Degradation Modeling Based on a Time-Dependent Ornstein-Uhlenbeck Process and Residual Useful Lifetime Estimation

In this paper, how to estimate residual useful lifetime (RUL) is discussed based on a model-based method when fluctuations exist in the degradation process around its average behavior. The main idea is to model the degradation process as a time-dependent Ornstein-Uhlenbeck (OU) process, where the first passage failure is adopted to consider corresponding RUL estimation. The time-dependent OU process is proved good by its statistical properties on the controllable mean, variance, and correlation. Its mean-reverting property is introduced to interpret temporary correlated fluctuations from an overall degrading trend in degradation records. The corresponding parameter estimation is proposed based on the maximum likelihood estimation method, and a Volterra integral equation of second kind with a non-singular kernel is then considered to calculate the probability density function (pdf) of failure time. Proposed methods are tested in a case study, where results are compared with a nonlinear-drift, linear-diffusion process.