Bearing Life Prediction with Informed Hyperprior Distribution: A Bayesian Hierarchical and Machine Learning Approach

Abstract

A Bayesian hierarchical model (BHM) is developed to predict bearing life using envelope acceleration data in combination with a degradation model and prior knowledge of the bearing rating life. The BHM enables the inference of individual bearings, groups of bearings, or bearings operating under certain conditions. The key benefit of the BHM approach is that the relationships between the bearing model parameters and their prior distributions can be expressed at different hierarchical levels. We begin our analysis using a bearing rating life calculation $L_{10h}$ and an estimate of its associated failure time distribution. Realistic variations to constrain our prior distribution of the failure time are then applied before measurements are available. When data become available, estimates more representative of our specific batch and operating conditions are inferred, both on the individual bearing level and the bearing group level. The proposed prognostics methodology can be used in situations with varying amounts of data. The presented BHM approach can also be used to predict the remaining useful life (RUL) of bearings both in situations in which the bearing is considered to be in a healthy state and in situations after a defect has been detected.