Stochastic sampling based Bayesian model updating with incomplete modal data

Abstract

© 2016 by Begell House, Inc. In this paper, we are interested in model updating of a linear dynamic system based on incomplete modal data including modal frequencies, damping ratios, and partial mode shapes of some of the dominant modes. To quantify the uncertain-ties and plausibility of the model parameters, a Bayesian approach is developed. The mass and stiffness matrices in the identification model are represented as a linear sum of the contribution of the corresponding mass and stiffness matrices from the individual prescribed substructures. The damping matrix is represented as a sum of the contribution from individual substructures in the case of viscous damping, in terms of mass and stiffness matrices in the case of classical damping (Caughey damping), or a combination of the viscous and classical damping. A Metropolis-within-Gibbs sam-pling based algorithm is proposed that allows for an efficient sampling from the posterior probability distribution. The effectiveness and efficiency of the proposed method are illustrated by numerical examples with complex modes.