Lévy process-based stochastic modeling for machine performance degradation prognosis

Accurate and robust monitoring, tracking and prognosis of machine performance degradation provides the technical basis for realizing predictive maintenance scheduling and improved operational reliability. To cope with nonlinearity and non-homogeneity that are typically seen in performance degradation, this paper presents a prognostic modeling technique based on the Lévy process, which expresses the variation of machine performance as an accumulation of successive and jump increments. Specifically, the proposed Lévy model is divided into two terms to address two types of degradations: a linear Brownian motion (LBM) model to describe gradual deterioration with time-varying rates, and a non-homogenous compound Poisson process (CPP) model to describe transient performance changes due to abrupt fault occurrence. The time-varying deterioration rate is captured in LBM by a stochastic drifting coefficient that is assumed to follow a Gaussian distribution, besides a diffusion term that accounts for temporal uncertainties and degradation-to-degradation variations. The non-homogeneous occurrence rate of transient changes is captured in CPP by a Poisson distribution with a time-varying jump intensity, with the sizes of transient changes assumed to follow a Gaussian distribution. By calculating the moments of the characteristic function of the proposed Levy model, explicit expressions for the probability distributions of predicted degradation and remaining useful life (RUL) have been derived. To estimate the time-varying parameters in the Lévy model, Markov Chain Monte Carlo (MCMC) as a batch estimation technique has been investigated. The proposed prognostic modeling technique is evaluated using rolling bearing run-to-failure tests.