A New Gibbs Sampling Based Bayesian Model Updating Approach Using Modal Data from Multiple Setups

This paper presents a new Gibbs sampling based approach for Bayesian model updating of a linear dynamic system based on modal data (natural frequencies and partial mode shapes of some of the dominant modes) obtained from a structure using multiple setups. Modal data from multiple setups pose a problem as mode shapes identified from multiple setups are normalized individually and the scaling factors to form the overall mode shape are not known a priori. For comprehensive quantification of the uncertainties, the proposed approach allows for an efficient update of the probability distribution of the model parameters, overall mode shapes, scaling factors, and prediction error variances. The proposed approach does not require solving the eigenvalue problem of any structural model or matching of model and experimental modes, and is robust to the dimension of the problem. The effectiveness and efficiency of the proposed method are illustrated by simulated numerical examples.