Tangential-projection algorithm for manifold representation in unidentifiable model updating problems

The problem of updating a structural model and its associated uncertainties by utilizing structural response data is addressed. In an identifiable case, the posterior probability density function (PDF) of the uncertain model parameters for given measured data can be approximated by a weighted sum of Gaussian distributions centered at a number of discrete optimal values of the parameters at which some positive measure-of-fit function is minimized. The present paper focuses on the problem of model updating in the general unidentifiable case for which certain simplifying assumptions available for identifiable cases are not valid. In this case, the PDF is distributed in the neighbourhood of an extended and usually highly complex manifold of the parameter space that cannot be calculated explicitly. The computational difficulties associated with calculating the highly complex posterior PDF are discussed and a new adaptive algorithm, referred to as the tangential-projection (TP) algorithm, allowing 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. Copyright (C) 2002 John Wiley Sons, Ltd