Bayesian Approach for Parameter Estimation in the Structural Analysis and Prognosis

Abstract

In this study, a Bayesian framework is outlined for the parameter estimation that arises during the uncertainty quantification in the numerical simulation as well as in the prognosis of the structural performance. In the framework, the parameters are estimated in the form of posterior distribution conditional on the provided data. Several case studies that implement the estimation are presented to illustrate the concept. First one is an inverse estimation, in which the unknown input parameters are inversely estimated based on a finite number of measured response data. Next one is a metamodel uncertainty problem that arises when the original response function is approximated by a metamodel using a finite set of response values. Third and fourth one are a prognostics problem, in which the unknown parameters of the degradation model are estimated based on the monitored data. During the numerical implementation, Markov Chain Monte Carlo (MCMC) method is employed, which is a modern computational technique for the efficient and straightforward estimation of parameters. Once the samples are obtained, one can proceed to the posterior predictive inference on the response at the unobserved points or at the future time in the form of confidence interval.