A novel method for subgrade cumulative deformation prediction of high-speed railways based on empiricism-constrained neural network and SHapley Additive exPlanations analysis

Understanding the long-term deformation of high-speed railway subgrade is essential for solving deformation issues and managing operations. Machine learning methods are commonly used to predict subgrade cumulative deformation (SCD). However, traditional machine learning models for SCD prediction have poor generalization to new data and lack visualization. Hence, this study proposes a novel method using an empiricism-constrained neural network (ECNN) and SHapley Additive exPlanations (SHAP) analysis for predicting SCD of high-speed railways. Firstly, the SCD prediction dataset is constructed and divided into training and test sets. Then, neural network models are developed using the training set, and the optimal model is determined based on the comprehensive scoring results on the test set. The optimal model couples empirical information into the neural network with loss function modification, to create the ECNN model. Finally, the interpretability of the ECNN model is analyzed using the SHAP method. The results indicate that the Bi-directional Gated Recurrent Unit (Bi-GRU) model is the optimal model with the highest CSI value of 23. The ECNN model outperforms the Bi-GRU in generalization to new data, especially in long-term SCD prediction with limited training data. Contribution analysis shows that the top two features influencing the prediction are S_t-1 (54.4%) and S_t-2 (30.4%), consistent with the findings of the ablation analysis. The research results can provide a new reference for predicting the SCD of high-speed railways.