Prognostics of fractional degradation processes with state-dependent delay

Abstract

In modern industrial processes, the remaining useful life (RUL) of core manufacturing equipments is regarded as an important indicator for assessing the continuous serving ability by considering safety and reliability. Accurate RUL predictions contribute to saving maintenance costs, and can be applied to the life extension technologies. Being subjected to complicated noise environments, the fractional characteristic usually exists in the stochastic heterogeneous diffusions. Traditional methods mostly utilize the fractional Brownian motion (FBM) to describe a simple class of memory effect in the time domain, but lose sight of potential time-varying state-dependencies from historical information. In view of uncertain lagging levels, the state-dependent delay (SDD) is introduced to construct a novel nonlinear fractional degradation model in this paper. Based on a specific discretization scheme, the unknown parameters are estimated by optimizing an approximate log-likelihood function. The RUL distribution is then derived under a Markovian statistical transformation. Finally, a case study on certain hearth wall degradation processes is provided to validate the proposed prognostic method in production practice.