Advancing Shear Capacity Estimation in Rectangular RC Beams: A Cutting-Edge Artificial Intelligence Approach for Assessing the Contribution of FRP

Abstract

Shear strength prediction in FRP-bonded reinforced concrete beams is crucial for ensuring structural integrity and safety. In this extensive investigation, advanced machine learning algorithms are harnessed to achieve precise shear strength predictions for rectangular RC beams reinforced with FRP sheets. The aim of this research is to enhance the accuracy and reliability of shear strength estimation, providing valuable insights for the design and assessment of FRP-strengthened structures. The primary contributions of this study lie in the meticulous comparison of various machine learning algorithms, including Xgboost, Gradient Boosting, Random Forest, AdaBoost, K-nearest neighbors, and ElasticNet. Through comprehensive evaluation based on predictive performance, the most suitable model for accurately estimating the shear strength of FRP-reinforced rectangular RC beams is identified. Notably, Xgboost emerges as the superior performer, boasting an impressive R² value of 0.901. It outperforms other algorithms and demonstrates the lowest RMSE, MAE, and MAPE values, establishing itself as the most accurate and reliable predictor. Furthermore, a sensitivity analysis is conducted using artificial neural networks to assess the influence of input variables. This additional research facet sheds light on the critical factors shaping shear strength outcomes. The study, as a whole, represents a substantial contribution to advancing the development of accurate and dependable prediction models. The practical implications of this work are far-reaching, particularly for engineering applications in the realm of structures reinforced with FRP. The findings have the potential to transform the approach to the design and assessment of such structures, elevating safety, efficiency, and performance to new heights.

1. Introduction

Concrete structures are extensively employed in the construction industry due to their high strength and durability. [1]. However, they often experience shear failures, which can lead to catastrophic consequences. In the pursuit of enhancing the shear strength of concrete beams, many methods have been developed, among which the external bonding of FRP composites has emerged as a subject of substantial research and scholarly focus [2]. The use of FRP composites as an external bonding technique has shown great promise in enhancing the structural performance of concrete elements, mitigating shear failures, and increasing their load-carrying capacity [3]. The extant literature exhibits a plethora of scholarly endeavors exploring the domain of shear strengthening of concrete beams through the utilization of FRP sheets. This compendium of studies exemplifies the substantial research endeavors and notable progress achieved within this realm. Encompassing a diverse array of subjects, these investigations span experimental inquiries, analytical modeling approaches, numerical simulations, and the development of design guidelines.

De Maio et al. [4] evaluated the impact of damage on the dynamic characteristics of RC structures retrofitted with FRP systems. A numerical model, utilizing a cohesive crack strategy and an embedded truss model, was performed to simulate the damage progression under quasi-static loading conditions. The dynamic response, specifically the natural vibration frequencies, was analyzed and compared to numerical and experimental results. The findings demonstrate that the FRP system positively influences both the static and dynamic behavior of the structures, enhancing their load-carrying capacity and mitigating natural frequency degradation. A comprehensive literature review on the utilization of natural fibers and biopolymers in FRP composites for concrete members was presented by Nwankwo et al. [5]. The study examines various FRP configurations and strengthening techniques, placing emphasis on the effectiveness of bio-based FRPs in enhancing the strength of concrete beams and columns. The review emphasizes the importance of factors such as laminate thickness, FRP anchorage, and member stiffness in determining the effectiveness of the strengthening process. Furthermore, analytical and numerical modeling methods are identified as valuable tools for predicting the behavior of concrete structures bonded with bio-based FRPs. The authors also acknowledge the impact of environmental factors on bio-based FRPs and discuss the potential for modifying natural fiber properties through appropriate treatments. Zhou et al. [6] presented a comprehensive review of stochastic multiscale analysis for FRP composite structures. The research focuses on the uncertainties in FRP structures that are caused by material variations and manufacturing processes. Key aspects discussed include the source of uncertainty, the prediction of effective material properties with uncertainties, and probabilistic structural analysis. Manufacturing weaknesses like fiber misalignment and matrix voids have a significant influence on the mechanical properties of FRP composites. Techniques based on micromechanics and probabilistic homogenization are employed to predict and quantify the impact of microscale uncertainties on overall material behavior. The integration of probabilistic homogenization and structural analysis enables multi-scale stochastic analysis, providing more accurate results than single-scale approaches. The review emphasizes the need for further research to consider realistic uncertainties, propagate non-probabilistic random variables across scales, and explore nonlinear problems and non-probabilistic reliability analysis.

Zhang et al. [7] investigated flexural design in RC structures strengthened by hybrid bonded-FRP. Their study addresses the lack of effective design methodologies for this strengthening technique. The authors analyze debonding mechanisms and failure modes, propose a design process, and introduce failure criteria that ensure good ductility. They develop a predictive model for bearing capacity and verify its accuracy. Numerical analysis confirms the effectiveness of the fastener design. Pohoryles et al. [8] studied the impact of slabs and transverse beams on the effectiveness of FRP retrofitting for existing RC structures under seismic loading. Through experimental investigations conducted on four beam-column joints, they revealed that the presence of slabs and transverse beams significantly influences damage progression and failure mechanisms. The retrofit effectiveness is found to be higher in specimens without slabs and transverse beams, indicating the inadequacy of focusing solely on joint shear strengthening. These findings caution against overestimating the effectiveness of retrofitting and emphasize the importance of accurately representing realistic structures in numerical and experimental assessments for assessing seismic performance in RC moment-resisting frames. In another research work, Wei et al. [9] conducted experiments to investigate the dynamic properties of eight footbridges constructed using FRP composites. They compare these properties to six additional FRP footbridges as well as 124 non-FRP footbridges. The comprehensive analysis reveals that FRP footbridges exhibit similar basic frequencies but higher damping ratios compared to conventional materials. The natural frequencies and damping ratios of FRP footbridges are found to be response amplitude dependent. The presence of accelerant peaks suggests that FRP footbridges exhibit approximately 3.5 times higher responsiveness to resonant excitation compared to conventional bridges of similar length and mode shape.

Ferracuti [10] proposed a model for retrofitting RC frames using FRP wrapping specifically for columns subjected to axial loading and cyclic bending, which is a common scenario in seismic areas. The present models for FRP-bonded RC frames primarily consider pure axial loads, neglecting the effects of cyclic bending. The proposed model takes into account the strain gradient effect caused by bending loads, which significantly affects the confinement level of the frame. The validation of the model was established through a comprehensive comparison of its results with the experimental data obtained from cyclic tests. Additionally, the model is incorporated into open-source software, enabling its utilization for conducting pushover analyses on an existing RC frame. This analysis investigates various retrofitting strategies aimed at improving column ductility in response to lateral forces. A novel numerical method for seismic assessment of RC structures, considering both bare and FRP-retrofitted conditions was proposed by Markou et al. [11]. The method incorporates a damage factor in the steel constitutive material model, which accurately represents the accumulated damage in the surrounding concrete and accounts for bar slippage. Experimental validation is performed using full-scale cyclic tests on deficient RC joints wrapped with CFRP, showing good agreement between the proposed model and observed nonlinear behavior. The results highlight the method’s robustness and accuracy in capturing extreme nonlinearities, providing a basis for reliable numerical tools and design guidelines for seismic evaluation of structures pre- and post-earthquake events. Furthermore, Ding et al. [12] introduced a novel vibration-based approach for detecting debonding in FRP-strengthened structures using an evolutionary model. The study addresses the limitations of conventional nondestructive testing methods by proposing a global vibration-based method that can identify debonding conditions even at locations far from the sensors. Experimental tests on an FRP-strengthened cantilever steel beam were conducted, simulating debonding scenarios through a stepwise bonding procedure. By extracting natural frequencies and mode shapes and employing model updating with l0.5 regularization, the proposed algorithm accurately locates and quantifies the debonding condition. The integration of K-means clustering in the Q-learning approach enhances the optimization process.

Zeng et al. [13] presented the development and flexural behavior of FRP bar-reinforced ultra-high-performance concrete (UHPC) plates with a grouting sleeve connection. By incorporating FRP bars and steel grouting sleeves, the innovative connection method offers a dependable solution for the prefabrication construction of UHPC structures reinforced with FRP bars. Through comprehensive flexural tests, the impact of the connection mode and the type of reinforcing fiber embedded in the UHPC is thoroughly examined. The findings demonstrate that the proposed system ensures reliable performance, as failure occurs outside the connection zone. Also, Wu et al. [14] introduced a novel approach for modeling and predicting the mechanical behavior of FRP-wrapped slabs through the development of two multilayer composite plates. These elements integrate the substrate, and FRP sheet into a single element, effectively addressing the challenges associated with geometric irregularities and time-varying adhesive properties. By offering the capability to simulate irregular structures and achieve enhanced accuracy, these elements enable the accurate analysis of various strengthening systems.

In light of the potential catastrophic consequences associated with shear failures in concrete structures, there is an urgent need to explore innovative approaches that can enhance their shear strength. Among the promising research avenues, the implementation of machine learning (ML) models arises as a compelling solution [15,16,17]. These models have the potential to provide invaluable insights into the intricate behavior of FRP-strengthened RC beams by leveraging the power of data-driven analysis.

This study addresses a significant research gap in the body of knowledge by improving our understanding of and ability to predict the shear strength of concrete beams wrapped with FRP. Shear failures in concrete structures can have detrimental effects, such as structural harm or safety risks. This study aims to provide engineers with reliable tools for evaluating the shear strength performance of FRP-strengthened RC beams by investigating novel approaches and utilizing the power of ML models.

The use of FRP composites as an external bonding technique has shown great promise in improving the structural performance of concrete members, mitigating shear failures, and increasing their load-carrying capacity. However, accurately predicting the shear strength of FRP-strengthened concrete beams is a complicated task due to the intricate interplay between various wrapping techniques and fiber types.

The application of FRP in enhancing the shear capacity of reinforced concrete beams offers a pathway to mitigate reliance on conventional materials like steel, known for its substantial environmental footprint. Optimizing existing structures with innovative materials such as FRP advocates for sustainable resource utilization and a reduction in carbon emissions. The focus on Durability extends beyond lessening environmental impact to encompass the longevity of structures. Emphasizing the bolstering of the shear capacity of RC beams correlates with the potential for prolonged infrastructure lifespan. This extension diminishes the necessity for frequent repairs and reconstructions, practices known for their resource-intensive and environmentally adverse consequences. Furthermore, the research addresses Waste Reduction, a crucial aspect of sustainable building practices. Introducing FRP for retrofitting existing structures holds promise in minimizing the demolition and disposal of outdated constructions. This strategy adheres to sustainability principles by curbing construction-related waste and mitigating associated environmental repercussions. Moreover, the study contributes to Energy Efficiency, a pivotal element in sustainable construction. Retrofitting RC beams with FRP enhances building performance, making structures more resilient to natural disasters and adverse conditions. This fortification diminishes the energy consumption and resources typically required for reconstruction.

2. Materials and Methods

This study aims to examine the effectiveness of ML models in predicting the shear strength of concrete beams externally bonded with FRP. The analysis includes a comprehensive database containing various types of wrapping techniques and fiber types commonly used in FRP strengthening applications. The database includes three types of wrapping techniques: U-wrap (U), side bonded (SB), and closed wrap (F). Each of these techniques provides a distinct method of applying FRP composites to concrete beams, thereby influencing their shear behavior. Furthermore, the database includes four types of fibers: carbon fiber-reinforced polymer (CFRP), basalt fiber-reinforced polymer (BFRP), glass fiber-reinforced polymer (GFRP), and polyethylene terephthalate fiber-reinforced polymer (PET-FRP). These fiber types have varying mechanical properties, which adds to the variability in shear performance of FRP-strengthened concrete beams.

The comprehensive database used in this study, which includes various wrapping techniques and fiber types, allows for an in-depth analysis of the factors influencing shear behavior, as presented in Appendix A. In pursuit of accomplishing the objective of shear strength prediction, we employ a range of ML models, each incorporating state-of-the-art methodologies. These models include eXtreme Gradient Boosting (Xgboost), Random Forest (RF), Adaptive Boosting (Adaboost), ElasticNet, K-nearest neighbors (KNN), and Gradient Boosting (GB). Using these models, we aim to develop accurate and reliable prediction frameworks that will aid engineers in assessing the shear strength of FRP-strengthened RC beams. The ML models were implemented using Python 3.7. The following Python libraries were used: NumPy, SciPy, Pandas, Matplotlib, and TensorFlow. The study aims to provide engineers with reliable tools that will help in the design and evaluation of FRP-strengthened beams, thereby improving the safety and performance of structures.

The significance of this study extends across multiple dimensions. Firstly, it addresses the critical issue of mitigating the risks associated with shear failures in concrete structures, thereby contributing to overall structural safety. Secondly, the use of ML models provides a robust and efficient solution for predicting shear strength, outperforming traditional methods and providing more precise and reliable assessments. This advancement has the potential to revolutionize the field of FRP strengthening, empowering engineers to make informed decisions regarding the design and performance evaluation of FRP-strengthened RC beams. Additionally, the comprehensive database employed in this research enhances the applicability and generalizability of the developed prediction frameworks, making them relevant to a wide range of practical scenarios. Overall, this study significantly contributes to advancing the understanding and implementation of FRP strengthening techniques, thereby promoting the development of resilient and sustainable concrete structures.

2.1. Extreme Gradient Boosting

XGBoost is a powerful ensemble learning algorithm that has gained widespread popularity in ML and data science applications. It belongs to the family of gradient-boosting algorithms, which are known for their high predictive accuracy and robustness in handling a variety of data types and complexities. XGBoost stands out for its efficiency and effectiveness in handling structured data, as well as its ability to handle missing values, making it a versatile tool for a wide range of applications, including classification, regression, ranking, and even more complex tasks like user-defined custom objectives. The algorithm is built on the principles of boosting, which involves combining the predictions of multiple weak learners (typically decision trees) to create a strong learner. It sequentially builds a series of trees, each attempting to correct the errors of the previous ones. This iterative process allows XGBoost to continually refine its predictions, resulting in a highly accurate model [18].

The advantages of the Xgboost algorithm can be summarized as follows:

• High Predictive Accuracy: XGBoost often outperforms other ML algorithms in terms of predictive accuracy. It effectively reduces bias and variance, leading to models that generalize well to new, unseen data.
• Efficiency and Scalability: XGBoost is engineered for efficiency and speed. It employs a number of optimization techniques, including parallelization and approximation algorithms, which make it highly scalable and capable of handling large datasets.
• Feature Importance: XGBoost provides a feature importance score, allowing users to understand which features have the most impact on the model’s predictions. This information is crucial for feature selection and understanding the underlying relationships in the data.
• Robustness to Overfitting: The algorithm includes regularization terms, such as L1 (Lasso) and L2 (Ridge) penalties, which help prevent overfitting. This ensures that the model does not become overly complex and remains capable of generalizing to unseen data.
• Handling Missing Values: XGBoost has a built-in mechanism to handle missing values during the training process, reducing the need for extensive data preprocessing.

The disadvantages of the Xgboost algorithm can be summarized as follows:

• Black-Box Nature: Like many ensemble methods, the interpretability of XGBoost models can be a challenge. Understanding the exact decision-making process within the model can be complex, especially when dealing with a large number of features and trees.
• Resource Intensive: Although XGBoost is efficient, it can be computationally demanding, especially when training very large models on limited hardware. This may limit its practicality in resource-constrained environments.
• Sensitivity to Hyperparameters: The proper tuning of hyperparameters is crucial for achieving optimal performance with XGBoost. This process can be time-consuming and may require some expertise.
• Limited Support for Unstructured Data: XGBoost is designed primarily for structured data. It may not perform as effectively when applied to unstructured data types, such as text, images, or audio, without appropriate feature engineering.
• Potential for Overfitting: While XGBoost is designed to mitigate overfitting, it is not immune to it. Improper hyperparameter tuning or the use of very complex models can still lead to overfitting issues. Regularization techniques must be applied judiciously.

In summary, XGBoost is a highly effective algorithm known for its predictive accuracy, efficiency, and robustness. However, it may require careful tuning and may not be the best choice for all types of data or applications. Researchers and practitioners should consider its advantages and disadvantages in the context of their specific use case.

2.2. Random Forest

RF is an ensemble learning method that is used in both classification and regression tasks [19]. It operates by constructing multiple decision trees during the training phase and outputs the class (in classification tasks) or mean prediction (in regression tasks) of the individual trees. During the training process, RF randomly selects a subset of features and a subset of the training data for each tree, which helps in reducing overfitting. It then builds multiple decision trees based on these subsets. In the case of classification, each tree ’votes‘ for a class, and the class with the most votes is considered the final prediction. For regression, the predictions of the individual trees are averaged to obtain the final output.

The advantages of the RF algorithm can be summarized as follows:

• High Predictive Accuracy: RF is renowned for its remarkable predictive accuracy. Combining the predictions of multiple decision trees effectively reduces overfitting, providing more reliable and accurate results compared to single decision trees.
• Robustness to Outliers: RF is robust against outliers and noisy data, as individual decision trees can be sensitive to extreme values. The ensemble nature of RF mitigates the impact of such anomalies on the overall model.
• Feature Importance: RF can evaluate the importance of features in the dataset. It assigns a relevance score to each feature, aiding in feature selection and providing insights into which attributes contribute most to the model’s predictions.
• Handling Missing Data: It can handle missing data without extensive data preprocessing. Using surrogate splits, RF can make predictions based on available information, making it more resilient to incomplete datasets.
• Reduction in Overfitting: RF reduces the risk of overfitting, a common problem in decision trees, by introducing randomness through feature subsampling and bootstrapping. This helps the model to generalize better to unseen data.
• Parallelization: RF can efficiently utilize parallel processing, as individual trees can be constructed independently. This makes it suitable for large datasets and computationally intensive tasks.
• Interpretability: While not as interpretable as a single decision tree, RF can provide insights into feature importance and how the model makes predictions, aiding in model understanding and feature engineering.

The disadvantages of the RF algorithm can be summarized as follows:

• Complexity: The ensemble of multiple decision trees can make the RF model complex, potentially requiring more memory and computational resources compared to single-decision trees.
• Computational Cost: Training an RF model can be computationally expensive, especially for large datasets or a high number of trees in the forest.
• Black-Box Nature: RFs are less interpretable compared to individual decision trees, making it challenging to understand the inner workings of the model, especially when dealing with a large number of trees.
• Not Suitable for Linear Relationships: RF may not perform as well as linear models when the underlying relationship between features and the target variable is linear, as it is inherently a non-linear model.
• Overhead in Hyperparameter Tuning: Tuning the hyperparameters of an RF, such as the number of trees and the depth of the tree, can be time-consuming and require careful experimentation to achieve optimal performance.

In conclusion, RF is a powerful and versatile ensemble learning method with several advantages, including high predictive accuracy, robustness, and feature importance analysis. However, it also has its disadvantages, such as complexity, computational cost, and reduced interpretability, which should be considered when choosing this method for a specific ML task.

2.3. AdaBoost

AdaBoost is an ensemble learning method used in classification and regression tasks [20]. It works by combining the predictions of multiple weak learners (typically decision trees) to form a strong learner. The key idea behind AdaBoost is to sequentially train a series of weak models, giving more weight to misclassified samples in each iteration. Therefore, subsequent models focus more on previously misclassified data points, leading to a refined and accurate prediction.

The advantages of the AdaBoost algorithm can be summarized as follows:

• High Accuracy: AdaBoost often yields high predictive accuracy compared to individual weak learners. This is because it focuses on misclassified samples and iteratively improves the model’s performance.
• Versatility: AdaBoost can be applied to various types of weak learners, not just decision trees. This makes it adaptable to different types of data and problem domains.
• Reduced Overfitting: AdaBoost tends to reduce overfitting compared to training a single complex model. It does this by combining multiple weak models, each focusing on different aspects of the data.
• Handles Noisy Data Well: AdaBoost can handle noisy data and outliers to some extent. Since it gives more weight to misclassified samples, it tends to focus on difficult-to-classify data points.
• Feature Selection: AdaBoost implicitly performs feature selection by assigning more importance to features that are more informative in the context of the problem.

The disadvantages of the Adaboost algorithm can be summarized as follows:

• Sensitivity to Noisy Data: While AdaBoost can handle some level of noise, it can still be sensitive to outliers or extremely noisy data. In extreme cases, it may overfit to the noise.
• Computationally Intensive: Training an AdaBoost model can be computationally intensive, especially when using a large number of weak learners or complex base models.
• Less Interpretable: The final ensemble model produced by AdaBoost may be less interpretable compared to individual weak models. It may not provide clear insights into the relationships between features and the target variable.
• Less Effective on Complex Relationships: AdaBoost may struggle with datasets where the underlying relationships are highly complex or not well-captured by simple weak models.
• Requires Sufficient Data: AdaBoost may not perform well on very small datasets or datasets with insufficient diversity. It relies on a variety of weak models to be effective.

Overall, AdaBoost is a powerful ensemble method that can significantly improve the performance of weak base learners. However, like any ML algorithm, its effectiveness depends on the characteristics of the data and the problem at hand [21].

2.4. ElasticNet

ElasticNet is a linear regression method that combines both L1 (Lasso) and L2 (Ridge) regularization techniques [22]. It is used for variable selection and to mitigate issues arising from multicollinearity in regression analysis. It employs a linear combination of both L1 and L2 penalties, which allows it to select a subset of important features while still benefiting from the grouping effect of L2 regularization. This is achieved by minimizing the sum of squared differences between observed and predicted values, subject to a penalty term that is a combination of both the L1 and L2 norms of the regression coefficients.

The advantages of the Adaboost algorithm can be summarized as follows:

• Variable Selection: ElasticNet can perform variable selection by encouraging some of the coefficients to be exactly zero, effectively removing irrelevant features from the model. This is especially beneficial when dealing with high-dimensional datasets, where feature selection is critical.
• Balancing L1 and L2 Regularization: The α parameter allows for fine-tuning the balance between L1 and L2 regularization. This flexibility enables ElasticNet to capture the advantages of both Lasso (sparsity) and Ridge (stability).
• Robust to Multicollinearity: ElasticNet can handle multicollinearity, a situation where independent variables are highly correlated, by shrinking and selecting groups of correlated variables simultaneously. This aids in stability and interpretability.
• Generalization: ElasticNet often yields models that generalize well to new, unseen data. It can prevent overfitting by adding a regularization penalty to the loss function, which is crucial for dealing with noisy or limited data.

The disadvantages of the ElasticNet algorithm can be summarized as follows:

• Complexity in Choosing Hyperparameters: Selecting appropriate values for hyperparameters can be challenging. The optimal combination depends on the specific problem, and choosing the wrong values may lead to suboptimal results.
• Computational Cost: Its objective function involves both the L1 and L2 regularization terms, which makes it computationally more expensive than simple linear regression. This cost can be significant for large datasets.
• Less Interpretability: Although ElasticNet provides a balance between L1 and L2 regularization, the resulting models may be less interpretable than simple linear regression models. This is because some coefficients may be shrunken towards zero or other coefficients, making their individual interpretation less straightforward.

In conclusion, ElasticNet is a powerful regression technique, offering a compromise between Lasso and Ridge regressions. Its ability to handle feature selection, multicollinearity, and regularization makes it a valuable tool in various ML and statistical applications, but careful parameter tuning is required to make the most of its advantages.

2.5. K-Nearest Neighbors

KNN algorithm is a non-parametric and instance-based supervised learning method used for both classification and regression tasks [23]. In this method, the prediction of a target variable for a given data point is determined by identifying the K training examples that are closest to it in the feature space. The predicted value is then computed based on the average (for regression) or majority vote (for classification) of the KNN.

The advantages of the KNN algorithm can be summarized as follows:

• Simplicity and Intuitiveness: KNN is relatively easy to understand and implement. It does not involve complex mathematical computations or assumptions about the underlying data distribution.
• No Training Phase: Unlike many other ML algorithms, K-NN does not require a training phase. This means that the model is readily available for prediction once the data is available.
• Flexibility to Data Distribution: KNN can be applied to both linear and non-linear relationships between features and the target variable. It is not sensitive to the underlying data distribution.
• Adaptability to New Data: As new data points become available, the KNN model can be easily updated to incorporate this new information.

The disadvantages of the KNN algorithm can be summarized as follows:

• Computational Complexity: The main computational cost of KNN arises from the need to compute distances between all pairs of data points. As the dataset grows, this can become computationally expensive.
• Sensitivity to Feature Scaling: The performance of KNN can be influenced by the scale of the features. Therefore, it is essential to normalize or standardize the features before applying this algorithm.
• Memory Consumption: KNN requires storing the entire training dataset in memory, which can be impractical for very large datasets.
• Optimal K Selection: Choosing the appropriate value of K (the number of nearest neighbors to consider) can be challenging. A suboptimal choice of K may lead to poor model performance.
• Imbalanced Data: In classification tasks with imbalanced classes, KNN may be biased towards the majority class since it gives equal weight to all neighbors.
• Lack of Interpretability: KNN does not provide explicit information on the underlying relationships between features and the target variable. It does not offer coefficients or feature importance scores.
• Vulnerability to Noisy Data: Outliers and noisy data points can significantly impact the performance of KNN, potentially leading to incorrect predictions.

In summary, while KNN offers simplicity and adaptability to various data distributions, it is important to consider its computational requirements and sensitivity to parameter choices when applying it in practice.

2.6. Gradient Boosting

GB is a powerful ensemble learning technique used in supervised ML tasks, particularly for regression and classification problems [24]. It builds an additive model in a forward stage-wise manner, where each new model attempts to correct the errors made by the previous models. This is achieved by fitting a weak learner, typically a decision tree with limited depth, to the residuals (the differences between the observed and predicted values) of the previous model.

The advantages of the GB algorithm can be summarized as follows:

• High Predictive Accuracy: GB often yields highly accurate predictions. GB incrementally improves its performance by iteratively addressing the shortcomings of the model, ultimately achieving superior performance compared to individual weak learners.
• Handles Heterogeneous Data: It is robust to different types of data (categorical or numerical) and can handle a mix of predictor variables effectively.
• Feature Importance: GB provides a measure of feature importance, indicating which variables are most influential in making accurate predictions.
• Handles Missing Data: It can handle missing data in a dataset without the need for imputation techniques. It does this by using the information from available predictors.
• Robust to Outliers: It is less sensitive to outliers in the data compared to other algorithms.

The disadvantages of the GB algorithm can be summarized as follows:

• Computationally Expensive: Training a gradient boosting model can be computationally expensive, especially when dealing with large datasets and complex weak learners.
• Prone to Overfitting: Without proper hyperparameter tuning, gradient boosting models can overfit the training data, leading to poor generalization performance on unseen data.
• Requires Careful Hyperparameter Tuning: Selecting the right hyperparameters is crucial for achieving optimal performance. This process can be time-consuming and may require domain knowledge.
• Less Interpretable: Unlike simpler models like linear regression, the inner workings of a gradient boosting model are more complex and less interpretable, making it challenging to explain the predictions to non-technical stakeholders.
• Less Efficient for High-Dimensional Data: GB may not perform as well in situations with a very large number of features, as it may struggle to effectively capture the interactions among them.

In summary, GB is a powerful ensemble learning method known for its high predictive accuracy and versatility in handling different types of data. However, it requires careful parameter tuning and may not be the most efficient choice for very high-dimensional data [25].

3. Experimental Database

This study presents a rigorously curated experimental database encompassing 196 beams, meticulously obtained from 29 conducted experimental studies [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]. The experimental database encompasses a comprehensive range of data attributes, including the following parameters: width (b) and effective depth (d) of the concrete beams, concrete compressive strength (f_c), yield strength of steel reinforcement (f_y), transverse steel ratio (A_sv), spacing of transverse reinforcement (Sv), shear span to effective depth ratio (a/d), types of fiber employed, and experimental scheme details. Additionally, the database includes information about the types of fiber used, experimental scheme details, as well as the elastic modulus (E_f), ultimate strain (ε_frp), tensile strength (f_frp), total thickness (n × t_f), width (wf), spacing (sf), height (hf), and angle of inclination (β) of the FRP strips. Lastly, the database also encompasses the shear capacity of beams (V_exp). These essential parameters collectively form a comprehensive representation of the experimental data and facilitate a holistic understanding of the shear behavior of concrete beams externally bonded with FRP.

Table 1. Overview of the comprehensive database utilized for AI-based models.

Variables	Notation	Unit	Min	Mean	Std.	Max
Beam Width	b	mm	75.00	180.40	52.02	406.00
Beam Effective Depth	d	mm	120.00	297.40	101.82	660.00
Concrete Compressive Strength	fc	MPa	13.30	34.13	12.20	71.00
Yield Strength of Steel Reinforcement	fy	MPa	240.00	458.20	90.47	665.30
Transverse Steel Ratio	Asv	%	0.00	0.12	0.11	0.41
Spacing of Transverse Reinforcement	Sv	mm	0.00	147.70	131.21	400.00
Shear Span to Effective Depth Ratio	a/d	---	1.00	2.78	0.55	4.08
Elastic Modulus of FRP	Ef	GPa	5.30	200.95	109.80	392.00
Ultimate Strain of FRP	εFRP	---	0.00	0.02	0.01	0.07
Tensile Strength of FRP	fFRP	MPa	112.00	3073.52	1151.52	4500.00
Total Thickness of FRP	n × tf	mm	0.07	0.38	0.35	1.50
Width of FRP Strips	wf	mm	1.00	42.94	74.07	304.80
Spacing of FRP Strips	Sf	mm	1.00	124.61	218.08	1195.00
Height of FRP Strips	hf	mm	150.00	323.52	115.90	720.00
Angle of Inclination of FRP Strips	βeta	°	45.00	84.57	14.62	90.00
Shear Capacity Contribution by FRP	Vexp	kN	3.90	58.86	48.97	343.20

provides a summary of the collected database. All the mechanical parameters shown in Table 1, except for ‘Shear Capacity Contribution by FRP,’ are used as prediction inputs. The output of the prediction model is the ‘shear capacity contribution by FRP’.

Moreover, the correlation matrix analysis, as depicted in Figure 1, provides valuable insights into the interrelationships between Vexp and the various parameters, offering a comprehensive understanding of the factors influencing the shear capacity contribution by FRP reinforcement in RC beams wrapped with FRP. Among the variables showing positive correlations with V_exp, the effective depth (d) exhibits the strongest positive interaction with a coefficient of 0.55, indicating that an increase in the effective depth of the concrete beams is associated with a higher shear capacity contributed by FRP reinforcement. Additionally, the height of FRP strips (h_f) demonstrates a positive correlation with Vexp, with a coefficient of 0.46. Similarly, the width of the beams (b) and the shear span to effective depth ratio (a/d) show positive correlations, with coefficients of 0.40 and 0.20, respectively. Other variables, such as S_v, f_c, n × tf, w_f, f_y, and f_frp, also exhibit positive correlations with V_exp, albeit with relatively smaller coefficients ranging from 0.01 to 0.13.

On the other hand, certain variables display negative correlations with V_exp. The ultimate strain of FRP (ε_frp) exhibits a negative correlation with a coefficient of −0.02, suggesting that higher ultimate strain values of FRP are associated with a lower shear capacity contribution. Similarly, the spacing of FRP strips (s_f), elastic modulus of FRP (E_f), transverse steel ratio (A_sv), and the angle of inclination of FRP strips (β) also show negative correlations with V_exp, with coefficients of −0.10, −0.10, −0.16, and −0.24, respectively. These negative correlations indicate that higher values of these variables are associated with a decrease in the shear capacity contributed by FRP reinforcement.

4. AI-Based Analysis

Python was used to perform AI-based analysis, including model training and evaluation.

Table 2. Evaluation metrics for algorithm comparison.

Model	RMSE	MSE	MAE	R2
XGBoost	20.065	402.608	13.856	0.901
GB	26.454	699.823	18.427	0.828
RF	32.148	1033.504	21.275	0.747
AdaBoost	32.163	1034.457	24.163	0.746
KNN	44.888	2014.893	26.398	0.506
Elastic Net	46.566	2168.379	30.654	0.468

presents a comprehensive comparison of the algorithms based on various evaluation metrics. R² values for each algorithm obtained indicate the goodness of fit between predicted and actual shear strength values. The Xgboost model achieved the highest R² value of 0.901, demonstrating its strong predictive capabilities. This result signifies that approximately 90.1% of the variance in the shear strength can be explained by the Xgboost model. It outperforms other algorithms in terms of predictive accuracy and provides reliable estimations for the shear strength of rectangular RC beams retrofitted with FRP sheets. The GB algorithm also exhibits satisfactory performance with an R² value of 0.828. This value indicates that around 82.8% of the variability in the shear strength can be attributed to the predictions of the GB model. Although slightly lower than Xgboost, it still demonstrates a strong correlation between the predicted and observed shear capacity values. The RF and AdaBoost models yielded R² values of 0.747 and 0.746, respectively. These values indicate that these models can explain approximately 74.7% and 74.6% of the variability in shear strength, respectively. While these algorithms are reasonably good predictors, they have a slightly lower correlation than Xgboost and GB. The R² values for the KNN and ElasticNet algorithms, on the other hand, are 0.506 and 0.468, respectively. These values indicate that the predictions from these models explain approximately 50.6% and 46.8% of the variability in shear strength, respectively. These algorithms have lower predictive capabilities than the other models.

Additional evaluation metrics, such as Root Mean Squared Error (RMSE), Mean Squared Error (MSE), and Mean Absolute Error (MAE), were computed to further assess the performance of the algorithms. The RMSE values calculate the average difference between predicted and actual shear strength values. The lower the RMSE, the more precise the predictions. The Xgboost model had the lowest RMSE of 20.065, followed by the GB model, which had an RMSE of 26.454. The RMSE values for the RF and AdaBoost models were 32.148 and 32.163, respectively. The KNN and ElasticNet algorithms demonstrated higher RMSE values of 44.888 and 46.566, respectively. These values suggest that the Xgboost and GB models yield more precise predictions compared to the other algorithms. Additionally, the MSE values were calculated to quantify the overall prediction error. The Xgboost model yielded the lowest MSE value of 402.608, followed by the GB model with a value of 699.823. MSE values for the RF and AdaBoost models were 1033.504 and 1034.457, respectively. KNN and ElasticNet algorithms had higher MSE values of 2014.893 and 2168.379, respectively. Furthermore, the MAE values were calculated to determine the average absolute difference between the predicted and actual shear strength values. The Xgboost model demonstrated the lowest MAE value of 13.856, followed by the GB model with a value of 18.427. The RF and AdaBoost models yielded MAE values of 21.275 and 24.163, respectively. The KNN and ElasticNet algorithms resulted in higher MAE values of 26.398 and 30.654, respectively. These metrics collectively demonstrate the superior performance of the Xgboost model, followed by GB, RF, and AdaBoost models, while KNN and ElasticNet exhibit relatively lower predictive accuracy. The performance comparison is visually depicted in Figure 2, where bar plots illustrate the MAE, MSE, R² Score, and RMSE values for each model.

Figure 3 provides a visual representation of the relationship between the predicted and actual shear strength values for rectangular RC beams wrapped with FRP sheets using a range of ML algorithms. The x-axis represents the true shear strength values in kilonewtons (kN), while the y-axis represents the predicted shear strength values. The scatter plot serves as a visual representation of the extent to which the predicted values align with the actual values. Ideally, a perfect alignment would result in a cluster of data points tightly distributed along the diagonal line, indicating a high degree of concordance between the predicted and experimental shear strength values. Conversely, greater dispersion and deviations from the diagonal line signify a weaker correlation and less accurate predictions.

Upon careful examination of the scatter plot, it becomes evident that the Xgboost model exhibits the most remarkable predictive capabilities among the examined algorithms. The data points cluster densely around the diagonal line, implying a substantial agreement between the predicted and actual shear strength values. This noteworthy alignment underscores the Xgboost model’s capacity to discern underlying patterns within the dataset and provide reliable predictions for the shear strength of the beams wrapped with FRP sheets. Likewise, the GB algorithm demonstrates a reasonably strong correlation between the predicted and observed values, albeit somewhat less precise when compared to Xgboost. The data points exhibit a moderate clustering pattern around the diagonal line, indicating that the GB model adeptly captures the inherent relationships within the data, thereby yielding predictions of shear strength with a commendable level of accuracy. Regarding the RF and AdaBoost algorithms, the scatter plot exhibits a moderate alignment between the predicted and actual values. Although there are some deviations from the diagonal line, the overall clustering of data points suggests that the RF and Adaboost models can provide reasonably accurate predictions for shear strength estimation. However, for the KNN, and ElasticNet algorithms, the scatter plots indicate less pronounced alignments between the predicted and actual values. The data points exhibit more significant deviations from the diagonal line, indicating a weaker correlation and less accurate predictions for the shear strength of the beams. In summary, the scatter plot figure validates the R² values obtained for each algorithm, further emphasizing the performance of the Xgboost algorithm in accurately predicting the shear strength of rectangular RC beams strengthened with FRP sheets. The GB, RF, and AdaBoost models also show promising performance while the KNN and ElasticNet algorithms exhibit relatively lower predictive accuracy.

The analysis of prediction errors, visually depicted in Figure 4, yields valuable insights into the efficacy of the ML algorithms in accurately estimating the shear strength of rectangular RC beams bonded with FRP sheets. Figure 4 illustrates the disparity between the predicted and actual shear strength values. Remarkably, the Xgboost model exhibits significantly smaller prediction errors compared to the other algorithms, indicating its superior predictive capabilities. This observation substantiates previous findings, underscoring the Xgboost model’s exceptional accuracy in estimating the shear strength of rectangular RC beams wrapped with FRP sheets. Conversely, the remaining models demonstrate comparatively larger prediction errors, suggesting relatively less precise predictions.

Under careful examination of Figure 5, depicting the residuals, we delve into the analysis of the disparities between the predicted and experimental values. Consistently, the Xgboost model displays the smallest residuals, with values closer to zero, indicating minimal bias in its predictions. In contrast, the residuals for the other models exhibit a broader distribution, implying a higher degree of variability and potential bias in their predictions.

Overall, the visual analysis of the prediction error and residual plots aligns with the earlier quantitative evaluation metrics, further validating the superior performance of the Xgboost model. The smaller prediction errors and tighter distribution of residuals observed for Xgboost provide strong evidence of its ability to accurately capture the underlying patterns in the dataset. Consequently, the Xgboost model emerges as a reliable tool for predicting the shear strength of rectangular RC beams wrapped with FRP sheets, offering significant practical utility in engineering applications.

It is important to note that these visual representations serve as complementary evidence to the previously discussed numerical evaluation metrics. Together, they provide a thorough assessment of the models’ performance and support the conclusion that the Xgboost model excels as the most accurate and reliable predictor in this study.

The analysis of the residual distribution, as depicted in Figure 5, provides further understanding of the models’ performance in predicting the shear strength of the beams. The histograms in Figure 6 showcase the distribution patterns of the residuals for each model. The shape, spread, and central tendency of the residuals offer crucial information regarding the accuracy and precision of the predictions made by the models. Examining the histograms, we observe that the residuals exhibit varying distributions for different models. A desirable characteristic is a distribution centered around zero, indicating minimal bias in the predictions. Additionally, a narrower spread of the residuals implies higher precision in the model’s predictions. In the visual representation, alongside the colored lines, multiple rectangular boxes are present along the x-axis (residuals), each corresponding to a specific algorithm employed in the analysis. The positioning of these boxes along the x-axis provides insight into the distribution and magnitude of residuals for each algorithm. A lower placement along the y-axis suggests a higher density of residuals, while a higher placement indicates a lower density. In essence, a box located lower on the y-axis signifies a more concentrated distribution of residuals for that particular algorithm.

To aid in clarity, a colored line is assigned to each algorithm. The position of the colored lines serves as an additional visual cue to interpret the overall performance of each algorithm. A colored line positioned lower along the y-axis and with a shorter span along the x-axis suggests fewer and more concentrated residuals. For example, the red line representing the XGBoost algorithm is located at the bottom of the y-axis and exhibits a narrow span along the x-axis, indicating a lower density and more accurate predictions.Comparing the histograms, we find that the Xgboost model demonstrates a distribution of residuals that is more concentrated around zero, suggesting reduced bias and improved accuracy. This aligns with the previous evaluation metrics, reinforcing the notion that the Xgboost model outperforms the other models in predicting the shear strength of rectangular RC beams wrapped with FRP sheets. Conversely, the histograms for the remaining models exhibit wider distributions of residuals, indicating a relatively higher degree of variability and potential bias in their predictions. The insights gained from the analysis of Figure 6 further corroborate the superiority of the Xgboost model in accurately estimating the shear strength. Its ability to generate predictions with smaller residuals and a narrower distribution underscores its capacity to capture the underlying patterns in the data more effectively. Overall, the examination of the distribution of the residuals depicted in Figure 6 supports and reinforces the conclusion that the Xgboost model is the most accurate and reliable predictor among the models evaluated in this study.

5. Sensitivity Analysis by ANN

Numerous approaches exist for depicting the significance of input parameters concerning the target variable. For instance, Zaitseva et al. [54] introduced a novel method for assessing the importance of attributes in classification tasks. The study acknowledges that various factors and input data quality can influence the effectiveness of classification techniques. Their method, based on Importance Analysis from reliability engineering, measures the sensitivity of input attributes in the classification process, highlighting which attributes have the most significant impact on classification results. The importance of attributes is determined using a specialized index known as structural importance. The authors demonstrate the method’s application using a Fuzzy Decision Tree, which considers uncertainty in the initial data, but it is adaptable for use with other classifiers as well.

Determining the relative importance of input variables on selected outputs can be achieved by analyzing neural network weights. Neural networks employ weights to quantify the contribution of each input variable to the final output. These weights represent the strength of connections between the input variables and the neurons in the network’s hidden layers. To assess the relative importance of input variables using neural network weights, the first step is to train the neural network. During the training process, the weights are adjusted iteratively to minimize the error between predicted outputs and experimental outputs. Once the network is trained, the weights associated with each input variable can be examined.

The magnitude of the weights is indicative of the relative importance of the corresponding input variables. Larger weights suggest a stronger influence of the input variable on the output. Positive weights indicate a positive relationship, while negative weights signify a negative relationship. It is often beneficial to normalize the weights before comparing their relative importance. Normalization techniques, such as dividing the weights by their sum or scaling them to a specific range, can facilitate fair comparisons between variables. By analyzing the weights, one can rank or compare them to identify the input variables with the highest relative importance. Variables with higher weights are considered more influential in determining the output. However, it is essential to exercise caution when interpreting neural network weights. The relationship between weights and the importance of input variables can be complex and nonlinear. Additionally, other factors such as network architecture, activation functions, and regularization techniques can influence the interpretation. Therefore, it is advisable to combine weight analysis with other techniques to obtain a comprehensive understanding of variable importance. In this regard, an ANN was created using all the input and target data. After training the data and satisfying the criteria, its results were utilized for sensitivity analysis. A flowchart of artificial neural networks representing its working algorithm is presented in Figure 7.

Table 3. Weights obtained from the idealized neural network.

0.488	0.610	−0.507	0.773	0.200	−0.900	−0.398	0.161	0.628	0.339
−0.568	0.373	0.565	−0.035	0.186	−0.649	−0.325	1.181	0.249	0.394
0.280	−0.685	0.454	0.470	0.172	0.384	0.297	−0.417	0.138	−0.516
0.203	−0.620	0.107	−0.345	−0.699	0.334	0.495	0.134	0.658	−0.210
−0.026	−0.399	0.359	0.285	−0.452	0.166	0.012	0.367	0.324	0.278
−0.328	−0.270	0.029	−0.206	−0.502	−0.023	1.001	−0.399	−0.083	−0.329
0.301	−0.854	0.384	0.747	0.323	0.568	0.032	−0.214	−0.589	−0.294
0.606	−0.382	0.399	−0.248	0.587	−0.321	−0.320	−0.694	0.107	−0.094
−0.277	0.500	0.175	0.380	0.457	−0.169	0.382	0.251	−0.106	0.000
−0.626	−0.364	−0.095	0.269	0.481	−0.408	0.317	−0.250	−0.707	0.030
−0.680	0.071	−0.006	−0.016	−0.595	0.332	−0.663	0.349	−0.033	0.424
−0.020	−0.388	−0.475	0.121	−0.295	0.208	0.311	0.428	−0.651	0.137
−0.661	0.647	−0.695	0.681	0.509	0.346	−0.461	−0.331	−0.514	0.731
−0.069	0.541	−0.792	−0.381	−0.564	−0.356	0.725	0.354	0.047	−0.382
0.701	0.078	−0.238	0.048	−0.338	−0.410	−0.177	−0.569	−0.456	−0.417
−0.148	−0.499	0.239	0.768	−0.200	−0.336	−0.309	0.683	−0.248	−0.545

presents the weights obtained from the idealized neural network. The results of the sensitivity analysis are summarized in Figure 8, which reflects the relative importance of each input data.

The results indicated that four parameters, including the tensile strength of FRP, yield strength of steel reinforcement, beam width, and total thickness of FRP, have a profound impact on the output as they directly influence the structural behavior and performance of the system.

The FRP material’s tensile strength is a significant factor in determining the output. It denotes the FRP’s ability to withstand tension and is critical in maintaining structural integrity and load-bearing capacity. FRP with a higher tensile strength has better reinforcement effectiveness and overall structural performance. The yield strength of the steel reinforcement is a vital parameter that greatly impacts the structural performance. It determines the maximum stress level at which the steel can undergo elastic deformation without permanent deformation. A higher yield strength enables greater load-bearing capacity and resistance to yielding, resulting in a more structurally robust system. The width of the beam is an important factor that has a significant impact on the output. It has a direct impact on the load-carrying capacity, stiffness, and behavior of the beam, as well as the overall structural performance. A wider beam offers increased resistance to bending and enhances the structural performance, making it a key parameter in achieving desired output goals. The total thickness of the FRP material is a significant parameter in structural reinforcement. It is crucial in determining the FRP system’s strength, stiffness, and durability. A thicker FRP layer improves the load-carrying capacity and overall performance of the strengthened structure, thereby contributing to the desired output objectives.

It is worth emphasizing the importance of FRP properties in influencing the output. The tensile strength of FRP and the total thickness of FRP are two of the most influential parameters in determining structural performance. The high tensile strength of FRP enables it to effectively resist tension and enhance the load-bearing capacity of structures. Additionally, increasing the thickness of the FRP layer contributes to improved structural stiffness and strength, making FRP an invaluable material for reinforcing and retrofitting applications. These FRP properties have a significant impact on the output by ensuring structural integrity, durability, and overall performance.

6. Conclusions

A comprehensive investigation into accurately predicting the shear strength of FRP-strengthened RC beams using sophisticated ML algorithms was conducted. The evaluation and comparison of various algorithms, including Xgboost, GB, RF, AdaBoost, KNN, and ElasticNet, provide valuable insights into their predictive performance.

The extensive experimental database curated in this study, encompassing 196 beams and a comprehensive range of data attributes, is a valuable resource for the research community and practitioners. The experimental database comprises a wide spectrum of data attributes, encompassing key parameters such as the dimensions of the concrete beams, concrete compressive strength, yield strength of steel reinforcement, transverse steel ratio, spacing of transverse reinforcement, shear span to effective depth ratio, types of fiber employed, experimental scheme details, as well as the elastic modulus, ultimate strain, tensile strength, total thickness, width, spacing, height, and angle of inclination of the FRP strips.

The evaluation metrics employed, namely R², RMSE, MSE, and MAE, served as robust measures for assessing the accuracy and precision of the algorithms. Among the evaluated algorithms, the Xgboost model demonstrated outstanding performance, exhibiting the highest R² score and the lowest RMSE and MAE values. These findings establish the superiority of the Xgboost algorithm in terms of its predictive capabilities compared to the other algorithms studied. The scatter plot analysis further emphasizes the remarkable predictive capabilities of the Xgboost model, with data points clustering closely around the diagonal line, indicating a high degree of concordance between the predicted and observed values. The analysis of prediction errors and residuals supports the superior performance of the Xgboost model, revealing smaller prediction errors and a narrower distribution of residuals, indicative of reduced bias and increased accuracy.

Furthermore, a sensitivity analysis was performed using Artificial Neural Networks (ANNs) to quantify the impact of input variables on shear strength prediction. By analyzing the weight assignments associated with each input variable in the trained neural networks, a precise evaluation was made regarding the relative contributions of these variables to the output. Significantly, the tensile strength of FRP, yield strength of steel reinforcement, beam width, and total thickness of FRP emerged as influential factors directly influencing the structural behavior and performance.

Future research endeavors can focus on expanding the dataset and exploring additional variables to further refine the predictive models and broaden their applicability in practical scenarios. Additionally, investigating alternative ML algorithms and incorporating hybrid approaches may provide further improvements in predictive accuracy. This research paves the way for improved prediction models and practical applications in engineering design and analysis involving FRP-strengthened structures, advancing the field and facilitating more efficient and reliable structural solutions.