A Perturbed Markovian process with state‐dependent increments and measurement uncertainty in degradation modeling

Abstract

AbstractIn structural reliability, the Markovian cumulative damage approaches such as Gamma process seem promising to model a nonreversible deterioration that involves gradually over time with small time increments. However, in many degradation phenomena, its evolution depends on the level of the degradation rather than the increments of time. Further, the measured data are usually collected with random error whose dispersion depends on the current degradation level. Therefore, the deterioration model should take in consideration such dependency and uncertainty for more accurate prediction. In this paper, a new statistical, data‐driven state‐dependent and perturbed model is proposed to model the state dependence (hidden level‐degradation) both in temporal increments and measurement uncertainty. The construction of the degradation model will be discussed within an application to the pitting corrosion and synthetic data. Numerical experiments will later be conducted to identify preliminary properties of the model in terms of statistical inferences. Algorithm and estimates are proposed to compute the parameters of the model, the hidden state, and failure probabilities.