Correlation‐driven multivariate degradation modeling and RUL prediction based on Wiener process model

Abstract For degraded products with multiple performance characteristics (PCs), one way to model their degradation process is by using a multivariate independent Wiener process model with random drift. However, it fails to capture the latent correlation in degradation paths for multiple PCs caused by the common environmental condition. In this paper, we model the degradation processes of multiple PCs using multiple correlated Wiener processes. The commonly shared environmental condition function incorporates the degradation correlation and random effect. Thus, it directly catches the strong correlation of degradation rates and volatilities to all dimensions of multiple PCs. Our model is more economical in the number of parameters than the multivariate independent Wiener process. The correlation coefficients and RUL distribution approximation are provided in closed forms. We extend the proposed model to a two‐stage degradation process to correlate multiple PCs in each stage. An adaptive drift is adopted in the Wiener process model for the real‐time degradation states updating with the help of the Bayesian and the expectation‐maximization (EM) algorithm. The proposed model's effectiveness is illustrated by numerical studies and a real‐world application to the wheel treads on high‐speed trains.