Degradation Modeling And Residual Life Estimation Based On Wiener Process With Measurement Errors

For products of high reliability or high price,it is usually impossible to obtain enough product failure data during a limited time so as to carry out relevant reliability analysis.As an alternative to traditional analysis method based on the failure data of target products,the method of degradation modeling and corresponding analysis which is based on the degradation data of product performance is playing an important role in current studies.According to the description of the hidden degradation states of target products,the analysis method proposed in this paper enables people to model the deterioration process of target products and estimate the parameters of corresponding degradation model in a limited period of time.Moreover,the proposed method based on the degradation model provides an effective access to the prediction of residual life of target products and improves the accuracy of the residual life prediction of target products.At the same time,this analysis method enables us to carry out the preventive maintenance on the system at a lower cost,reduce the probability of system failure in the operation process as well as improve the reliability of target products and equipments such that ensures the stable operation of the system.Since wiener process is a non-monotonous stochastic process,this paper will adopt the wiener process to describe the fluctuation of product degradation data.Because of the influences of the external environment and the restriction of the internal factors,the degradation of the target product directly observed in the process of using this product is bound to be different from the real degradation of the product.Therefore,the effects of the measurement errors should be considered in the research of the degradation modeling and the prediction of the residual life.This paper will construct the degradation model based on the Wiener process with the assumption that the measurement errors all follow Logistic distributions,and exploit the combination of the Gibbs sampling technique,rejection method and Monte Carlo expectation maximization algorithm to filter the observed degradation data with noise so as to obtain the approximate potential degradation states as well as the estimated values of the degradation model parameters.At the same time,this paper will also construct the degradation model based on the Wiener process with measurement errors that follow normal distributions.According to the comparison of the Monte Carlo simulation results of the two kinds of wiener degradation models,it can be verified that the degradation model which is based on the Wiener process with measurement errors following Logistic distributions brings out a more comprehensive characterization on the cases where extreme values are easily appeared.The Wiener degradation model constructed in this paper is more robust and takes on a more excellent fitting performance for the real degradation data.Finally,through the case study of capacity loss of Lithium ion batteries,the rationality and effectiveness of the proposed degradation method is verified again.