Unbiased parameters estimation and mis-specification analysis of Wiener process-based degradation model with random effects

Abstract

Accurate parameters estimation is one of the most crucial components in remaining useful life (RUL) prediction. This paper proposes an unbiased parameters estimation method and analyzes the impact of model mis-specification of Wiener process-based degradation model with random effects. First, we obtain an analytical expression of parameters estimation for the linear Wiener process. Then, by analyzing the natures of parameters estimation, an unbiased parameters estimation method is proposed and applied to other types of Wiener process-based degradation models. This unbiased estimation method is very similar to the sample variance of normal distribution. Since the sample size of degradation data is typically small, hence the proposed unbiased estimation method is suggested. After that, we present an empirical unbiased parameters estimation method with a closed-form solution when the degradation data is measured at different times. The proposed unbiased estimation method could increase computational speed and avoid falling into local minimum. In addition, based on parameters estimation results, the mis-specification issue about whether the random effects should be considered in the degradation modeling is analyzed in theory. Finally, several numerical examples and case studies are used for experimental verification. The experimental results demonstrate that the proposed unbiased parameters estimation method is superior to other parameters estimation methods and the random effects are suggested to be considered.