Remaining useful life prediction for a machine with multiple dependent features based on bayesian dynamic linear model and copulas

Degradation modeling and remaining useful life (RUL) prediction for products with multiple degradation features are hot topics in the prognostic and health management. The key to this problem is to describe the dependence among multiple degradation features effectively. In this paper, a multivariate degradation modeling approach based on the Bayesian dynamic linear model (BDLM) is proposed to calculate the RULs of degradation features, and the Copula function is employed to capture the dependence among RUL distributions. A combined BDLM is used to establish the multivariate degradation model, which includes two typical BDLMs, namely, the linear growth model and seasonal factors model. After the model parameters get calibrated by the maximum likelihood estimation, the model can predict the degradation process of features. Once the failure thresholds are given, the probability density function and cumulative distribution function (CDF) of RUL for each degradation feature can be obtained. Since these RUL distributions are not independent of each other, the Copula function is adopted herein to couple the CDFs. Finally, some practical testing data of a microwave component, which has two degradation features, are utilized to validate our proposed method. This paper provides a new idea for the multivariate degradation modeling and RUL prediction.