values were 18.33% and 28.46%, and the RRSE values were 30.04% and 33.93%, respectively. The agreement plot between actual and predicted compressive strength of concrete mix is shown in Figure 2.  Tables 6 and 7 presents analytical performance measures for training and testing datasets to aid in the evaluation of proposed models for FS and CS of concrete, respectively. To achieve a precise performance, the CC should be close to one and the RMSE and MAE values should be close to zero. The SVM algorithm predicts compressive strength better than flexural strength with higher CC (0.9450) value.

GPs Based Assessment
Gaussian Processes are a type of regression that uses a PUK function and certain user-defined parameters such as L, omega (O) and sigma (S). Several experiments were conducted in order to arrive at the optimal value, which was the maximum CC value with the lowest errors. The dataset utilized in this investigation yielded the best results with L values of 0.01, O = 3 and S as 3.   Tables 6 and 7 show that when SVM, SVM-Bagging, and SVM-Stochastic were evaluated, SVM-Stochastic is more reliable for predicting compressive strength with highest CC value of 0.9462.

GPs Based Assessment
Gaussian Processes are a type of regression that uses a PUK function and certain userdefined parameters such as L, omega (O) and sigma (S). Several experiments were conducted in order to arrive at the optimal value, which was the maximum CC value with the lowest errors. The dataset utilized in this investigation yielded the best results with L values of 0.01, O = 3 and S as 3.    Figure 4 depicts the agreement plot between the actual and predicted compressive strength of concrete mix.

LR Based Assessment
LR based model predict the relationship between two variables or factors. The results of Table 6 show the linear regression model technique for flexural strength for both training and testing dataset Figure 5 is the graphical representation of actual versus predicted flexural strength with coefficient of correlation CC is 0.7802, RMSE is 2.7717, MAE is 2.3822, RAE is 68.93% and RRSE is 67.66%, for testing dataset as listed in Table 6. Equation

LR Based Assessment
LR based model predict the relationship between two variables or factors. The results of Table 6 show the linear regression model technique for flexural strength for both training and testing dataset Figure 5 is the graphical representation of actual versus predicted flexural strength with coefficient of correlation CC is 0.7802, RMSE is 2.7717, MAE is 2.3822, RAE is 68.93% and RRSE is 67.66%, for testing dataset as listed in Table 6. Equation (10) was developed by LR algorithm from Weka 3.9.5 for the prediction of flexural strength of concrete. FS = 0.0563 × curing days + 4.4332 (10) LR based model predict the relationship between two variables or factors. The results of Table 7 show the linear regression model technique for the compressive strength for both training and testing dataset. Figure 6 is the graphical representation of actual versus predicted compressive strength with coefficient of correlation CC is 0.8712, RMSE is 3.3921, MAE is 2.6909, RAE is 44.26% and RRSE is 50.24%, for testing dataset listed in Table 7. Equation (11) was developed by LR modelling through Weka 3.9.5 for the prediction of compressive strength for a given set of data. CS = −0.0164 * Marble Powder(kg/m 3 ) + 0.087 * Curing Days + 13.6919 (11) ing and testing dataset Figure 5 is the graphical representation of actual versus predicted flexural strength with coefficient of correlation CC is 0.7802, RMSE is 2.7717, MAE is 2.3822, RAE is 68.93% and RRSE is 67.66%, for testing dataset as listed in Table 6. Equation (10) was developed by LR algorithm from Weka 3.9.5 for the prediction of flexural strength of concrete.  Table 7 show the linear regression model technique for the compressive strength for both training and testing dataset. Figure 6 is the graphical representation of actual versus predicted compressive strength with coefficient of correlation CC is 0.8712, RMSE is 3.3921, MAE is 2.6909, RAE is 44.26% and RRSE is 50.24%, for testing dataset listed in Table 7. Equation (11) was developed by LR modelling through Weka 3.9.5 for the prediction of compressive strength for a given set of data.

Comparison
Various machine learning approaches were used in this research. When these models are compared, it appears that the GP model outperforms the others for both training and testing datasets for FS. Figure 7 represents the scatter plot for the observed and predicted FS values using SVM, GP, and LR. Table 6 indicate that the GP model has the greatest CC value for both training and testing datasets for FS, i.e., 0.9170 and 0.8235, respectively, as well as the lowest error values, i.e., MAE (2.2808) and RAE (66%), for the testing dataset. It can be seen from Figure 8 that the error band width is lesser in GP based model as compared to other applied models for the prediction of FS of concrete mix [63].

Comparison
Various machine learning approaches were used in this research. When these models are compared, it appears that the GP model outperforms the others for both training and testing datasets for FS. Figure 7 represents the scatter plot for the observed and predicted FS values using SVM, GP, and LR. Table 6 indicate that the GP model has the greatest CC value for both training and testing datasets for FS, i.e., 0.9170 and 0.8235, respectively, as well as the lowest error values, i.e., MAE (2.2808) and RAE (66%), for the testing dataset. It can be seen from Figure 8 that the error band width is lesser in GP based model as compared to other applied models for the prediction of FS of concrete mix [63]. Figures 1, 3 Figure 9 represents the scatter plot for the observed and predicted compressive strength values using SVM, GP, and LR. Table 7 indicate that the SVM model has the greatest CC value for testing datasets for the compressive strength, i.e., 0.9450, as well as the lowest error values, i.e., MAE (1.7305), RMSE (2.2908), RAE (28.46%) and RRSE (33.93%) for the testing dataset. It can be seen from Figure 10 that the error band width is lesser in SVM based model as compared to other applied model for the prediction of CS of concrete mix. Figure 11 represents the scatter plot between no. of observation and ratio of actual and predicted strength. It shows that SVM-Schotastic based model is reliable for compressive strength prediction followed by SVM [64] as compared to GP model for flexural strength because the values are more scatter in the ratio of actual and predicted flexural strength.   Figure 9 represents the scatter plot for the observed and predicted compressive strength values using SVM, GP, and LR. Table 7 indicate that the SVM model has the greatest CC value for testing datasets for the compressive strength, i.e., 0.9450, as well as the lowest error values, i.e., MAE (1.7305), RMSE (2.2908), RAE (28.46%) and RRSE (33.93%) for the testing dataset. It can be seen from Figure 10 that the error band width is lesser in SVM based model as compared to other applied model for the prediction of CS of concrete mix. Figure 11 represents the scatter plot between no. of observation and ratio of actual and predicted strength. It shows that SVM-Schotastic based model is reliable for compressive strength prediction followed by SVM [64] as compared to GP model for flexural strength because the values are more scatter in the ratio of actual and predicted flexural strength.  Figure 9 represents the scatter plot for the observed and predicted compressive strength values using SVM, GP, and LR. Table 7 indicate that the SVM model has the greatest CC value for testing datasets for the compressive strength, i.e., 0.9450, as well as the lowest error values, i.e., MAE (1.7305), RMSE (2.2908), RAE (28.46%) and RRSE (33.93%) for the testing dataset. It can be seen from Figure 10 that the error band width is lesser in SVM based model as compared to other applied model for the prediction of CS of concrete mix. Figure 11 represents the scatter plot between no. of observation and ratio of actual and predicted strength. It shows that SVM-Schotastic based model is reliable for compressive strength prediction followed by SVM [64] as compared to GP model for flexural strength because the values are more scatter in the ratio of actual and predicted flexural strength.       In addition to the actual value, quartile values of 25%, 50%, and 75% were assessed for the evaluation of FS and CS of concrete containing marble powder, as shown in Table 8. The inter quartile range (IQR) of SVM-Schotastic and SVM Bagging is closer to the IQR of real data, as seen in Figures 12 and 13 for FS and CS, respectively. Materials 2022, 15, 5811 17 In addition to the actual value, quartile values of 25%, 50%, and 75% were asse for the evaluation of FS and CS of concrete containing marble powder, as shown in T 8. The inter quartile range (IQR) of SVM-Schotastic and SVM Bagging is closer to the of real data, as seen in Figures 12 and 13 for FS and CS, respectively.

Sensitivity Analysis
Using sensitivity analysis, the most significant factor among input factors for pre ing the CS and FS with WMP was determined. Since GP and SVM-Schotastic model formed the best among the other models for FS and CS for this dataset, sensitivity ana was carried out on it by changing the input combination and taking out one input pa eter at a time, as shown in Tables 9 and 10. Statistical assessment metrics such as CC, M and RMSE were used to assess each model's performance [72][73][74][75][76][77][78][79][80][81][82]. Tables 9 and 10, dem strates that the number of curing days followed by CA, C, w and MP is critical in pre ing the flexural and compressive strength of a concrete mix. Due to the pozzolanic tions, concrete recovers 60% of its strength after 7 days of curing and increases by after 28 days, resulting in a low CC value after removing the aforementioned characte [76][77][78][79]. The pozzolanic reaction is a slow process, and as the curing period lengthens amount of gel produced in the mix increases, resulting in greater strength [65]]. Hydr products form when water is added to cement mixes, filling gaps between aggregate ticles and increasing the density and strength of the concrete.

Sensitivity Analysis
Using sensitivity analysis, the most significant factor among input factors for predicting the CS and FS with WMP was determined. Since GP and SVM-Schotastic model performed the best among the other models for FS and CS for this dataset, sensitivity analysis was carried out on it by changing the input combination and taking out one input parameter at a time, as shown in Tables 9 and 10. Statistical assessment metrics such as CC, MAE, and RMSE were used to assess each model's performance [72][73][74][75][76][77][78][79][80][81][82]. Tables 9 and 10, demonstrates that the number of curing days followed by CA, C, w and MP is critical in predicting the flexural and compressive strength of a concrete mix. Due to the pozzolanic reactions, concrete recovers 60% of its strength after 7 days of curing and increases by 99% after 28 days, resulting in a low CC value after removing the aforementioned characteristic [76][77][78][79]. The pozzolanic reaction is a slow process, and as the curing period lengthens, the amount of gel produced in the mix increases, resulting in greater strength [65]. Hydration products form when water is added to cement mixes, filling gaps between aggregate particles and increasing the density and strength of the concrete.

Conclusions
This study compared the CS and FS using WMP by three machine learning techniques: SVM, LR, and GP based models. CC, MAE, RMSE, RAE, and RRSE were applied to evaluate the performance of these models. The following is a summary of the study's findings: The GP and SVM model's results were shown to be the best for predicting concrete flexural and compressive strength of concrete mix, respectively. For the testing dataset, GP predicts better outcomes followed by SVM with CC values of 0.8235 and 0.8153, lower MAE values of 2.2808 and 2.3456, and lower RMSE values of 2.8527 and 3.0367, respectively, for flexural strength of concrete. SVM-Schotastic predicts better results with CC values of 0.9462, lower MAE values of 1.8104 and lower RMSE values of 2.3430 for compressive strength of concrete. The scatter plot reveals that the GP and SVM-Schotastic has the smallest error band width and is a strong match for predicting flexural and compressive strength as output, respectively.
In comparison to input factors for this data set, the number of curing days followed by the CA, C, w and MP is essential in predicting the flexural and compressive strength of a concrete mix for this data set. These findings are restricted to a 0-20% cement sand substitute with marble powder. Additionally, CD is a more sensitive parameter, and some further investigation is warranted. In addition, Tables 9 and 10 demonstrate that CA, C, FA, MP and w have minimal effects on CC. This indicates that additional study is required to examine the input variables.