An Improved Variational Bayesian Analysis for Wiener Process With Multi‐Source Variability

ABSTRACT In the degradation with multi‐source variability under the Variational Bayesian method, the true degradation state is not directly observable, necessitating effective tracking of the latent state. The unidirectional dependence of the latent states on drift coefficients, which reflect unit‐to‐unit variability, induces a hierarchical structure that significantly complicates joint estimation of the latent variables. To address this, a dual‐layer Variational Bayesian method is developed based on a carefully constructed state‐space model to enable joint estimation of both states and parameters. Furthermore, the state‐parameter covariance matrix is explicitly decomposed, and a block filtering strategy is proposed to control the propagation of cross‐covariance caused by the unidirectional dynamic coupling. In applications, validation using both simulated data and lithium‐ion battery degradation data demonstrates that the proposed method significantly outperforms Markov Chain Monte Carlo, Maximum Likelihood Estimation, and traditional Variational Bayesian methods in terms of parameter estimation accuracy and computational efficiency. The proposed approach is particularly well‐suited for high‐efficiency reliability analysis in large‐scale degradation scenarios.