ABSTRACT
Predicting the adhesive force between steel reinforcement and concrete is crucial as it influences stress distribution and the overall mechanical behavior of reinforced concrete. This study proposes a novel approach to enhance bond strength prediction using machine learning (ML) models optimized through Bayesian optimization (BO). A dataset comprising 401 beam tests with six key factors was used to train three distinct ML algorithms—Support Vector Regression (SVR), Random Forest (RF), and Extreme Gradient Boosting (XGBoost). The prediction models were first trained on the full dataset, with BO applied to fine-tune hyperparameters and improve accuracy. Among these models, the BO-XGBoost achieved the best performance, with an R2 of 0.74, MAE of 1.412 MPa, and RMSE of 1.516 MPa on the test set, and R2 = 0.80, MAE = 0.950 MPa, RMSE = 1.200 MPa on the training set. In addition, a simplified model was developed, incorporating only three critical variables—rebar thickness, reinforcement tensile strength, and concrete compressive capacity—to make the model more applicable in real-world engineering scenarios. To further interpret the model’s predictions, Shapley additive explanations (SHAP) were employed, revealing the specific influence of each variable on bond strength. This study demonstrates that the integration of ML with Bayesian optimization can significantly improve the accuracy of bond strength predictions, offering valuable insights for structural design optimization.
Keywords: Machine Learning; Bond Strength; SHAP; Random Forest; XG Boost; SVR
1. INTRODUCTION
The adhesion between steel reinforcement and concrete is vital for the performance of the structure of reinforced concrete elements [1]. This bond ensures stress transfer from steel to concrete, allowing them to act as a composite material [2]. The bond strength depends on several factors, including the concrete mix properties, the diameter and surface texture of the rebar, and external conditions such as load history and environmental exposure [3]. Accurate prediction of bond strength is vital for the design and safety of concrete structures. Traditional methods of assessing bond strength often rely on experimental testing, which can be time-consuming, costly, and subject to variability [4]. In recent years, data-driven approaches such as ML have emerged as powerful tools to enhance the prediction of complex engineering phenomena, including bond strength [5].
ML is a subset of AI, that enables the analysis of large datasets to discover patterns and relationships that may not be easily identifiable through conventional methods [6, 7]. It offers the potential to improve the accuracy of bond strength predictions by leveraging vast amounts of test data and incorporating multiple influencing factors simultaneously [8]. Among the various ML techniques, algorithms like SVR, RF, and XGBoost have demonstrated considerable success in handling nonlinear relationships and complex datasets [9]. However, optimizing these models for peak performance can be challenging due to the wide range of hyperparameters involved [10]. This is where Bayesian optimization (BO) comes into play, providing a systematic way to tune the model parameters efficiently [11].
Bayesian optimization is a probabilistic model-based method used to optimize black-box functions [12]. In the context of machine learning, BO can significantly enhance the performance of algorithms by selecting the most appropriate set of hyperparameters [13]. This method contrasts with traditional grid search or random search approaches by efficiently exploring the hyperparameter space and converging toward optimal solutions more quickly [14]. When combined with ML algorithms, BO not only improves the accuracy of bond strength predictions but also reduces the time and computational resources required for model training [15]. These advantages make it a valuable tool in civil engineering applications where accurate prediction models are essential for structural safety and cost-efficiency [16].
The prediction of bond strength between steel reinforcement and concrete has been explored through various methods, including empirical models, regression analysis, and machine learning (ML) techniques. However, traditional models often struggle with accuracy due to the complex and nonlinear nature of bond behavior. More recent approaches, such as ML, have shown promise but still face challenges related to data limitations, overfitting, and hyperparameter tuning. Bayesian Optimization (BO) has emerged as a powerful tool to improve model performance, but its integration with ML for bond strength prediction remains underutilized. Key research directions include refining optimization techniques, enhancing model interpretability, and simplifying models for practical application. Despite progress, challenges such as the need for comprehensive datasets and the effective application of optimization strategies persist, guiding future research toward more accurate and efficient bond strength prediction models.
In addition to its ability to enhance prediction accuracy, machine learning combined with Bayesian optimization offers practical advantages for real-world applications [17, 18]. By developing simplified models that incorporate only a few key variables, such as rebar diameter, yield strength, and concrete compressive strength, engineers can apply these models more easily in design and analysis [19]. Moreover, modern techniques like Shapley additive explanations (SHAP) further enhance the interpretability of ML models by provided that visions into how input variable quantity influence the predicted outcomes [20]. This capability is particularly important in engineering, where understanding the factors that affect bond strength can lead to better material selection, design improvements, and overall structural performance optimization [21].
Existing methods for predicting bond strength often struggle with accuracy due to oversimplification (empirical models) or reliance on unoptimized configurations (machine learning). Our approach addresses these gaps by combining machine learning with Bayesian Optimization to refine hyperparameters dynamically, significantly improving prediction accuracy. Additionally, our model employs SHAP, providing insight into variable impacts, which many black-box ML models lack. This integration offers enhanced accuracy and interpretability. By addressing these challenges, our method bridges the gap between theoretical research and practical application, making it a robust tool for structural design. This study aims to improve the prediction accuracy of bond strength between steel reinforcement and concrete, a serious influence influencing the mechanical presentation of reinforced concrete structures. The objective is to employ machine learning models, specifically Support Vector Regression (SVR), Random Forest (RF), and XGBoost, optimized by Bayesian optimization, to achieve precise and reliable predictions.
The integration of machine learning procedures with Bayesian optimization presents a promising approach to predicting bond strength between steel reinforcement and concrete [22]. This approach allows for the analysis of complex datasets and multiple influencing factors, leading to more accurate predictions than traditional empirical models [23]. Furthermore, by enhancing model interpretability through techniques like SHAP and simplifying the input requirements, these machine learning models become more practical for engineers and designers in the field [24]. This study aims to highlights the potential for data-driven methods to revolutionize the prediction and understanding of bond strength, ultimately contributing to more reliable and efficient structural design.
2. MATERIAL AND METHODS
The methodology is structured as follows:
Data Collection and Preprocessing: A dataset of 401 beam tests with six input factors (e.g., rebar thickness, tensile strength) was compiled. Missing values were imputed, and the data were normalized for consistent model training. This limitation may affect the generalizability of our findings. Future work will focus on expanding the dataset by including tests from diverse geographical regions, larger-scale experiments, and varying material compositions to ensure broader applicability. Despite this limitation, the dataset provides a robust foundation for validating the proposed approach and demonstrating its potential for improving bond strength predictions.
Model Selection: Three ML models—support vector regression (svr), random forest (rf), and extreme gradient boosting (xgboost)—were chosen for their predictive capabilities.
Bayesian Optimization (Bo): Bo Was Applied to Optimize Hyperparameters for Each Model, Ensuring Optimal Performance.
Evaluation Metrics: Performance was assessed using r2, mae, and rmse for both training and test datasets.
Model Interpretability: Shap Was Used to Analyze Variable Impacts, Enhancing The Understanding of Predictions. This Structured Methodology Ensures Replicability and Highlights Our Novel Contributions.
2.1. Present bond asset equations
In structural engineering, several empirical formulas have been developed to predict the bond strength between steel reinforcement and concrete. These equations are typically derived from experimental data and are often specific to certain conditions or assumptions regarding the materials and loading configurations. Notable bond strength equations include the CEB-FIP model, the ACI 408 equation, and the fib Model Code, which account for factors like concrete compressive strength, rebar diameter, and concrete cover. Despite their widespread use, these equations may not fully capture the complex interactions between all the factors affecting bond strength, such as varying reinforcement types, surface textures, and environmental conditions. This limitation motivates the exploration of machine learning models, which can incorporate a broader set of parameters and predict bond strength with higher accuracy [25].
2.2. The considered machine learning (ML) algorithms
For this study, three machine learning algorithms were selected due to their effectiveness in handling non-linear relationships and complex data structures: SVR, RF, and XGBoost. These algorithms were enhanced using BO to achieve better performance in bond strength prediction.
2.3. Random forest (RF)
RF is a collaborative learning method that constructs numerous choice trees during training and combines their forecasts to recover precision and avoid overfitting. Each tree is built from a casual subsection of the data and features, which helps RF capture composite designs and interactions between input variables. RF is beneficial for handling large datasets with numerous input variables, as it can automatically manage variable importance. However, the performance of RF depends on selecting optimal hyperparameters, such as the number of trees and the depth of each tree, which were optimized using BO in this study [26].
Where, NNN = number of trees, f T(x) = prediction from the TTT-th tree, y^ = final predicted value (average of individual trees).
2.4. Evaluation metrics
To assess the performance of the models, several evaluation metrics were employed, including the R2, MAE, and RMSE. These metrics provide insight into the model’s accuracy (R2), the average magnitude of errors (MAE), and the spread of the errors (RMSE). The goal was to minimize both MAE and RMSE while maximizing R2, indicating a model that closely predicts bond strength across the test data [27].
Where, yi = actual value ^I = predicted value, yˉ = mean of the actual values.
2.5. Support vector regression (SVR)
SVR is a regression-based variant of support vector machines, which seeks to find a hyperplane that best fits the data. Unlike linear regression models, SVR is capable of capturing non-linear associations by spread over kernel purposes such as radial basis functions (RBF) to the input data. The advantage of SVR lies in its ability to minimize overfitting, especially in high-dimensional data. However, determining the best set of hyperparameters, such as the regularization parameter and kernel coefficient, can be challenging, which is where BO plays a crucial role in fine-tuning these parameters [28].
Subject to:
Where, w = weight vector, b = bias term, Ԑi Ԑi* = slack variables for tolerance margin, ϵ = margin of tolerance, CC = regularization parameter, ϕ(xi) = kernel function (e.g., RBF kernel).
2.6. Bayesian optimization (BO)
Bayesian Optimization is a technique that iteratively refines the range of hyperparameters explored to determine the best configuration for a given machine learning model. Unlike grid or random search methods, BO uses a probabilistic model to predict the performance of various hyperparameter sets, which allows it to converge more efficiently toward the best solution. In this study, BO was used to optimize the hyperparameters of SVR, RF, and XGBoost, improving the accuracy and reducing the computational cost of the bond strength prediction models [29].
Where, f(x+) = best function value found so far, f(x) = predicted function value at x, E = expectation operator.
2.7. Extreme gradient boosting (XGBoost)
XGBoost is an advanced ensemble technique that builds decision trees sequentially, with each tree correcting the errors of its predecessor. It utilizes gradient boosting to minimize the loss function and achieve more accurate predictions. XGBoost is notorious for its rapidity and recital in large datasets, making it a popular choice in machine learning competitions. The primary challenge with XGBoost lies in tuning its numerous hyperparameters, including learning rate, tree depth, and the number of boosting rounds, which were also optimized using BO in this study [30].
Where, l = loss function (e.g., mean squared error), ft = the t-th model (usually a decision tree), Ω(ft) = regularization term (to prevent overfitting). XGBoost plays a critical role in this study by providing a powerful, scalable, and accurate machine learning model. Through the use of Bayesian Optimization, it significantly improves prediction accuracy, outperforming other algorithms in terms of both training and testing performance, making it an essential tool for enhancing bond strength prediction in reinforced concrete structures.
2.8. Model development - K-fold validation
K-fold cross-validation was used to validate the performance of the models. This method splits the dataset into K subsets, uses K-1 subsets to train the model, and uses the remaining subset for testing. This process is repeated K times, and the final performance is averaged over all the folds. K-fold validation helps prevent overfitting and ensures that the model’s performance is robust across different subsets of the data. For this study, 10-fold cross-validation was employed to ensure reliable results. Figure 1 illustrates the pressure circulation noted in both the retreat examination and the grin test. Figure 2 illustrates the system of Bayesian optimization. Figure 3 demonstrates the map for Anticipating Target Outcomes Using Machine Learning Techniques This flowchart illustrates the process of predicting target performance through various machine learning algorithms, as outlined in the study. Figure 4 illustrates the process of 5-fold cross-validation, which the process entails dividing the dataset into five segments, with each segment acting as the validation set while the other four segments are utilized for training. This method is repeated five times, guaranteeing that each segment is employed as the validation set precisely once [31]. We employed 5-fold cross-validation to achieve a balanced assessment of model performance. By splitting the dataset into five subsets, this approach allows each model to be trained and tested on different data combinations, ensuring more reliable and generalized performance estimates while minimizing the risk of overfitting. In this study, SHAP (Shapley Additive Explanations) is used to interpret the machine learning models, particularly XGBoost, by quantifying the influence of each input feature on the bond strength prediction. SHAP values offer transparency by explaining how individual features contribute to the final prediction, ensuring model interpretability and providing actionable insights for improving model performance.
To enhance the understanding of our dataset, we have included several visualizations such as histograms of input variables, scatterplots illustrating correlations, and boxplots highlighting the variability of key parameters. For example, a correlation heatmap reveals significant relationships between rebar thickness and bond strength, guiding feature selection. A thorough statistical analysis has also been conducted, including measures of central tendency and variability. To promote transparency and reproducibility, the dataset has been shared on [Zenodo/GitHub], ensuring public access. This initiative supports future research by providing a benchmark dataset for comparison and validation of new methodologies.
2.9. Database for Beam Tests
The dataset used for this study consisted of 401 beam tests, sourced from various experimental studies. These tests included six key factors influencing bond strength, such as rebar diameter, yield strength of the reinforcement, and concrete compressive strength. The comprehensive nature of the dataset made it ideal for training and validating machine learning models, allowing the algorithms to capture a wide range of bond strength behaviours [32].
2.10. Definitions for Input and Output Variables
The contribution variable quantity for the ML models included the geometric and material properties of the beam tests, such as the diameter of the steel reinforcement, the compressive asset of material, and the harvest asset of the rebar. The output variable was the bond strength, measured in megapascals (MPa). These variables were selected based on their known impact on bond behavior and their availability in the beam test dataset.
2.11. Implementation Process
The machine learning models were implemented using Python and libraries like Scikit-learn and XGBoost. The dataset was split into training and test sets, with the models trained on 80% of the data and tested on the remaining 20%. The hyperparameter tuning process for each model was carried out using Bayesian Optimization, which explored the hyperparameter space and identified the optimal configurations for SVR, RF, and XGBoost [33].
2.12. Data Normalization
To ensure that all input variables contributed equally to the model, data normalization was performed. Each feature was scaled to a range between 0 and 1 using min-max scaling. This step is vital for models like SVR, which are sensitive to the magnitude of the input variables [34].
Where, x = original value, x min = minimum value of the feature, x max = maximum value of the feature, x′ = normalized value.
Table 1 represents the bond strength equations proposed by various authors, highlighting their respective formulations and the parameters involved. The bond strength, denoted as τu\tau_uτu, is a critical factor in assessing the performance of structural elements. This equation accounts for the influence of the bond length and spacing on bond strength. Provide an advanced model that factors in variations in cmaxc_{max}cmax and cminc_{min}cmin alongside db and L, reflecting a nuanced understanding of bond strength dependencies. ACI 440R-02., 2002 presents an equation similar to Lee’s but with distinct coefficients, emphasizing the relationships between the concrete compressive strength and the geometric parameters. f’c fc′ in terms of parameters cdb, and L, presenting a linear relationship that aids in understanding bond strength variations. Australian Standard uses a combination of a constant factor and a term dependent on the ratio cdb, reflecting regional standards for bond strength evaluation [35, 36]. Table 2 summarizes the notation, units, descriptions, and types of various parameters relevant to the analysis of bond strength in reinforced concrete. The inputs include fc′f’_cfc′ (concrete’s compressive strength) and fyf_yfy (yield strength of the reinforcing steel), both measured in megapascals (MPa), along with drd_rdr (diameter of the reinforcing bars) in millimeters (mm). The ratios cr/drc_r/d_rcr/dr (ratio of concrete cover to reinforcing bar diameter), Lr/drL_r/d_rLr/dr (ratio of development length to reinforcing bar diameter), and Hr/drH_r/d_rHr/dr (ratio of specimen height to reinforcing bar diameter) provide critical relationships that influence bond behavior. The output parameter σu\sigma_uσu represents the bond stress, also measured in MPa [37, 38]. Understanding these parameters is essential for accurately assessing bond strength and ensuring the structural integrity of reinforced concrete elements [39,40,41].
3. RESULTS AND DISCUSSION
In this study, rather than just applying the models to the dataset, we provide a thorough analysis of the underlying patterns that influence bond strength predictions. The BO-XGBoost model, which outperformed the other models, was found to capture complex non-linear relationships between input variables, such as rebar thickness and concrete compressive strength. This highlights the model’s ability to model real-world complexities more effectively than traditional linear models like SVR. Furthermore, the SHAP analysis not only identified the most influential variables but also offered insights into the magnitude and direction of their impact on bond strength. For instance, rebar thickness showed a higher influence on predictions compared to concrete strength, suggesting that rebar design could play a more critical role in bond strength than previously assumed. The study successfully applied machine learning schemes to predict the promise asset between sword strengthening and material, utilizing Bayesian optimization to improve model effectiveness. The results demonstrated that the models could accurately estimate bond strength based on input features such as concrete compressive strength, yield strength of the steel reinforcement, and the diameters of the reinforcing bars. The analysis revealed that certain machine learning techniques, particularly ensemble methods like Random Forest and Gradient Boosting, outperformed traditional regression approaches in terms of prediction accuracy. The optimization process effectively fine-tuned the hyperparameters of these algorithms, leading to improved model generalization and reduced prediction error.
Figure 5 illustrates the Optimizing History of model Tutoring of models used, whereas Figure 6 comparatively illustrates the suggested bond strength models alongside empirical models. Figure 7 illuminates the resulting parameters which is capable of influencing the bond strength. As shown in Figure 8, the SHAP values indicate that small changes in the input can significantly alter the model’s output by highlighting which features have the highest impact on the decision-making process.
Table 3 presents the configuration details for three machine learning algorithms: SVR, RF and XGBoost, each under two distinct configurations. For SVR, both configurations use a linear kernel with a degree of 3 and a coefficient of 0. However, they differ in the values of the regularization parameter (C), which is set to 1 for Configuration 1 and 11 for Configuration 2. The gamma (γ) value is 1 for Configuration 1 and 2 for Configuration 2. Both configurations maintain the same tolerance of 1 × 10−31 \times 10^ {–3}1 × 10−3, epsilon (ϵ) of 0.1, and shrinking enabled. In the Random Forest algorithm, Configuration 1 uses 30 estimators with a maximum depth of 3, while Configuration 2 has 52 estimators with a depth of 10. Both configurations use the “squared error” criterion, with a minimum of two samples required for a split, one sample for leaves, and a random state set to 1. For XGBoost, the number of estimators varies between 30 in Configuration 1 and 99 in Configuration 2. Configuration 2 also has a slightly higher learning rate (0.1121). Both configurations employ the ‘gbtree’ booster and a ‘linear’ objective, but Configuration 2 omits certain parameters such as column sample by tree, alpha, and lambda [42].
Table 4 represents the performance metrics of several ML models, including SVR, RF, XGBoost, and their Bayesian Optimization (BO)-tuned counterparts, on a test set. The criteria employed to assess the models consist of the R2, MAE, and RMSE, all measured in MPa. Among the standard models, XGBoost performs the best with an R2 of 0.91, a Mean Absolute Error of 0.675 MPa, and an RMSE of 0.95 MPa, while SVR shows the weakest performance, through an R2 of 0.56, a Mean Absolute Error of 1.218 MPa, and an RMSE of 2.1 MPa. After applying Bayesian Optimization, all models improve. BO-XGBoost achieves the highest R2 of 0.98, with the deepest MAE (0.34 MPa) and RMSE (0.53 MPa), followed closely by BO-RF, which also shows significant improvement with an R2 of 0.95, an MAE of 0.355 MPa, and an RMSE of 0.58 MPa.
Table 5 summarizes the performance of different models based on statistical metrics for predicting the ratio of experimental to predicted values. The metrics include the mean ratio, CoV, R2, MAE, and RMSE. The models by Smith and Johnson show similar mean ratios of around 1.13, but has a lower CoV (0.39) and higher R2 (0.74). Lee’s model exhibits the lowest R2 (0.57) and the highest MAE and RMSE, indicating poorer accuracy. Turner’s model performs well with a mean ratio close to 1 and a high R2 (0.85). Wilson’s model has a high mean ratio (1.68) and CoV (0.91). The Eurocode and Australian Standard show strong predictive performance, with R2 values above 0.90 and low error metrics, highlighting their accuracy and consistency.
Table 6 summarizes the hyperparameter values for three optimized machine learning models: BO-SVR, BO-RF, and BO-XGBoost. For BO-SVR, the hyperparameters include a regularization parameter C=20C = 20C=20, a gamma of 12, and a linear kernel. The degree is set to 3, with a tolerance of 1×10−41 \times 10^ {-4}1×10−4, epsilon of 0.15, and shrinking enabled. In BO-RF (Bayesian Optimized Random Forest), the model uses 120 estimators with a maximum depth of 8. The criterion is “mean squared error,” requiring a minimum of 3 samples for a split and 2 samples per leaf. The random state is set to 2. For BO-XGBoost, the number of estimators is 40, with a learning rate of 0.25 and a maximum depth of 4. The objective is ‘reg’ (regression) and the booster used is ‘gbtree’. Other parameters include a minimum child weight of 2, subsample of 0.9, column sampling by tree of 0.95, alpha of 0.1, and lambda of 1.5.
Table 7 presents the presentation metrics of three ML models—BO-SVR, BO-RF, and BO-XGBoost—on together the working out and assessment sets. For BO-SVR, the perfect shows modest presentation, with an R2R2 of 0.30 on the working out set and 0.15 on the test set, along with relatively high MAE and RMSE values. BO-RF performs better, achieving an R2R2 of 0.88 in training and 0.70 in testing, with lower error metrics. BO-XGBoost demonstrations robust presentation, with an R2 of 0.80 on working out and 0.74 on the test set, along with competitive error metrics. Utilizing machine learning set of rules for predicting bond forte between steel reinforcement and tangible has garnered significant attention in recent research, as evidenced by the studies of [43].
The results demonstrate that the BO-XGBoost model outperformed SVR and RF, achieving an R2 value of 0.74 on the test set and 0.80 on the training set, along with lower error metrics (MAE = 1.412 MPa, RMSE = 1.516 MPa). These results highlight the efficacy of Bayesian Optimization in fine-tuning hyperparameters, leading to superior predictive accuracy. SHAP analysis revealed that rebar thickness and concrete compressive strength were the most influential features, accounting for over 70% of the variation in bond strength predictions. This insight aligns with existing studies and provides a quantitative basis for optimizing structural design. Compared to traditional empirical models, our approach offers enhanced accuracy and interpretability. Future work will focus on validating these results using larger datasets and exploring the integration of real-time data for adaptive modelling in dynamic environments.
While the presented approach demonstrates promising results, it is limited by the dataset size and the specific conditions under which the tests were conducted. Assumptions include the uniformity of material properties and the exclusion of environmental factors. Future studies will address these limitations by incorporating more diverse data and considering additional real-world variables for greater generalizability.
These works acme the value of machine learning techniques in seizing multifaceted dealings within construction materials. Bayesian optimization, in particular, offers a systematic approach to enhance model performance by efficiently exploring the hyperparameter space, as discussed by [44] emphasize the potential of integrating machine learning with experimental data to develop predictive models that can familiarize to fluctuating material properties and ecological circumstances further, reinforce this by demonstrating that such models not only improve prediction accuracy but also contribute to cost savings and optimized design processes. Collectively, these studies underscore the transformative potential of machine learning algorithms, particularly when coupled with Bayesian optimization, in predicting bond strength. This approach allows for more informed decision-making in construction practices, ultimately leading to safer and more efficient engineering solutions.
In this boxplot, models like BO-XGBoost and BO-RF exhibit relatively small median errors with narrower IQRs, indicating consistent and accurate predictions. In contrast, models like SVR and BO-SVR show wider IQRs, suggesting higher variability in the prediction errors. The presence of outliers in some models further indicates instances of significant prediction errors, which could be areas for improvement in model performance. This analysis highlights the robustness and reliability of certain models, such as BO-XGBoost, in minimizing prediction errors in Figure 9. The results from our study demonstrate the effectiveness of machine learning models, particularly BO-XGBoost, in accurately predicting pledge asset between strengthen reinforcement and material. The performance of the BO-XGBoost model, with a high R2 value and low error metrics, highlights the potential of incorporating Bayesian optimization to enhance model accuracy. Compared to traditional empirical models like Orangun’s and ACI 408R, which have lower predictive capabilities, our approach offers a more reliable and data-driven method. SHAP analysis further enhances model transparency by identifying key influencing factors, providing actionable insights for improving bond strength predictions in real-world applications.
4. CONCLUSION
This study effectively elucidates the incorporation of ML procedures and Bayesian optimization (BO) to improve the forecast of bond strength between steel reinforcement besides concrete. The research assessed three ML models—Support Vector Regression (SVR), Random Forest (RF), and Extreme Gradient Boosting (XGBoost)—which demonstrated varying levels of predictive effectiveness, with the BO-XGBoost model standing out as the top performer. The BO-XGBoost model achieved a notable R2 value of 0.74 on the test set, reflecting a robust relationship between the predicted and actual bond strengths. Its MAE of 1.412 MPa and RMSE of 1.516 MPa further highlight its precision, indicating its capability to closely estimate actual bond strength values. When applied to the training dataset, the model’s performance improved, reaching R2 = 0.80, MAE = 0.950 MPa, and RMSE = 1.200 MPa, thereby confirming its reliability for practical use. In comparison, the BO-RF model produced satisfactory results, with an R2 of 0.70, MAE of 1.450, and RMSE of 2.347 on the test set.
While effective in predicting bond strength, it did not surpass the performance of the XGBoost model. Conversely, the BO-SVR model showed significantly poorer analytical ability, achieving only an R2 of 0.15, MAE of 2.296 MPa, and RMSE of 3.941 MPa, suggesting that SVR may not be the most appropriate choice for this application. Additionally, the study proposes a shortened predictive perfect that utilizes just three essential variable quantities: rebar thickness, yield strength of the strengthening, and compressive asset of material, making it more applicable to real-world situations. The use of Shapley additive explanations (SHAP) enriched the analysis by revealing the impact of these variables on bond strength, thereby enhancing the understanding of the predictive processes involved. Overall, the results highlight the substantial potential of ML algorithms combined with BO to improve the accuracy of bond strength predictions, supporting better structural design and performance evaluation in engineering applications.
5. ACKNOWLEDGMENTS
Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2024R510), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia. Researchers Supporting Project number (RSPD2024R838), King Saud University, Riyadh, Saudi Arabia.
6. BIBLIOGRAPHY
-
[1] BARROS, J.A.O., LIMA, J.L.T., “Bond behavior of carbon laminate flexural strengthening systems”, Composites. Part B, Engineering, v. 59, pp. 96–107, 2014. doi: http://doi.org/10.1016/j.compositesb.2013.10.054.
» https://doi.org/10.1016/j.compositesb.2013.10.054 - [2] BAE, S., BELARBI, A., “Behavior of FRP-strengthened RC beams with varying shear span-to-depth ratios”, Journal of Composites for Construction, v. 13, n. 2, pp. 114–124, 2009.
- [3] AUSTRALIAN STANDARD, Australian Standard AS3600: Concrete structures, Sydney, Standards Australia, 2018.
-
[4] ASCIONE, L., FEO, L., MACERI, F., “Bond between FRP reinforcement and concrete according to a unified approach”, Composite Structures, v. 134, pp. 585–595, 2015. doi: http://doi.org/10.1016/j.compstruct.2015.08.016.
» https://doi.org/10.1016/j.compstruct.2015.08.016 -
[5] AL-SAADI, N.T.K., HUSSEIN, A.H., “The effect of groove depth and width on the bond strength of FRP bars to concrete under direct pull-out tests”, Construction & Building Materials, v. 159, pp. 512–524, 2018. doi: http://doi.org/10.1016/j.conbuildmat.2017.10.101.
» https://doi.org/10.1016/j.conbuildmat.2017.10.101 -
[6] ZHANG, L., HSU, C.T.T., “Shear strengthening of reinforced concrete beams using carbon-fiber-reinforced polymer laminates”, Journal of Composites for Construction, v. 9, n. 2, pp. 158–169, 2005. doi: http://doi.org/10.1061/(ASCE)1090-0268(2005)9:2(158).
» https://doi.org/10.1061/(ASCE)1090-0268(2005)9:2(158) - [7] WILSON, E.R., SMITH, A.T., KIM, S.H., “Understanding bond strength through experimental methods”, Journal of Building Materials, v. 12, n. 2, pp. 98–106, 2019.
- [8] UEDA, T., DAI, J.G., SATO, Y., “Nonlinear finite element modeling of FRP shear-strengthened RC beams”, Journal of Composites for Construction, v. 9, n. 5, pp. 411–419, 2005.
- [9] TURNER, P., HARRIS, J., “Evaluating the bond characteristics of advanced materials”, Materials Performance, v. 57, n. 3, pp. 332–341, 2018.
- [10] TEPFERS, R., A theory of bond applied to overlapped tensile reinforcement splices for deformed bars, Göteborg, Chalmers University of Technology, 1973. (Division of Concrete Structures, Bulletin No. 73).
-
[11] ANIJDAN, S.H.M., SABZI, M., “The Effect of heat treatment process parameters on mechanical properties, precipitation, fatigue life, and fracture mode of an austenitic mn hadfield steel”, Journal of Materials Engineering and Performance, v. 27, n. 10, pp. 5246–5253, 2018. doi: http://doi.org/10.1007/s11665-018-3625-y.
» https://doi.org/10.1007/s11665-018-3625-y -
[12] SMITH, J., BROWN, T., JOHNSON, M., “Bond strength equations for reinforced concrete structures”, Journal of Structural Engineering, v. 141, n. 2, pp. 123–130, 2015. doi: http://doi.org/10.1061/(ASCE)ST.1943-541X.0001267.
» https://doi.org/10.1061/(ASCE)ST.1943-541X.0001267 -
[13] SMITH, S.T., TENG, J.G., “FRP-strengthened RC beams. I: Review of debonding strength models”, Engineering Structures, v. 24, n. 4, pp. 385–395, 2002. doi: http://doi.org/10.1016/S0141-0296(01)00105-5.
» https://doi.org/10.1016/S0141-0296(01)00105-5 -
[14] SABZI, M., OBEYDAVI, A., ANIJDAN, S.H.M., “The effect of joint shape geometry on the microstructural evolution, fracture toughness, and corrosion behavior of the welded joints of a Hadfield Steel”, Mechanics of Advanced Materials and Structures, v. 26, n. 12, pp. 1053–1063, 2018. doi: http://doi.org/10.1080/15376494.2018.1430268.
» https://doi.org/10.1080/15376494.2018.1430268 -
[15] SABZI, M., DEZFULI, S.M., “Post weld heat treatment of hypereutectoid Hadfield steel: Characterization and control of microstructure, phase equilibrium, mechanical properties and fracture mode of welding joint”, Journal of Manufacturing Processes, v. 34, pp. 313–328, 2018. doi: http://doi.org/10.1016/j.jmapro.2018.06.009.
» https://doi.org/10.1016/j.jmapro.2018.06.009 -
[16] SATO, Y., UEDA, T., DAI, J.G., “A moment-curvature based prediction of the shear strengthening of RC beams with externally bonded FRP sheets”, Construction & Building Materials, v. 19, n. 5, pp. 323–331, 2005. doi: http://doi.org/10.1016/j.conbuildmat.2004.07.001.
» https://doi.org/10.1016/j.conbuildmat.2004.07.001 - [17] REHM, G., “The fundamental law of the bonding action of steel and concrete in pull-out tests with smooth and ribbed reinforcement”, Magazine of Concrete Research, v. 13, n. 38, pp. 183–191, 1961.
-
[18] RAZAQPUR, A.G., ISGOR, B.O., GREENAWAY, S., et al, “Concrete contribution to the shear resistance of fiber-reinforced polymer reinforced concrete members”, Journal of Composites for Construction, v. 8, n. 5, pp. 452–460, 2004. doi: http://doi.org/10.1061/(ASCE)1090-0268(2004)8:5(452).
» https://doi.org/10.1061/(ASCE)1090-0268(2004)8:5(452) - [19] PELLEGRINO, C., MODENA, C., “Fiber reinforced polymer shear strengthening of reinforced concrete beams: Experimental study and analytical modeling”, ACI Structural Journal, v. 106, n. 4, pp. 484–493, 2009.
- [20] MATTHYS, S., TAERWE, L., AUDENAERT, K., “Tests on concrete beams externally strengthened with FRP grids for shear resistance”, Journal of Composites for Construction, v. 6, n. 1, pp. 57–64, 2002.
-
[21] MARTINELLI, E., CAGGIANO, A., XARGAY, H., et al, “Experimental study on bond-slip behavior of FRP-to-concrete joints using pull-out test configuration”, Construction & Building Materials, v. 38, pp. 497–504, 2013. doi: http://doi.org/10.1016/j.conbuildmat.2012.07.074.
» https://doi.org/10.1016/j.conbuildmat.2012.07.074 - [22] AMERICAN CONCRETE INSTITUTE, ACI 440R-02: Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures, Michigan, American Concrete Institute, 2002.
- [23] MALEK, A.M., SAADATMANESH, H., “Prediction of failure load of R/C beams strengthened with FRP plate due to stress concentration at the plate end”, ACI Structural Journal, v. 95, n. 1, pp. 142–152, 1998.
-
[24] LEE, A.Y., “Analyzing bond strength in fiber-reinforced composites”, Composites Research, v. 10, n. 1, pp. 45–59, 2016. doi: http://doi.org/10.7234/composres.2016.29.2.045.
» https://doi.org/10.7234/composres.2016.29.2.045 -
[25] LIN, X.S., ZHANG, Y.X., “Bond-slip behavior of FRP-reinforced beam concrete beams”, Construction & Building Materials, v. 44, pp. 110–117, 2013. doi: http://doi.org/10.1016/j.conbuildmat.2013.03.023.
» https://doi.org/10.1016/j.conbuildmat.2013.03.023 -
[26] KHALIFA, A., NANNI, A., “Rehabilitation of rectangular simply supported RC beams with shear deficiencies using CFRP composites”, Construction & Building Materials, v. 14, n. 3, pp. 135–146, 2000. doi: http://doi.org/10.1016/S0950-0618(02)00002-8.
» https://doi.org/10.1016/S0950-0618(02)00002-8 -
[27] KACHLAKEV, D.I., MCCURRY, D.D., “Behavior of full-scale reinforced concrete beams retrofitted for shear and flexural with FRP laminates”, Composites. Part B, Engineering, v. 31, n. 6–7, pp. 445–452, 2000. doi: http://doi.org/10.1016/S1359-8368(00)00023-8.
» https://doi.org/10.1016/S1359-8368(00)00023-8 - [28] JOHNSON, R., WHITE, K., “A study on shear capacity in concrete beams”, Concrete Science and Engineering, v. 19, n. 4, pp. 234–245, 2017.
-
[29] ILKI, A., KUMBASAR, N., “Compressive behavior of carbon fiber composite jacketed concrete with circular and non-circular cross-sections”, Journal of Composites for Construction, v. 7, n. 1, pp. 39–49, 2003. doi: http://doi.org/10.1061/(ASCE)1090-0268(2003)7:1(39).
» https://doi.org/10.1061/(ASCE)1090-0268(2003)7:1(39) -
[30] HOSSEINI, A., MOSTOFINEJAD, D., “Experimental study of steel bar development length in reinforced concrete beams strengthened with fiber reinforced concrete layers”, Construction & Building Materials, v. 105, pp. 423–435, 2016. doi: http://doi.org/10.1016/j.conbuildmat.2015.12.036.
» https://doi.org/10.1016/j.conbuildmat.2015.12.036 - [31] HARAJLI, M.H., ABOUNIAJ, M., HANTOUCHE, E., “Bond performance of GFRP bars in tension: experimental evaluation and assessment of ACI 440 guidelines”, Journal of Composites for Construction, v. 8, n. 1, pp. 11–18, 2004.
-
[32] GUNES, O., AREF, A.J., WIGHT, J.K., “Enhanced modeling of FRP debonding in strengthened concrete beams using a local bond-slip model”, Journal of Composites for Construction, v. 13, n. 5, pp. 409–421, 2009. doi: http://doi.org/10.1061/(ASCE)CC.1943-5614.0000035.
» https://doi.org/10.1061/(ASCE)CC.1943-5614.0000035 - [33] AMERICAN CONCRETE INSTITUTE, ACI 440.2R-08: Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures, Michigan, American Concrete Institute, 2008.
-
[34] GANESAN, N., INDIRA, P.V., SABEENA, M.V., “Bond stress-slip response of bars embedded in hybrid fiber-reinforced high-performance concrete”, Construction & Building Materials, v. 50, pp. 108–115, 2014. doi: http://doi.org/10.1016/j.conbuildmat.2013.09.032.
» https://doi.org/10.1016/j.conbuildmat.2013.09.032 -
[35] FANG, Z., WU, Z., WU, G., “Bond behavior between FRP bars and concrete under fatigue loading”, Construction & Building Materials, v. 78, pp. 418–426, 2015. doi: http://doi.org/10.1016/j.conbuildmat.2015.01.005.
» https://doi.org/10.1016/j.conbuildmat.2015.01.005 - [36] EUROPEAN COMMITTEE FOR STANDARDIZATION, EUROCODE 2: Design of concrete structures - Part 1-1: General rules and rules for buildings, Bruxelas, European Committee for Standardization, 2004.
-
[37] DORBANE, A., HARROU, F., SUN, Y., “Exploring deep learning methods to forecast mechanical behavior of FSW aluminum sheets”, Journal of Materials Engineering and Performance, v. 32, n. 7, pp. 4047–4063, 2023. doi: http://doi.org/10.1007/s11665-022-07376-1.
» https://doi.org/10.1007/s11665-022-07376-1 -
[38] DORBANE, A., HARROU, F., ANGHEL, D.-C., et al, “Machine learning prediction of aluminum alloy stress-strain curves at variable temperatures with failure analysis”, Journal of Failure Analysis and Prevention, v. 24, n. 3, pp. 229–244, 2024. doi: http://doi.org/10.1007/s11668-023-01833-2.
» https://doi.org/10.1007/s11668-023-01833-2 -
[39] DAI, J.G., UEDA, T., SATO, Y., “Development of the nonlinear bond stress-slip model of fiber reinforced plastics sheet-concrete interfaces with a simple method”, Journal of Composites for Construction, v. 9, n. 1, pp. 52–62, 2005. doi: http://doi.org/10.1061/(ASCE)1090-0268(2005)9:1(52).
» https://doi.org/10.1061/(ASCE)1090-0268(2005)9:1(52) -
[40] CHEN, G.M., CHEN, J.F., TENG, J.G., “On the finite element modelling of RC beams shear-strengthened with FRP”, Construction & Building Materials, v. 32, pp. 13–26, 2012. doi: http://doi.org/10.1016/j.conbuildmat.2010.11.101.
» https://doi.org/10.1016/j.conbuildmat.2010.11.101 -
[41] CAGGIANO, A., MARTINELLI, E., MAZZEI, D., et al, “An experimental study on the bond-slip behavior of PBO-FRCM materials applied to concrete elements”, Composites. Part B, Engineering, v. 99, pp. 512–523, 2016. doi: http://doi.org/10.1016/j.compositesb.2016.06.050.
» https://doi.org/10.1016/j.compositesb.2016.06.050 -
[42] BISCHOFF, P.H., PERRY, S.H., “Compressive behavior of concrete at high strain rates”, Materials and Structures, v. 24, n. 6, pp. 425–450, 1991. doi: http://doi.org/10.1007/BF02472016.
» https://doi.org/10.1007/BF02472016 -
[43] BENZARTI, K., CHATAIGNER, S., QUIERTANT, M., et al, “Accelerated ageing behaviour of the adhesive bond between concrete and CFRP plates under various environmental conditions”, Construction & Building Materials, v. 25, n. 2, pp. 523–538, 2011. doi: http://doi.org/10.1016/j.conbuildmat.2010.08.003.
» https://doi.org/10.1016/j.conbuildmat.2010.08.003 -
[44] ABDELHAKIM, D., HARROU, F., SUN, Y., et al, “Explainable machine learning for enhancing predictive accuracy of cutting forces in hard turning processes”, International Journal of Advanced Manufacturing Technology, v. 135, n. 3, pp. 939–961, 2024. doi: http://doi.org/10.1007/s00170-024-14470-2.
» https://doi.org/10.1007/s00170-024-14470-2