A mechanism-based hybrid Transformer-GRU network for bridge pier hysteresis curves prediction: an interpretable research

To address the complexity and accuracy requirements for predicting the hysteretic behaviour of bridge piers, this study developed a hybrid deep learning method that integrates physical mechanisms. A mechanism-based Transformer-GRU hybrid network was proposed, which introduces physical constraints through multi-head attention mechanisms and a specially designed dataset, combining the global modelling capabilities of Transformers with the temporal capture advantages of GRUs. A comprehensive dataset incorporating geometric parameters, material properties, load conditions, and historical information was constructed, and an improved training strategy was adopted to mitigate the error propagation issues in multi-step predictions. In comparison with alternative prediction models, the proposed method demonstrated superior performance on key performance metrics: R² improved by 1.2%, RMSE reduced by 6.3%, and MAE decreased by 8.9%. The model demonstrated good predictive performance, even with limited training data. The SHAP interpretability analysis confirmed that the model effectively captured the key physical relationships. This interpretable method provides an efficient and accurate tool for predicting the hysteretic behaviour of bridge piers, offering significant engineering application value in structural health monitoring and seismic performance assessment.