Model selection in finite element model updating using the Bayesian evidence statistic

This paper considers the problem of finite element model (FEM) updating in the context of model selection. The FEM updating problem arises from the need to update the initial FE model that does not match the measured real system outputs. This inverse system identification-problem is made even more complex by the uncertainties in modeling some of the structural parameters. Such uncertainty often results in a number of competing forms of FE models being proposed which leads to lack of consensus in the field. A model can be formulated in a number of ways; by the number, the location and the form of the updating parameters. We propose the use of a Bayesian evidence statistic to help decide on the best model from any given set of models. This statistic uses the recently developed stochastic nested sampling algorithm whose by-product is the posterior samples of the updated model parameters. Two examples of real structures are each modeled by a number of competing finite element models. The individual model evidences are compared using the Bayes factor, which is the ratio of evidences. Jeffreys scale is then used to determine the significance of the model differences obtained through the Bayes factor.