Bayesian Model Updating Using Modal Data Based on Dynamic Condensation

Abstract

This paper introduces a methodology for Bayesian model updating of a linear dynamic system using the modal data that consists of the posterior statistics of the modal properties, identified from dynamic test data using a Bayesian modal identification method. To avoid direct mode matching or solving the eigenvalue problem, Eigen system equation is used to establish the relationship between modal data and the structural model parameters. The dynamic condensation technique is proposed to reduce the full system model to a smaller model with the degrees of freedom (DOFs) in the reduced model corresponding to the observed DOFs. This eliminates the need for selecting the observed DOFs of the full system mode shape. The proposed methodology is computationally efficient because neither iteration nor numerical optimization is required to obtain the reduced model. The performance and effectiveness of the proposed methodology was demonstrated by means of two simulated examples. The transitional Markov chain Monte Carlo (TMCMC) method is used to obtain samples distributed according to the posterior distribution.