Remaining useful life prognostic for degrading systems with age- and state-dependent jump-diffusion processes

The prediction of the remaining useful life (RUL) holds significant importance within the field of prognostics and health management (PHM), which may provide lifetime information about the system. The foundation for effectively estimating RUL is constructing an applicable degradation model for the system. However, the majority of existing degradation models only consider the issue of age dependence and disregard state dependence. In addition, variations to the system's operating environment will cause degradation state jumps, which will impact degradation paths and the precision of RUL estimation. Nevertheless, existing studies have only accounted for some of the influencing factors, neglecting to simultaneously consider age dependence, state dependence, and jumps. To account for both age-state dependent (ASD) and jump, a generalized age-state dependent jump-diffusion (ASDJD) model is proposed for RUL estimation in this paper. Approximate analytic expressions for the RUL distribution are derived based on first hitting time (FHT). Expectation conditional maximization (ECM) and maximum likelihood estimate (MLE) are used to estimate the model's unknown parameters. The simulation dataset and the Xi'an Jiaotong University bearing dataset validate the proposed model, demonstrating that state dependence and jumps should be considered in the RUL estimation process.