Hierarchical Bayesian uncertainty quantification of dynamical models utilizing modal statistical information

Abstract

Updating dynamical models based on experimental modal information has become an important topic in structural health monitoring. This paper revisits this significant problem and develops a new two-stage hierarchical Bayesian framework, aiming to improve the quantification of uncertainty. This framework employs the Bayesian FFT approach to identify the modal parameters along with their identification uncertainty, and then, it utilizes this modal information to update the stiffness matrix. It can quantify the variability of both modal and structural parameters over multiple data sets while characterizing their identification uncertainty as well. This framework also proposes a new basis to assign optimal and appropriate weights for modal features. It weights different modal parameters based on the sum of identification uncertainty and the ensemble variability such that more uncertain parameters will be assigned smaller weights. As a result, a coherent quantification of uncertainty is attained by following Bayesian probability logic. Ultimately, experimental data from a shear building structure is used for demonstrating the proposed framework. © 2020 European Association for Structural Dynamics. All rights reserved.