Approximate Bayesian Inference Of Gamma And Inverse Gaussian Random Process Degradation Models

The advancement of intelligent sensing technology,the development of network transmission materials and the improvement of solid-state storage technology have enabled managers to collect more and more types of data,with increasing magnitude and speed.The rich operational data not only brings convenience to the full-cycle health management of products,but also brings new challenges to statistical modeling and inference of data,for example,multiple types of variables lead to increased model complexity,and large magnitude leads to low computational efficiency of models.Therefore,when modeling and inferring,the traditional maximum likelihood method and Bayesian method in statistical inference sometimes can not meet the actual needs of calculation and modeling.To solve the problem,scholars in the fields of machine learning,spatiotemporal statistics,and population dynamics have proposed many approximation inference methods,such as variational Bayes inference algorithm,Deep neural networks,Laplace approximation algorithm,etc.In the field of reliability,the stochastic degradation model is one of the main models for degraded data analysis.Its statistical inference still relies on the traditional expectation maximization(EM)and Bayesian methods,but these two methods cannot meet the accuracy and computational efficiency at the same time,which may hinder the application of stochastic degradation model in practical problems.Therefore,this paper aims to integrate a variety of approximate Bayesian inference methods to carry out approximate Bayesian inference on two stochastic process degradation models(gamma and inverse Gaussian processes)that characterize monotonicity degradation laws,and in addition,due to intrinsic and extrinsic factors such as differences in raw materials and unobservable properties,the physical or chemical properties of products from the same batch may show different degradation trends.To address the heterogeneity between these unobservable product units,random effects are also introduced into the degenerate model,as follows:(1)The approximate Bayesian inference of the gamma process degradation model with the scale parameter of random variable was studied.Under the framework of variational Bayes,the conjugate feature is used to directly approximate Bayesian inference on the scale parameters of the gamma process.Approximate Bayesian inference based on Lindley Approximation to solve the set of non-conjugated parameters of random effects part.In order to verify the superiority of variational Bayesian algorithm,this paper compares the accuracy and computational efficiency of variational Bayesian method with traditional EM method and Bayesian method by combining numerical simulation and case analysis.(2)The approximate Bayesian inference of the inverse Gaussian process degeneration model with mean and shape parameters are random variables is studied.Through a clever setup of the two random effects distributions,Under the variational Bayes framework,the analytic expression of the variational posterior of the set of mean random effect partial parameters is obtained,and the remaining parameters in the model are estimated by the Lindley approximation method.For comparative research,this paper also gives traditional EM and Bayesian algorithms.Finally,a combination of numerical simulation and example analysis is used to demonstrate the advantages of the proposed model and algorithm.