High-speed train dynamics modeling based on end-edge–cloud collaboration: An efficient distributed online correction method

The construction of accurate dynamic models for high-speed trains (HSTs) and their rapid online correction mechanisms constitute the core guarantee for safe and efficient operation. However, conventional mechanism-based models suffer from poor transferability, while data-driven models struggle to simultaneously achieve interpretability, lightweight design, and global multi-mass-point modeling. Furthermore, existing correction strategies exhibit significant deficiencies in cross-operating-condition generalization, tracking capability under strongly time-varying dynamics, and resource efficiency. To address these challenges, this paper proposes a novel hybrid modeling approach along with a end-edge–cloud collaborative online correction framework. First, a hybrid model is constructed based on longitudinal dynamic analysis: the Nonlinear Autoregressive with Exogenous Inputs (NARX) model is employed to characterize the fundamental dynamics of a single mass-point, while an innovatively designed Temporal–Spatial Attention (TSA) module is utilized to extract multi-mass-point temporal dependencies and spatial coupling features in parallel. The outputs are processed through a Feedforward Neural Network (FNN) to compensate for unmodeled dynamics, thereby forming a lightweight and interpretable global model. Second, a hierarchical correction strategy is proposed: (1) At the cloud level, cross-operating-condition parameter transfer is achieved via low-rank matrix reconstruction to maintain the model’s generalization capability across diverse operating conditions; (2) At the edge level, a self-organizing stochastic configuration algorithm is developed, leveraging node freezing and sequential projection optimization to enable rapid, anti-forgetting correction; (3) On the end side, a Recursive Ridge Regression with time-varying forgetting factors and ridge parameters is developed, which handles multicollinearity while enhancing the capability of tracking time-varying dynamics. Finally, validation using real-world data from the Beijing–Guangzhou high-speed railway train system demonstrates the effectiveness and superiority of both the proposed model and the collaborative correction framework. Furthermore, ablation studies on a gas turbine dataset further confirm the efficacy and advancement of each individual correction algorithm.