Remaining useful life prediction for multi-phase deteriorating process based on Wiener process

Owing to the environmental stress and internal materials, the degradation signals show multiple phases characteristics, which have frequently been encountered in practice. In this paper, a multi-phase degradation model with jumps based on Wiener process is formulated to describe the multi-phase degradation pattern. The modified information criterion is adopted to determine the change-point number, and a simple yet effective algorithm is proposed for obtaining the change-point locations, which are critical for remaining useful life prediction. In the proposed model, to take into account the unit heterogeneity, all model parameters are assumed to be random variables. A Bayesian approach is used for integrating historical data and real-time data, which involves two stages, the off-line stage and on-line stage. Meanwhile, by treating the drift parameter and the diffusion parameter of each phase as latent parameters, the corresponding hyper-parameters are estimated based on the expectation maximization (EM) algorithm. The model parameters are updated under Bayesian rule at the on-line stage. Then, considering the multiple random change points and the corresponding jumps, the expressions of remaining useful life are derived under the concept of first passage time. Finally, a numerical simulation and a practical case study are provided for demonstrating the effectiveness.