A generalized diffusion model for remaining useful life prediction with uncertainty

Forecasting the remaining useful life (RUL) is a crucial aspect of prognostics and health management (PHM), which has garnered significant attention in academic and industrial domains in recent decades. The accurate prediction of RUL relies on the creation of an appropriate degradation model for the system. In this paper, a general representation of diffusion process models with three sources of uncertainty for RUL estimation is constructed. According to time-space transformation, the analytic equations that approximate the RUL probability distribution function (PDF) are inferred. The results demonstrate that the proposed model is more general, covering several existing simplified cases. The parameters of the model are then calculated utilizing an adaptive technique based on the Kalman filter and expectation maximization with Rauch-Tung-Striebel (KF-EM-RTS). KF-EM-RTS can adaptively estimate and update unknown parameters, overcoming the limits of strong Markovian nature of diffusion model. Linear and nonlinear degradation datasets from real working environments are used to validate the proposed model. The experiments indicate that the proposed model can achieve accurate RUL estimation results.