Two novel mixed effects models for prognostics of rolling element bearings

Rolling element bearings are widely used in various machines to support rotating shafts. Due to harsh working environments, the health condition of a bearing degrades over time. A typical bearing degradation process includes two phases. In Phase I, the health condition of the bearing is in normal and it exhibits a stable trend. In Phase II, the health condition of the bearing degrades exponentially. To analytically model the bearing degradation process, two novel mixed effects models are proposed in this paper. Each of the two mixed effects models is able to simultaneously model Phases I and II of the bearing degradation process. The main difference between the two mixed effects models is that different error assumptions including multiplicative normal random error and multiplicative Brownian motion error are respectively considered in the two mixed effects models. Consequently, two different closed-form distributions of bearing remaining useful life are derived from the two mixed effects models via Bayes' theorem once real-time bearing condition monitoring data are available. 25 sets of bearing degradation data collected from an experimental machine are used to illustrate how the two mixed effects models work. Comparisons are conducted to show that the mixed effects model with multiplicative Brownian motion error results in lower prediction errors than the mixed effects model with multiplicative normal random error for bearing remaining useful life prediction.