Degradation Modeling and RUL Prediction in Dynamic Environments Using a Wiener Process With an Autoregressive Rate

Since the degradation process is dependent on the environmental stresses, degrading products operating under dynamic environments can have time-varying degradation rates. Existing studies generally exploit a random walk to model the time-varying degradation rate, considering the randomness of the environmental effects. The random walk is not stationary, while the real environments, although dynamic, are often stationary. The degradation process under a stationary environment would have a stationary degradation rate. Therefore, instead of the random walk, we propose to model the stochastic degradation rate by an autoregressive model. The autoregressive rate can accommodate the randomness and stationarity of the environmental effects. Conditional on the autoregressive degradation rate, a Wiener process is used to model the degradation process. We develop an Expectation-Maximization algorithm to perform maximum likelihood estimation of model parameters. Moreover, to facilitate remaining useful life prediction, we derive the explicit probability density function for the remaining useful life (RUL). We validate the proposed model by a simulation study and justify the applicability and performance of the proposed model by two real degradation datasets.