Abstract: In the existing research on the remaining useful life prediction of stochastic degradation equipment with imperfect maintenance, only the single influence of maintenance activities on the degradation state or degradation rate is usually considered,while the research that considers both two influences ignores the unit-to-unit variability of degradation equipment. In view of this, an adaptive remaining useful life prognostic approach based on a multi-stage diffusion process is proposed, which takes into account the influence of imperfect maintenance activities on the degradation state and degradation rate, and describes the update process of degradation rate with observation data by using a random walk model to characterize the unit-to-unit variability of equipment. Based on the historical degradation data, the initial values of degradation model parameters are obtained by the maximum likelihood estimation method. Based on the state observation data, the Kalman filtering and expectation-maximization algorithm are used to adaptively update the model parameters. The probability density function of the remaining useful life in the sense of the first hitting time is derived by the convolution operator and the Monte Carlo method. Finally, the effectiveness and superiority of the proposed approach are verified by the simulation example and the case study of gyroscopes.

Key words: imperfect maintenance, degradation equipment, remaining useful life, unit-to-unit variability, adaptive prediction