An improved exponential model for machine remaining useful life prediction using empirical Bayes

The exponential model with Gaussian random error term is widely used in machine remaining useful life (RUL) prediction. However, this model is highly impacted by the prior parameter settings. To tackle this issue, this paper provides an improved exponential model for the machine RUL prediction. The empirical Bayesian analysis is adopted to update both the posterior distribution and the prior distribution based on the degradation observations. In particular, the posterior distribution is updated using conjunct Bayesian inference, and the prior distribution is updated based on the expectation maximum algorithm. Two schemes of empirical Bayesian analysis are designed in this study as, robust empirical Bayes (REB) and sensitive empirical Bayes (SEB). In REB, one-dimensional prior parameter is updated during the inference. In SEB, all the prior parameters are updated. The comprehensive experimental results and theoretical analysis show that REB outperforms the original exponential model for the RUL prediction, while SEB results in an inference divergence. As a result, REB is recommended for usage. The presented work will facilitate the RUL prediction of safety-critical machine with higher accuracy.