Studies On Approximate Bayesian Inference For Complicated Degradation Models And Applications

With the development of sensors,storage,and transmission technologies,data collection has been completely changed,which has driven the age of big data.In the age of big data,the data exhibits new characteristics of fast collection speed,large volume,and complex structure.These new features also bring new challenges to the statistical analysis of data.Meanwhile,the statistical models are becoming more complexity to describe the observed data high fidelity.As a result,the traditional statistical inference methods-the maximum likelihood and Bayesian methods-may not meet the practical computational needs and modeling demands.In this context,many approximate Bayesian inference methods have emerged,such as the variational Bayesian method to accelerate the training efficiency of neural networks,integrated nested Laplace approximation algorithm to alleviate the computational burden of spatiotemporal models,and Bayesian synthetic likelihood methods to solve the intractable likelihood.However,in the field of reliability,the statistical inference of most models still relies on the traditional maximum likelihood and Bayesian methods,which may hinder the application of many models in practical engineering.Additionally,with the limitations of statistical inference methods and the mathematical nature of the models,a compromise modeling framework has to be made in many situations,which is usually away from the nature of the data.For some complex stochastic process-based degradation models in the realm of reliability,this paper gives new statistical inference schemes for them through various approximate Bayesian methods.Meanwhile,benefiting from the superiority of some approximate Bayesian methods,we can relax some assumptions of the existing models and make it feasible to model degradation data high fidelity.The main points of this paper are as follows:(1)Approximate Bayesian inferences are studied for the Wiener degradation model with random effects and the parameter-dependent Wiener degradation model with random effects under the variational Bayesian approach,respectively.To solve some intractable variational posteriors under two models,we respectively embed a three-step procedure and the Lindley approximation in the variational Bayesian framework.For comparative study,we also give the statistical inference process of the two models under the traditional estimation methods.Finally,the given variational Bayesian algorithms are validated by comprehensive numerical simulations and a case study.(2)Approximate Bayesian inference for a noval reparameterization gamma degradation model with random effects is investigated.Compared with the existing gamma degradation model with random effects,the proposed model has a more intuitive physical interpretation.Additionally,combining the Gauss-Hermite quadratic integration and the Laplace approximation,an analytic variational posterior estimate for the proposed model can be developed.We also provide the statistical inference procedure for the proposed model under the conventional estimation method for comparison.Finally,the superiority of the given model and the proposed algorithm is verified by the comprehensive numerical simulations and a case study.(3)Under step-stress accelerated degradation tests,approximate Bayesian inference for the Wiener process-based degradation model is investigated.We first give a step-stress accelerated degradation model based on the Wiener process,and then use the integrated nested Laplace approximation for its statistical inference.To take advantage of the existing integrated nested Laplace approximation framework,we first convert the model into a latent Gaussian model using the Taylor linearization technique and then evaluate the model using a fixed-point iterative method in the framework of integrated nested Laplace approximation.Finally,the superiority of the given algorithm is verified by numerical simulations and case studies.(4)Approximate Bayesian inference for exponential dispersion process-based degradation model with measurement errors is studied.We first introduce the exponential dispersion degradation model with time-independent measurement errors.For the given model,it is challenging to write its likelihood function.To this end,three learning-based Bayesian synthetic likelihood approaches are develpoed.It indirectly obtains the posterior estimates of the model parameters by extensive learning of the summary statistics of the model.Finally,the given model and the proposed algorithm is verified by the comprehensive numerical simulations and a case study.