Operational modal analysis using variational Bayes Li, Binbin; Der Kiureghian, Armen
Operational modal analysis is the primary tool for modal parameters identification in civil engineering. Bayesian statistics offers an ideal framework for analyzing uncertainties associated with the identified modal parameters. However, the exact Bayesian analysis is usually intractable due to the high computation demanding in obtaining the posterior distributions of modal parameters. In this paper, the variational Bayes is employed to provide an approximated solution. Working with the state space representation of a dynamic system, the joint distribution of the state transition matrix and observation matrix as well as the joint distribution of the process noise and measurement error are firstly obtained analytically using conjugate priors, then the distributions of modal parameters are extracted from these obtained joint distributions based on sampling because no closed form solution exists. A numerical simulation example demonstrates the performance of the proposed approach. The variational Bayes yields a consistent estimation of modal parameters although the variability is slightly under-estimated. Moreover, the variational Bayes is more flexible than the Laplace approximation and much more efficient than Monte Carlo sampling.
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