An Online Bayesian Framework for Identifying Latent System Degradation States

In industrial settings, the health state of a product is often difficult to observe directly. Instead, it is typically inferred from noisy degradation data that are related to the system’s operational condition. However, existing methods commonly neglect parameter uncertainty and lack the ability to perform real-time state estimation. To address these challenges, this article proposes a Bayesian inference framework for accurate online identification of system degradation states. Specifically, a Wiener process model with measurement noise is developed, and prior distributions are introduced to capture parameter uncertainty. In the offline training stage, historical measurement data are utilized to approximate the joint posterior distribution of the latent degradation states and model parameters via variational Bayesian methods. In the online stage, a state-space formulation is adopted to dynamically update the posterior distribution using real-time observations, enabling dynamic estimation of the degradation state. The proposed approach significantly reduces both storage and computational costs. Numerical simulations and real-world case studies demonstrate that the proposed method achieves superior performance in terms of both accuracy and efficiency.