An Age-Dependent Prognostic Model for Nonlinear Degrading Devices Based on Diffusion Process

Degradation modeling-based remaining useful life (RUL) predicting has become a significant basis of prognotics and system health management (PHM) and has drawn much favor of both scholars and engineers in the field of reliability. Based on a purely time-dependent diffusion process, this article presents a nonlinear degradation model with a special focus on the proportional relationship between the age-dependent expectation and variance of the degradation processes of the concerned devices. Exact probability density function (pdf) and cumulative distribution function (cdf) of lifetime and RUL in explicit forms are derived under the concept of first hitting time (FHT), incorporating the item-to-item variability. A framework of maximizing the likelihood function has been proposed to estimate the unknown parameters utilizing condition monitoring (CM) data of the devices. Case studies of fatigue crack length data of alloy and capacity data of electrolytic capacitors have been presented to illustrate the proposed prognostics model. The results show that the proposed degradation model can be well fitted to the nonlinear degradation data and provide an accurate prediction of RUL, and thus demonstrate the effectiveness of the proposed model.

Automated summary

Degradation modeling-based remaining useful life (RUL) predicting has gained significant attention as a basis for reliability prognotics and system health management (PHM) in the field of reliability. This article presents a nonlinear degradation model based on a purely time-dependent diffusion process, focusing on the proportional relationship between the age-dependent expectation and variance of the degradation processes. The article derives explicit expressions for probability density function (pdf) and cumulative distribution function (cdf) of lifetime and RUL, incorporating item-to-item variability using the concept of first hitting time (FHT). A framework for estimating unknown parameters using condition monitoring (CM) data is proposed, and case studies are conducted to validate the proposed prognostics model using fatigue crack length data of alloy and capacity data of electrolytic capacitors. The results demonstrate the effectiveness of the proposed model in accurately predicting RUL.