Bayes-Mode-ID: A Bayesian modal-component-sampling method for operational modal analysis

Abstract

A Bayesian modal-component-sampling system identification (Bayes-Mode-ID) method is developed in this paper. This method can efficiently identify the modal parameters of civil engineering structures under operational conditions even when the number of measured degrees of freedom (DOFs) is large. The mathematical model of the dynamic system is constructed with the modal parameters being the system parameters and the posterior probability density function (PDF) of these modal parameters is formulated using Bayes theorem. Bayesian modal analysis is conducted through generating samples of the modal parameters in the important regions of the posterior PDF. The proposed method can identify the most probable (maximum posterior) values (MPVs) of the modal parameters, together with the corresponding posterior uncertainties based on the generated samples, without assuming an approximate form for the posterior PDF. There are two main difficulties in sampling modal parameters from the posterior PDF. Firstly, it is not possible to analytically normalize the posterior PDF. Secondly, the number of the modal parameters is usually large so the samples cannot be efficiently generated in the important region of the posterior PDF. The proposed component sampling algorithm is tailor made to handle these two problems. This paper covers the theoretical development of the Bayes-Mode-ID for operational modal analysis together with two experimental case studies under laboratory conditions.