Development of the New Prediction Models for the Compressive Strength of Nanomodified Concrete Using Novel Machine Learning Techniques

Abstract

Concrete is a heterogeneous material that is extensively used as a construction material. However, to improve the toughness and mechanical properties of concrete, various ingredients (fillers) have been added in the past. The addition of nanomaterials for the improvement of the aforementioned properties has attracted many researchers worldwide. The high surface area, high reactivity, and finer size of various nanomaterials have made them preferable for the enhancement of durability, as well as compressive and flexural strength. The aim of the current research is focused on the estimation of compressive strength for the concrete modified with various nanomaterials using two machine learning techniques, namely decision tree technique (DTT) and random forest technique (RFT), and comparison with existing models. The database is collected for different percentages of four major widely used nanomaterials in concrete, i.e., carbon nanotubes, nano silica, nano clay, and nano alumina. The other four input variables used for the calibration of the models are: cement content (CC); water–cement ratio (W/C); fine aggregate, i.e., sand (FA); and coarse aggregate (CA). Both DTT and RFT models were developed for 94 collected experimental datasets from the published literature. The predicted results are further validated through K-fold cross-validation using correlation coefficient (R²), mean absolute error (MAE), root mean square error (RMSE), relative root mean square error, relative square error (RRMSE), and performance index factor (PiF). The RFT model was found to have the lowermost MAE 3.253, RMSE 4.387, RRMSE 0.0803, and performance index factor (PiF) 0.0061. In comparison, predicted results overall revealed better performance and accuracy for the RFT-developed models than for DTT and gene expression programming (GEP) models, as illustrated by their high R² value, equal to 0.96, while the R² value for DTT and GEP was found 0.94 and 0.86, respectively.

1. Introduction

Concrete is an extensively used building material obtained from the mixing of sand aggregate and cement as a binding material. However, with the advancement in technology, the application of nanomaterials to make special concrete, such as high strength and durable concrete has gained much importance worldwide. Concrete is a brittle material that has a low tensile strength [1]. Nanomaterials can be used as additives or as a replacement for cement to induce special properties [2]. Nanomaterials have a high specific surface area. In concrete, nanomaterials make dense structures having few pores because of their fineness and high specific surface area. Common weaknesses of concrete due to porosity and deterioration can be controlled by adding a specific amount of nanoparticles [3]. Since the breakthrough in the construction industry, various nanomaterials have been employed by researchers to obtain the required enhanced properties [4,5,6]. In 1964, Steins and Stevens firstly reported the employment of nano silica (NS) in pure alite paste [7]. The addition of NS facilitated faster and more complete hydration. Similar results were reported by [8]. However, the addition of nanomaterials negatively affects the flowability and reduces the workability of cement mortars, paste, and concrete [9]. Many researchers utilized various proportions and types of nanomaterials, such as nano clay (NC), carbon nanotubes (CNTs), nano aluminum (NA), and nano-silica (NS) to modify the mechanical properties of concrete. The rate of hydration was significantly increased which provided additional nucleation sites for precipitation, thus forming a denser structure having better compressive strength (CS) and durability properties [10,11,12]. Glenn, 2013, stated that through the addition of CNTs and graphene oxide (GO), certain unique properties, such as self-sensing, self-healing, and electric resistivity of concrete were achieved [13]. CNTs, NS, NC, and NA are all intriguing materials with unique mechanical, electrical, dynamic, and chemical enhancement capabilities [14]. These components are mixed with cement to obtain special concrete with enhanced aforementioned properties. For example, NC addition not only improves the CS and endurance but also enhances the rheological properties which are more important parameters for 3D concrete printing and self-compacting concrete (SCC) [15]. Similarly, the addition of NA to cementitious materials enhances the pozzolanic reactivity by increasing the formation of aluminate and silicate phases by evolving the high heat of hydration [16].

The ML techniques have been significantly useful in predicting the CS and fresh properties of concrete using various raw and waste materials [17,18,19,20]. In 2001, Ferreira proposed GEP as a better kind of genetic programming (GP) [21]. It makes use of a straight-line string and a parse tree with different lengths. Function sets, boundary sets, boundary conditions, control limitations, and goal functions are all part of the GEP model. GEP starts with a small group of entities and transforms them into expression trees of various dimensions and shapes. DT is a tree shape ML algorithm, where the description of the dataset (experimental inputs) is represented by internal nodes, branches classify the algorithm rules adapted for modeling, and the outcome is represented in form of leaves [22]. Ref. [23] proposed RFT in 2001 and it is considered as an enhanced classification regression method. It is a type of ensemble ML technique, which utilizes several decision trees. The random forest technique (RFT) and decision tree technique (DTT) are implemented in the current investigation. more description of these employed techniques is explained in Section 4.

The addition of nanomaterials enhances both the CS and durable properties of concrete by reducing the porosity and permeability [24]. However, an addition in access amount may lead to a negative effect [25]. Therefore, the prediction of these properties through machine algorithms may ease their suitable use in the mix design. The current study is performed to predict the performance of nanomaterials in concrete in terms of CS using individual and ensemble ML techniques, such as RFT and DTT. These techniques have been employed by various investigators recently, for the prediction of CS and tensile properties of normal and modified concrete with various natural and industrial pozzolanic wastes [26,27]. Large datasets and predict the results with higher efficiency. In 2021, Murad Y. employed the GEP to predict the CS of concrete mixed with different nanomaterials. However, the estimation of CS of the concrete modified with various nanomaterials has been rarely explored by using the ensemble ML technique. Therefore, this study focuses on the estimation and comparison of CS of nano-modified concrete by using both individual (DTT) and ensemble (RFT) ML techniques using the Anaconda Python script. A dataset of 94 experimental points was collected from previously published literature [28]. Four types of nanomaterials, such as NS, CNTs, NA, and NC have been used. The results obtained by the modeling from GEP, DTT, and RFT have been compared. The efficiency of the models was checked by the following statistical checks, coefficient of determination R², mean absolute error (MAE), root mean square error (RMSE), relative root mean square error (RRMSE), relative square error (RSE), and performance index factor (PiF). Thereafter, these models were validated by external K-fold cross-validation. Results are compared in terms of efficiency and predictability. The adapted research methodology for the current study is shown in the flow chart (see Figure 1).

2. Literature Review

Machine learning ideas have been effectively employed in a kind of field in recent years for the prediction of various properties. Similarly, to avoid time-consuming testing methods, the civil engineering construction sector has used such strategies. Examples of these approaches include: multivariate adaptive regression spline (MARS) [29,30]; genetic engineering programming (GEP) [31,32,33,34]; support vector machine (SVM) [35,36]; artificial neural networks (ANN) [37,38,39]; DTT [27,40,41]; adaptive boost algorithm (ABA); and adaptive neuro-fuzzy interference (ANFIS) [42,43,44]. RFT is one of the most developed ensemble techniques, with variable importance measures (VIMs), a small number of model parameters, and strong resistance to overfitting [23,45]. The decision tree is the basis predictor of RF, as its name implies. The RFT model even gives better efficient results with default parameter settings [46]. The number of choices of base predictors and factor settings can be limited when using RFT. RFT has been used in a variety of domains, including ecology [47,48,49] and bioinformatics [50,51,52], but it has rarely been used in concrete [53,54,55,56]. Mohamed used the RF algorithm to forecast the CS of sustainable self-consolidating concrete [54]. To evaluate the effects of ground granulated blast furnace slag (GGBFS) and waste tire rubber powder (WTRP) [55] developed an RFT model. [56] used several techniques to forecast the CS of HPC and discovered the best performance of the RFT model. Using a beetle antenna search-based random forest algorithm, [57] estimated the CS of self-compacting concrete. With experimental results, the author obtained an unwavering strong correlation of R² of 0.97. To forecast the CS of HPC, [27] used a random forest technique. [58] used an evolved random forest algorithm with 138 data samples taken from the literature to forecast the CS of rubberized concrete. With a good coefficient correlation of R² of 0.96, this advanced-based strategy performed better. Ref. [59] established two models with random forest technique (RFT) and GEP to forecast the CS of HSC. RFT has a significant connection with strong projected values and provides a stable performance [60]. The machine learning approach is not only restricted to predicting the compressive or tensile properties of concrete; it may be used for any reaction in the engineering field [61]. In the last few years, the application of AI techniques has gained performance to forecast various outcomes in the field of civil engineering [19,62,63,64,65,66,67,68]. These techniques were commonly utilized to predict concrete’s mechanical properties [69,70,71,72]. Genetic programming (GP), a resilient soft computing technique (SCT), is beneficial since it develops the model without assuming the prior form of the existing correlation [73,74].

3. Datasets

The datasets for nano-modified concrete were collected from peer-reviewed published literature [28]. The data collected show the compressive strength as a response parameter and eight factors, i.e., cement (C); coarse aggregate (CA); fine aggregate, i.e., sand (FA); carbon nanotubes % (CNT); W/C; nano silica % (NS); nano clay % (NC); and nano alumina % (NA) were chosen as main influencing input variables. The nanomaterials are used in concrete as a percentage of binder content. Therefore, the input values of nanomaterials are shown in percentages. Two models of RFT and DTT were formed. The datasets were trained and tested to develop a numerical-based empirical model for nano-modified concrete. In total, 80% of datasets were used for training and 20% were used for testing according to a previous study [75].

4. Description of Used ML Approaches

The decision tree technique (DTT) is widely used for regression and classification-related problems. DTT is easier to comprehend as compared to other ML algorithms as it mimics human thinking to reach a decision. The tree shape structure with roots, branches, and leaf nodes is formed for possible outcomes (predictions) during modeling which is relatively easily understandable [76]. The flow chart of the DT starts from root nodes, and tree branches and ends with the leaves nodes which represent outcomes. The classification of the real dataset starts from the root node which usually represents the whole dataset, which later splits into various homogenous branch nodes (sets). This splitting process is performed based on a comparison of the values attributed to the parent (root) node. The further algorithm compares the assigned values of these newly formed nodes and splits them. Once the leaf node is reached, it cannot be further subdivided into sets. The pruning is a continuous process during modeling, which removes the unwanted branches to reach a decision. The most efficient modeling depends on the attributes assigned to each root node. The classification principle depends upon the path taken by each parent (root) node approaching the leaf (see Figure 2). These nodes are classified into three geometric shapes, i.e., triangle, rectangle, or circle. DT is an overall simple classified technique and easy to comprehend and interpret. However, overfitting may occur sometimes which can affect the efficiency of the model [77].

The random forest (RF) algorithm is a typical parallel ensemble ML technique, popular for both regression and classification analysis. It works on the principle of linking various classifiers to solve a more complex problem, therefore, improving the efficiency of the predicted results. However, the variance in the final predicted results depends upon the initial classification of supplementary data during the training phase. The random forest algorithm is the combination of various decision trees, for each subgroup of the dataset [78]. The efficiency of prediction is improved by taking an average of these decision trees The outcome is predicted based on the estimates of all these decision trees. The greater the number of trees, the greater would be the accuracy of the predicted model [77,79]. Figure 3 shows the schematic diagram of a random forest. Overall RF algorithms take a very short time even for large datasets and predict the results with higher efficiency. In this study, two subsets of training and testing are formed with 80% and 80% of the original dataset, respectively. Python programming is used to run the random forest algorithm. RF works in the following steps in Python [80].

• Pre-processing of collected dataset;
• Running and fitting the training set in the RF algorithm;
• Running the model and prediction of test results;
• Accuracy and efficiency of test results.

Figure 2. Example of the decision tree.

Figure 2. Example of the decision tree.

Figure 3. Schematic of random forest generation and prediction.

Figure 3. Schematic of random forest generation and prediction.

5. Model Development and Performance Evaluation

The most critical step before the creation of the model is the choice of input variables from the existing database that can considerably affect the strength of concrete [81]. Various types of nanomaterials have been employed in concrete to improve the CS, as well as the durability of concrete. The most common are NS, NC, CNTs, and NA. Other than nano-materials, compressive strength is significantly influenced by the cement (CC), sand (S), coarse aggregate (CA) content, and water/cement.

$$\mathrm{CS}=\mathrm{f}\left(\frac{\mathrm{W}}{\mathrm{C}},\mathrm{CC},\mathrm{S},\mathrm{CA},\mathrm{CNT}\%,\mathrm{NC}\%,\mathrm{NS}\%,\mathrm{NA}\%\right)$$

The efficiency of the finally developed model was checked by the following statistical checks, coefficient of determination R², MAE, RMSE, RSE, RRMSE, and PiF. MAE must be less than RMSE for better prediction results [81,82]. A value of R² higher than 0.8 shows a good correlation between the predicted and experimental values [83,84]. A PiF less than 0.2 indicates a better performance of the model [85].

Equations (1)–(6) shows the six statistical factors (RMSE, MAE, RSE, RRMSE, R, and PiF) used to compute the efficiency of both established models.

$$\mathrm{RMSE}=\sqrt{\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{e}}_{\mathrm{i}}-{\mathrm{m}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}$$

(1)

$$\mathrm{MAE}=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{e}}_{\mathrm{i}}-{\mathrm{m}}_{\mathrm{i}}\right|}{\mathrm{n}}$$

(2)

$$\mathrm{RSE}=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{m}}_{\mathrm{i}}-{\mathrm{e}}_{\mathrm{i}}\right)}^2}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left(\overline{\mathrm{e}}-{\mathrm{e}}_{\mathrm{i}}\right)}^2}$$

(3)

$$\mathrm{RRMSE}=\frac{1}{\left|\overline{\mathrm{e}}\right|}\sqrt{\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{e}}_{\mathrm{i}}-{\mathrm{m}}_{\mathrm{i}}\right)}^2}{\mathrm{n}}}$$

(4)

$$\mathrm{R}=\frac{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{e}}_{\mathrm{i}}-\overline{{\mathrm{e}}_{\mathrm{i}}}\right)\left({\mathrm{m}}_{\mathrm{i}}-\overline{{\mathrm{m}}_{\mathrm{i}}}\right)}{\sqrt{{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{e}}_{\mathrm{i}}-\overline{{\mathrm{e}}_{\mathrm{i}}}\right)}^2{{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{m}}_{\mathrm{i}}-\overline{{\mathrm{m}}_{\mathrm{i}}}\right)}^2}}$$

(5)

$$\mathrm{PiF}=\frac{\mathrm{RRMSE}}{1+\mathrm{R}}$$

(6)

where e_i and m_i illustrate the actual (tested) and model outcomes, $\overline{{\mathrm{e}}_{\mathrm{i}}}$, $\overline{{\mathrm{m}}_{\mathrm{i}}}$, and n reveals the average values of the collected dataset (tested) values and predicted output values from the developed model, and the overall quantity of samples, respectively.

The division of input variables significantly affects the efficiency of the model in terms of generalization capability. The frequency histograms in Figure 4 and descriptive analysis in

Table 1. Statistical description of input variables.

Parameters	W/C	CNT	NS	NC	NA	CC	CA	FA	CS
mean	0.414	0.023	0.938	0.27957	0.0019	442.379	976.656	1018.093	57.215
standard deviation	0.1084	0.090	1.608	1.386	0.0065	88.907	679.422	918.044	22.418
standard error	0.011	0.0093	0.166	0.144	0.0006	9.219	70.453	95.197	2.325
median	0.450	0	0.050	0	0	430	920	757	51.799
mode	0.250	0	0	0	0	430	920	0	80.492
kurtosis	−0.866	24.442	12.021	33.118	11.425	−0.201	2.135	−0.579	−0.281
skewness	−0.652	4.979	2.983	5.615	3.484	0.685	1.219	0.849	0.837
range	0.350	0.500	10	10	0.030	364.5	2720.343	2648.607	86.805
minimum	0.200	0	0	0	0	325.5	0	0	23.5948
maximum	0.550	0.500	10	10	0.030	690	2720.343	2648.607	110.4
sample variance	0.012	0.008	2.587	1.920	4.19 × 10−5	7904.498	461,614.6	842,804.2	502.5577

clearly show the non-uniform higher frequency distribution of these input variables. These histograms are formulated from the collected datasets of input variables. The nanomaterials are shown in different percentages, while cement, coarse aggregate, and fine aggregate are shown in Kg/m³. The range of utilization for nanomaterials has been found in very few percentages, while cement, water-to-cement ratio, fine aggregate, and coarse aggregate have larger data ranges.

6. Results and Discussion

6.1. Decision Tree Technique Outcome

The statistical analysis explanation of both tested and predicted values for the compressive strength of nano-modified concrete for the DTT-developed model is illustrated in Figure 5. Overall, 80% of the collected dataset was used for training the algorithm and 20% was used for testing. DTT efficiently predicts the output with a high value of correlation factor and low error is found between experimental (tested) and model outcome values. The correlation factor (R²) was found 0.94 for testing dataset values and 0.89 for the training dataset, which shows the better accuracy of the developed DT model. Figure 6 shows the distribution of experimental values, predicted values, and overall errors for the DT-based developed model for the compressive strength of nano-modified concrete. The highest, lowest, and average values of the error were found to be 10.966, −4.810, and 3.786 MPa, respectively.

6.2. Random Forest Technique Outcome

Figure 7 reveals the statistical analysis description of the experimental (actual) and projected results for the CS of the nano-modified concrete utilizing the random forest algorithm. DTT model creates an output with a high degree of accuracy and a small difference between actual and expected values. R² of 0.96 for the testing dataset and 0.90 for the training dataset indicates the higher correctness of the model in forecasting outcomes as compared to the DTT algorithm, which logically supports the basic idea of using several decision trees in the RFT. Figure 8 illustrates the scattering of experimental (actual) values, predicted outcome values, and overall errors for the RFT-based model for compressive strength of nano-modified concrete. The maximum, smallest, and average error values for the division were determined to be 11.339, −3.391, and 3.381 MPa, respectively.

7. Performance Evaluation of Developed Models

Past studies proposed the ratio of a total quantity of datasets to a quantity of inputs variable must be at least three, to obtain efficient results from developed models. Higher ratios lead to a better and more efficient prediction of the outcomes [86,87,88]. Therefore, this ratio is kept at around 12 in this study.

Table 2. Statistical parameters of the developed models (DTT and RFT).

Model	RSE	MAE	RMSE	RRMSE	PiF
DTT model	0.9128	3.863	4.865	0.0891	0.0086
RFT model	0.895	3.253	4.387	0.0803	0.0061

illustrates the statistical analysis of the dataset and predicted values for both DTT and RFT, respectively. Overall, the results represent a better correlation between the predicted and tested values for the RFT model as compared to the DTT model. The RSE, MAE and RMSE, RRMSE, and PiF values are found 0.9128, 3.863, 4.865, 0.089, and 0.008, respectively for the developed model by the DTT. Likewise, values of MAE and RMSE, RRMSE, RSE, and PiF for the RFT were found 3.253, 4.387, 0.0803, 0.893, and 0.006, respectively. The values of PiF are much less than 0.5 which shows good efficiency and predictability of the developed models.

8. Statistical and K-Fold Analysis

The K-fold analysis is used to evaluate the effectiveness and skill of the machine learning model. It follows the principle of Jack’s knife test, which is usually used to minimize the overfitting results and also reduces the biases during sampling of the training set. K-fold is popular because of its ease of understanding, and, also, it is less optimistic in estimating the skill of the model. In K-fold cross-validation, the set of observations is divided into k groups or equal folds of the same size. The value of these K groups is dependent upon the statistical classification of the datasets. The larger the value of K, the smaller will be the difference between training and resampling subsets.

K-fold cross-validation measures the efficiency of the developed model in terms of coefficients of determination (R²) and calculation of errors for the data selected for test and train data (MAE, MSE, RMSE). The higher value of R² and minimum value of errors illustrate the better prediction through a developed model. The collected experimental database was divided into ten groups, nine belong to training and one was used for validation. After ten repetitions, a significant improvement in results was achieved with excellent accuracy. Overall, 80% of the collected dataset values were used for the training and 20% were used for testing purposes. Statistical analysis of the errors (MAE, MSE, and RMSE) is illustrated in

Table 3. Validation indicators and results through K-fold.

	DTT				RFT
K-Fold	R2	MAE	MSE	RMSE	R2	MAE	MSE	RMSE
1	0.623	3.354	4.295	2.072	0.791	4.692	5.863	2.422
2	0.790	5.310	9.138	3.023	0.690	4.167	5.291	2.300
3	0.421	1.549	6.760	2.600	0.797	4.457	5.412	2.326
4	0.468	7.177	6.105	2.471	0.660	5.737	5.152	2.269
5	0.738	4.600	6.614	2.572	0.932	3.465	4.148	2.036
6	0.568	6.013	9.209	3.035	0.971	5.056	7.121	2.668
7	0.453	5.139	6.183	2.487	0.435	4.242	4.952	2.225
8	0.249	6.698	8.648	2.941	0.831	4.631	4.329	2.081
9	0.906	3.096	5.754	2.399	0.980	1.991	1.497	1.224
10	0.369	6.220	9.430	3.071	0.933	5.500	3.844	1.960

for the decision tree and random forest developed models. The tabular results clearly show that the values of MAE, MSE, and RMSE errors were found less for the RFT model than in the DTT model.

Figure 9 and Figure 10 show the R², MAE, MSE, and RMSE values extracted after evaluating both models through k-fold cross-validation. However, as shown in Table 3, the maximum, minimum, and average MAE values for the DTT model in terms of compressive strength (CS) were 7.177 MPa, 1.549 MPa, and 4.912 MPa, respectively, during the K-fold cross-validation process. The highest value of the RMSE was noted as 3.070 MPa. Moreover, the MAE, RMSE, and R² maximum values for RF in terms of CS were 5.737 MPa, 2.421 MPa, and 0.980, respectively, as illustrated in Figure 10. Similarly, the highest, lowest, and average mean squared error (MSE) values for the RFT about the CS were 5.863 MPa, 1.497 Pa, and 4.760 MPa, respectively, as shown in Figure 10.

9. A Comparative Study with Existing Models

CS forecast models for nano-modified concrete have been very rarely presented in past studies. However, Murad Y. investigated the mechanical performance of concrete modified with nanomaterials [28]. GEP was used for modeling and prediction purposes, and a mathematical equation (see Equation (7)) was presented as an end product of constitutive modeling. NS, CNT, W/C, CA, and CC represent the nano-silica, carbon nanotubes, water–cement ratio, coarse aggregate, and cement content, respectively. In this part of the current research, the GEP-developed mathematical model has been compared with the DTT and RFT models. The same type and number of inputs were used to develop DTT and RFT models for the comparative investigation. The results are presented in Figure 11. The correlation coefficient factor is used to compare the performance of all three models. The random forest (RFT) algorithm produced the most efficient model with an R² of 0.96. However, the decision tree (DTT) algorithm and GEP gave R² values of 0.94 and 0.86, respectively.

$$\mathrm{CS}=\left(\mathrm{NS}+\left(\frac{\left(\frac{5.85+\mathrm{CNTs}}{\mathrm{W}/\mathrm{C}}\right)-\left(\frac{\mathrm{CA}}{\mathrm{CC}}\right)}{0.34}\right)\right)+\left(\left(\frac{10.53}{\left(\frac{\mathrm{CA}}{\mathrm{CC}}\right)-\mathrm{W}/\mathrm{C}}\right)+17.03\right)$$

(7)

10. Conclusions

Overall, the compressive strength of nano-modified concrete has been very rarely explored. These predictions can reduce the overall cost and time consumed for laboratory testing. The present research compares the two, machine learning (ML)-based algorithms, i.e., random forest technique (RFT) and decision tree technique (DTT) to assess the compressive strength of nano-modified concrete. The ML models were developed using RFT and DTT using four types of nanomaterials, i.e., carbon nanotubes (%CNT), nano silica (%NS), nano clay (%NC), nano alumina (%NA), and other input variables are cement content (CC), water–cement ratio (W/C), a quantity of fine aggregate (FA), and coarse aggregate (CA). The two models were trained and tested based on data obtained from published literature. Based on the results and analysis, the following conclusions are deduced:

• The ensemble ML technique RFT reveals better performance with fewer variations between the experimental datasets and the projected outcomes. Additionally, the efficiency level of the random forest technique was found higher with an R² value of 0.96 than the individual ML DTT having an R² of 0.94.
• The smaller values of the statistical performance indicators MAE (3.253), RMSE (4.387), RSE (0.895), and RRMSE (0.0803) for RFT confirm the better accuracy than the 3.863, 4.865, 0.912, and 0.0891 values for the DTT algorithm. Additionally, a better performance index factor (PiF) for RFT was found at 0.0061 than the DTT approach with a PiF of 0.0086.
• K-fold cross-validation findings confirmed the effectiveness and better performance of the RFT-developed model.
• The performance of the established RFT (R² of 0.96)and DTT (R² of 0.94) models was found much better than the GEP model (R² of 0.864) developed in previous studies.

11. Future Recommendation

The results proved that ensemble machine learning techniques produce better results for the prediction of CS of nanomodified concrete. To achieve more accuracy in the results, it is recommended to increase the number of databases for the training and testing of the models. For a better understanding and development of the model, laboratory work is further recommended to conduct experimental work. In addition, sensitivity and parametric analysis are recommended to understand the effect of each input parameter on modeling.