Prognostics of Non-Markovian Degradation Processes with Fractal Property and Measurement Uncertainty

Abstract

Non-Markovian stochastic degradation processes exist extensively in the practical industrial systems. For instance, a blast furnace should be operated continuously subject to harsh conditions of high temperature, sulfuration, and nitration, resulting in biased random walks among the degrading performance variables. This phenomenon can be well interpreted as the memory effects, which implies the future states may rely on each of the past ones. The other tough issue is that the degradation processes would be contaminated with measurement noises from unidentified sources. Large level of measurement uncertainty seems adverse to the accurate extraction of non-Markovian diffusions, and hence impacts the prognostics of the system. To overcome these difficulties, we mainly present a remaining useful life (RUL) prediction method on the framework of a state space model incorporating both the fractional Brownian motion (FBM) and the Gaussian noise. Attributing to the fractal property of longterm dependency, FBM naturally adapts to the non-Markovian degradation modeling. Considering the nonlinearity, a variant form of sigmoid function is also adopted as the fixed drift item. The hidden states and the unknown parameters are estimated synchronously using a composite identification algorithm, while the RUL distributions are derived by a Monte Carlo method. A simulation example further verifies the validity of the proposed prognostics scheme.