Modeling And Research Of Degradation Data Based On Wiener Process

With the development of industrial manufacturing technology and the development of science and technology,many devices in the fields of electronic communication,aerospace,transportation facilities have the characteristics of small sample,long life and high reliability.Therefore,reliability-based modeling analysis based on the stochastic process has become a hot spot in the academia and the industrial research.Wiener process has good mathematical characteristics and data fitting ability,which can model and analyze the degradation data of many typical devices.Therefore,Wiener process has become one of the most widely used models in current degradation modeling.However,because of the structural complexity of modern equipment and the impact of the operating environment,the individual degradation process has more random and heterogeneous.In order to carry out more suitable reliability modeling for the degradation process of modern equipment,this paper proposes three reliability modeling methods based on Wiener process to improve the degradation modeling system.Firstly,a generalized Wiener model with random drift,random diffusion,and measurement errors is presented for the individual heterogeneity and measurement errors in degradation data.A multi-step parameter estimation method is proposed.Based on random drift effect and random diffusion effect,the proposed model also considers the influence of measurement errors during degradation modeling.In addition,the failure time distribution of product is analyzed.The numerical simulations and the 2017-T4 aluminum alloy degradation data are applied to demonstrate the effectiveness of the proposed method.Secondly,an adaptive Wiener model with measurement errors is proposed to obtain the remaining useful life(RUL)prediction under the dynamic conditions.In the degradation modeling,the proposed model applies a continuous Brownian motion to model the fluctuation of the adaptive drift factor,which increases the randomness of the proposed model.The adaptive drift factor and the influence of measurement error are considered,simultaneously.In addition,according to the definition of the first hitting time(FHT),the probability density function(PDF)of the online RUL distribution is derived with the explicit formulation.The unknown parameters are estimated by the principle of the maximum expectation(EM)algorithm.The effectiveness of the proposed method is validated by the numerical simulations and the lithium battery capacity degradation data study.Thirdly,the measurement error in the existing Wiener model is usually assumed to be a random variable,which follows a Gaussian distribution.However,due to the thick tail of outliers,the Wiener model with Gaussian measurement error is not suitable for degenerate modeling of degradation data with outliers.To solve the problem that the Gaussian errors are sensitive to outliers,a Wiener process model with t-distribution errors and random drift is proposed.However,the multiple integral problem of the likelihood function is caused by the t-distribution error.To solve this problem,the combination of the EM and the variational Bayes(VB)method is applied to estimate the parameters in the proposed model.The Monte Carlo simulations and the case study are used to demonstrate the effectiveness of the proposed model.Finally,the research results and contents of this paper are summarized,which makes a useful exploration for further research on degradation-based reliability degradation modeling.