Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method

Ensemble learning (EL) models are designed to enhance the accuracy and efficiency in predicting the flexural ultimate capacity of reinforced ultra-high-performance concrete (UHPC) beams with aim to provide more reliable and efficient design experience for structural applications in this study. For model training and testing, a comprehensive database is initially established for flexural ultimate capacity of reinforced UHPC beams, composed of 339 UHPC-based specimens with varying design parameters compiled from 56 published experimental investigations. Furthermore, multiple machine learning (ML) algorithms, including both traditional and EL models, are employed to develop optimized predictive models for the flexural ultimate capacity of reinforced UHPC specimens derived from the established database. Four statistical indicators of model performance are utilized to assess the accuracies of the prediction results with ML models used. Subsequently, a highly efficient evaluation of ML models is taken by analyzing the sensitivity of ML models to varying data subsets. Finally, a Shapley Additive Explanations (SHAP) method is employed to interpret several EL models, thereby substantiating their reliability and determining the extent of influence exerted by each feature on the prediction results. The present ML models predict accurately the flexural ultimate capacity Mu of reinforced UHPC beams after optimization, with EL models providing a higher level of accuracy than the traditional ML models. The present study also underscores the significant impact of the database division ratios of training-to-testing set on the effectiveness of performance prediction for the ML models. The optimal model functionality may be accomplished by properly considering the effects of database subset distribution on the performance prediction and model stability. The CatBoost model demonstrates superior performance in terms of predictive accuracy, as evidenced by its highest R² value, the lowest RMSE value, lowest MAE value, and lowest MAPE value. This substantial improvement in performance prediction of flexural capacity for reinforced UHPC beams is notable when compared to existing empirical methods. The CatBoost model displays a more uniform distribution of SHAP values for all parameters, suggesting a balanced decision-making process and contributing to its superior and stable model performance. The current study identifies a significant positive relationship between the increases in height, and reinforcement ratio of steel rebars and the growth in normalized SHAP values. These findings contribute to a deeper understanding of the role played by each feature in the prediction of flexural ultimate capacity of reinforced UHPC beams, thereby providing a foundation for more accurate model optimization and for a more refined feature section strategy.