Kernel dynamic orthonormal subspace analysis for monitoring hybrid electric vehicle powertrain faults

Hybrid electric vehicle (HEV) powertrain systems exhibit complex dynamic and nonlinear characteristics due to the coupling effects among mechanical, electrical, and thermal subsystems. Traditional multivariate statistical process monitoring (MSPM) methods based on the time lag shift method (TLSM) may suffer from redundant information problems where historical data not used for prediction can contaminate the extracted features and reduce fault detection sensitivity. To address this limitation, this paper proposes a kernel dynamic orthonormal subspace analysis (KDOSA) method for monitoring HEV powertrain faults. The proposed method extends the OSA framework to the kernel feature space using Gaussian kernel functions, aiming to capture nonlinear dependencies while maintaining orthogonal separation between dynamic and static components. By decomposing real-time data into dynamic and static subspaces in the reproducing kernel Hilbert space, KDOSA is designed to mitigate the redundant information problem inherent in TLSM-based kernel methods such as dynamic kernel PCA. A comprehensive monitoring framework is developed with [Formula: see text] indices for both dynamic and static subspaces, providing fault detection capability and diagnostic information about fault origins. The effectiveness of the proposed method is examined through numerical simulations and real-world HEV powertrain experiments. Experimental results demonstrate that KDOSA achieves favorable fault detection performance with performance index (PI) values exceeding 95% across all test scenarios without triggering false alarms in the tested cases, showing improved performance compared with existing OSA-based nonlinear dynamic methods.