One of the main issues associated with steel fiber–reinforced concrete (SFRC) beams is the ability to anticipate their flexural response. With a comprehensive grid search, several stacked models (i.e., chained, parallel) consisting of various machine learning (ML) algorithms and artificial neural networks (ANNs) were developed to predict the flexural response of SFRC beams. The flexural performance of SFRC beams under bending was assessed based on 193 experimental specimens from real-life beam models. The ML techniques were applied to predict SFRC beam responses to bending load as functions of the steel fiber properties, concrete elastic modulus, beam dimensions, and reinforcement details. The accuracy of the models was evaluated using the coefficient of determination (R²), mean absolute error (MAE), and root mean square error (RMSE) of actual versus predicted values. The findings revealed that the proposed technique exhibited notably superior performance, delivering faster and more accurate predictions compared to both the ANNs and parallel models. Shapley diagrams were used to analyze variable contributions quantitatively. Shapley values show that the chained model prediction of ductility index is highly affected by two other targets (peak load and peak deflection) that show the chained algorithm utilizing the prediction of previous steps for enhancing the prediction of the target feature. The proposed model can be viewed as a function of significant input variables that permit the quick assessment of the likely performance of SFRC beams in bending.

中文翻译：

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用于预测钢纤维混凝土梁的承载能力和延展性的链式机器学习模型

与钢纤维混凝土（SFRC）梁相关的主要问题之一是预测其弯曲响应的能力。通过全面的网格搜索，开发了由各种机器学习（ML）算法和人工神经网络（ANN）组成的多个堆叠模型（即链式、并行）来预测 SFRC 梁的弯曲响应。基于来自真实梁模型的 193 个实验样本，评估了 SFRC 梁在弯曲下的弯曲性能。应用机器学习技术来预测 SFRC 梁对弯曲载荷的响应，作为钢纤维特性、混凝土弹性模量、梁尺寸和钢筋细节的函数。使用实际值与预测值的确定系数 ( R ² )、平均绝对误差 (MAE) 和均方根误差 (RMSE) 来评估模型的准确性。研究结果表明，所提出的技术表现出明显优越的性能，与人工神经网络和并行模型相比，可以提供更快、更准确的预测。沙普利图用于定量分析变量贡献。Shapley 值表明，延展性指数的链式模型预测受到其他两个目标（峰值载荷和峰值挠度）的高度影响，这表明链式算法利用先前步骤的预测来增强目标特征的预测。所提出的模型可以被视为重要输入变量的函数，可以快速评估 SFRC 梁在弯曲方面的可能性能。