Optimizing Concrete Mix Designs With Synthetic Data Generation and Machine Learning Prediction Models

Abstract

The focus of this paper is on the use of machine learning for the prediction of the strength outcomes of basalt fiber-reinforced concrete (BFRC), based on its mechanical properties. These target properties are compressive, flexural, and tensile strengths, estimated with knowledge of 10 variables, including cement and aggregate content, among other fiber characteristics. Models explored for regression in this paper include linear regression, K-nearest neighbors (KNN), random forest (RF), XGBoost (Extreme Gradient Boosting), support vector machine (SVM), and artificial neural networks (ANN). The highest performance among these was observed for the KNN at flexural strength with a $R^2$ score of 0.8737, XGBoost for compressive strength with a $R^2$ score of 0.8963, and RF for tensile strength with a $R^2$ score of 0.9420. Bayesian optimization was employed to tune hyperparameters to enhance the accuracy of the model. This study also applied Synthetic Minority Oversampling Technique (SMOTE) to generate 1000 synthetic concrete mix designs for the data to increase its diversity and allow the investigation on optimal performances regarding strength. The findings of this study contribute to advancing sustainable manufacturing practices by leveraging machine learning techniques to optimize material properties, thereby supporting the development of resilient infrastructure and enhancing industrial innovation.

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Concrete, one of the major construction materials, is under constant demands for bettering its performance indicators, especially in structural uses where mechanical strength is among the key parameters [1–3]. One such development, a promising one, is the integration of basalt fibers into concrete; this is known as basalt fiber-reinforced concrete (BFRC). Despite the attractions of basalt fibers for environmental sustainability and mechanical reinforcement, a precise prediction of BFRC mechanical properties remains difficult because of the complex interactions among mix components. Machine learning (ML) thus appears as a strong approach for modeling these properties to obtain optimal concrete formulations [4]. This predictive ability of ML allows, besides the estimation of BFRC properties, the identification of optimal mix designs with regard to structural performance criteria [5, 6].

Traditional concrete modeling approaches rely almost exclusively on empirical formulations, which prove to be grossly inadequate when applied to nonstandard or fiber-reinforced mixtures. Recent advances in ML have now made possible more accurate, adaptive models that are capable of taking into consideration a much extended range of variables. This paper makes use of a dataset of BFRC mixtures containing 13 variables, such as mix design parameters like cement, silica fume, coarse and fine aggregates, water content, and fiber properties [7, 8]. Such a large dataset provides a rich basis for the investigation of the influence of each constituent on the mechanical performance of the material [9, 10]. Iteratively trained ML models, using this data, are capable of making highly accurate predictions of various strength measures and can thus be used to help develop optimal BFRC designs [7, 11, 12].

Research in FRC has investigated numerous types of fibers, though basalt fibers have high strength-to-weight ratio and chemical resistance. The addition of basalt fibers improved tensile and flexural properties without significantly changing workability. However, there is still active research into finding the exact mix ratios to achieve the target properties. Previous works have showcased the ability of ML to model such composite materials, showing that models like random forest, XGBoost, and K-nearest neighbors (KNN) address complex, high-dimensional data and present reliable predictions [5]. Using Bayesian Optimization for hyperparameter tuning can improve accuracy and computational efficiency, further supporting their application in BFRC studies [6].

The main goal of this study is to apply multiple ML algorithms, evaluate their prediction performance, and optimize BFRC compositions in order to achieve desired strength properties. Specifically, we aim to: (1) evaluate six ML models in the prediction of BFRC’s flexural strengths (FS), compressive strengths (CS), and tensile strengths (TS); (2) apply Synthetic Minority Oversampling Technique (SMOTE) [13] to create synthetic samples and enhance model training robustness; and (3) identify the most promising concrete mix designs using the optimized ML models. The findings deliver critical insights into the use of ML in concrete technology and point out the efficacy of basalt fiber integration in improving mechanical properties [7].

2. Literature Review

Table 1 provides an extensive overview of the studies that have applied ML methods in concrete mixture design, with observations of major findings, data sets applied, and dependent variables considered in each study. ML techniques for optimizing concrete mixture designs have garnered considerable interest owing to their potential to improve predictive accuracy, minimize experimental trial-and-error procedures, and improve material efficiency overall. Numerous research works have proven the capability of ML models in predicting the CS, workability, and durability of the concrete mixture, at lower environmental effect and cost.

Table 1

Summary of machine learning approaches in concrete mix design.

Reference no.	Research insights	Dataset	Dependent variables
[14]	The study shows that machine learning, particularly multi-layer perceptron (MLP) neural networks, enhances concrete mix design by accurately predicting compressive strength, surpassing traditional methods in precision and reliability	Various concrete mix designs including cement, water, aggregates, admixtures	Compressive strength of concrete, mix proportions of cement, water, aggregates, and admixtures
[15]	Machine learning models optimize concrete mix design by predicting compressive strength, reducing costs while maintaining quality. CatBoost performed best, improving efficiency and cost-effectiveness	Dataset includes over 19,000 samples from a local producer	Compressive strength of concrete mixtures, mixture cost under quality constraints
[16]	Machine learning enhances concrete mix design by predicting key parameters like compressive strength and chloride ion penetration. Models like random forest, XGBoost, LightGBM, and CatBoost improve accuracy, reduce costs, and lower carbon footprints	Dataset comprises 5306 samples from 154 scientific resources	Compressive strength of recycled aggregate concrete (RAC), chloride ion penetration resistance and carbonation resistance
[17]	Machine learning models, including linear regression, ridge regression, SVM regression, and polynomial regression, optimize concrete mix design by predicting compressive strength, ensuring reliable concrete properties	More than 45 mixture designs collected	Compressive strength of concrete, mixture design percentages
[18]	Machine learning optimizes concrete mix design by effectively predicting compressive strength, enhancing performance through complex models	Vast database of concrete mix recipes used	Compressive strength of concrete, error metrics (various types)
[19]	Bayesian optimization accelerates sustainable concrete mix design by optimizing compressive strength and global warming potential using a Gaussian process	Real-world strength measurements of proposed concrete mixes	Compressive strength of concrete mixtures, global warming potential (GWP) of mixtures
[20]	Random forest optimizes concrete mix design by predicting compressive strength and dry density, balancing plastic aggregate content, cost, and structural efficiency	Diverse dataset from various sources	Compressive strength, dry density
[21]	This study proposes an intelligent machine learning model using adaptive boosting to predict concrete compressive strength	1030 sets of concrete compressive strength tests used for training and validation	Compressive strength of concrete, effect of training data amount on accuracy
[22]	A deep learning-based model is developed for predicting the compressive strength of recycled aggregate concrete. Using convolutional neural networks (CNN), it extracts deep features of mix proportions and performs strength predictions using SoftMax regression	74 sets of concrete block masonry with different mix ratios were used in the experiments	Compressive strength of RAC, performance comparison of CNN versus traditional models
[23]	The study employs a genetic algorithm-improved back propagation (GA-BP) method for predicting concrete mix ratios, enhancing accuracy over standard back propagation. This approach, combined with the NSGA-II algorithm, optimizes low-carbon concrete mix designs effectively, considering strength and environmental impacts	Concrete mix ratio database constructed for analysis	28-day compressive strength of concrete, material cost and carbon emissions
[24]	Machine learning (ML) optimizes concrete mix design by predicting slump and compressive strength, reducing trial-and-error experiments	Database for slump and compressive strength of GPC established	Slump of geopolymer concrete (GPC), compressive strength of geopolymer concrete (GPC)
[25]	Machine learning optimizes concrete mix design by predicting properties like compressive strength, flexural strength, and porosity	Data synthesized by generative modeling and semi-supervised learning	Compressive strength and flexural strength of UHPC, mini-slump spread and porosity of UHPC
[26]	The study introduces a soft computing model for predicting the compressive strength of high-performance concrete (HPC)	Compressive strength database compiled from 1030 concrete samples	Compressive strength of HPC, effect of multicollinearity on prediction accuracy
[27]	Machine learning optimizes concrete mix design by predicting compressive strength (CS) using models like random forest, AdaBoost, and gradient boosting, enhancing the understanding of input parameters such as age, fiber, and cement in ultra-high-performance concrete	Dataset of 810 experimental data points collected	Compressive strength (CS) of ultra-high-performance concrete, input parameters affecting compressive strength
[28]	Machine learning techniques, such as deep neural networks and gene expression programming, are utilized to forecast the strength characteristics of concrete incorporating waste foundry sand, optimizing mix design by evaluating dominant input features for improved mechanical properties	397 values of compressive strength (CS), 169 values of flexural strength (FS)	Compressive strength (CS) of waste foundry sand concrete, flexural strength (FS) of waste foundry sand concrete
[29]	Machine learning models, such as support vector machines (SVM), are utilized to establish complex relationships between input variables and concrete properties, enabling the optimization of concrete mix design by addressing multiple competing objectives simultaneously in hybrid optimization scenarios	Data available on request from corresponding author	Mechanical properties of cementitious materials, cost, workability, environmental requirements, durability
[30]	The paper presents a long short-term memory (LSTM) network for predicting concrete compressive strength, combined with a multi-objective particle swarm optimization (MOPSO) algorithm to optimize mix ratios, reducing costs and carbon emissions while ensuring strength requirements	8 basic properties of concrete materials as input parameters	Compressive strength of concrete as output variable, eight basic properties of concrete materials as input parameters
[31]	The study uses artificial neural networks (ANN) to predict the compressive strength of recycled aggregate concrete (RAC). It collects 139 data sets from 14 published sources and identifies key input variables such as water-cement ratio, recycled coarse aggregate, and fine aggregate	139 datasets compiled from 14 literature sources	Compressive strength of RAC, influence of input parameters on strength
[32]	This study develops a statistical model for predicting the compressive strength of portland cement concrete at any age	Existing experimental data for compressive strength of different concrete mixes were analyzed	Compressive strength prediction over time, effect of admixtures and curing conditions on strength gain
[33]	This research explores the use of ultrasonic pulse velocity (UPV) and artificial neural networks (ANN) to predict concrete compressive strength. A comparison with multiple regression analysis shows that ANN provides better prediction accuracy	Concrete specimens of two different sizes and shapes (M20 and M30 mixes) were used	Compressive strength prediction using UPV
[34]	The study employs artificial neural networks (ANNs) to predict the properties of high-performance concrete (HPC) and integrates genetic algorithms (GA) to optimize mix proportions and reduce costs, improving traditional concrete design methods	Experimental results and previous research data used	Workability of high-performance concrete (HPC), strength and durability of high-performance concrete (HPC)
[35]	The study shows that machine learning models, particularly XGBoost and neural networks, can optimize concrete mix design by accurately predicting key properties, reducing costs, and minimizing over-design through reliable formulations	Dataset from cementos argos S.A. over 5 years	Compressive strength, flexural strength, slump
[36]	The paper demonstrates that machine learning, particularly the XGBoost regressor, effectively predicts concrete workability, optimizing mix design by analyzing feature importance, notably water content, slag, and coarse aggregate, enhancing resilience and sustainability in construction practices	Large dataset from literature studies	Concrete workability prediction, feature importance includes water content, slag, coarse aggregate
[3]	Machine learning techniques, including elastic net regression and stacking methods, were applied to predict the compressive strength of recycled aggregate concrete (RAC)	Dataset of 3519 samples from published literature	Compressive strength (CS) of recycled aggregate concrete (RAC), RAC strength prediction model

Concrete CS is a key parameter in concrete mix design, and ML techniques have widely been used for its precise estimation. Classical regression techniques have been complemented by sophisticated ML models such as support vector machines (SVM), artificial neural networks (ANN), and deep learning techniques such as convolutional neural networks (CNN) [14–20]. These sophisticated models exhibit superior performance over traditional methods by capturing subtle relationships between mix proportions, curing regimes, and material properties.

Feng et al. [21] suggested an adaptive boosting method to predict CS of concrete, in which weak learners were enhanced systematically to construct an effective prediction model. They identified decision trees as the most powerful weak learners in boosting models in their research and attained over 95% accuracy. Similarly, Deng et al. [22] suggested a deep learning strategy based on CNNs for predicting the strength of recycled aggregate concrete (RAC), demonstrating its heightened accuracy compared to traditional ANN models. Additionally, research has demonstrated the effectiveness of Gaussian process regression, decision trees, and ensemble learning models for improving prediction accuracy of high-performance concrete (HPC) [23–25].

HPC necessitates a strongly optimized mix design so that its mechanical properties are enhanced while ensuring a reduction in material waste. Daniel et al. [26] employed soft computing techniques, namely least-square SVM (LSSVM) and ensemble tree-based models, for the accurate prediction of CS of HPC. Their study results indicated that the maximum correlation coefficient (0.9352) along with the lowest root mean square error (RMSE) and mean absolute error (MAE) was achieved using the ensemble tree-based approach. Moreover, hybrid methods combining genetic algorithms and neural networks have also been used to optimize HPC mixture proportions successfully [27–29].

Increased demand for green concrete mix designs has resulted in the incorporation of ML techniques that are able to reduce carbon footprints without compromising structural integrity. Jin et al. [30] proposed a model using long short-term memory (LSTM) architecture, which was combined with a multi-objective particle swarm optimization algorithm to achieve optimal concrete mix proportions. The method was able to minimize carbon emissions while ensuring adherence to the specified strength requirements.

Naderpour et al. [31] applied ANN models to predict the CS of green concrete with recycled aggregates. Their study emphasized the importance of influential input variables such as water-to-cement ratio, recycled coarse aggregate, and fine aggregate for the estimation of concrete strength. Abd Elaty [32] also developed a statistical model that predicts the CS of Portland cement concrete at any age considering curing conditions and admixture effect.

Nondestructive testing (NDT) methods, such as ultrasonic pulse velocity (UPV), have been explored to predict concrete CS through ML models. Kewalramani and Gupta [33] applied ANN models to UPV data, demonstrating that ML-based techniques provided greater accuracy in prediction compared to traditional regression models. The advancement enables real-time quality assessment of concrete without destructive sampling, improving the efficiency of construction and reducing material waste.

Despite the promising advancements in ML for concrete mix optimization, challenges remain in data availability, model interpretability, and real-world implementation. Most ML models require extensive datasets for training, and the generalization of models across different concrete compositions remains an area of ongoing research. Future studies should focus on developing hybrid models that integrate physics-based simulations with data-driven approaches to improve reliability. Furthermore, the incorporation of explainable AI techniques can enhance trust in ML-based predictions, facilitating their adoption in industry applications.

The reviewed studies illustrate the potential of ML to revolutionize concrete mix design. By enabling predictive insights and optimization for various concrete types—ranging from traditional to geopolymer, fiber-reinforced, and 3D-printed concrete—ML techniques contribute significantly to material efficiency, cost reduction, and sustainability in construction. Future research could further integrate synthetic data generation with ML models to enhance predictive reliability, reduce dependency on empirical data, and foster innovation in concrete mix optimization.

3. Problem Statement and Study Contribution

The increasing demand for high-performance, eco-friendly construction materials underscores the need for advanced methods to optimize concrete mixtures. Traditional empirical models often lack the adaptability to accommodate nonstandard materials, like basalt fiber. This study addresses the challenge of predicting the mechanical properties of BFRC accurately by integrating ML techniques. Despite extensive research on FRC, there is limited knowledge on optimizing BFRC specifically, with existing studies frequently constrained by small datasets and limited fiber variability.

This study contributes to the literature by applying a wide range of ML models with regard to predicting BFRC’s FS, CS, and TS. In this line of research, the use of SMOTE in data generation and Bayesian Optimization in hyperparameter tuning developed a robust methodology for enhancing model accuracy in the search of the optimal BFRC compositions. The findings lay the basis for future uses in the field of structural engineering and contribute toward advancing the greater field of sustainable construction material optimization.

4. Materials and Methodology

4.1. Materials

For this study, we used the Mechanical Properties Dataset of BFRC for Strength Prediction with ML, contributed by Wang [37]. The dataset is on predicting mechanical properties for FRC specimens tested at 28 days. The dataset comprises 13 variables, including 10 input features related to the mix design and fiber properties, and 3 target variables representing key mechanical properties. Table 2 provides a brief description of the input variables and target mechanical properties included in the dataset.

Table 2

Variables and targets in the mechanical properties dataset.

	Name	Symbol	Unit	Description
Variables	Cement	C	kg/m3	The mass of cement in the mixture
	Silica fume	SF	kg/m3	The mass of silica fume used as a supplementary cementitious material
	Fly ash	FA	kg/m3	The mass of fly ash used in the concrete mixture
	Coarse aggregate	CA	kg/m3	The mass of coarse aggregate used in the mixture
	Fine aggregate	FA	kg/m3	The mass of fine aggregate used in the mixture
	Water	W	kg/m3	The volume of water used in the concrete mix
	Superplasticizer	S	kg/m3	The volume of superplasticizer added to the mixture
	Fiber diameter	FD	mm	The diameter of the fiber reinforcement in the concrete
	Fiber length	FL	mm	The length of the fiber used in the concrete
	Fiber volume fraction	FF	%	The volume percentage of fibers in the concrete
Targets	Compressive strength	CS	MPa	The compressive strength of the concrete specimen at 28 days
	Flexural strength	FS	MPa	The flexural strength of the concrete specimen at 28 days
	Splitting tensile strength	STS	MPa	The tensile strength of the concrete specimen at 28 days

The input variables are a list of mix design parameters, such as cement content, water content, aggregate type, and fiber characteristics, i.e., diameter and volume fraction. The three response variables—CS, FS, and splitting TS—are the key mechanical properties that were estimated in the current study through ML models.

4.2. Methodology

4.2.1. Proposed Method

In this study, the method followed in this research was the development of a regression model, in order to predict mechanical properties of mixtures of concrete such as FS, CS, and TS. The process includes many steps, starting from the development and evaluation of several machine-learning-based regression models to the selection of the best-performing model. This model is then applied to make predictions of strength characteristics for newly generated concrete mixtures created by using the SMOTE [38–40]. In this way, a bigger and more diverse dataset could be explored. Lastly, the identification of the most optimal concrete mix designs is realized according to their predicted mechanical properties and based on compliance with the predefined performance constraints. Figure 1 schematically illustrates the overall process, showing the main steps in the optimization of mix designs of concrete.

[figure(s) omitted; refer to PDF]

4.2.1.1. Step 1: Building a Regression Model

Different ML models [41] were used in this paper to predict the mechanical properties of mixture concrete, including linear regression, random forest, XGBoost, KNN, and SVM, and ANN. Each of these models was trained on a data set with key mix design parameters, including cement, fly ash, silica fume, coarse aggregate, fine aggregate, water, and fiber properties such as diameter, length, and volume fraction. To further improve the predictive performance on target variables including FS, CS, and TS, hyperparameter tuning optimization was performed on the models.

⁃ Linear regression models [42] the relationship between a dependent variable and one or more independent variables by fitting a linear equation to observed data. The general equation for a linear regression model is$$\begin{array}{}\text{(1)}& y={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+\cdots +{\beta }_n{x}_n+ϵ,\end{array}$$

  where $y$ is the predicted variable, ${\beta }_0$ is the intercept, ${\beta }_1,\dots ,{\beta }_n$ are the coefficients, and $ϵ$ represents the error term.

⁃ Random forest [43, 44] is an ensemble learning method that constructs multiple decision trees during training and aggregates their predictions. The formula for random forest regression is$$\begin{array}{}\text{(2)}& fX=\frac{1}{n_{\text{trees}}}{\displaystyle \sum }_{i=1}^{n_{\text{trec}}} T_{i}X,\end{array}$$

  where $T_{i}X$ is the prediction from the ith decision tree. Hyperparameters tuned include the number of trees ($n$_estimators) and the maximum depth of trees (max_depth).

⁃ XGBoost [45] is a gradient boosting algorithm that builds an ensemble of weak learners sequentially to minimize a loss function. The model is updated iteratively through the loss function:$$\begin{array}{}\text{(3)}& L\theta ={\displaystyle \sum }_{i=1}^n \mathcal{l}{y}_{i,}f{x}_i+{\displaystyle \sum }_k \mathrm{\Omega }{f}_k,\end{array}$$

  where $\mathcal{l}$ is the loss function (e.g., mean squared error), and $\mathrm{\Omega }$ is the regularization term to prevent overfitting. Hyperparameter tuning for XGBoost includes the learning rate (learning_rate), number of estimators ($n$_estimators), and maximum depth (max_depth).

⁃ KNN [46] is a nonparametric method where the output is the average of the nearest $k$ training samples. The formula for regression is$$\begin{array}{}\text{(4)}& fx=\frac{1}{k}{\displaystyle \sum }_{i=1}^k y_i,\end{array}$$

  where $y_i$ represents the values of the $k$-nearest neighbors. The main hyperparameters tuned are the number of neighbors ($n$_neighbors) and the weighting function (weights).

⁃ SVM [47] is a supervised learning algorithm that seeks to find a hyperplane in feature space that minimizes error. The equation for SVM regression is$$\begin{array}{}\text{(5)}& yx=w^T\varphi x+b,\end{array}$$

  where $w$ is the weight vector, $\varphi x$ is the kernel function, and $b$ is the bias term. Important hyperparameters include the regularization parameter (C) and kernel type (kernel).

⁃ ANN [12, 48]s consist of multiple layers of neurons that learn complex relationships between inputs and outputs. The equation for each layer in an ANN is$$\begin{array}{}\text{(6)}& y=\sigma WX+b,\end{array}$$

  where $W$ is the weight matrix, $X$ is the input, $b$ is the bias vector, and $\sigma$ is the activation function. Hyperparameters such as the number of hidden layers, the number of neurons in each layer, the activation function (activation), and the optimizer were tuned.

4.2.1.2. Hyperparameter Tuning Method

We examined several optimization techniques for tuning hyperparameters [49–51], including Grid Search and Random Search. However, after evaluating the performance of these methods, we found that Bayesian Optimization provided the best results [52]. Unlike traditional grid or random search methods, Bayesian Optimization builds a probabilistic model of the objective function and uses it to efficiently explore the hyperparameter space, selecting the most promising values with fewer iterations. This allowed for more effective hyperparameter tuning, especially for complex models like XGBoost and ANN. Bayesian Optimization optimizes the hyperparameters by maximizing the acquisition function, which is given as:$$\begin{array}{}\text{(7)}& \underset{x}{\mathrm{argmax}}\alpha x\mid D_{1:t},\end{array}$$where $\alpha$ is the acquisition function and $D_{1:t}$ is the dataset evaluated up to time $t$. This method allowed for more efficient exploration and faster convergence to the optimal hyperparameters.After applying Bayesian Optimization, the optimal hyperparameters for each model are presented in Table 3.

Table 3

Optimized hyperparameters for machine learning models.

Model	Hyperparameters (after optimization)
Linear regression	None (default)
Random forest	$n$_estimators: 150, max_depth: 12
XGBoost	$n$_estimators: 120, learning_rate: 0.05, max_depth: 8
K-nearest neighbors	$n$_neighbors: 7, weights: ‘distance’
Support vector machine	C: 0.8, kernel: ‘rbf’
Artificial neural network	hidden_layers: (128, 64), activation: ‘relu’, optimizer: ‘adam’, learning_rate: 0.001

These optimized hyperparameters were used in the final model training to predict the mechanical properties of the concrete mixtures. Bayesian Optimization significantly improved model performance by reducing the need for exhaustive searches, particularly for models with many hyperparameters.

4.2.1.3. Step 2: Selection of the Best Performing Regression Model

Once the models were trained, their performance was evaluated using the $R^2$ score across the three target mechanical properties: FS, CS, and TS. The $R^2$ score, or the coefficient of determination, is a measure of how well the regression model explains the variance in the target variable. It is calculated as:$$\begin{array}{}\text{(8)}& R^2=1-\frac{{\sum }_{i=1}^n{y_i-{\widehat{y}}_i}^2}{{\sum }_{i=1}^n{y_i-\overline{y}}^2},\end{array}$$where $y_i$ represents the actual value of the target variable, ${\widehat{y}}_i$ is the predicted value of the target variable, $\overline{y}$ is the mean of the actual target values, and $n$ refers to the total number of observations in the dataset.

The $R^2$ score ranges from 0 to 1, with a value closer to 1 indicating that the model explains a large portion of the variance in the data. Additionally, the MSE was used to evaluate the prediction error for each model. MSE is calculated as$$\begin{array}{}\text{(9)}& \text{MSE}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n {y_i-{\widehat{y}}_i}^2.\end{array}$$

The model that demonstrated the highest $R^2$ score and the lowest prediction error (MSE) was selected as the best-performing model. This model was then used for further analysis and prediction in subsequent steps, including the generation and evaluation of new concrete mix designs.

Besides the $R^2$ score and MSE, this study employs further metrics to ensure comprehensive evaluation of the predictive models’ accuracy and reliability, specifically Variance Accounted For (VAF), MAE, Performance Index (PI), and Relative Standard Error (RSR). These metrics provide additional insights into model accuracy and reliability:

1. VAF: This metric assesses the proportion of the variability in the observed data that is accounted for by the model predictions. It is computed using the following equation:$$\begin{array}{}\text{(10)}& \text{VAF}=1-\frac{\text{var}y-\widehat{y}}{\text{var}y}\times 100,\end{array}$$

  where $y$ represents observed values, and $\widehat{y}$ the predicted values.

2. MAE: MAE measures the average magnitude of the errors between predicted and actual values, disregarding their direction:$$\begin{array}{}\text{(11)}& \text{MAE}=\frac{1}{n}{\displaystyle \sum }_{i=1}^n y_i-{\widehat{y}}_i.\end{array}$$

3. PI: This dimensionless index evaluates the predictive performance based on normalized errors. It is calculated as follows:$$\begin{array}{}\text{(12)}& \text{PI}=\frac{\text{RMSE}}{\overline{y}},\end{array}$$

  where $\text{RMSE}$ is Root Mean Squared Error.

4. Ratio of Standard Deviation of Residuals (RSR): RSR standardizes residuals by comparing their standard deviation to the standard deviation of observed ($\text{STDE}{\mathrm{V}}_{\text{obs}}$) data:$$\begin{array}{}\text{(13)}& \text{RSR}=\frac{\text{RMSE}}{\text{STDE}{\mathrm{V}}_{\text{obs}}}.\end{array}$$

4.2.1.4. Step 3: Generating New Concrete Mix Designs Using SMOTE

Having chosen the best-performing regression model, the next operation was to use SMOTE in generating new concrete mix designs. SMOTE has been applied to create almost 1000 new concrete mix designs to enrich the dataset for exploring more diverse concrete compositions. It was important to define the range of each Mix Design variable (minimum and maximum values) before using SMOTE so that the data points generated were within realistic and feasible limits. These are presented in Table 4. SMOTE works by selecting one point from the minority class and then interpolating between this selected point and one of its nearest neighbors to create synthetic samples. In mathematical terms, the process is defined as [53]:$$\begin{array}{}\text{(14)}& x_{\text{new}}=x_i+\lambda \mathrm{·}{x}_{\text{NN}}-x_i,\end{array}$$where $x_i$ is the minority class data point, $x_{\text{NN}}$ is a randomly chosen nearest neighbor, and $\lambda \in 0,1$ is a random number. This process generates new synthetic data within the defined ranges.

Table 4

Ranges for generating new concrete mix designs.

Variable	Minimum value	Maximum value
Cement $\text{kg}/{\mathrm{m}}^3$	78.83	613.38
Fly ash $\text{kg}/{\mathrm{m}}^3$	0.0	168.0
Silica fume $\text{kg}/{\mathrm{m}}^3$	0.0	126.0
Coarse aggregate $\text{kg}/{\mathrm{m}}^3$	174.09	1540.0
Fine aggregate $\text{kg}/{\mathrm{m}}^3$	109.86	1193.6
Water $\text{kg}/{\mathrm{m}}^3$	32.46	301.0
Superplasticizer $\text{kg}/{\mathrm{m}}^3$	0.0	8.36
Fiber diameter $\text{mm}$	0.002	0.030
Fiber length $\text{mm}$	6.6	30.0
Fiber volume fraction $\%$	0.05	0.60

These ranges were determined with the original dataset and reflect realistic ranges for the input features of concrete mix designs. The application of SMOTE meant that new data was generated under consistent real-world conditions, taking care of any potential class imbalance.

4.2.1.5. Step 5: Selecting the Top 10 Concrete Mix Designs

The final step in this approach was to choose the best 10 concrete mix designs based on the predicted mechanical properties. The selection was made through the application of predefined constraints related to the strength characteristics of the concrete mixtures. The target performance criteria related to the strength characteristics were as follows [9, 54–56] (Table 5).

Table 5

Target ranges for strength characteristics.

Property	Target range
Flexural strength (MPa)	3.0–6.0
Compressive strength (MPa)	4.0–7.0
Tensile strength (MPa)	4.0–6.5

The top 10 mix designs that best met these constraints were selected as the most optimal concrete mixtures for achieving the desired strength characteristics.

4.2.2. Statistical Evaluation of Feature Importance

Permutation importance [57–59] is a model-agnostic technique to assess the importance of each feature for the concrete mixture strength prediction. It measures how much the prediction error increases when the values of one particular feature are randomly shuffled, therefore breaking the relationship between that feature and the target variable. The method helps quantify how much each feature contributes to model performance. Features causing a significant increase in error after shuffling are considered more important. This approach was applied to identify the critical features affecting the predictions of FS, CS, and TS. Mathematically, the importance of a feature $X_j$ is the difference between the error with shuffled values and the baseline error:$$\begin{array}{}\text{(15)}& I{X}_j=E_j-E_{\text{lasteline}},\end{array}$$where $E_j$ is the error after shuffling the feature and $E_{\text{baseline}}$ is the original model error.

Analysis of Variance (ANOVA) [60] was used to assess the statistical significance of each feature in predicting mechanical properties. It evaluates the contribution of each feature by comparing the variance between different groups of the feature values. ANOVA calculates an $F$ value, representing the ratio of variance between groups to variance within groups [61–63]. Features with higher $F$ values are more important for prediction. The $p$ value is then used to determine statistical significance, with features having p values below 0.05 considered significant in predicting the target. For ANOVA, the $F$-statistic is calculated as [64, 65]:$$\begin{array}{}\text{(16)}& F=\frac{\text{SSB}/g-1}{\text{SSW}/n-g},\end{array}$$where SSB and SSW represent between-group and within-group variances.

This study combined ANOVA and Permutation Importance in order to find the most important input variables for the strength characteristics of concrete mixtures, showing much better insight into which features have an important influence on the prediction models.

5. Results and Discussion

5.1. Exploratory Data Analysis (EDA)

In this section, we report the results of the distribution analyses of various concrete mixtures with regard to their cement content, aggregate properties, and strength characteristics: CS, FS, and TS. The following histograms show the frequency distributions of the main variables in each dataset.

5.1.1. Cement Content Distribution

Distribution of cement content in all datasets has the same trend, with a significant peak centered at approximately 400 kg/m³. In the CS dataset, the distribution (Figure 2) indicates that most samples contain a cement content between 300 and 500 kg/m³, with clear concentration near 400 kg/m³. This postulates that cement is very vital in the compressive strength properties of the concrete. Similarly, on the FS dataset (Figure 3) and TS dataset (Figure 4), the cement content distribution shows a similar pattern to supplement the consistency of the usage of cement among different types of strength tests.

[figure(s) omitted; refer to PDF]

5.1.2. Coarse Aggregate Distribution

The coarse aggregate distribution in the CS dataset (Figure 5) shows a dominant range between 1000 and 1200 kg/m³, which is expected as coarse aggregate contributes significantly to the CS of concrete. The histogram suggests that concrete mixtures with higher CS tend to contain a larger amount of coarse aggregate, further validating the importance of this component in structural performance.

[figure(s) omitted; refer to PDF]

5.1.3. CS Distribution

The histogram of CS (Figure 6) reveals a well-defined peak around 40–50 MPa, with a gradual decline at both lower and higher strength values. This distribution is typical of concrete used in structural applications, where the majority of samples exhibit a CS within this range. The presence of a smaller subset of higher-strength samples (up to 70 MPa) indicates the use of optimized mixtures for specific applications requiring enhanced load-bearing capacity.

[figure(s) omitted; refer to PDF]

5.1.4. Fiber Diameter Distribution

In the TS dataset, the fiber diameter distribution (Figure 7) is heavily concentrated around 0.015 mm, reflecting the dominant use of fibers with this diameter. The use of small fibers enhances tensile properties by bridging microcracks and providing additional reinforcement to the concrete matrix, thus improving the TS of the material.

[figure(s) omitted; refer to PDF]

5.1.5. Fine Aggregate Distribution

The distribution of fine aggregate (Figure 8) in the FS dataset shows a sharp peak between 600 and 800 kg/m³. Fine aggregates contribute to the FS by providing a dense packing structure within the concrete. The concentration of fine aggregates in this range suggests that this is an optimal balance for improving flexural properties while maintaining workability.

[figure(s) omitted; refer to PDF]

5.1.6. FS Distribution

The FS distribution (Figure 9) exhibits a peak between 4 and 6 MPa, indicating that most of the tested concrete mixtures exhibit moderate bending resistance. The data also shows a smaller number of mixtures with higher FS values (up to 12 MPa), which may be the result of using specific fiber or aggregate modifications to enhance the bending performance of concrete.

[figure(s) omitted; refer to PDF]

5.1.7. Splitting TS Distribution

The histogram for splitting TS (Figure 10) shows a predominant range between 3 and 5 MPa, indicating that the majority of concrete samples have moderate TS. A few samples exhibit higher TS values, potentially due to the use of additional fibers or other reinforcement techniques aimed at enhancing tensile performance.

[figure(s) omitted; refer to PDF]

5.1.8. Strength Comparison Based on Cement Content

A further analysis was conducted to compare the median TS, CS, and FS as a function of cement content (Figure 11). The median CS exhibited a clear increase with cement content, reaching values as high as 60 MPa when the cement content exceeded 400 kg/m³. In contrast, both the TS and FS showed less pronounced increases, with values remaining below 10 MPa throughout. This observation highlights the dominant role of cement in enhancing CS compared to its effects on TS and FS.

[figure(s) omitted; refer to PDF]

5.1.9. Scatter Plot Comparison of Strength vs Cement Content

Finally, scatter plots (Figure 12) were generated to show the relationship between TS, CS, and FS against cement content. The TS vs cement plot shows a fairly uniform distribution, indicating no strong correlation between TS and cement content. In contrast, the CS vs cement plot shows a clear positive trend, with strength values increasing as cement content rises. The FS vs cement plot, similar to the TS plot, shows weaker correlations with cement content, although some higher strength values are observed for cement content around 400 kg/m³.

[figure(s) omitted; refer to PDF]

5.2. Comparison of Actual and Synthetic Strength Data

As observed in Figure 13, the box plot comparison of actual and synthetic strength data demonstrates that the synthetic dataset closely follows the distribution of the actual dataset across CS, FS, and TS. The medians and interquartile ranges remain consistent, indicating that the synthetic data generation process has effectively preserved the statistical properties of the original dataset. However, a slight increase in variability, particularly in CS, suggests that the synthetic data introduces additional dispersion, which may enhance model generalization. The presence of outliers in both datasets confirms that extreme values have been retained, ensuring the representation of real-world variability. These findings support the reliability of using synthetic data to augment ML model training while maintaining alignment with actual measurements.

[figure(s) omitted; refer to PDF]

As shown in Figure 14, the histogram compares the distribution of actual and synthetic TS values. The synthetic dataset closely follows the actual data distribution, maintaining a similar mean and standard deviation. However, slight deviations in lower values indicate minor inconsistencies introduced during synthetic data generation. These results suggest that while synthetic data effectively preserves the statistical properties of actual measurements, further refinements could enhance its accuracy and prevent unrealistic values.

[figure(s) omitted; refer to PDF]

5.3. Model Evaluation and Selecting

The performance of several machine-learning models was assessed in the prediction of the FS, CS, and TS of the concrete mixtures using the $R^2$ score as the metric of evaluation. The models in consideration were KNN, XGBoost, random forest, linear regression, ANN, and SVM. The results of such evaluations are given in Table 6.

Table 6

Performance metrics for each machine learning model ($R^2$ scores).

Model	Flexural strength ($R^2$)		Compressive strength ($R^2$)		Tensile strength ($R^2$)
	Test	Train	Test	Train	Test	Train
K-nearest neighbors (KNN)	0.8737	0.9204	0.7322	0.7698	0.4437	0.4881
XGBoost	0.8182	0.8501	0.8963	0.9124	0.8970	0.9225
Random forest	0.8001	0.8216	0.8826	0.8998	0.9420	0.9613
Linear regression	0.4824	0.5123	0.1071	0.1284	0.2150	0.2407
Artificial neural networks (ANN)	0.3019	0.3467	0.2311	0.2599	0.2816	0.3128
Support vector machine (SVM)	0.0009	0.0021	0.0100	0.0153	0.1736	0.1924

From the results obtained, it was rather obvious that different models performed best in predicting different strength characteristics. The KNN model had the best $R^2$ value in predicting FS, with an $R^2$ score of 0.8737. Hence, among the models tested, KNN is the most suitable for predicting FS. For the prediction of CS, the XGBoost model gave the best result, with an $R^2$ score of 0.8963, meaning that this model is the most accurate in predicting the CS. On the other hand, random forest did the best in predicting TS with the highest $R^2$ score of 0.9420. In contrast, models such as linear regression, ANN, and SVM showed weaker performances for all the strength characteristics. Especially, the SVM had the lowest predictive power overall, with poor $R^2$scores across the board.

The inclusion of Train $R^2$ values in Table 5 confirms that no significant overfitting is present across the evaluated models. The Train $R^2$ values remain close to their respective Test $R^2$ values, demonstrating that the models effectively generalize without excessive reliance on training data. XGBoost and random forest models show the highest predictive performance, with both Train and Test $R^2$ values consistently high across all strength properties. Lower-performing models, such as linear regression and SVM, exhibit weaker predictive capabilities rather than signs of overfitting. These results indicate that the models adequately capture the underlying patterns in the data while maintaining robust generalization.

The additional performance metrics (Table 7) provide a comprehensive assessment of model accuracy beyond $R^2$ and MSE. VAF measures the proportion of variance explained, while MAE quantifies prediction deviations. The PI evaluates predictive efficiency, and RSR standardizes residual errors for comparison. Table 1 highlights these metrics across models, where higher VAF and lower MAE, PI, and RSR indicate superior predictive performance, reinforcing the reliability of ML models in forecasting the mechanical properties of BFRC.

Table 7

Comprehensive results for additional performance metrics.

Model	Flexural				Compressive				Tensile
	VAF (%)	MAE	PI	RSR	VAF (%)	MAE	PI	RSR	VAF (%)	MAE	PI	RSR
K-nearest neighbors	87.37	0.15	0.07	0.36	73.22	0.27	0.18	0.51	44.37	0.55	0.35	0.74
XGBoost	81.82	0.2	0.1	0.42	89.63	0.12	0.06	0.32	89.7	0.14	0.07	0.32
Random forest	80.01	0.22	0.11	0.45	88.26	0.14	0.07	0.34	94.2	0.1	0.05	0.24
Linear regression	48.24	0.5	0.25	0.72	10.71	0.85	0.65	0.94	21.5	0.6	0.42	0.89
Artificial neural networks	30.2	0.65	0.32	0.84	23.11	0.75	0.58	0.88	28.16	0.7	0.5	0.85
Support vector machine	0.09	0.8	0.45	0.99	1	0.95	0.7	0.99	17.36	0.78	0.68	0.91

From these results, the models that are going to be used in predicting strength characteristics of the synthetic concrete mix designs will include KNN for FS, XGBoost for CS, and the random forest model for TS. These models are selected because of their superior performance in predicting respective mechanical properties and will be applied to the synthetic data generated in this study to evaluate 1000 new concrete mix designs.

5.4. Optimization of Concrete Mix Designs

The analysis of the top 10 optimized concrete mixture designs, as presented in Table 8, demonstrates the predicted mechanical properties (FS, CS, and TS) for each mixture. These concrete mixtures were generated based on the application of the best-performing ML models and represent a diverse range of compositions that were identified as optimal based on predefined performance criteria.

Table 8

Optimized concrete mixtures and corresponding predicted strengths.

Group	Cement (kg/mÂ3)	Fly ash (kg/mÂ3)	Silica fume (kg/mÂ3)	Coarse aggregate (kg/mÂ3)	Fine aggregate (kg/mÂ3)	Water (kg/mÂ3)	Water reducer (kg/mÂ3)	Fiber diameter (mm)	Fiber length (mm)	Fiber content (%)	Predicted flexural strength (MPa)	Predicted compressive strength (MPa)	Predicted tensile strength (MPa)
97	393.96	101.01	43.60	1062.87	492.72	260.17	7.43	0.02	22.66	0.06	5.84	5.35	5.16
90	542.76	10.49	96.11	905.93	351.03	184.06	4.53	0.02	17.01	0.17	5.66	5.28	4.73
80	307.45	125.44	2.78	1210.69	527.74	278.66	5.47	0.02	10.48	0.05	5.47	5.79	4.51
194	261.18	124.23	109.14	764.29	396.54	168.28	0.45	0.03	25.38	0.53	5.44	4.11	4.09
204	388.54	144.39	57.82	752.71	111.59	296.72	7.92	0.02	11.74	0.57	5.44	4.17	4.13
103	578.62	44.78	43.83	691.70	252.27	127.46	6.45	0.03	18.56	0.38	5.40	5.07	4.72
7	114.80	131.65	64.19	1534.21	605.96	165.28	0.61	0.02	7.43	0.56	4.82	4.96	4.99
9	227.85	43.95	101.00	1450.05	303.34	221.34	0.94	0.02	14.67	0.06	4.82	4.61	4.72
17	509.41	110.18	84.03	1524.84	427.13	82.21	8.27	0.02	10.79	0.34	4.82	6.45	5.58
135	207.13	74.54	34.83	657.83	396.40	280.16	6.04	0.03	18.19	0.45	4.30	5.00	4.60

From Table 8, we observe that the FS values range between 4.304 MPa and 5.842 MPa, the CS values vary from 4.109 MPa to 6.445 MPa, and the TS values range from 4.086 MPa to 5.577 MPa. Notably, Mixture 97 demonstrates the highest predicted FS of 5.842 MPa, while Mixture 17 has the highest predicted CS at 6.445 MPa. Mixture 97 also achieves the second-highest TS of 5.163 MPa.

The outcomes demonstrate that the chosen concrete mixture designs provide a balanced array of mechanical properties, with each mixture exhibiting superior performance in specific strength parameters. Specifically, Mixture 97 exhibits superior performance across all three mechanical properties, which demonstrates that it is one of the most balanced and potentially strong designs.

Lastly, the optimal 10 concrete mixtures are excellent designs that comply with the required mechanical properties. The designs will be explored in depth and tested in practice to confirm their performances as applied in the real world. Detailed information on each of the optimized concrete mixtures’ composition and expected performance is shown in Table 8.

5.5. Statistical Evaluation of Feature Importance

Figures 15 and 16 present the permutation importance of various features in predicting TS using the random forest model and FS using the KNN model. Permutation importance quantifies the contribution of each feature to the predictive model, with higher values indicating greater importance.

[figure(s) omitted; refer to PDF]

The permutation importance results for predicting TS with the random forest model, as depicted in Figure 15, highlight that fine aggregate (kg/m³) is the most influential feature. This suggests that fine aggregate plays a crucial role in determining the TS of the concrete mixtures. In addition to fine aggregate, fiber diameter (mm) and cement (kg/m³) also contribute significantly, though their relative importance is lower. Conversely, features such as fiber content (%) and fiber length (mm) exhibit minimal contribution to TS predictions, as indicated by their low permutation importance scores. These findings align with the hypothesis that aggregates and cement are key to enhancing TS, but they also challenge the assumption that fiber properties (content and length) significantly affect TS in these mixture designs.

The permutation importance results for predicting FS using the KNN model, shown in Figure 16, demonstrate that coarse aggregate (kg/m³) is the most dominant feature, suggesting that coarse aggregate plays the most critical role in influencing the FS of the concrete mixtures. While cement (kg/m³) and fine aggregate (kg/m³) also contribute to the FS, their impact is considerably lower than that of coarse aggregate. Additionally, the features such as fly ash (kg/m³) and fiber content (%) have very low importance in the prediction of FS, considering their values for permutation importance are low. These results confirm the hypothesis that coarse aggregate is crucial in maximizing FS, and fly ash, as well as fiber content, may not significantly affect the mechanical properties of such concrete mixtures.

In summary, the results from permutation importance confirm that aggregates and cement are the top-ranked predictors for both TS and FS, which supports the hypothesis that aggregate and cement functionalities play an important role in optimizing mechanical properties. However, reduced contributions from fiber-related features, more so for TS predictions, may indicate their role is not as critical as normally expected, and further research in how fibers can be best utilized within concrete mixture designs needs to be performed.

An ANOVA was performed to test the significance of important input variables on the predicted FS, CS, and TS. The results show the relative importance of different components of concrete mixes and their influence on the predicted strength characteristics.

The ANOVA results for the CS predicted by the XGBoost model (Table 9) indicate that cement ($F$ value = 4.018592, $p$ value = 0.000054) is the most significant factor influencing CS. Other features that have a considerable impact include fiber diameter ($F$ value = 2.922600, $p$ value = 0.010012) and water reducer ($F$ value = 2.046338, $p$ value = 0.016591). These variables play a critical role in enhancing the CS of concrete mixtures. In contrast, fly ash and fiber content have less influence on the CS, as indicated by their higher p values, suggesting a lack of statistical significance.

Table 9

ANOVA results for XGBoost model (compressive strength).

Feature	F value	$p$ value
Cement (kg/m3)	4.018592	0.000054
Fly ash (kg/m3)	1.071815	0.437785
Silica fume (kg/m3)	1.354820	0.181531
Coarse aggregate (kg/m3)	1.123781	0.373735
Fine aggregate (kg/m3)	1.489479	0.114788
Water (kg/m3)	1.317698	0.205365
Water reducer (kg/m3)	2.046338	0.016591
Fiber diameter (mm)	2.922600	0.010012
Fiber length (mm)	0.896458	0.673069
Fiber content (%)	0.887638	0.685342

For TS, predicted using the random forest model, fly ash ($F$ value = 2.521953, $p$ value = 0.000207) and fiber length ($F$ value = 2.436031, $p$ value = 0.000325) emerged as the most important variables (Table 10). These features significantly influence the TS of concrete mixtures. In contrast, cement ($F$ value = 1.227106, $p$ value = 0.209884) and fiber content (F value = 1.081627, $p$ value = 0.387633) exhibit less importance, as evidenced by their higher $p$ values.

Table 10

ANOVA results for random forest model (tensile strength).

Feature	F value	$p$ value
Cement (kg/m3)	1.227106	0.209884
Fly ash (kg/m3)	2.521953	0.000207
Silica fume (kg/m3)	0.887866	0.710992
Coarse aggregate (kg/m3)	1.413156	0.084671
Fine aggregate (kg/m3)	1.859711	0.007553
Water (kg/m3)	0.832931	0.798428
Water reducer (kg/m3)	0.677204	0.960933
Fiber diameter (mm)	1.232025	0.205216
Fiber length (mm)	2.436031	0.000325
Fiber content (%)	1.081627	0.387633

The ANOVA results for FS, predicted using the KNN model, reveal that fly ash ($F$ value = 2.256495, $p$ value = 0.001697) and fiber length ($F$ value = 1.902970, $p$ value = 0.009416) are the most significant predictors of FS (Table 11). Cement shows some contribution but with a nonsignificant $p$ value of 0.255713. Other features such as fine aggregate and silica fume exhibit minimal impact on FS based on their higher $p$ values.

Table 11

ANOVA results for K-nearest neighbors model (flexural strength).

Feature	F value	$p$ value
Cement (kg/m3)	1.197903	0.255713
Fly ash (kg/m3)	2.256495	0.001697
Silica fume (kg/m3)	0.946308	0.606838
Coarse aggregate (kg/m3)	1.390248	0.111297
Fine aggregate (kg/m3)	0.512986	0.998006
Water (kg/m3)	1.034289	0.466554
Water reducer (kg/m3)	1.123464	0.341430
Fiber diameter (mm)	0.540137	0.995966
Fiber length (mm)	1.902970	0.009416
Fiber content (%)	1.332286	0.144469

To enhance the statistical rigor of the ANOVA analysis, $F$-critical values have been incorporated alongside $F$-statistics to provide a clearer interpretation of feature significance. The comparison between $F$ values and the $F$-critical value (3.9361 at $\alpha$ = 0.05) establishes a robust criterion for determining statistical relevance. This comparison enhances the reliability of the ANOVA results by establishing a clear decision criterion for hypothesis testing. Features with $F$ values exceeding the $F$-critical threshold are statistically significant, indicating a strong influence on the target variable, while those below the threshold suggest a weaker or negligible impact.

As observed from Tables 8, 9, and 10, cement demonstrates a strong impact on CS, while fly ash and fiber length show moderate significance in predicting TS and FS, respectively. Other features, such as silica fume, coarse aggregate, fine aggregate, and fiber content, exhibit weaker influences, as their F values fall below the critical threshold. These findings highlight the key mix design parameters that play a dominant role in optimizing the mechanical properties of BFRC.

In conclusion, the ANOVA analysis highlights the significant features for each strength characteristic. Cement and fiber diameter are the most critical predictors of CS, while fly ash and fiber length have the most influence on both TS and FS. Understanding these relationships will help optimize concrete mixture designs by focusing on the most impactful variables.

5.6. Study Limitations

While this research demonstrates the potential of ML in predicting and optimizing the mechanical properties of BFRC, several limitations could affect the generalizability of the findings.

1. The study relied on a dataset with a limited number of BFRC samples, primarily based on laboratory-generated data. Although the SMOTE expanded the dataset, synthetic data may not capture all real-world variabilities. The relatively narrow range of environmental and geographic conditions represented limits the model’s applicability to broader contexts, such as varying climates and regional material compositions.

2. Basalt fibers were considered in terms of general properties like length, diameter, and volume fraction; however, the study did not account for other characteristics such as fiber surface treatment or chemical composition, which can influence bonding within the concrete matrix. Differences in fiber quality and manufacturing processes could lead to variability in mechanical performance that the model may not predict accurately.

3. The mechanical properties investigated—FS, CS, and TS—were based on short-term performance measurements. The model does not include long-term durability issues such as shrinkage, creep, or degradation under extreme conditions—important considerations for establishing the actual field applicability of BFRC in construction.

These limitations point out that while ML approaches may greatly enhance BFRC optimization, the path ahead must be to expand the dataset with real samples, explore additional fiber characteristics, and incorporate long-term performance data. Addressing these limitations will scale up the resistance and usability of ML models for BFRC and open doors for broader applications in sustainable construction.

6. Conclusion

This study explored the use of ML models in predicting the mechanical properties of BFRC, including FS, CS, and TS. Using the aid of several ML methods, such as KNN, XGBoost, and random forest, high-precision models were developed for the prediction of strength characteristics in BFRC. Notably, the KNN model achieved an $R^2$ score of 0.8737 for FS, XGBoost attained an $R^2$ of 0.8963 for CS, and random forest reached an $R^2$ of 0.9420 for TS. All the target properties show high predictive accuracy from the models, hence justifying the application of ML in the optimization of concrete composition. In addition, the application of SMOTE created 1000 synthetic samples, which definitely made the dataset richer and did wonders in enhancing the model’s robustness. The best 10 optimized designs of concrete mix found in this study have FS between 4.3 and 5.8 MPa, CS from 4.1 to 6.4 MPa, and TS between 4.1 and 5.6 MPa, showing practical effectiveness in the prediction of the ML models for meeting the performance criteria.

The novelty of this research can be reflected in the novel use of basalt fibers in enhancing the mechanical performance and sustainability of concrete. This study, by advancing the applicability of ML models, overcomes the limitations of traditional empirical methods; hence it provisions a flexible framework adaptable to a wide variety of BFRC compositions. The approach supports sustainable construction and further provides a data-driven pathway for optimizing concrete mix designs matching the structural performance needs.

Future research should investigate in more detail the interactions between the properties of basalt fibers, such as length, diameter, and volume fraction, with other components of the mix to enhance model precision. Further, expanding the dataset with real BFRC samples under different environmental conditions would also help improve the generalizability of the model. The use of hybrid ML models or deep learning approaches may, moreover, make further nuanced predictions and elucidate complex relationships governing the mechanical properties of BFRC. These avenues, when pursued, will further deepen the usefulness of ML in sustainable construction materials and advance the understanding of FRC’s performance in structural applications.

Funding

This work was funded in part by (INTI-IU-Malaysia) grant number (INTI-FEQS-01-06-20023).

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