Lifelong dictionary learning for dynamical system fault detection: A Bayesian perspective

Dynamical-system fault detection is essential for maintaining safe and reliable operation. However, industrial systems often evolve across operating modes, causing fixed monitoring models to lose accuracy when the data distribution shifts. Updating the model with new mode data can alleviate this problem, but it may also overwrite representations learned from previous modes, leading to catastrophic forgetting. To address this issue, this paper proposes a Bayesian lifelong dictionary learning method for fault detection in evolving dynamical systems. Starting from a maximum a posteriori formulation, the proposed method introduces atom-wise elastic penalties that protect dictionary atoms according to their importance to historical modes while allowing less constrained atoms to adapt to newly observed modes. A recursive weight update is further derived, enabling sequential model updates without replaying historical training data. Numerical simulations, a CSTH process benchmark, and the Paderborn University bearing benchmark show that the proposed method improves detection accuracy and knowledge retention compared with representative baselines under sequential operating-mode transitions.