Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method
In this study, 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 the aim of providing a more reliable and efficient design experience for structural applicatio...
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MDPI AG
2025-03-01
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| author | Zhe Zhang Xuemei Zhou Ping Zhu Zhaochao Li Yichuan Wang |
| author_facet | Zhe Zhang Xuemei Zhou Ping Zhu Zhaochao Li Yichuan Wang |
| author_sort | Zhe Zhang |
| collection | DOAJ |
| description | In this study, 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 the aim of providing a more reliable and efficient design experience for structural applications. For model training and testing, a comprehensive database is initially established for the flexural ultimate capacity of reinforced UHPC beams, comprising 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 <i>M<sub>u</sub></i> 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 sets 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 <i>R</i><sup>2</sup> value and lowest RMSE, MAE, and MAPE values. This substantial improvement in performance prediction of the 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 the flexural ultimate capacity of reinforced UHPC beams, thereby providing a foundation for more accurate model optimization and a more refined feature section strategy. |
| format | Article |
| id | doaj-art-d6cfe38810814bebafec53925e68c46f |
| institution | Kabale University |
| issn | 2075-5309 |
| language | English |
| publishDate | 2025-03-01 |
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| series | Buildings |
| spelling | doaj-art-d6cfe38810814bebafec53925e68c46f2025-08-20T03:43:02ZengMDPI AGBuildings2075-53092025-03-0115696910.3390/buildings15060969Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP MethodZhe Zhang0Xuemei Zhou1Ping Zhu2Zhaochao Li3Yichuan Wang4School of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, ChinaSchool of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, ChinaResearch Institute of Hunan University in Chongqing, Chongqing 401135, ChinaSchool of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, ChinaSchool of Civil Engineering, Hunan University of Technology, Zhuzhou 412007, ChinaIn this study, 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 the aim of providing a more reliable and efficient design experience for structural applications. For model training and testing, a comprehensive database is initially established for the flexural ultimate capacity of reinforced UHPC beams, comprising 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 <i>M<sub>u</sub></i> 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 sets 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 <i>R</i><sup>2</sup> value and lowest RMSE, MAE, and MAPE values. This substantial improvement in performance prediction of the 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 the flexural ultimate capacity of reinforced UHPC beams, thereby providing a foundation for more accurate model optimization and a more refined feature section strategy.https://www.mdpi.com/2075-5309/15/6/969performance predictionflexural ultimate capacityreinforced UHPC beammachine learning (ML)ensemble learning (EL)SHAP |
| spellingShingle | Zhe Zhang Xuemei Zhou Ping Zhu Zhaochao Li Yichuan Wang Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method Buildings performance prediction flexural ultimate capacity reinforced UHPC beam machine learning (ML) ensemble learning (EL) SHAP |
| title | Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method |
| title_full | Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method |
| title_fullStr | Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method |
| title_full_unstemmed | Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method |
| title_short | Prediction of Flexural Ultimate Capacity for Reinforced UHPC Beams Using Ensemble Learning and SHAP Method |
| title_sort | prediction of flexural ultimate capacity for reinforced uhpc beams using ensemble learning and shap method |
| topic | performance prediction flexural ultimate capacity reinforced UHPC beam machine learning (ML) ensemble learning (EL) SHAP |
| url | https://www.mdpi.com/2075-5309/15/6/969 |
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