A Bayesian Probability Approach to Updating Structural Models and Their Uncertainties

The problem of updating a structural model and its associated uncertamt1es by utilizing structural response data is addressed using a Bayesian statistical framework which can handle the inherent ill-conditioning and possible nonuniqueness in model updating applications. The model updating is done by using Bayes theorem to update the probability model for the parameters of the structural model set and the parameters of the prediction-error probability model set. From this perspective, model updating is viewed as part of robust analysis where modeling uncertainties are explicitly addressed in the analysis of a system. The exact expressions for updated model predictions are given by multi-dimensional integrals whose direct evaluation is usually computationally prohibitive. Asymptotic approximations are presented for both identifiable and unidentifiable model sets. An illustrative example is given using robust and updated reliabilities to achieve a more effective optimal design of a tuned-mass damper for a simple bridge system.