Lévy Process-Based Stochastic Modeling for Machine Performance Degradation Prognosis

Accurate and reliable machine performance degradation tracking and remaining useful life (RUL) prognosis establish the foundation for predictive maintenance scheduling toward improved safety and productivity of machine operations. In general, machine performance degradation exhibits a nonlinear and nonhomogeneous pattern that arises from time-varying degradation rate and abrupt performance changes. To address this challenge and improve the generalizability of degradation modeling, in this article, we present a stochastic modeling technique based on the Lévy process, which generalizes system variations as the accumulations of successive and jump increments. The developed Lévy process model consists of two terms: a linear Brownian motion term for capturing the gradual degradation with time-varying rates and a nonhomogenous compound Poisson process term for capturing transient performance changes. By calculating the moments of the characteristic function of the Lévy model, explicit expressions for the probability distributions of predicted performance degradation and RUL are derived. To obtain the time-varying parameters in the Lévy model, Markov chain Monte Carlo is investigated. The developed technique is evaluated through simulation and run-to-failure tests of roller and ball bearings, and the good performance of the developed Lévy model is confirmed.