Treatment of unidentifiability in structural model updating
The present study addresses the issues of non-uniqueness and unidentifiability arising in structural model updating. A Bayesian probabilistic frame-work is used for model updating which properly handles the uncertainties due to model error and measurement noise associated with model updating. Uncertainties in the model parameters are quantified by probability density functions (PDF) specifying the relative plausibilities of the possible values of the parameters. The Bayesian formulation is well-suited for updating the PDF of the uncertain model parameters taking into account engineering experience and measured dynamic data. Methods are presented for approximating this updated PDF for the general unidentifiable case for which the region of significant probabilities is concentrated in the neighborhood of a manifold of lower dimension than the original parameter space. This PDF is useful for both model updating and structural damage predictions. Asymptotic approximations are also developed for computing the uncertainties in the model response predictions. It is demonstrated that unidentifiable cases are not treatable by existing results valid only for identifiable cases for which the dimension of the manifold is exactly zero. Two examples involving simulated model error and measurement noise are presented to demonstrate the advantages of the new proposed method in effectively addressing unidentifiability issues.