Correlation-Driven Bivariate Wiener Process Modeling Subjects to Random Effects

For many high reliable products, the degradation can be characterized in terms of two performance characteristics (PCs). Under this circumstance, both the degradation rates and degradation volatilities between two PCs are correlated due to the common working environment. However, most studies either assume only one PC for the target product, neglecting the commonly encountered bivariate situation, or fail to capture the inevitably degradation volatility correlation between two PCs. This significantly weaken the accuracy of degradation modeling and remaining useful life (RUL) prediction. To solve the issue, we developed a correlation-driven bivariate Wiener process model subject to random effects. Both the degradation rate and volatility are positive functions of the working stress. The expectation maximization method and the Bayesian algorithm are combined to update the model parameters, based on which the degradation path and RUL are predicted accordingly. A case study about bearing vibrations is carried out for illustrating the effectiveness of our method.