Probabilistic model updating using dynamic data

Abstract

The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. Using a Bayesian probabilistic formulation, the posterior probability density function (PDF) of the uncertain model parameters for given measured data can be obtained. Previous results provide asymptotic approximations to the posterior PDF under the assumption of relatively small model error and measurement noise, relatively small number of model parameters to be identified, and large number of data. Using such results one can approximate-the posterior PDF as a weighted sum of Gaussian distributions centered at some optimal values of the parameters at which some positive measure-of-fit function is minimized. The present paper addresses the problem of model updating in the general case for which the assumptions for the previous asymptotic approximations are not satisfied. In this case the posterior PDF is distributed in the neighborhood of an extended and extremely complicated manifold of the parameter space. The computational difficulties associated with calculating the highly complex posterior PDF are discussed and an algorithm for an efficient approximate representation of the above manifold and the posterior PDF is presented. Using this approximation, expressions for calculating the uncertain predictive response are established. A numerical example involving noisy data is presented to demonstrate the proposed method