A novel prognostic method for degrading devices with nonlinear degradation processes indexed by both continuous and discrete time scales

Remaining useful life (RUL) prediction techniques based on degradation modeling to ensure the safety and reliability of stochastic degraded devices are of critical value. However, although the performance degradation of various devices in engineering practice is affected by multi-timescales, there are few RUL prediction methods for stochastic degraded devices with dual time scales in the existing literature. The research of prediction methods considering continuous and discrete time scales is blank. Toward this end, this paper proposes a novel prognostic method for nonlinear degradation devices based on the continuous-discrete dual time scales. First, the performance degradation with a discrete timescale is determined with a compound Poisson process and integrated into the diffusion process model to establish a nonlinear dual-timescale degradation model. Subsequently, the joint expression of the dual-timescale RUL distribution of the device in the first hitting time sense solves with threshold transformation. Finally, the effectiveness and superiority of the proposed method are verified through a numerical simulation and a gyroscope example. The experimental results show that the proposed method can provide more comprehensive information about the life distribution and effectively improve the accuracy of the RUL prediction.