Fuzzy Bayesian estimation for the identification of fuzzy-parameterized models in the framework of model updating

The fuzzy Bayesian estimation is motivated by the Bayesian inference and enables estimating the uncertain parameters of a model on the basis of given reference outputs as well as some prior information about the parameters. The method is based on fuzzy arithmetic which allows the performing of computations with uncertain quantities modeled by fuzzy numbers. The fuzzy Bayesian estimation is particularly suitable for model updating problems, where the uncertainty often emerges from model deficiencies. Originally, the method was defined for problems with discrete distributions of information such as a sparse sample of observations of an uncertain quantity. In this paper, the method is extended in order to be able to perform computations on the basis of continuous distributions of epistemic information. The extended fuzzy Bayesian estimation is applied to real-world model updating problem, where the parameters of a finite element model are estimated based on information from an experimental modal analysis and given prior information.