Order-adaptive subspace scale learning for unsupervised anomaly detection under time-varying rotational speed conditions

Under time-varying speeds, rotating machinery experiences pronounced dynamic effects, making this operational phase highly susceptible to faults. Anomaly detection under such non-stationary condition is challenging, as speed-induced distribution shifts in vibration signals often lead conventional methods to mistake normal variations for faults, resulting in false alarms. Although data driven methods aim to learn speed-invariant representations, its generalization to unseen speed profiles remains limited. To address this, we propose a physics-informed Order-Adaptive Subspace Scale Learning (OASSL) method that integrates order tracking grounded in the physical relationship between vibration harmonics and shaft rotation. This approach resamples time-domain signals into the angular domain to generate unified order-frequency features, considerably eliminating the influence of speed fluctuations. Furthermore, a novel multi-subspace sampling and subspace scale learning strategy is introduced within the network, which enhances the extraction of subtle fault signatures and improves robustness against varying operating conditions. Experimental results on time-varying speed datasets demonstrate that the proposed OASSL significantly outperforms existing methods in reducing false alarms and accurately identifying faults under complex speed variations. © 2026 Elsevier Ltd.