Physically grounded quantification of high-speed train hunting instability via phase-space divergence and nonlinear feature fusion

This study proposes a physics-informed framework for early warning and severity assessment of hunting instability in high-speed trains. A high-fidelity CR400AF vehicle dynamics model was established to reproduce three typical instability scenarios: overspeed operation, anti-yaw damper degradation, and increased wheel–rail equivalent conicity. A Local Trajectory Divergence Index (LTDI) was formulated to characterise the phase-space transition from weakly correlated or stochastic vibration to limit-cycle-like hunting motion. LTDI was integrated with Sample Entropy and vibration-energy information to construct a multidimensional state representation, from which a normalised Hunting Severity Index (HSI) was developed for continuous severity quantification and stable–moderate–severe state discrimination. The framework was evaluated using model-based simulations, onboard condition-monitoring data from operating high-speed trains, and independent field-alarm records with event-level reference annotations. The results show that the proposed method can identify hunting-related state transitions and provide interpretable severity assessment under both simulated and measured operating conditions, supporting intelligent condition monitoring and proactive safety warning of railway vehicles.