Predicting flexural strength of sustainable basalt fiber-reinforced concrete using machine learning algorithms incorporating a graphical user interface

1.1. Significance of this research

The accurate prediction of FS may be hindered by issues with conventional empirical formula approaches, including the scarcity of experiments and the time-consuming nature of the procedure. This current study proposes a novel method to assess the compressive and FSs of BFRC, including different parameters, such as fly ash, fibers, and silica fume, using advanced ML models. This research also optimized Shapley additive explanations (SHAP) for model interpretability and developed a user-friendly graphical user interface (GUI) to benefit more applied in different domains. This study tackles the challenges of predicting FS by combining advanced ML. The novelty of this study lies in the integrated use of ensemble ML algorithms and a symbolic tree regression model and calculate the behavior of BFRC enhanced with fly ash, silica fume, and fiber using cutting-edge ML approaches. Ultimately, our study supports more sustainable and effective building methods by fortifying the basis for implementing explainable ML in civil engineering materials.

2.1. Data describes

In this research, BFRC concrete data parameters were gathered from previously published articles. In the study, a total of 245 data samples are utilized to forecast the FS of the BFRC concrete. These datasets were randomly separated into two parts: the training phase and the testing phase. 30% data points were designed for the testing stage, and 70% of the data variables were designated for the training stage. AI models are often trained with a certain degree of output information accuracy to assess their predictive performance. Testing is regarded as a second check of the models’ output prediction capabilities, utilizing various data sets. However, in this research, a total of ten inputs and one output were used to predict the FS of the BFRC concrete. The inputs parameters are cement (kg/m³), fly ash (kg/m³), silica fume (kg/m³), coarse aggregate (kg/m³), fine aggregate (kg/m³), water (kg/m³), water reducing agent (kg/m³), fiber diameter (mm), fiber length (mm), and fiber content (%). On the other hand, the output parameter is FS. The statistical information gathered regarding each data point has been explained in Table 1. As can be observed, most studies used specified input variables that varied at numerous levels and supplemental materials in different amounts, ranging from 5% to more. The descriptions of the collected input data for the training and testing phases have been shown in Table 1. Furthermore, it is well recognized that the proper distribution of the input variables is essential to the model’s success. The input variables are the primary input parameters that significantly affect the CS of concrete. As shown in Table 2, the count, mean, standard deviation, minimum, 25%, 50%, 75%, and maximum values are examples of input variables that provide information on the total number of data points.

Fig. 2 displays the correlation coefficient values between the input and output variables. The Seaborn heatmap approach, which depicts the matrix of coefficients between the input and output parameters, was used to create this relationship. It can be shown that different colours display the correlation value. The red colour shows positive correlation coefficient values, and the blue color indicates negative values. From the correlation analysis, the cement input variable has the highest positive influence on FS, with a +0.40 value. The second positive influence parameter is silica fume, which has a 0.36 positive value impact on the FS. It is also notable that positive value is represented by fly ash, water, and fiber length input parameters. Conversely, the fiber diameter input variable shows the highest negative correlation coefficient value, which is -0.34. In addition, the Fine aggregate and fiber content input variables also have a negative influence on the FS.

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Fig. 2.

The correlation coefficient relationship between input and output.

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2.2. DT algorithm

The most widely recognized ML algorithm is the DT, which is used to discover and classify regression issues and other types of problems (Nasir Amin et al., 2023). Additionally, this technique is notable for its simplicity in data preprocessing, representation, and interpretation, as well as its ability to handle data outliers. The DT techniques consist of three different nodes: root, internal, and leaf (Abushanab et al., 2023). Notably, the initial root node specifies the major property of the data, while internal and leaf nodes branch from it. The internal nodes indicate attribute tests, while the leaf nodes predict responses. On the other hand, leaf nodes have multiple decision-making branches and, therefore, can make any decision. Finally, the DT algorithm starts at the base and involves many branches, replicating the structure of a real tree (Ben Chaabene et al., 2020).

The input observation space R^N is iteratively divided into K different subspaces {R₁,..., R_k}, where aggregation takes place for observations with comparable objectives, in order to create the tree predictor. This is done by applying the RMSE for ML regression problems and the Gini Index for classification problems, respectively. To minimize the overfitting issues of the DT model, the tree is subsequently trimmed utilizing a lower-cost, comprehensive pruning technique (Segal, n.d.). The DT structure is described as follows in Eq. (1).

where R_K represents the k^th unique subspace, b_k indicates the estimation of the subspace of R_k, and finally $I_{\left(xϵR_k\right)}$ denotes the indicator function $(I_{\left(xϵR_k\right)}=1 \text{when} x\in R_K).$ The decision rule accurately predicts the final results of fresh or unseen actual observations that have input findings but may not contain target values (Karbassi et al., n.d.).

2.3. KNN

KNN is an extraordinary ML method that is well known for its ability to solve regression problems and classify big data (Najmoddin et al., 2024). The KNN models retain all of the data that is accessible and use similarity to classify new data points. In regression problems, KNN uses the average value of the K closest observations to forecast a simultaneous target variable, such as FS and CS (Cakiroglu et al., 2023b). The new data point’s KNN are found using the algorithm, then it uses their majority vote to determine the class label, and it depends on the KNN (Rahman et al., 2021). However, when there are a lot of features or dimensions in the data, KNN cannot perform accurately because it becomes more challenging to determine the distance between observations (Hastie et al., n.d.). Additionally, in the training stage, this makes KNN computationally efficient, but in prediction, it may be slow (Song et al., 2017). The architecture of the KNN model is described in Eq. (2), where N_K (x) consists of the neighborhood of data sample x, and $y_i$ and $x_i$ are the desired values in the neighborhood of the K nearest samples are,

2.4. Adaptive boosting regression (ABR)

The statistical classification meta-algorithm, recognized as AdaBoost, was established in 1997 by Yoav Freund and Robert Schapire (1997). It is an ensemble learning technique that enhances performance when combined with different kinds of other learning methods (Najmoddin et al., 2024). Accordingly, the boosting techniques are a consolidated learning framework that combines several weak learners to generate an effective model. The fundamental principle of AdaBoost is capable of weakening frequent learners in favor of those cases where prior classifiers misclassified the dataset. Therefore, compared to other ML algorithms, AdaBoost is less vulnerable to the overfitting issue and produces accurate prediction results (Zheng et al., 2023b). AdaBoost uses iterative training of multiple base learners utilizing reweighted bootstrap variables from the training data sets, for example, in order to learn the link between the response variable (Y) and the input parameters (X). Additionally, every subsequent base learner in the series, except the first iteration, is taught from the one before it by placing greater focus on occurrences that were mistakenly predicted. In the training phase, an example of n instances of Eq. (3), here ($x_i)$, and ($y_i)$ denotes the $i^{th}$ observation values, ($x_i)$ represents the vector of input parameters and ($y_i)$ indicates the predicted outcomes. To develop a single better model F(X), the AdaBoost algorithm iteratively trains multiple base learners $f_t$(X) given a training database of Z samples in Eq. (4),

where K represents the optimum base learners and $w_k$ signifies the k^th learner’s weight. For the initial iteration, the weight is equally divided across the weak learners, with a consistent weight of $\{w_{1 }i$ = $\frac{1}{Z}, \forall i$} (Shrestha and Solomatine, n.d.). Furthermore, the observations that were readjusted in the first iteration are then given a larger weight to reconsider the weighting technique. Eq. (5) is used for modifying the weight distribution per training step t, where $\beta$t $\in$ [0, 1] is the variable associated with the distribution upgrade in Eq. (6) and ${\overline{L}}_K$ denotes the average loss function in Eq. (7). The current investigation also employed a linear loss function to evaluate the base learner’s performance. The framework of AdB algorithms is as follows in Eq. (8),

2.5. RFR

According to Ehrman et al. (2007), RFR is the most used ML algorithm that utilizes many DTs to categorize or forecast the results of an accurate answer. RF learning techniques utilize bootstrap sampling to develop datasets of random samples to simulate each algorithm’s base tree, following the conventional RF formula. This means that every RF regression tree is evaluated on a subset of the actual observations, compared to being evaluated among the observations (Gupta and Sihag 2022). Subsequently, two predetermined user variables are needed for RF regression: all of the trees developed (k) and an input parameter (m) that must be assigned to a different node to generate a tree (“scma-breiman,” n.d.). The technique depends on the trial-and-error method, with the best split being used to choose the variables. In addition, the RFR technique generates RFs by gathering a set of random trees (RT) (Erdal and Karahanoğlu 2016). Notably, RF is a combination of the bagging learning and the random subspace algorithm, which utilizes DTs as its basis classifier (Gupta and Sihag 2022). This methodology can deal with continuous, categorical, and binary data, as well as missing values, making it appropriate for multi-directional data modeling. The architecture of the RFR algorithm is presented in Eq. (9), where ${\hat{m}}_i\left(x\right)$ represents the prediction of a single DT, and n is the total number of DTs (Feng et al., 2021),

2.6. SVR

Applying the training data points, the SVR method creates a data mapping by a kernel function and uses a hyperplane that optimally from the labeled classes as much as possible in order to reduce generalization error (Rahman et al., 2021). The hyperplane enhances the performance between the observed and estimated values; this hyperplane additionally exceeds a predetermined tolerance margin, represented by ε (Cakiroglu et al., 2023b). To estimate the best outcomes, the SVR algorithms develop highly dependable regression equations by integrating many kernel functions (Zheng et al., 2023a). The SVR model is assessed using the following Eq. (10),

where $\left(X_i\right)$ and $\left(W_i\right)$ present the input feature and optimum model weight n-dimensional vectors, and (b) denotes the bias function of the predicting algorithm equation ($f)$.

2.7. Hyperparameter optimization

Table 3 outlines the hyperparameter tuning process for five ML models: DTR, SVR, KNN, RFR, and ABR. For each model, the primary hyperparameters are listed along with their respective value ranges and the selected settings for FS prediction. Key parameters such as max_depth, learning_rate, and n_estimators play a crucial role in defining model complexity and learning effectiveness. The tuning process is essential for determining the optimal hyperparameter combinations to improve the overall predictive performance of each mode. The optimization was performed in Python using the scikit-learn framework with a standard computing setup (Intel i7, 16 GB RAM).

2.8. SHAP

SHAP is a novel method for investigating ML models that draws from the well-known Shapley value theory developed originally by mathematician Lloyd Shapley (Vega García and Aznarte, 2020). SHAP measures how every single variable contributes to the predicted result using a concept known as ‘force-directed’ (Wang et al., 2024). Additionally, SHAP values provide a precise knowledge of the degree to which an individual parameter influences the desired outcomes that rely on cooperative game theory. Based on the cooperative game theory, a positive SHAP number indicates a feature that influences the prediction effectively, whereas a negative value indicates a feature that influences the prediction unfavorably.(Abood et al., 2024). The variability from the estimated (average) values and the model’s estimate for a particular instance is the same as the total of the SHAP values for all characteristics (Asghar et al., 2023). Furthermore, SHAP is a widely used and effective model interpretability tool that improves the integrity and transparency of ML models (Zheng et al., 2023b),

In this Eq. (11), f(x) represents the initial frame of the method, and x is the real input variable. g(x′) denotes the model explained, and (xi′) is the simplified input, M is the total number of all parameter matrices, and $\left({\varphi }_o\right)$ indicates the predicted mean value of ML algorithms, finally, $\left({\varphi }_i\right)$ exhibit the SHAP value of the i-th variable in Eq. (12),

Where |n| is the optimum feature set, and |S| denotes the optimum amount of non-zero entries in the subset of S. Similarly, $f_x(S\cup \{i\left\}\right)$ indicates the forecasting algorithms when the features are involved in subset S.

2.9. Model performance indicators

For estimating the performance accuracy of ML models, distinct parameters are evaluated to estimate the BF FS and the exhibited reliability of these models. In the current study, four performance metrics are utilized to calculate the model’s quality: R², RMSE, MAE, and MAPE, and the experimental outcomes of the five models are compared as shown below in Eqs. (13,14,15, and 16),

Where n represents the optimum parameters records and $p_i$, $q_i$ denotes the observed and predicted values. Evaluation matrix $R^2$ value range from (-1, 1) shows a strong correlation between actual and observed values, indicating that the model more accurately captures the data’s variance (Sun et al., 2025a). In contrast, the lowest values found within both parameters, MAE and RMSE, and their ranges are zero to infinity, which means less error between better prediction and measurement values (Kashyap et al., 2024, Sun et al., 2025b). Furthermore, this current research implemented the Taylor diagram, and other predictive indicators can be developed in Python without requiring other toolboxes or compilers, allowing for relatively straightforward model comparison.

3.1. ML models FS prediction performance

In Fig. 3, the FS predicted results are shown employing ML models at both stages, with predicted accuracy based on the dataset. To verify their data adjustments, each of the actual and predicted datasets were combined. The bar below indicates the error of the actual and predicted resulting datasets of the FS. At both stages, it is evident that the SVR and RFR models were accuracy calibrated for the actual and predicted data points. It is also noteworthy that the error range was kept to a maximum from +1 MPa to -1MPa. The ABR, DT, and KNN models are moderately adjusted in predicted and actual data points in both phases, with an error range between +2 MPa and -2 MPa. Most notably, although the SVR and RFR models display a few error ranges over 2 MPa, overall, they perform well in predicting the FS on BFRC concrete. The SVR and RFR models have better performance than the DT, KNN, and ABR models because they capture the actual data points and have a lower error value.

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Fig. 3.

FS prediction performances of ML models for BFRC specimens.

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In Fig. 4, the performance of actual and real data points for FS during the training and testing stages is shown. Additionally, they draw attention to the linear fit’s error margins, which range from +15% to -15%. It is seen that for all models, the maximum datasets fall close to the linear fit line, and almost 90% of data points are adjusted within the error range between +10% and -10%. In addition, the ABR, DT, and KNN models show around 90% of data points within the error range. However, it is notable that the RFR and SVR models display above 95% data points adjusted into the error range from +10% to -10% for the training and testing stages of the prediction of BFRC concrete. Most importantly, the RFR and SVR models perform well compared to ABR, DT, and KNN models because every few data points are adjusted out of the error range between +10% and -10%. Overall, it is considered that although the RFR and SVR models are very close to the linear fit line, all models have good performance because a significant number are adjusted within the error range.

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Fig. 4.

Scatter plot displays the relationship between the predicted and actual outcomes of the ML models.

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In Fig. 5, the performance metrics for all ML models of predicted FS of the BFRC concrete are represented. The evaluation metrics include R², RMSE, MAE, and MAPE, computed for training and testing phases. All models exhibit an R² value above 0.90 and 0.85 at the training and testing stages, respectively. The RFR and SVR models’ R² values were found to be almost 0.9196 and 0.9164 during the testing phase, respectively. The R² values at the testing stage for DT, KNN, and ABR are 0.8845, 0.8958, and 0.8463, respectively. However, the RMSE value at the testing stage for SVR and RFR models shows 0.5853 and 0.5743, respectively, for the predicted BFRC concrete. The DT, KNN, and ABR models exhibit RMSE values of 0.6881, 0.6536, and 0.7941 at the testing phase, respectively. It is shown that the SVR and RFR models have good performance compared to other models. In addition, Fig. 4 shows that the SVR and RFR models have good performance with MAE values of 0.3872 and 0.4168, correspondingly, at the testing phases. In the training stage, the MAE value demonstrations are around 0.1661 and 0.2178 for the SVR and RFR models, respectively. Furthermore, it displays that the SVR and RFR models show a better MAPE value than the DT, KNN, and ABR models. Finally, it is notable that the SVR and RFR models show slightly better evaluation metric values compared to the DT, KNN, and ABR models at the training and testing stages of the BFRC concrete.

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Fig. 5.

Model performance evaluation for the radar diagram predicting FS.

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The Taylor diagram provides a more comprehensive explanation of the results by comparing all of the algorithm’s outcomes as shown in Fig. 6. More specifically, the Taylor diagram, which examines standard deviations in two dimensions (vertically and horizontally), is a powerful tool for illustrating which ML models perform best in both the training and validation stages. Furthermore, the position on the Taylor diagram that is nearest to the predicted results indicates that the implemented ML algorithms function is at their highest efficiency. The desired results of the ongoing computational study suggest that all pertinent advanced optimization models have demonstrated satisfactory performance during both the training and testing phases. According to the Taylor diagram (Fig. 6), ML approaches RFR and SVR indicate that the model aligns closely with the obtained data points, performing superior accuracy in both stages, with an R² of 0.980 during the training stage and an R² of 0.919 in the testing stage. Similarly, the DT, KNN, and regression models (R² = 0.953, R² = 0.960, and RMSE = 0.519, RMSE = 0.478) performed moderately in both phases compared to the ABR models. Ultimately, it was demonstrated that RFR and SVR models possess a greater ability to compute experimental data points and exhibit overall better performance.

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Fig. 6.

The correlation coefficient and standard deviation for models are displayed in a Taylor diagram.

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3.2. Sensitivity analysis with SHAP algorithms

Sensitivity analysis frequently explains how an estimate is produced by comparing a dataset’s inputs and outcomes. Therefore, the SHAP technique was employed in the previous study to explain the main reasons why certain of the input variables were effective in predicting the BFRC matrices’ output FS data. For a specific case, SHAP can also describe the distinct effects of each input feature on the outcome. It is important to note that parameters with higher absolute SHAP magnitudes are thought to have the most influence. The ML model SVR model determines the average SHAP magnitude of all input variables, which is used to show the parameter relevance in Fig. 7. The x-axis runs from left to right, and the SHAP values were arranged from smallest to largest. It is evident that the Cement (kg/m³) parameter, which is around 0.51, had the most significant impact on the FS enhancement. The silica fume and fine aggregate input parameters had a good influence on FS, and they were almost 0.35 and 0.33, respectively. Notably, the strong influence of cement and silica fume highlights their role in hydration reactions, improved pozzolanic activity, and crack resistance, which informs optimal mix design. From a sustainability perspective, identifying silica fume as a dominant contributor supports supplementary cementitious material use to reduce clinker content and carbon emissions. Cakiroglu et al. (2023a) demonstrated that cement and silica fume were the most influential parameters in predicting the splitting tensile strength of BFRC, while fiber geometry variables exhibited complex, nonlinear effects. Similarly, Najmoddin et al. (2024) found that cement and supplementary cementitious materials dominated the prediction of FS and CSs in hybrid-fiber concrete. These cross-study similarities validate the physical credibility of our model and highlight the capacity of SHAP to produce interpretable, mechanistically consistent explanations across datasets. In addition, the water, coarse aggregate, and fiber diameter input parameters moderately affected the output of BFRC concrete. However, the lowest input parameters found from SHAP analysis were water-reducing agent and fly ash parameters, whose values were around 0.09 and 0.08, respectively. Finally, it can be concluded that the most significant parameter that the FS of BFRC concrete predicted is cement.

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Fig. 7.

Model output depends on input parameters with mean SHAP values.

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The summary plot of SHAP impact values, whether positive or negative, between input variables and model outputs is shown in Fig. 8. The figure shows the SHAP values summary plot for global explanations on the prediction of the SVR model. Fig. 8 shows the results of the SHAP analysis of the input parameters that affect the output. Most importantly, the red hue indicates a large feature magnitude that corresponds to a higher SHAP value, whereas the blue color indicates a lower SHAP value. The description of Fig. 7 also showed that the input samples had a similar rank of contribution, as Fig. 8 explains. It is noteworthy that, as the SVR model explains, the growth of FS is significantly influenced by the effective cement. Additionally, the silica fume input variable and the Fine aggregate appeared as the second and third dominant samples, respectively. However, the water-reducing agent and fly ash input parameters represented the lowest positive and negative values.

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Fig. 8.

SHAP impact value summary plotted with model outputs.

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Fig. 9 illustrates how the input variables relate to one another and affect the FS of BFRC. Fig. 9 shows that up to 400 kg/m³, the impact pattern of cement with water is less prominent; after that, it appears to be growing until it reaches about 500 kg/m³. It shows that the fly ash interaction has a less impactful pattern with the coarse aggregate from 0 to 120 kg/m³; a higher impact pattern is then observed. Fig. 7, which depicts a prospective relationship between silica fume and fine aggregate, indicates that the correlation with fine aggregate gets stronger as silica fume values increase. In addition, the coarse aggregate with a water-reducing agent has a positive impact on the FC of BFRC between 800 kg/m³ and 1100 kg/m³, after which this negative pattern is noticed. According to findings from Fig. 8, from 500 kg/m³ to 700 kg/m³, positive influences on FS of BFRC, and after that, fine aggregate concentrations should be kept low, between 700 kg/m³ and 900 kg/m³ strength. Moreover, it is noticeable that using 125-175 kg/m³ to reduce water content with cement has a beneficial influence that decreases the FS, and from 175 kg/m³ to 225 kg/m³, to increase water content with cement has a beneficial influence. According to Fig. 8, the ideal water-reducing agent amount with coarse aggregate is between 2 kg/m³ and 8 kg/m³. It shows that the fiber length with cement between 5 kg/m³ and 20 kg/m³ has less impact on the FS of BFRC; after 20-30 kg/m³, it has the most significant beneficial impact. Finally, there are both negative and positive interactions seen in the fiber content and water-reducing agent parameters.

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Fig. 9.

SHAP dependence for FS of the BFRC.

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The present findings are consistent with recent advances in deep learning and hybrid optimization frameworks, which also emphasize the importance of model interpretability and parameter sensitivity in construction material prediction.

An intuitive Graphical User Interface (GUI) was established to link the differences between powerful ML algorithms and real-world structural design applications. Fig. 10 illustrates applying all of the input key mix design parameters, such as cement, fly ash, silica fume, coarse and fine aggregates, water, water-reducing agents, and fiber characteristics (diameter, length, and content). The application is powered by an RFR model, trained with optimized hyperparameters for accurate prediction of FS. The interface, developed using Python’s Tkinter package, provides an immediate prediction upon clicking the “Predict” button, eliminating the need for time-consuming laboratory tests or complex simulations. In the example shown, entering a specific mix composition results in a predicted FS of 7.91 MPa, demonstrating the tool’s capability to deliver rapid, cost-effective, and data-driven insights. Validation of the GUI against known experimental data demonstrated an average prediction deviation below 5%, confirming its reliability for preliminary design purposes. This implementation significantly enhances the practical usability of ML in concrete design, supporting more efficient and informed engineering decisions.

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Fig. 10.

GUI tool of the ML model and FS prediction.

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