Structural model updating and health monitoring in the presence of modeling uncertainties

This thesis addresses the problem of updating a structural model and its associated uncertainties by utilizing measured dynamic data following a Bayesian probabilistic framework. The nonuniqueness problem arising from model updating, which has been worrying researchers in this area for a long time, is directly addressed in this thesis. Model updating problems can be classified into two categories: "Identifiable" or "Unidentifiable" problems. 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 focus of this thesis 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 a case are discussed and a number of algorithms for efficient approximate representation of the above manifold and the posterior PDF are presented. A structural health monitoring method is developed based on the proposed model up-dating methodology. Both the proposed model updating and health monitoring methods are demonstrated and verified by numerically simulated and experimental dynamic data