Assessing Waste Marble Powder Impact on Concrete Flexural Strength Using Gaussian Process, SVM, and ANFIS

Abstract

The study’s goal is to assess the flexural strength of concrete that includes waste marble powder using machine learning methods, i.e., ANFIS, Support vector machines, and Gaussian processes approaches. Flexural strength has also been studied by using the most reliable approach of sensitivity analysis in order to determine the influential independent variable to predict the dependent variable. The entire dataset consists of 202 observations, of which 120 were experimental and 82 were readings from previous research projects. The dataset was then arbitrarily split into two subsets, referred to as the training dataset and the testing dataset, each of which contained a weighted percentage of the total observations (70–30). Output was concrete mix flexural strength, whereas inputs comprised cement, fine and coarse aggregates, water, waste marble powder, and curing days. Using statistical criteria, an evaluation of the efficacy of the approaches was carried out. In comparison to other algorithms, the results demonstrate that the Gaussian process technique has a lower error bandwidth, which contributes to its superior performance. The Gaussian process is capable of producing more accurate predictions of the results of an experiment due to the fact that it has a higher coefficient of correlation (0.7476), a lower mean absolute error value (1.0884), and a smaller root mean square error value (1.5621). The number of curing days was identified as a significant predictor, in addition to a number of other factors, by sensitivity analysis.

1. Introduction

Cement, fine and coarse aggregates and water are the main ingredients of concrete. Every one of the components, with the exception of cement, is easily accessible in every region of the world. The only way to create cement is through the process of manufacturing it. The manufacture of cement results in the emission of carbon dioxide, which is harmful to the environment. Because of their extensive application, there is currently an increase in the overexploitation of several resources. As a result of industrialization and urbanization, concrete is used in a significant amount of construction projects, and the rising demand for the material will eventually lead to its depletion. If the waste material could meet the required criteria, then it could be used in the development of the infrastructure, which would make it economically viable [1,2]. The process of industrialization results in the production of a variety of hazardous wastes, the management of which can be accomplished by mixing these wastes into the fundamental components of concrete. There is a possibility that fly ash, silica fumes, and slag will raise the water demand of the concrete mix. This issue can be remedied by using a superplasticizer [3]. Waste marble powder (WMP) can be utilized in place of cement or fine aggregates as an alternative [4,5,6]. WMP is a potentially useful material that might be used to partially replace sand and cement. CaO, SiO₂, Al₂O₃, Fe₂O₃ are significant constituents, whereas MgO, SO₃, K₂O, and Na₂O are minor constituents. India produces the most marble waste throughout the mining process. The marble industry’s waste can harm the environment and the economy if not properly managed. The demand for marble on the market is driven in part by its widespread application in ornamental settings. The production of marble results in the generation of a number of different chemical forms that are considered to be hazardous waste. The disposal of waste is not an efficient use of resources, and it also raises concerns for the environment. When appropriately integrated, the use of waste from industrial processes has the potential to reduce the amount of cement that must be added to concrete [7]. Marble sludge can be recycled and utilized as one of the primary components of concrete mix, which can subsequently be used as a building material or in the construction of road pavements, amongst other potential applications [8]. Soliman [9] found that as marble powder (MP) replaces cement in the nominal mix, the concrete strength decreases. Both the effect of substituting MP for cement (C) and the findings show that the tensile strength of WMP starts to decrease as the amount of WMP increases [10]. By replacing 10% of the cement with marble dust, Dhoka [11] noticed a 25% improvement in 28-day tensile strength compared to the composite samples. Many researchers use waste MP as a replacement of cement by weight [12,13,14,15,16]. In the experiment that was carried out by Kelestemur [14], on a concrete mix that contained various amounts of glass fiber, it can be seen that by adding marble dust, it achieves the highest CS. Workability was not affected by the capillarity properties of self-compacting concrete caused by the addition of waste marble dust as a cement replacement, but tensile strength was reduced as a result [15]. Uysal and Yilmaz [17] investigated the usage of lime, basalt, and MP as Portland cement substitutes. In addition, the tensile strength after 28 days was improved when both gravel and sand were used as a substitute [18]. It was determined that the utilization of MP as a filler was satisfactory [19]. According to the findings of the study, replacing sand with 10% mineral powder delivers the highest possible CS while maintaining a level of workability that is comparable to that of cement. MP offers good cohesiveness to mortar because of its fineness. MP can also be used as a substitute for SCC [20]. After 28 days of curing, Demirel [21] found that the porosity of the matrix began to decrease as the quantity of small particles in the matrix increased after being replaced with WMP. However, the CS rating improved. The mechanical and physical qualities of the concrete are altered when WMP is used as a filler ingredient in the production of SCC [22].

Waste marble powder (WMP) can be utilized in place of cement or fine aggregates as an alternative [5,6]. Researchers are currently employing methods of soft computing in an effort to find solutions to the problems [23,24,25,26,27,28,29,30,31,32]. The amount of cement, aggregates, water, admixtures, and waste products that are included in the mix are the primary factors that define the strength of the concrete. These elements can be incorporated into the model as input variables to facilitate more accurate forecasting of the ultimate outcome. In classic methodologies, the approaches of linear and non-linear regression are utilized the majority of the time in order to anticipate results. However, in recent years, techniques from the field of AI such as artificial neural networks (ANN), linear regression, group method of data handling (GMDH), random forest, and random tree (RT) have been utilized to estimate the concrete mechanical characteristics [33,34,35,36,37,38]. The majority of the research effort is being put towards attempting to forecast the mechanical characteristics of various concrete mixes. In order to accurately estimate the strength of no-slump concrete, a number of regressions, neural networks (NNT), and adaptive neuro-fuzzy inference system (ANFIS) models have been created [25,32]. These models use components of concrete as input parameters. The findings indicate that the NNT and ANFIS models are superior to the proposed standard regression models in terms of accuracy when it comes to forecasting the 28-day CS for non-slumping concrete. In Madandoust’s [39] research, a neural network of the GMDH type was combined with ANFIS modelling to make a prediction about the strength of concrete made from cementitious components. During the course of the research, a genetic algorithm was utilized to construct a neural network of the GMDH variety. Input parameters consisted of things like ratios of length to diameter, core diameter, and other similar measurements in order to forecast the output strength. Ayat [40], in the year 2018, directed the study to analyses the affectability of the developed model to some basic factors influencing concrete CS. The goal of the investigation was to determine whether or not the constructed model is affected by these factors. It was found that the ANNs model that had been suggested was remarkable as a practical and very effective method for simulating the CS forecast of lime filler (LF) concrete. When it comes to forecasting the CS of concrete mixtures, tree-based models perform admirably.

In this paper, the effect of marble powder on flexural strength of concrete is demonstrated. Experimental investigations to study the effect of marble dust on flexural strength exploring possible reasons for the gain in strength have been conducted. Techniques from the field of soft computing have found widespread use in a variety of technical fields over the course of the past few decades. Fewer studies have been identified on the performance of soft computing techniques for predicting the FS of concrete mixtures that include waste MP. Some of the soft computing techniques that were utilized in this work are the Support Vector Machine (SVM), the Gaussian Process (GP), and the Adaptive Neuro-Fuzzy Inference System (ANFIS). The results were compared in order to identify the modelling strategy that proved to be the most reliable in predicting the FS of concrete mix includes waste marble powder. Additional sensitivity analysis was done to identify the most important input parameter.

2. Machine Learning Techniques

2.1. ANFIS

An artificial neural network that is built on the Takagi-Sugeno fuzzy inference system is called an adaptive neuro-fuzzy inference system (ANFIS). It wasn’t until the early 1990s that the methodology was created. It offers the chance to use the benefits of both types of systems under a single framework because it combines neural networks and fuzzy logic concepts. Its inference system is made up of a collection of fuzzy IF–THEN rules with the capacity to approximate nonlinear functions through learning. As a result, ANFIS is regarded as a universal estimator. The best parameters acquired by genetic algorithm may be used to employ the ANFIS in a more efficient and optimal manner. Figure 1 presents the ANFIS architecture [41]. There are five layers in the ANFIS model. Each layer has its own set of nodes, which are specified by the node function. Layer one is the layer in which all of the nodes have a node function and are adaptive nodes. The second layer is where nodes multiply incoming signals, and the output is the sum of all the incoming signals. The firing strength of the ith rule is compared to the total firing strength of all node rules, which is the focus of Layer 3’s calculation. Each node in layer 4 is responsible for calculating the contribution that the ith rule makes to the overall output. The signal node in layer 5 calculates the final output as the sum of all input signals.

Within the framework of this ANFIS system, the hybrid algorithm was implemented. The input and output membership functions of the ANFIS model each have their own unique shape. The ‘trimf’ membership function was chosen out of all the other MF’s because it displays the lowest test error and the lesser value of mean absolute percentage error compared to the other membership functions. The ‘trimf’ membership function, which stands for ‘triangular membership function,’ also has incline and decline features with a specific value [42].

2.2. Support Vector Machine (SVM)

Vapnik initially demonstrated the SVM in 1995. Researchers utilize this method to tackle categorization, prediction, and regression difficulties. It’s a part of artificial intelligence (AI) [43,44]. SVM analysis involves training and testing data sets and input/output parameters. The optimal margin classifier is used in SVM analysis to segment the decision surface. The product of two vectors is determined using the kernel function approach. Fixed mapping is used to fit a non-linear kernel function in high-dimensional space after input data has been mapped using n-dimensional characteristics. When high-dimensional data is mapped using a kernel, the information separates linearly without altering the input space [44]. The input space is converted into a high-dimensional feature space via the kernel function, which enables non-linear relationships to be expressed in a linear fashion. The particular selection of a kernel function to map the non-linear input space into a linear feature space is highly dependent on the nature of the data, which refers to the type of underlying relationship that needs to be estimated in order to relate the input data with the desired output property. Finding such a kernel will be quite valuable. The Pearson VII Universal Kernel was utilized for use as the basis for the GP and SVM kernel function. The Pearson VII function offers outstanding flexibility and the opportunity to simply shift from a Gaussian into a Nonlinear peak shape and more by modifying its parameters. It also has the ability to transition from a Nonlinear peak shape to a Gaussian peak shape. As a result, the Pearson VII function can be utilized in place of a generic kernel [45].

2.3. Gaussian Processes (GPs)

Over the course of the last several years, a large amount of research and development effort has been concentrated on the study of machine learning as an area of study. The Gaussian process is a method for machine learning that involves performing analyses of models using kernels. It gives kernel machine novices hands-on experience [46,47]. Each finite random variable has a joint normal distribution. This collection is called a random variable ensemble. It is generally agreed that the mean function, which is represented by the symbol m(x), and the kernel function, which is represented by the symbol n(x,x′), are the two most important functions of the Gaussian process, which is represented by the symbol l (x).

2.4. Purpose of the Study

A comprehensive literature analysis found that fewer studies had utilized these modelling methodologies to assess the FS of concrete mixes including WMP. In civil engineering, their ability to predict the FS of concrete mixtures was evaluated using literature and lab data. In this paper, the effect of marble powder on flexural strength of concrete is demonstrated. Experimental investigations to study the effect of marble dust on flexural strength exploring possible reasons for the gain in strength have been conducted. The study’s goal is to assess the flexural strength of concrete that includes waste marble powder using machine learning methods, i.e., ANFIS, Support vector machines, and Gaussian processes approaches. Other algorithms were also tested on the dataset used for the study in addition to GP, SVM, and ANFIS, but they showed a poor coefficient of correlation value for the dataset. Therefore, in place of other conventional methodologies, ANFIS, support vector machine, and Gaussian process methods were used to predict the flexural strength of concrete.

In order to determine which modelling technique was the most effective at predicting the FS of concrete mix, the results were compared. This was done so that the most dependable modelling strategy could be selected. Flexural strength has also been studied by using the most reliable approach of sensitivity analysis in order to determine the influential independent variable to predict the dependent variable.

3. Methodology

In order to accomplish the goal of the study, which was to predict the FS of concrete, the following approach was taken: data was gathered on the FS of concrete, and various forms of soft computing were utilized. It was important to collect adequate data for the purpose of predicting the FS, and this was accomplished by carrying out experimental study and data from previously published studies.

3.1. Experimental Investigation

Each of the 120 beam specimens measuring 700 mm × 150 mm × 150 mm provided the following information regarding the testing materials and procedures:

3.1.1. Aggregate

CA with nominal diameters between 10 and 20 mm was incorporated in the concrete mixture. The particle size distribution of the aggregate was graded [48]. The SG, crushing, and impact were found to be 2.61, 23.67, and 6.74 percent, respectively, by ASTM C-128 and ASTM C-127 [49,50]. The mechanical characteristics of FA and CA are shown in

Table 1. Mechanical Characteristics of Fine and Coarse Aggregates.

Experiment	Unit	Observed Value	Permissible Limit	Standard
Impact test of CA	%	6.74	<10	[50]
Crushing value of CA	%	23.67	>45	[50]
SG of CA	gm/cm3	2.61	-	[49]
Apparent SG of CA	gm/cm3	2.82	-
WA of CA	%	2.82	-
SG of FA	gm/cm3	2.47	-	[49]
Apparent SG of FA	gm/cm3	2.51	-
WA of FA	%	0.6	-

.

3.1.2. Cement

Cement according to ASTM C-150 [51] Type-I cement was utilized in this study.

Table 2. Mechanical Characteristics of cement.

Test	Unit		Value	Permissible Limit	Standard
Fineness	%		5.77	<10	[52]
Consistency	%		32	>45	[53]
Soundness	mm		3.33	<10	[54]
SG	gm/cm3		3.1	-	[55]
Setting Time	min	Initial	40	-	[56]
		Final	360	-

lists the mechanical characteristics of cement.

3.1.3. Marble Powder

The Waste Marble Powder that was obtained came from its source, which was a marble company that was located locally. While

Table 3. Mechanical Characteristics of MP.

Test	Unit	Value
Fineness	%	2.01
SG	gm/cm3	2.44
Apparent SG	gm/cm3	2.56
WA	%	1.96
Bulk SG	gm/cm3	1.63

provides an explanation of the WMP’s mechanical qualities, Figure 2 depicts the chemical analysis of the marble powder. An EDS analysis was carried out so that the elemental make-up of the WMP could be ascertained. The X-ray spectra, which can be seen in the image, are laid out with the energy, which is measured in keV, along the x-axis and the number of counts, which is measured along the y-axis. The information shown in Figure 2 makes it abundantly evident that Calcium and Oxygen have the highest weightage of all the elements.

3.1.4. Mix Design

When making batches, the amounts of C, FA, and MP that were specified were employed. Other components, such as CA and the ratio of water to cement, were always used in the same proportions throughout the process. Several unique sets of specimens, each of which had three beams, were manufactured as a part of the experiment. A total of one hundred and twenty beams were manufactured. The composition of the control specimens, as well as the composition of the specimens with 5, 10, 15, and 20% replacement by the weight of cement and sand, is detailed in

Table 4. Mix Design.

Sr. No.	Mix-ID	Materials in kg/m3
		Cement	FA	CA	Water	MP
1	M0	395.74	600.15	1103.09	217.65	0
2	A04	395.74	570.14	1103.09	217.65	30.00
3	A13	390.79	577.65	1103.09	214.93	27.44
4	A22	385.85	585.15	1103.09	212.21	24.89
5	A31	380.89	592.64	1103.09	209.49	22.34
6	A40	375.95	600.15	1103.09	206.77	19.78
7	B04	395.74	540.13	1103.09	217.65	60.01
8	B13	385.85	555.13	1103.09	212.21	54.90
9	B22	375.95	570.14	1103.09	206.77	49.75
10	B31	366.06	585.15	1103.09	201.33	44.68
11	B40	356.16	600.15	1103.09	195.89	39.57
12	C04	395.74	510.12	1103.09	217.65	90.02
13	C13	380.89	532.63	1103.09	209.49	82.35
14	C22	366.06	555.13	1103.09	201.33	74.69
15	C31	351.21	577.65	1103.09	193.16	67.02
16	C40	336.37	600.15	1103.09	185.00	59.36
17	D04	395.74	480.12	1103.09	217.65	120.03
18	D13	375.95	510.12	1103.09	206.77	109.80
19	D22	356.16	540.13	1103.09	195.89	99.58
20	D31	336.37	570.14	1103.09	185.00	89.43
21	D40	316.59	600.15	1103.09	174.12	79.14

M0 = control mix; (A represents 5% MP, B represents 10% MP, C represents 15% MP, D represents 20% MP) replacement.

.

ASTM D790 and ASTM C78 determine flexural strength using a two-point loading test. This method determines the flexural strength of hardened concrete test specimens by two-point loading [57,58]. Figure 3 shows a schematic of a flexural machine with two supports and two loads. Two supports considered as simply supported. The specimen’s center was loaded and then two points until failure. The flexural test machine directly measured the load.

3.1.5. Result and Discussion

The samples A04 and D40 that contained marble powder instead of sand and cement, respectively, showed an extra improvement in strength in the strength activity results as shown in Figure 4. After 28 days, the strength ratio for the samples was 15% and 3% higher, respectively, showing that a chemical reaction was occurring. The components with the biggest weightage, according to an EDS study, are calcium and oxygen in marble powder, which contribute to the increase in strength.

4. Statistical Analysis

4.1. Data Collection

The dataset is absolutely necessary for making an accurate prediction.

Table 5. Range of the dataset used.

Sr. No.	Independent Variable Range						Dependent Variable Range	Reference
	(kg/m3)					CD	FS (MPa)
	C	FA	CA	W	MP
1.	316.59– 395.74	480.12– 600.15	1103.09	174.13– 217.66	0.00– 120.03	7.00–28.00	0.71– 11.73	Experimental Reading
2.	225.00– 300.00	450.00	900.00	120.00	0.00– 75.00	7.00-28.00	0.40– 3.10	[59]
3.	383.00	273.00– 546.00	1187.00	191.60	0.00– 273.00	28.00	4.18– 5.73	[60]
4.	340.00– 400.00	672.00	1113.00	120.00– 160.00	0.00– 60.00	7.00– 28.00	3.30– 4.21	[61]
5.	240.00– 300.00	312.30	1721.40	150.000	0.00– 30.00	7.00– 90.00	4.80– 6.10	[62]
6.	270.20– 337.80	741.40– 927.00	1046.20	189.140– 212.800	0.00– 185.20	7.00– 90.00	1.76– 3.40	[63]

contains the range of the 202 observations that were gathered for this study from various sources, including the literature (82 readings), as well as laboratory data (120 readings).

Table 6. Detail of dataset.

Sr. No.	1	2	3	4	5	6	Total
Author	Mansoor [59]	Anitha Selvasofia [60]	Sounthararajan and Sivakumar [61]	Ergun [62]	Kirgiz [63]	Experimental Readings	202
No. of observation	18	6	14	22	22	120

contains detailed information regarding the observations that were analyzed as part of the investigation. After then, the 202 observations were divided into two subgroups at random, with a ratio of 70–30 for the training and testing subsets, respectively. In this study, FS served as the output variable, while ANFIS, SVM, and GP were the three methods that were employed to obtain the intended outcome. The input variables included C, FA, CA, w, MP, and CD. The software platforms that were used were MATLAB and Weka 3.9. In order to achieve the desired outcome, the researchers used independent variables including C, FA, CA, w, MP, and CD. In

Table 7. Characteristics of Datasets.

Dataset	Statistics	Minimum	Maximum	Mean	Standard Deviation	Kurtosis	Skewness
Total Dataset (202 observations)	C	225.00	400.00	345.23	48.54	−0.43	−0.89
	FA	273.00	927.00	556.21	132.14	0.59	0.12
	CA	900.00	1721.40	1149.32	209.67	3.40	2.07
	w	120.00	217.66	186.23	31.89	−0.32	−1.01
	MP	0.00	273.00	59.71	46.51	2.48	1.29
	CD	7.00	90.00	20.10	16.64	8.33	2.44
	FS	0.40	11.73	4.55	2.52	0.01	0.67
Training Dataset (142 Observations)	C	225.00	400.00	343.55	50.30	−0.60	−0.82
	FA	273.00	927.00	554.14	137.09	0.53	0.15
	CA	900.00	1721.40	1155.17	218.49	2.80	1.96
	w	120.00	217.66	185.80	32.29	−0.45	−0.95
	MP	0.00	273.00	59.21	48.52	2.95	1.44
	CD	7.00	90.00	21.05	18.62	6.82	2.39
	FS	0.40	11.73	4.59	2.62	0.04	0.75
Testing Dataset (60 Observations)	C	225.00	395.74	349.21	44.23	0.14	−1.05
	FA	312.30	834.30	561.10	120.60	0.81	0.05
	CA	900.00	1721.40	1135.46	188.16	5.90	2.46
	w	120.00	217.66	187.26	31.15	0.13	−1.17
	MP	0.00	185.20	60.89	41.72	0.34	0.73
	CD	7.00	28.00	17.85	10.34	−2.02	−0.05
	FS	0.71	10.31	4.46	2.27	−0.44	0.32

, the characteristics of the complete dataset, the dataset used for training, and the dataset used for testing are outlined. Consideration was given to the CC, MAE, RMSE, RAE, and RRSE when attempting to ascertain which model produced the most accurate results. These factors were helpful in determining which model was the most accurate. Better results are likely to have a higher CC value as well as a lower error value.

Table 8. Use Defined Parameters.

Model Used	User Defined Parameters
SVM	C = 1.5, PUK kernel O = 0.7, S = 0.7
GP	Noise = 0.1, PUK kernel O = 0.8, S = 0.8
ANFIS	Epoches = 10

is a listing of the user-defined criteria that must be met when evaluating the FS of a concrete mixture using WMP. These user-defined optimal settings for various procedures are the product of a significant amount of research that were conducted. The effectiveness of each model was determined by the optimal configurations. Because the optimal parameters will have an effect on the performance of the model, it is essential that they be determined with extreme care. As a consequence of this, the example parameters were perfectly suitable for both the datasets used for training and for testing.

Figure 5, show how distinct each data point’s colors are. The color alterations on the pair charts depend on the output’s level of intensity. Figure 5 shows how the color for flexure strength, which ranges from 0.4 MPa to 11.73 MPa, varies from blue to orange depending on the intensity of the output. As a result, each data point’s color is unique for each variable and ranges from blue at 0.4 MPa to orange at 11.73 MPa. In addition, Figure 5 illustrates a pair plot that was created to visualize the given dataset and discover their relationship. Figure 5 depicts the complex relationship that exists between the flexural strength of concrete and the constituent elements of marble powder, curing days, water, and cement. As can be seen, an increase in the dependent variables such as cement, water, marble powder, and curing days has an effect on the FS of the concrete.

4.2. Criteria for Evaluative Assessment

Using evaluating parameters ensures that algorithms perform to their greatest capacity. The CC, MAE, RMSE, RAE, and RRSE were used in this investigation.

$$\mathrm{CC}=\frac{x\left({{\displaystyle \sum }}_{i=1}^{x}OV\right)-\left({{\displaystyle \sum }}_{i=1}^{x}O)({{\displaystyle \sum }}_{i=1}^{x}V\right)}{\sqrt{[x{{\displaystyle \sum }}_{i=1}^x{O}^2-{({{\displaystyle \sum }}_{i=1}^{x}O)}^2] }\sqrt{[x{{\displaystyle \sum }}_{i=1}^x{V}^2-{({{\displaystyle \sum }}_{i=1}^{x}V)}^2] }}$$

(1)

$$\mathrm{RMSE}=\surd \frac{1}{x}\left({\displaystyle \sum }_{i=1}^x{\left(V-O\right)}^2\right)$$

(2)

$$\mathrm{MAE}=\frac{1}{x}({\displaystyle \sum }_{i=1}^x\left|V-O\right|)$$

(3)

$$\mathrm{RAE}=\frac{{{\displaystyle \sum }}_{i=1}^x\left|O-V\right|}{{{\displaystyle \sum }}_{i=1}^x\left(\left|O-\overline{O}\right|\right)}$$

(4)

$$\mathrm{RRSE}=\sqrt{ \frac{{{\displaystyle \sum }}_{i=1}^x{\left(O-V\right)}^2}{{{\displaystyle \sum }}_{i=1}^x{\left(\left|V-\overline{V}\right|\right)}^2}}$$

(5)

• O = Observed readings; $\overline{O}$ = the average of the Observed readings
• V = Predicted readings; $\overline{V}$ = Predicted Values Average
• x = the total number of readings.

The numbers assigned to the CC might range from minus one to plus one. The higher the CC number, the more favorable the outcomes are projected to be. Lower values of evaluation parameters such as RMSE, MAE, RAE, and RRSE, on the other hand, predict better outcomes; that is, if the computed error is low, it means that the output results will be better [64,65,66,67,68,69,70].

5. Findings and Discussion

5.1. ANFIS Based Assessment

Trial-and-error is used in the development of ANFIS-based models. Matlab can be used to predict FS. The model used in the study is triangular. The performance metrics for each membership function-based ANFIS model are listed in the later section. ANFIS model based on triangular membership function (MFs) predicts FS of concrete mix containing WMP. The CC values for training and testing were 0.8592 and 0.4687, respectively. The RMSE, MAE, RAE, and RRSE values were 1.3351 and 2.5116, 0.8487, 39.77% and 59.93%, respectively. Figure 6 illustrates observed and predicted ANFIS-based results for both phases. These numbers show how well the ANFIS trimf-based model predicts the FS of concrete mixes containing WMP. Reliable outcomes are predicted by a value that is closer to the line of perfect agreement [71,72,73,74,75,76].

5.2. Support Vector Machine (SVM) Based Assessment

The Pearson VII function kernel, often known as the PUK kernel, is used in this model along with a number of user-defined parameters, such as C, omega (O), and sigma (S). The ideal method, which involved getting the maximum CC value while also minimizing the number of errors, was found after a substantial number of experiments were run [77,78,79,80]. The dataset that was used in this investigation yielded the most successful outcomes, with a c value of 1.5, O = 0.7, and S = 0.7, respectively. The performance metrics of the SVM are listed in

Table 9. Performances of SVM, GP, and ANFIS.

Machine Learning Techniques	CC	MAE	RMSE	RAE	RRSE
Training
GP	0.8967	0.7180	1.1563	33.64%	44.32%
SVM	0.8656	0.6720	1.3275	31.49%	50.88%
ANFIS_trimf	0.8592	0.8487	1.3351	39.77%	59.93%
Testing
GP	0.7476	1.0884	1.5621	57.79%	69.19%
SVM	0.7020	1.1604	1.7691	61.61%	78.36%
ANFIS_trimf	0.4687	1.6305	2.5116	86.99%	98.74%

, and it includes both the training and testing datasets. The RRSE was 50.88 percent during the training phase and 78.36 percent during the testing phase. The RAE was 31.49 percent during the training phase and 61.61 percent during the testing phase. The MAE was 0.6720 during the training phase and 1.1604 during the testing phase. The CC values were 0.8656 and 0.7020. A comparison of the actual and anticipated FS values of the concrete mix resulted in the creation of the agreement plot, which is depicted in Figure 7.

5.3. Gaussian Processes (GPs) Based Assessment

The type of regression known as Gaussian Processes makes use of a Pearson VII function kernel, often known as a PUK kernel, together with specific user-defined parameters such as L, Omega (O), and Sigma (S). Numerous trials had to be conducted in order to find the optimal value, which was defined as the greatest CC value that could be achieved with the fewest errors [81,82,83,84]. With L values of 0.1, O = 0.8, and S = 0.8, respectively, the dataset employed in this experiment yielded the most effective findings. Table 9 can be accessed here and contains the performance metrics for the general practice training and testing datasets. The training and testing phases’ respective RMSE values were 1.1563 and 1.5621, the training and testing phases’ respective MAE values were 0.7180 and 1.0884, the training and testing phases’ respective RAE values were 33.64 percent and 57.79 percent, and the training and testing phases’ respective RRSE values were 44.32 percent and 69.19 percent. The actual FS of the concrete mix is compared to the projected FS in Figure 8, which illustrates the agreement plot.

6. Comparison

Throughout the course of this investigation, a variety of distinct strategies for machine learning were utilized. The GP model appears to outperform the others when these models are compared, both in terms of the training datasets and the testing datasets [65]. Both the training dataset and the testing dataset showed that the GP model had the greatest possible CC values of 0.8967 and 0.7476, respectively, for the testing dataset. Figure 9a,b illustrates the disparity that exists between the projected dataset and the actual dataset on which machine learning methods were performed.

GP model also had the lowest MAE (1.0884), RMSE (1.5621), RAE (57.79%), and RRSE (69.19%) for the testing dataset. These results can be seen in Table 9 and Figure 10.

In order to determine the FS of concrete mix that included MP, it was necessary to evaluate not only the actual value but also the quartile values of 25%, 50%, and 75% in addition to the actual value.

Table 10. Statistics of observed and predicted output of testing dataset utilizing soft computing algorithms.

Output	Statistic Criteria	Actual	GP	SVM	ANFIS_Trimf
FS	Minimum	0.71	1.23	0.90	1.29
	Maximum	10.31	10.38	10.68	14.48
	1st Quartile	2.90	2.81	2.42	2.58
	Mean	4.46	4.50	4.41	4.83
	3rd Quartile	5.96	6.31	6.40	6.48
	IQR	3.06	3.50	3.98	3.90

displays the findings obtained from the aforementioned assessments. Interquartile range (IQR) of GP is relatively near to IQR of the real data that was followed by ANFIS trimf, as can be shown in Figure 11 and Table 10, respectively.

In addition, based on the examination of the data, the set of data has been separated into two groups, which are FS < 10 MPa and FS > 10 MPa.

Table 11. Performances of SVM, GP, and ANFIS for FS < 10 MPa and FS > 10 Mpa.

MAE
	GP	SVM
FS < 10	1.3511	1.6208
FS > 10	0.6411	0.6647

and Figure 12 show the increasing trend in error with decreasing FS based on the modelling methodologies that were used, and they indicate that the error increases from 0.6411 to 1.3511 MPa for FS > 10 to FS < 10, respectively, for GP based model.

7. Sensitivity Assessments

The most important component of the input variable that affects the prediction of the FS of concrete mixes containing waste MP was identified as a possible variable using sensitivity analysis. It can be seen from Figure 4, which shows the experimental results, that curing days and the change in quantity of MP affects the concrete flexural strength of concrete. Further, sensitivity study was undertaken on the GP model because it performed the best among the other models for this dataset [85,86,87]. As shown in

Table 12. GP-based sensitivity model results.

Removed Variable	GP Based Model
	CC	MAE	RMSE
NIL (no parameter has been removed)	0.7713	1.2034	1.6713
CD	0.5441	1.5499	2.0857
w	0.7365	1.3137	1.8028
FA	0.7419	1.3177	1.7863
CA	0.7690	1.2135	1.6808
C	0.7641	1.2367	1.6909
MP	0.7774	1.1642	1.6194

, this analysis involved changing the input combination and removing one input parameter one by one. For the purpose of determining which model performed the best, the study utilized statistical evaluation criteria such as CC, MAE, and RMSE. Table 12 indicates that one of the most important factors to consider when attempting to predict the FS of a concrete mixture is the number of curing days followed by the water. Figure 13 represents the relationship between removed parameter and the CC value based on the GP model. The following equation represents the best-fit model for independent variables:

y = −0.003x⁵ + 0.0648x⁴ − 0.5341x³ + 2.0406x² − 3.4785x + 2.68

(6)

where, x = independent variable, y = dependent variable

In addition, sensitivity analysis has been performed to check the sensitive variable when FS is divided into two parts, i.e., FS < 10 Mpa and FS > 10 Mpa. It can be seen from

Table 13. GP-based sensitivity model results for FS < 10 and FS > 10.

Removed Variable	MAE
	FS > 10	FS < 10
NIL (no parameter has been removed)	0.6411	1.3511
C	0.6378	1.0110
FA	0.6340	1.0131
CA	0.6411	0.9268
w	0.6379	1.0267
MP	0.6570	0.9492
CD	4.8163	1.4743

that curing days has an influential effect on the flexural strength of the concrete with maximum MAE value, i.e., 4.8163 Mpa and 1.4743 Mpa for FS > 10 Mpa and FS < 10 Mpa, respectively. A gel is created during the pozzolanic reaction, which causes the FS to increase. Concrete can become stronger when the curing time is extended because it is a gradual process [66].

8. Conclusions

In this study, the algorithms that were used to predict the FS of concrete mixes that included WMP were compared using three different machine learning techniques. These techniques were ANFIS, SVM, and GP. The effectiveness of these models was assessed using the CC, MAE, RMSE, RAE, and RRSE metrics, respectively.

According to the results of the research, the GP model yields the most reliable predictions of the FS of concrete. This conclusion may be drawn from the data of the investigation. GP also predicts more accurate outcomes for the testing dataset than SVM, with corresponding CC values of 0.7476 and 0.7020, lower MAE values of 1.0884 and 1.1604, and lower RMSE values of 1.5621 and 1.7691, respectively.

The scatter plot demonstrates that the GP has the least error band width and is an important predictor of output. This is demonstrated by the fact that the GP has the smallest error band width. The amount of curing days that are subsequently followed by water is the most significant variable to take into consideration when attempting to estimate the FS of concrete. This is because, when compared to the other variables that are utilized as input for this data set, it is the most relevant variable.