Degradation modeling and remaining useful life prediction with dual-time-scale considering system state and individual variability

Most recent studies on system degradation modeling and remaining useful life (RUL) prediction assume a stable system state, overlooking its influence on system degradation evolution. Additionally, individual variability among identical systems can affect the accuracy of the RUL prediction. To address these limitations, this study proposes a nonlinear Wiener process model with time-varying degradation rates that accounts for both system state and individual variability. The influence of fast-varying system states is captured using an average function, whereas individual variability is represented by a random-effect parameter. For cases where the system state changes rapidly while the degradation state evolves more slowly, a dual-time-scale Kalman filter algorithm is adopted to jointly estimate system state and random-effect parameters. The expectation–maximization algorithm is used to estimate the remaining unknown parameters of the degradation model. Furthermore, based on first hitting time definition, the approximate analytical expression for probability density function (PDF) of the RUL is derived. Finally, the effectiveness and practicality of proposed method are validated through both a numerical example and a motor case study.