A Data-Driven Modeling Method for Stochastic Nonlinear Degradation Process With Application to RUL Estimation

Abstract

This article proposes a novel modeling method for the stochastic nonlinear degradation process by using the relevance vector machine (RVM), which can describe the nonlinearity of degradation process more flexibly and accurately. Compared with the existing methods, where degradation processes are modeled as the Wiener process with a nonlinear drift function formulized as the power law or exponential law, this kind of modeling method can characterize degradation processes with more nonlinear behavior. Instead of modeling the drift coefficient of the Wiener process directly, the weighted combination of basis functions is utilized to express the increment of the Wiener process and the parameters are calculated by a sparse Bayesian learning algorithm. Based on the proposed model, a numerical approximation formula for the probability density function (PDF) of the remaining useful life (RUL) is derived. Finally, comparison studies, including a numerical simulation and a practical case, are provided to demonstrate the effectiveness and the accuracy of the proposed methods for RUL estimation.