Fault Diagnosis of High-Speed Rail Vehicle Suspension Systems: A Comparative Study of Koopman Operator and T–S Fuzzy Modeling Based Data-Driven K-Gap Metric

This paper proposes a novel data-driven K-Gap metric method based on the Koopman operator for the detection and isolation of multiplicative faults in high-speed train suspension systems. A systematic comparison is conducted with a data-driven K-Gap approach implemented through the fuzzy modeling framework. First, Takagi–Sugeno (T–S) theory is employed to extend the K-Gap metric for nonlinear dynamic modeling of the suspension system. Subsequently, the Koopman operator framework is introduced to lift the system states into a high-dimensional observable space, enabling a globally linear representation of the system. Building upon Koopman-based stable kernel representation (SKR), a more accurate K-Gap residual metric is constructed. Finally, a unified fault diagnosis scheme is developed with the K-Gap metric as the core indicator, and the two approaches are experimentally compared in terms of their performance in detecting and isolating multiplicative faults. The experimental results demonstrate that the Koopman-based method significantly outperforms the T–S fuzzy model in terms of residual separability, fault classification accuracy, and diagnostic stability, confirming its effectiveness and superiority for fault diagnosis in complex nonlinear systems.