Degradation Modeling Based on Wiener Process Considering Multi-Source Heterogeneity

Abstract

Degradation modeling using heterogeneous degradation data of a system population is critical for prognostics and health management. The heterogeneity may result from the inherent differences in the degrading systems and measuring instruments, as well as from the extrinsic environmental differences, making it difficult to predict the failure. Current studies have not considered the multiple sources of heterogeneity simultaneously, and consequently, have failed to capture the actual degradation process. To explain and quantify the combined effect of multi-source heterogeneity, we present a random effects Wiener process model with heteroscedastic measurement errors, where the parameters of the drift, diffusion, and error variance are assumed as random variables following a certain distribution. The Markov chain Monte Carlo method is adopted to estimate the posterior distributions of the actual degradation states and the model parameters under a hierarchical Bayesian framework. Based on the concept of first hitting time, the failure time distribution is estimated. To verify the presented approach, comparative studies are conducted with simulation and laser degradation data. The results show that considering multi-source heterogeneity can further eliminate the inter-individual variation in degradation data and improve the model fitting and prediction accuracy.

Keywords

• Degradation modeling
• Wiener process
• heterogeneity
• Bayesian analysis