Multivariate Relevance Vector Regression Based Degradation Modeling and Remaining Useful Life Prediction

Relevance vector regression (RVR) is a useful tool for degradation modeling and remaining useful life (RUL) prediction. However, most RVR models are for 1-D degradation processes and can only handle univariate observations. This article proposes a degradation path-based RUL prediction framework using a dynamic multivariate relevance vector regression model. Specifically, a multistep regression model is established for describing the degradation dynamics and extending the classical RVR into a multivariate one with consideration of the multivariate environment. The article introduces a matrix Gaussian distribution-based RVR approach and then estimates the hyperparameters with Nesterov’s accelerated gradient method to avoid the exhausting re-estimation phenomenon in seeking analytical solutions. It further forecasts the degradation path for monitoring the degradation status. Based on the forecasted path, the RUL is predicted by the first hitting time method. Finally, the proposed methods are illustrated by two case studies, one is presented in this article and the other in the supplement, which investigate the capacitors’ and bearings’ performance degradations.