Degradation modeling plays an important role in system health diagnosis and remaining useful life (RUL) prediction. Recently, a class of Wiener process models with adaptive drift was proposed for degradation-based RUL prediction, which has been proven flexible and effective. However, the existing studies use an autoregressive model of order 1 for the adaptive drift, which can result in difficulties in both model estimation and RUL prediction. This paper proposes a new adaptive Wiener process model that utilizes a Brownian motion for the adaptive drift. The new model shares the flexibility of the existing models, but avoids the difficulties in model estimation and RUL prediction. A model estimation procedure based on maximum likelihood estimation is developed, and the RUL prediction based on the proposed model is formulated. The effectiveness of the model in RUL prediction is validated using simulation and through an application to the lithium-ion battery degradation data.

Most industrial products degrade with usage. To capture degradation patterns and schedule condition-based maintenance actions, it is necessary to model the degradation process and predict the system remaining useful life (RUL). In practice, the operating environments and loading conditions are dynamic and stochastic, which introduces extra randomness in the degradation process. To account for the dynamic environmental impacts, this article proposes a nonlinear Wiener process model with a random time-varying covariate. We model the dynamic covariate with an Ornstein–Uhlenbeck process, and link it to the time-varying degradation rate by an exponential form covariate-effect function. Therefore, the proposed Wiener process has a time-varying degradation rate impacted by the dynamic environment. We propose to estimate the model parameters by maximum likelihood estimation based on given observations of the degradation and covariate. We also propose a simulation-based procedure to obtain the RUL for the proposed model. The model is verified by Monte Carlo simulations. We apply the proposed model to a dust-cleaning fan degradation dataset and a lithium-ion battery degradation dataset, and the results show that the proposed model outperforms the existing degradation models in fitting the real data and RUL prediction.