Interpretable machine learning methods for clarification of load-displacement effects on cable-stayed bridge

Cable-stayed bridges play a crucial role in various transportation systems, facilitating the movement of pedestrians, automobiles, and trains. Accurately estimating structural displacements and comprehending the impact of loads on these displacements are vital for bridge management and maintenance. This study develops an interpretable ensemble learning model called eXtreme Gradient Boosting (XGBoost) to predict the critical displacements of a cable-stayed bridge's girder and pylon using monitoring data. A model tuning approach is proposed to select the hyperparameters of the learning algorithm, ensuring the prediction performance. To assess the importance of input variables in predicting structural displacements, the SHapley Additive exPlanations (SHAP) method is employed to enable both individual and global interpretations of the input-output relationships with physical and correlative insights. To validate the proposed methodologies, data on critical loads and displacement responses from a cable-stayed bridge are collected. The performance of the ensemble learning model is compared with other machine learning and conventional methods, demonstrating an average accuracy with R² of 84.13% for all five displacement predictions. The SHAP analysis reveals that temperature emerges as the most significant feature influencing the displacements of both the girder and pylon. Furthermore, traffic loads exhibit a greater impact on girder displacement, while wind loads exert a stronger influence on pylon displacement. Notably, the effects of temperature and wind on the girder and pylon displacements can be decoupled. The findings of this study could aid in the effective management and maintenance of cable-stayed bridges by enhancing our understanding of bridge displacement.