Two-stage degradation modeling for remaining useful life prediction based on the Wiener process with measurement errors

Remaining useful life prediction (RUL) is a key component in the application of prognostics and health management associated with devices or systems. But such RUL predictions are cumbersome owing to complexities from external effects and internal degradation mechanisms within systems. Specifically, it is common for degradation processes to comprise distinct multiple stages rather than just one uniform stage in many mechanical systems. In particular, the two-stage degradation modeling for RUL prediction based on the Wiener process with linear drift has received significant attention in recent years. However, negative effects of measurement errors and stochasticity of the degradation states are generally excluded from current degradation modeling, which causes inaccuracy problems that can impact system maintenance schedules and operational efficiency. Therefore, to solve such problems, measurement errors are considered in this paper and a two-stage degradation model is proposed, in which an adaptive term is also characterized by the Wiener process. The transition probability density function (TPDF) of the degradation state at the two-stage changing point is derived and an analytical solution for the RUL is obtained under the concept of the first hit time (FHT). A Kalman filter and smoothing algorithm are introduced to estimate variables, and the expectation maximization (EM) algorithm is applied to update and estimate model parameters. Finally, the effectiveness and applicability of the proposed model in RUL predictions are verified through numerical simulation and a case study of bearings.

Automated summary

Remaining useful life (RUL) prediction is crucial for prognostics and health management of devices or systems. However, the complexity of external effects and internal degradation mechanisms makes RUL predictions challenging. This paper proposes a two-stage degradation model considering measurement errors, and utilizes the Wiener process and expectation maximization algorithm for RUL estimation. Numerical simulation and a case study of bearings validate the effectiveness and applicability of the proposed model.