Wiener degradation models with scale-mixture normal distributed measurement errors for RUL prediction

When the field collected data is biased by unexpected errors due to sensors and measurement, simple Wiener process may fail to correctly estimate the true degradation path. Most existing studies assume additive Gaussian errors in the true degradation path to account for the effects of measurement errors. This assumption is prone to unexpected outliers during the data collection. To achieve a robust estimation for the underlying degradation process, we propose to model the measurement errors using a family of thick-tailed distributions, called Scale-Mixture Normal (SMN) distributions. The SMN distribution can be expressed as a Gaussian hierarchy structure, which is more robust to unexpected outliers. We develop an efficient Expectation-Maximum (EM) algorithm incorporating the Variational Bayesian method to estimate the model parameters. We also derive the distribution of the remaining useful life for online monitoring. The efficiency of the model is verified by Monte Carlo simulations, and the performance of the proposed model on real data is illustrated by the application on hard disk drivers and thrust ball bearing degradation data.