An Interpretable Ensemble Machine Learning Framework for Predicting the Ultimate Flexural Capacity of BFRP-Reinforced Concrete Beams

Abstract

Prediction of the ultimate moment capacity (Mu) of BFRP-reinforced concrete beams is complicated by nonlinear parameter interactions and the linear-elastic response of BFRP, reducing the accuracy of conventional design models. This study develops an optimized machine learning (ML) framework incorporating random forest, extra trees, gradient boosting, adaboost, bagging, support vector regression, histogram-based gradient boosting, and ensemble voting and stacking strategies for reliable prediction of the Mu of BFRP-reinforced concrete beams. A comprehensive database of material, geometric, reinforcement, and BFRP mechanical parameters was analyzed, and model performance was evaluated using an 80/20 train–test split and 10-fold cross-validation based on R2, RMSE, MAE, and MAPE. The stacking regressor demonstrated superior predictive performance, achieving an R2 of 0.999 (RMSE = 0.590) in training and an R2 of 0.988 (RMSE = 2.487) in testing, indicating excellent robustness and strong generalization capability in predicting Mu. Furthermore, interpretability analyses based on SHAP, PDP, ALE, and ICE demonstrate that span length (L) and beam depth (h) constitute the governing parameters in the prediction of Mu. Unlike prior studies focused mainly on predictive accuracy, this work proposes an optimized and interpretable stacking ensemble framework that integrates explainable AI with classical flexural mechanics for physically consistent and reliable prediction of the ultimate moment capacity of BFRP-reinforced concrete beams.