RUL Prediction: Reducing Statistical Model Uncertainty Via Bayesian Model Aggregation

Abstract

It is important to predict the remaining useful life (RUL) for evaluating the performance of industrial equipment. Many simple and complex methods have been proposed to predict RUL based on stochastic processes. However, these methods have different prediction accuracies. The uncertainty associated with using one of these methods instead of another is called statistical model uncertainty. Therefore, some problems naturally arise: How can we reduce the uncertainty among different methods? Is it possible to obtain a more exact prediction of RUL, compared with the individual method? In this study, we apply a Bayesian model aggregation (BMA) approach to solve these problems. For a Wiener degradation process with unknown parameters, assume that there are $P$ types of methods to predict RUL, for example, maximum likelihood estimation (MLE), stochastic Newton algorithm (SNA), and Kalman filter (KF)- based methods. Then, there are 2P- 1 distinct combinations of these $P$ types of methods, each with a corresponding statistical model and an estimated parameter vector. BMA can statistically combine these estimated parameter vectors through a weighted average, and thus, the probability density function (PDF) of RUL can be obtained. BMA can be successfully applied to realistic bearing data, and simulation results show that BMA achieves higher prediction accuracy than an individual method.