A probabilistic approach to structural model updating

The problem of updating a structural model and its associated uncertainties by utilizing measured dynamic response data is addressed. A Bayesian probabilistic formulation is followed to obtain the posterior probability density function (PDF) of the uncertain model parameters for given measured data. The present paper discusses the issue of identifiability of the model parameters and reviews existing asymptotic approximations for identifiable cases. The focus of the paper is on the treatment of the general unidentifiable case where the earlier approximations are not applicable. In this case the posterior PDF of the parameters is found to be concentrated in the neighborhood of an extended and extremely complex manifold in the parameter space. The computational difficulties associated with calculating the posterior PDF in such cases are discussed and an algorithm for an efficient approximate representation of the above manifold and the posterior PDF is presented. Numerical examples involving noisy data are presented to demonstrate the concepts and the proposed method.