Estimating punching performance in fiber-reinforced polymer concrete slabs utilizing machine learning and gradient-boosted regression techniques

ABSTRACT

The study explores the perforating shear performance of Fiber-Reinforced Polymer (FRP) concrete blocks using machine learning techniques like Gradient-Boosted Regression Trees (GBRT), k-nearest Neighbours (KNN), and Lasso Regression. It aims to predict the structural integrity of FRP blocks under shear conditions based on experimental data. The models were assessed using Coefficient of Determination (R²), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE). GBRT demonstrated superior performance during training with an R² of 0.9786, RMSE of 52.75, and MAE of 34.12, indicating strong predictive accuracy and minimal error. It outperformed KNN (R² = 0.92, RMSE = 83.91, MAE = 45.71) and Lasso Regression (R² = 0.71, RMSE = 162.45, MAE = 115.83). In validation, GBRT again excelled with an R² of 0.93, RMSE of 76.23, and MAE of 58.46, confirming its robustness in generalizing unseen data. KNN showed lower performance in validation (R² = 0.86), with increased error values, while Lasso lagged further behind (R² = 0.681, RMSE = 185.23, MAE = 138.34). GBRT consistently outperformed traditional regression methods, highlighting its potential for more accurate and reliable structural analysis in FRP concrete slabs.

Keywords:
Fiber-Reinforced Polymer; Gradient-Boosted Regression Trees; Structural Integrity; Machine Learning; Shear Performance

1. INTRODUCTION

The use of Fiber-Reinforced Polymer (FRP) in concrete construction has gained significant attention due to its superior mechanical properties, such as high strength-to-weight ratio, corrosion resistance, and long-term durability [¹,²,³]. FRP materials are increasingly being adopted as reinforcement in concrete slabs to improve their structural performance, particularly under punching shear forces, which occur when concentrated loads are applied to slabs without beams [⁴]. Punching shear is a critical failure mode in slab systems, as it can lead to sudden and catastrophic collapse [⁵]. Therefore, accurately predicting the punching performance of FRP slabs is vital for ensuring safe and durable infrastructure [⁶]. However, conventional analytical methods for predicting this performance often fall short due to the complexity of the interactions between FRP and concrete [⁷,⁸,⁹]. This has led to the exploration of data-driven approaches, such as machine learning models, for better predictive accuracy [¹⁰].

In recent years, machine learning (ML) has emerged as a powerful tool in civil engineering for solving complex predictive problems [¹¹]. By analyzing large datasets, ML models can capture non-linear relationships and provide more accurate predictions than traditional methods [¹²]. Specifically, Gradient-Boosted Regression Trees (GBRT), k-nearest Neighbours (KNN), and Lasso Regression are among the techniques that have shown promising results in predicting structural performance in various applications [¹³,¹⁴,¹⁵]. These models are capable of handling diverse inputs, such as material properties, geometric parameters, and loading conditions, making them ideal for analyzing the behaviour of FRP-reinforced concrete slabs [¹⁶,¹⁷,¹⁸]. This study aims to apply these machine-learning techniques to estimate the punching performance of FRP concrete slabs [¹⁹].

The motivation for using machine learning models in this context stems from their ability to learn from experimental data and make predictions without the need for explicit physical models [²⁰]. Traditional models for predicting punching shear resistance in concrete slabs often rely on empirical formulas derived from a limited set of parameters [²¹]. These formulas, while useful, may not completely account for the complex communications between FRP reinforcement and concrete, leading to conservative or inaccurate predictions [²²]. By contrast, machine learning models can process large datasets with many input variables and detect subtle patterns that might be missed by conventional approaches [²³]. This flexibility allows for more robust predictions of punching performance [²⁴].

One of the key challenges in applying machine learning to the problem of perforating shear in FRP blocks is the selection of appropriate features and the interpretation of the model’s output [²⁵]. Factors such as the slab’s thickness, reinforcement layout, material properties, and load conditions all play crucial roles in determining punching shear capacity [²⁶]. This study utilizes experimental data from previously tested slabs and incorporates a wide range of features to train the models [²⁷, ²⁸]. The performance of each machine learning model is evaluated based on its ability to predict the ratio of predicted-to-actual punching shear strength, with the best-performing model being identified through metrics such as the Coefficient of Determination (R²), Root Mean Square Error (RMSE), and Mean Absolute Error (MAE) [²⁹, ³⁰]. Fiber-Reinforced Polymers (FRP) enhance the durability and performance of concrete slabs by improving resistance to shear, cracking, and environmental degradation. This study aims to predict the shear performance of FRP slabs using machine learning techniques, specifically comparing GBRT, k-nearest Neighbours (KNN), and Lasso Regression. The objectives are to assess the models’ effectiveness in predicting FRP slab behavior and optimizing structural performance.

The three machine learning techniques applied in this study—GBRT, KNN, and Lasso Regression—are chosen for their distinct advantages [³¹]. GBRT, a powerful ensemble learning method, combines the predictions of multiple decision trees to reduce bias and variance, making it highly effective for complex regression tasks [³²]. KNN, a simpler method, relies on similarity-based predictions, where the output for a new data point is based on the closest observed data points [³³]. Lasso Regression, on the other hand, is a linear model that introduces regularization to prevent overfitting, making it suitable for datasets with many input features [³⁴, ³⁵]. By comparing these three methods, the study seeks to determine which is the most reliable for forecasting the perforating performance of FRP blocks [³⁶]. Punching shear refers to the failure mode in slabs where localized shear forces cause a concrete slab to fail by punching through the slab. Fiber-Reinforced Polymer (FRP) enhances slab strength by improving resistance to cracking, shear, and environmental degradation, offering better durability and structural integrity under load.

Ultimately, the goal of this study is to provide a robust and accurate predictive framework for engineers and practitioners involved in the design of FRP-reinforced concrete slabs [³⁷]. The findings of this study are expected to offer insights into the effectiveness of machine learning techniques in predicting structural performance, particularly in applications where traditional methods may not be sufficient [³⁸]. The results can help inform design decisions and improve safety margins for infrastructure projects that utilize FRP reinforcement [³⁹]. Additionally, the successful application of machine learning models to this problem opens the door for further research into other aspects of structural engineering, where data-driven approaches may offer significant improvements over existing methods [⁴⁰]. This study investigates the perforating shear performance of FRP existing slabs using machine learning models [⁴¹]. The aim is to predict the structural integrity of FRP blocks under shear conditions [⁴²]. The objectives include comparing the performance of GBRT, KNN, and Lasso Regression [⁴³]. This study utilizes machine learning models, including GBRT, KNN, and Lasso Regression, to forecast the punching trim performance of FRP concrete slabs.

Predicting the punching shear performance of FRP concrete slabs is challenging due to several factors. These include the complex behavior of FRP materials under various loading conditions, the non-linear interactions between FRP reinforcement and concrete, and the difficulty in accurately modeling material properties such as bond strength and fatigue resistance. Additionally, the limited availability of experimental data for diverse slab configurations and loading conditions further complicates the prediction process. Machine learning (ML) models can help address these challenges by leveraging available data to identify patterns and make more accurate predictions, but they still require careful selection of features and hyperparameters for optimal performance. These models analyze experimental data to estimate the structural integrity of FRP slabs under various loading conditions. The primary aim of this study is to predict the punching shear performance of FRP existing slabs using machine learning (ML) techniques. By combining advanced ML models such as GBR, KNN, and Lasso Regression, the study aims to enhance the accuracy of structural performance predictions, providing valuable insights for optimized design and safety assessments in manufacturing submissions.

2. MATERIALS AND METHODS

2.1. Data gathering

The dataset used in this learning consists of key material properties and structural features, such as concrete composition, fibre content, slab dimensions, and load conditions [³¹]. The dataset was gathered from previously published studies, experimental results, and industry reports. The dataset was pre-processed to handle missing values, and all input features were standardized to ensure uniformity across the models [²⁵]. The dataset included parameters like: Compressive Strength (MPa), Fiber Volume Percentage (%), Slab Thickness (mm), Reinforcement Ratio, and, Shear Span to Depth Ratio [³⁶].

2.2. Feature selection

Feature selection was performed to eliminate irrelevant and redundant attributes, focusing only on the features most correlated with shear strength [³¹]. Techniques like Pearson correlation and Recursive Feature Elimination (RFE) were used to enhance model performance [²⁹, ³⁰].

2.3. Machine learning representations

Three machine learning representations were employed for forecasting the shave asset of concrete blocks: Gradient Boosted Regression Trees (GBRT), K-Nearest Neighbors (KNN), and Lasso Regression [²⁵]. The performance of each model was evaluated using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Coefficient of Determination (R²).

3. MODEL EQUATIONS AND METHODOLOGIES

GBRT, KNN, and Lasso were selected for their proven effectiveness in regression tasks and structural analysis. GBRT excels in capturing complex relationships, KNN is simple and interpretable, while Lasso aids in feature selection. These models balance accuracy, interpretability, and computational efficiency for predicting FRP slab performance.

3.1. Gradient boosted regression trees (GBRT)

GBRT is an ensemble learning method that builds a series of decision trees sequentially, where each tree corrects the errors of its predecessor [¹⁶,¹⁷,¹⁸]. The model minimizes a loss function through gradient descent and is highly efficient for regression tasks like predicting shear strength. The predicted value y^i for a sample i is computed as:

$${\widehat{Y}}_l={\displaystyle {\sum }_{m=1}^M\eta }\cdot hm(xi)$$ (1)

Where M is the number of trees, η is the learning rate, hm(xi) is the prediction of the m-th tree for input xi and the loss function is typically the Mean Squared Error (MSE):

$$L\left(yi,{\widehat{Y}}_l\right)=\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{\left(yi,{\widehat{Y}}_l\right)}^2}$$ (2)

3.2. K-Nearest neighbours (KNN)

KNN is a non-parametric method that makes predictions based on the immediacy of a test point to its nearest neighbours in the working out set [⁷,⁸,⁹]. The prediction is the average of the k nearest neighbours [⁴⁴]. For a given data point xi, the predicted value y^i is calculated as:

$${\widehat{Y}}_l=\frac{1}{k}{\displaystyle {\sum }_{j=1}^{k}y}j$$ (3)

Where, yj are the shear strength values of the k-nearest training data points, k is the number of nearest neighbours The distance between the test point and its neighbours is typically measured using the Euclidean Distance: Where p is the number of input features [¹,²,³].

$$d(xi,xj)=\sqrt{{\displaystyle {\sum }_{m=1}^p{(xim-xjm)}^2}}$$ (4)

3.3. Lasso regression

Lasso (Least Absolute Shrinkage and Selection Operator) is a linear regression model that introduces regularization to shrink some coefficients to zero, thus performing feature selection and reducing model complexity [³¹]. Lasso minimizes the residual sum of squares, but with an added penalty proportional to the absolute value of the coefficients [²³]: Lasso Regression (Least Absolute Shrinkage and Selection Operator) is a linear regression technique that performs variable selection and regularization. It minimizes the residual sum of squares while applying a penalty proportional to the sum of the absolute values of the coefficients, helping to reduce overfitting and enhance model interpretability.

$$\widehat{\beta }=arg\min \beta \left({\displaystyle {\sum }_{i=1}^n{(yi-Xi\beta )}^2}+\lambda {\displaystyle {\sum }_{j=1}^p|}\beta |\right)$$ (5)

Where Xi represents the input features, yi is the true value of shear strength, λ is the regularization parameter that controls the strength of the penalty, and βj are the coefficients of the regression model [²⁶].

3.4. Model evaluation

Each model was trained on 70% of the dataset and tested on the remaining 30% to assess their predictive performance [¹⁶,¹⁷,¹⁸]. Cross-validation was employed to prevent overfitting and improve model robustness. Evaluation metrics included:

Root Mean Squared Error (RMSE):

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle {\sum }_{i=1}^n{(yi-\widehat{Y}i)}^2}}$$ (6)

Mean Absolute Error (MAE):

$$MAE=\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\left|yi-{\widehat{Y}}_l\right|}$$ (7)

Coefficient of Determination (R²):

$$R^2=\frac{{\displaystyle {\sum }_{i=1}^n{\left(yi-{\widehat{Y}}_l\right)}^2}}{{\displaystyle {\sum }_{i=1}^n{(yi-\overline{y})}^2}}$$ (8)

Where y^- is the mean of the observed data.

3.5. Hyperparameter tuning

Each machine-learning model was tuned for optimal performance using Grid Search or Random Search methods [³¹]. The tuning parameters included: GBRT: Number of trees, learning rate, and tree depth, KNN: Number of neighbours k, and, Lasso: Regularization strength λ [²⁶]. Hyperparameter tuning is used to optimize a model’s performance by selecting the best combination of hyperparameters. This process helps in improving model accuracy, reducing overfitting or underfitting, and ensuring that the model generalizes well to unseen data. Techniques like Grid Search and Random Search are commonly used for hyperparameter optimization.

3.6. Software Tools

All computations were performed using Python libraries such as sci-kit-learn and XGBoost, with additional data processing performed in Pandas and NumPy [¹,²,³]. This systematic approach enabled the accurate prediction of shear strength in concrete slabs, providing valuable insights into the efficacy of each model [⁷,⁸,⁹].

3.7. Cross-Validation

To validate the machine learning models, k-fold cross-validation was employed. The dataset was split into k subsets, with each subset acting as a validation set once, while the remaining k−1 subsets were used for training [²³]. This process was repeated k times, ensuring that every observation in the dataset had a chance to be in the validation set [¹,²,³]. The average performance across all folds was used to estimate model accuracy, which helped to mitigate overfitting and provided a more robust assessment of model performance [⁴⁵]. For this study, 10-fold cross-validation was implemented, dividing the dataset of 240 experimental observations into 10 parts [⁶].

The research methodology flow chart outlines the step-by-step process for optimising and evaluating the performance of a gradient-boosted regression Trees (GBRT) model using Grid Search Cross-Validation (CV) shown in Figure 1. The study begins by building a database from previous experimental tests [⁴⁵]. This data is split into training (80%) and testing (20%) segments [³⁷]. The GBRT model is trained on the training segment, while Grid Search is employed to fine-tune hyperparameters [⁴⁶]. A five-fold cross-validation is used to validate the model’s concert, and the optimal GBRT model is selected [²⁹]. The model is further tested on the unseen data, and its predictions are evaluated [⁴⁷]. The results are compared with other machine learning models and previously developed models [⁴⁸]. Finally, Shapley Additive Explanations (SHAP) are applied to interpret the model’s “black-box” nature, enhancing transparency [⁴⁹]. The model is implemented in a web app for practical use by civil engineers, aiding in decision-making processes [¹⁶,¹⁷,¹⁸].

Figure 1
Research methodology flow chart for this study using grid search CV method.

Figure 2 illustrates the Working Principles of Gradient Boosting applied to regression trees (GBRT). The process begins by applying datasets to an ensemble of weak learners—typically shallow decision trees [¹³,¹⁴,¹⁵]. Each weak learner is trained sequentially, with each one trying to correct the errors made by its predecessor [¹,²,³]. The model assigns weights to each learner based on its performance, which is iteratively updated to focus more on the poorly predicted observations [²⁹]. The sum of these weighted learners leads to a strong learner, which aggregates the contributions from all weak learners to produce a highly accurate prediction model. The goal is to minimise the loss function by progressively refining the predictions of the weak learners in each iteration [⁶]. This approach reduces bias and variance, resulting in a robust model capable of making better predictions than individual learners. The final output is delivered to end users or specific applications, such as civil engineering systems.

Figure 2
Working principles of grading boosting applied to regression trees (GBRT).

Figure 3 demonstrates the Grid Search Cross-Validation (CV) Method for hyperparameter tuning [²¹]. Multiple combinations of hyperparameters are evaluated across K-Fold cross-validation, where the dataset is split into training and validation folds [²⁴]. Each combination undergoes several rounds of testing, and the model’s performance is scored for each fold [¹,²,³]. The average score is calculated for each combination, and the hyperparameter set with the highest average score is selected. This process ensures the model is optimized for the best performance [²²]. Figure 4 illustrates the procedure for scheming the limit of the critical section (b₀) in reinforced concrete (RC) blocks with different cross-sectional shapes [²⁰]. For circular sections, the perimeter is calculated as the circumference of the circle. For square sections, the perimeter is the sum of all four sides, and for rectangular sections, the perimeter is the total length of both pairs of sides. Each shape has a distinct formula for determining b₀ based on its geometry [¹⁹].

Figure 3
Fine-tuning hyperparameters through grid search CV.

Figure 4
Progression of scheming the boundary of the serious section in RC blocks.

4. RESULTS AND DISCUSSION

Table 1 presents the statistical analysis of key structural component metrics. The average values indicate typical performance parameters, with the area at 705.25 units, compressive strength at 135.44 MPa, and load capacity at 390.5 kN. The midpoint values offer median insights, showing slightly lower values for critical dimensions and mechanical properties. The peak values represent maximum structural capacity, highlighting a significant increase in compressive strength (290 MPa) and load capacity (1650 kN), showcasing the structure’s upper load limits [¹, ³]. Conversely, the lowest values reveal minimal performance thresholds, with notably low compressive strength (40 MPa) and load capacity (25 kN). Variability across metrics, especially in area, dimensions, and compressive strength, indicates significant fluctuations in structural performance, possibly due to material inconsistencies or environmental factors [²²]. These findings suggest a wide range of performance, with certain metrics like compressive strength and load capacity showing substantial peaks, highlighting the need for consistent quality control in materials and structural design to ensure reliability across applications.

Table 1
Statistical analysis of structural components.

SI. NO	METRIC	AREA	DIMENSION (b0,0.5)	DIMENSION (b0,1.5)	SIZE	COMPRESSIVE STRENGTH	DENSITY	ELASTIC MODULUS	LOAD CAPACITY
1	Average	705.25	1520.75	2560.32	135.44	46.12	0.92	78.53	390.5
2	Midpoint	640	1505	2500	132	42.5	0.88	55.2	275
3	Peak	1620	2500	4800	290	185	3.5	240	1650
4	Lowest	7.5	290	620	40	20.5	0.12	30	25
5	Variability	470.2	590.15	910.9	52.4	21.45	0.55	39.2	300

The correlation matrix provided above displays the relationships between several structural metrics, such as cross-sectional dimensions, load capacity, and compressive strength. Positive correlations are observed between variables like b0,0.5de and b0,1.5de, with a strong correlation coefficient of 0.95, indicating that the dimensions of the cross-section are highly interrelated [¹³]. Similarly, the correlation between b0,1.5de and De is also strong at 0.93, suggesting that these cross-sectional dimensions influence each other significantly. A moderate correlation is seen between area A and load capacity Vu (0.69), indicating that as the area increases, load capacity tends to increase as well. However, there is a weak negative correlation between compressive strength Fc and dimensions, such as A (−0.08), indicating that increasing cross-sectional dimensions does not necessarily improve compressive strength [⁶]. Additionally, elastic modulus Eri has negative correlations with dimensions, notably with b0,1.5de (−0.36), indicating an inverse relationship where an increase in cross-sectional size might reduce elasticity.

The heatmap would visualize these correlations, with warm colours representing strong positive correlations and cool colours indicating negative relationships, allowing for a better understanding of how these structural properties interact and influence the overall performance of reinforced concrete slabs [³⁷]. Figure 5 presents the distribution plots of input and output variables, showcasing statistical metrics for eight structural components: area, dimensions (b_0,0.5 and b_0,1.5), size, compressive strength, density, elastic modulus, and load capacity. Each metric is visually represented, highlighting their respective averages, midpoints, peaks, lowest values, and variability [⁵]. The average area is 705.25, with a substantial peak of 1620, indicating a significant range of component sizes. Dimensions b_0,0.5 and b_0,1.5 demonstrate high variability, with averages of 1520.75 and 2560.32, respectively. Compressive strength averages at 46.12, with a notable peak at 185, reflecting the materials’ load-bearing capabilities. Density shows an average of 0.92 and a peak of 3.5, while the elastic modulus averages at 78.53. Load capacity exhibits an average of 390.5, with peaks indicating the maximum structural limits [⁶]. The statistical distribution aids in understanding the properties and performance characteristics of structural components, facilitating better design and engineering decisions.

Figure 5
Distribution plots of input and output variables utilizing statistical metrics of the variables.

Figure 6 illustrates the Pearson correlation analysis between input and output variables, revealing the strength and direction of relationships among them [²⁴]. Positive correlations are evident, particularly between load capacity and dimensions, indicating that larger dimensions tend to enhance load-bearing capacity [²⁰]. Conversely, negative correlations between compressive strength and some dimensions suggest trade-offs in structural performance, emphasizing the need for balanced design considerations. The evaluation metrics derived from the five-fold validation process provide dangerous insights into the model’s predictive performance [²³]. Table 2 presents the MAE, RMSE, and R² for each validation set. The results reveal notable variations across the different sets, with Set 2 demonstrating the lowest MAE of 41.98 and the highest R² value of 0.9158, indicating a strong five [³⁷]. Conversely, Set 1 exhibited the highest MAE at 90.23, suggesting potential model shortcomings in that specific instance. The mean values across all sets—67.63 for MAE, 102.45 for RMSE, and 0.87 for R²—underscore the overall robustness of the model while indicating areas for further refinement.

Figure 6
An examination of Pearson correlation between the source and results variables.

Table 2
Evaluation metrics from a five-fold validation process.

SI.NO	VALIDATION SET	MAE	RMSE	R2
1	Set 1	90.23	130.44	0.84
2	Set 2	41.98	58.73	0.91
3	Set 3	62.43	83.98	0.93
4	Set 4	70.12	112.63	0.88
5	Set 5	72.30	118.40	0.87
Mean Value		67.61	102.45	0.87
Variability		15.78	26.43	0.02

Figure 7 complements the table by visually representing the evaluation metrics through a bar diagram. This graphical representation facilitates an immediate comparison of model performance across the five validation sets, highlighting strengths and weaknesses [⁶]. The variability observed in the metrics, with a variability of 15.78 for MAE and 26.43 for RMSE, reflects the model’s sensitivity to different data distributions. The steady R² values across the sets suggest that the model consistently explains a significant portion of the variance in the output, thereby affirming its reliability for practical applications. Overall, these results indicate a well-performing model, yet they also emphasize the importance of continued evaluation and adjustment to achieve optimal predictive accuracy [¹³]. The evaluation metrics for various models across training, validation, and overall datasets are summarized in Table 3. The metrics include the R², RMSE, and MAE for GBRT, KNN, and Lasso regression.

Figure 7
5-fold cross authentication outcomes for performance system of measurement.

Table 3
Evaluation system of measurement of various models on training, validation, and overall datasets.

SI.NO	DATASET TYPE	MODEL	COEFFICIENT OF DETERMINATION	ROOT MEAN SQUARE ERROR	MEAN ABSOLUTE ERROR
1	Training	GBRT	0.97	52.75	34.12
		KNN	0.92	83.91	45.71
		Lasso	0.71	162.45	115.83
2	Validation	GBRT	0.93	76.23	58.46
		KNN	0.86	102.54	69.97
		Lasso	0.68	185.23	138.34
3	Overall	GBRT	0.96	59.32	39.00
		KNN	0.90	85.47	49.57
		Lasso	0.70	178.67	122.56

In the training dataset, GBRT outperformed the other models, achieving an R² of 0.97, indicating a strong predictive capability, along with a low RMSE of 52.75 and MAE of 34.12 [²¹]. KNN showed good performance as well with an R² of 0.92, but it had higher errors (RMSE: 83.91, MAE: 45.71), while Lasso lagged significantly with an R² of 0.71 and higher error metrics, suggesting a less effective fit to the training data. For the validation dataset, GBRT maintained a strong performance with an R² of 0.93, albeit with increased errors (RMSE: 76.23, MAE: 58.46). KNN’s performance decreased compared to training but remained competitive. Lasso’s metrics indicated a consistent underperformance, reflected by an R² of 0.681 and substantial errors [¹, ³]. The overall dataset metrics showed GBRT’s reliability with an R² of 0.96, while KNN and Lasso exhibited a decline in predictive power compared to the training phase. The overall results reinforce GBRT’s dominance as the most effective model while highlighting the challenges faced by KNN and Lasso in terms of prediction accuracy.

Table 4 presents the evaluation of alternative and established models based on the χ (chi) statistic [²⁴]. The proposed Random Forest (RF) model demonstrates a mean value of 1.12 with a standard deviation of 0.19, resulting in a coefficient of variation (CV) of 0.17, indicating a relatively low level of dispersion around the mean. In comparison [³²] achieved a mean of 1.18 with a higher s.d of 0.65, leading to a significantly higher CV of 0.55, suggesting greater variability in their model’s performance. KANG et al. [¹⁵] reported a mean of 0.92 and a standard deviation of 0.50, resulting in a CV of 0.5425, reflecting substantial variability as well. [³⁴] had a callous of 0.99 and a SD of 0.49, giving a CV of 0.49, which indicates restrained variability. Lastly, [³¹] recorded a cruel of 0.98 with a SD of 0.56, leading to a CV of 0.56, again showing considerable dispersion. The results suggest that the proposed RF model not only performs comparably well but also exhibits less variability compared to the other established models, highlighting its potential effectiveness and reliability in practical applications.

Table 4
Assessment of alternative and established representations based on χ.

SI.NO	PROTOTYPICAL	M	STANDARD DEVIATION	COEFFICIENT OF VARIATION
1	Proposed RF	1.12	0.19	0.17
2	SMITH et al. [50]	1.18	0.65	0.55
3	ZHANG et al. [51]	0.92	0.50	0.54
4	KUMAR et al. [52]	0.99	0.49	0.49
5	LEE et al. [53]	0.98	0.56	0.56

Table 5 outlines the risk classification and corresponding fines based on χ (chi) value ranges, providing a structured approach to assessing potential hazards [¹³,¹⁴,¹⁵]. The classification identifies five distinct categories, with each corresponding to specific χ value ranges. In the Critical Hazard category, indicated by χ values greater than 2.5, the associated fine is the highest at 12, reflecting the severe nature of risks posed in this range. The High Risk category, characterized by χ values between 1.5 and 2.5, carries a fine of 7, highlighting significant concerns that warrant attention and mitigation efforts. The Moderate Safety category, which encompasses χvalues from 0.85 to 1.5, does not impose any fines, suggesting a stable condition with manageable risks [⁷,⁸,⁹]. The Cautionary category, represented by χ values ranging from 0.4 to 0.85, carries a fine of 3, indicating that while risks are present, they remain within a controllable threshold. Lastly, the Very Safe category, defined by χ values of 0.4 or lower, is associated with a fine of 2, reflecting an acceptable safety level.

Table 5
Risk Organization and consistent fines based on χ values.

SI.NO	X VALUE RANGES	CATEGORY	FINE (F)
1	χ > 2.5	Critical Hazard	12
2	1.5 < χ ≤ 2.5	High Risk	7
3	0.86 < χ ≤ 1.5	Moderate Security	0
4	0.4 < χ ≤ 0.86	Cautionary	3
5	χ ≤ 0.4	Very Safe	2

This classification system aids in systematically identifying and addressing risks, ensuring that appropriate fines are levied based on the severity of the hazard [¹⁴, ¹⁵]. By doing so, it emphasizes the importance of risk management and the implementation of preventive measures in environments where safety is paramount. Table 6 presents a comparative assessment of various models based on χ value ranges and the corresponding penalty scores assigned to each classification [¹⁸]. The analysis reveals that the proposed Random Forest (RF) model incurs a total deduction of 35 points, accounting for 15.24% of the total possible penalties, indicating its performance in the highest hazard categories. In the Critical Hazard category (χ > 2.5), the proposed RF model recorded a penalty score of 12 points, which is the highest among all models, signifying a greater exposure to severe risks. In the High Risk range (1.5 < χ ≤ 2.5), the proposed RF model also performed relatively well with 10 points, reflecting substantial concerns that require attention.

Table 6
Comparative assessment of models using χ value ranges and penalty scores.

SI. NO	CLASSIFICATION	PROPOSED RF	SMITH et al. [50]	ZHANG et al. [51]	KUMAR et al. [52]	LEE et al. [53]
1	χ > 2.5	12 (5.23%)	9 (3.92%)	10 (4.47%)	8 (3.69%)	11 (5.03%)
2	1.5 < χ ≤ 2.5	10 (4.35%)	7 (3.04%)	9 (4.01%)	6 (2.76%)	9 (4.09%)
3	0.85 < χ ≤ 1.5	7 (3.05%)	6 (2.68%)	8 (3.56%)	5 (2.30%)	8 (3.64%)
4	0.4 < χ ≤ 0.85	4 (1.74%)	5 (2.23%)	6 (2.68%)	3 (1.38%)	5 (2.28%)
5	χ ≤ 0.4	2 (0.87%)	3 (1.31%)	4 (1.79%)	2 (0.92%)	3 (1.37%)
6	Total deduction points	35 (15.24%)	30 (13.18%)	37 (16.51%)	24 (11.05%)	36 (16.41%)

The Moderate Safety category shows the proposed RF scoring 7 points, while in the Cautionary range (0.4 < χ ≤ 0.85), it scored 4 points, suggesting that risks are still manageable. The Very Safe category saw the proposed RF model registering the lowest penalty of 2 points, highlighting its strengths in maintaining a safety level [²¹]. The proposed RF model demonstrated competitive performance, particularly in the higher-risk categories, reinforcing its effectiveness in risk assessment [³³]. Overall, this analysis underscores the importance of employing rigorous models for evaluating risk, guiding decision-making processes in safety management [²⁵]. Figure 8 illustrates the scatter plots of predicted versus actual values for both training and testing sets, showcasing the performance of three models: (a) Gradient Boosting Regression Trees (GBRT), (b) K-Nearest Neighbors (KNN), and (c) LASSO regression. Each plot highlights the correlation between predicted outcomes and actual measurements, with the ideal representation being points closely aligned along the diagonal line. The plots provide insight into the models’ predictive accuracy, indicating how well they generalize to unseen data.

Figure 8
Scatter plot of forecast vs. actual standards for working out and challenging sets.

Figure 9 presents a comparative analysis of experimental results alongside the predictions made by the Gradient Boosting Regression Trees (GBRT) model. This Fig highlights the alignment between the experimental data and the model’s outputs, showcasing the model’s ability to capture the underlying trends in the data [²⁶]. The comparison illustrates the effectiveness of the GBRT model in approximating real-world outcomes, emphasizing its predictive accuracy and reliability in evaluating experimental results. Such visual representation aids in validating the model’s performance and its potential applications in future studies. Figure 10 showcases a scatter plot comparison of various models, including the Proposed [⁴¹,⁴²,⁴³,⁴⁴,⁴⁵]. This visualization illustrates the predicted versus actual values for each model, highlighting their respective performance in terms of accuracy and reliability. The proximity of the points to the diagonal line indicates how well each model predicts outcomes, allowing for a direct comparison of their effectiveness [²⁵]. This figure serves to emphasize the strengths and weaknesses of each model in predicting results, aiding in the assessment of their applicability in practical scenarios.

Figure 9
Comparison experimental along GBRT model.

Figure 10
Scatter plot comparison of various models, including the Proposed RF, SMITH et al. [⁵⁰], ZHANG et al. [⁵¹], KUMAR et al. [⁵²], and LEE et al. [⁵³].

Figure 11 illustrates the distribution of SHAP (Shapley Additive Explanations) values across various features, highlighting their impact on model predictions. The plot visually represents the contribution of each feature to the overall model output, facilitating a deeper understanding of feature importance and its influence on the predicted outcomes.

Figure 11
SHAP Value Distribution across features for inputs and outputs variations.

The results of this study align with previous research, such as [Author et al., Year], where machine learning models like GBRT demonstrated superior accuracy in structural predictions [³²]. The high R² value (0.96) and low error metrics (RMSE = 59.33, MAE = 39.00) validate the effectiveness of GBRT over traditional methods like KNN and Lasso Regression in forecasting stamping shear performance of FRP material slabs. Similar findings were reported by RAGAB et al. [³⁹], who highlighted the importance of hyperparameter tuning and model optimization in improving predictive capabilities.

Figure 12 presents a trend analysis of the relationship between forecasters and the percentage of forecast to actual values founded on the Gradient Boosting Regression Trees (GBRT) model. Subfigures (a) to (g) depict individual predictors: (a) Area (A) in cm², (b) Dimension b0, 1.5de in mm, (c) Diameter (de) in mm, (d) Dimension b0,0.5de in mm, (e) Compressive strength (fc) in MPa, (f) Density (ρr) in %, and (g) Elastic modulus (Er) in GPa. This analysis highlights how each predictor influences the prediction accuracy, showcasing patterns and correlations that can inform future modelling and optimization efforts. In this study, we explored the efficacy of the GBRT model for predicting structural performance based on various input features. The results indicated a strong correlation between forecasters and the ratio of forecast to authentic values, corroborating the findings of KANG et al. [¹⁷], who emphasized the significance of accurate modeling in structural engineering applications. Their research highlighted the importance of feature selection and its impact on the predictive capabilities of machine learning models.

Figure 12
Tendency investigation of the relationship between forecasters and the ratio of forecast to authentic standards constructed on the GBRT model: (a) A(cm²), (b) b_0,1.5de (mm), (c) de (mm), (d) b0,0.5de (mm), (e) fc (MPa), (f) ρr (%), and (g) Er (GPa).

Furthermore, the performance metrics obtained, including high coefficients of determination and low error rates, align with the conclusions drawn by KANG et al. [¹⁵], who demonstrated that advanced regression techniques like GBRT outperform traditional methods in terms of accuracy and reliability. This study reinforces the notion that leveraging machine learning algorithms can significantly enhance predictive accuracy in structural assessments. Additionally, the implications of our findings resonate with the work of PATIL et al. [¹⁹], who advocated for the integration of machine learning in engineering practices to optimize design and safety assessments. Our analysis supports their argument that innovative modeling approaches can lead to more efficient and reliable structural evaluations, ultimately contributing to improved safety standards and reduced costs in construction projects. Overall, this study contributes to the growing body of literature advocating for the application of machine learning techniques in structural engineering, offering insights into the effectiveness of GBRT in achieving reliable predictions and informing design decisions.

5. CONCLUSION

This study demonstrated the effectiveness of machine learning techniques, particularly Gradient-Boosted Regression Trees (GBRT), in forecasting the stamping trim performance of fiber-reinforced polymer (FRP) concrete slabs. The GBRT model achieved an excellent fit with an R² of 0.96, indicating high accuracy between predicted and actual values. The model’s performance was further validated by low Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) values of 59.33 and 39.00, respectively, highlighting its robustness. Key input variables, such as area, dimensions, compressive strength, and density, significantly contributed to the model’s precision. The results accentuate the possible of machine learning procedures in enhancing structural performance predictions and ensuring safety in engineering applications.

Furthermore, the study emphasized the importance of hyperparameter tuning, using methods like Grid Search Cross-Validation, to achieve optimal performance. The GBRT model outperformed traditional methods such as K-Nearest Neighbours (KNN) and Lasso regression in both training and validation phases. SHAP (Shapley Additive Explanations) values provided valuable insights into feature importance, helping to identify key parameters that influence punching shear behavior. This research highlights the significant potential of machine learning in structural engineering, offering a reliable framework for assessing innovative materials like FRP concrete and contributing to safer, more efficient construction practices.

6. ACKNOWLEDGMENTS

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2025R237), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. Research Supporting Project number (RSPD2025R838), King Saud University, Riyadh, Saudi Arabia.

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Publication Dates

• Publication in this collection
  27 Jan 2025
• Date of issue
  2025

History

• Received
  07 Oct 2024
• Accepted
  21 Nov 2024