A Markov chain Monte Carlo-based Bayesian framework for system identification and uncertainty estimation of full-scale structures

Identifying modal parameters and updating finite element models (FEMs) of real structures through ambient tests is essential in Structural Health Monitoring (SHM). However, efficiently solving the high-dimensional identification problem for full-scale structures and rigorously quantifying the uncertainties remain challenging. To address these two difficulties, a novel Bayesian framework based on Markov chain Monte Carlo (MCMC) is developed. The basic idea is to identify the high-dimensional posterior probability density functions (PDFs) in both modal analysis and model updating through constructing Markov chains by sampling in the important region of the parameter spaces. The sampling is done by Bayes-Mode-ID and the adaptive sequential Monte Carlo (ASMC) for modal analysis and model updating, respectively. A new formulation is developed to link the results from modal analysis, model updating and model class selection using the Markov chain samples. Thus, the propagation of the posterior uncertainties from the identified modal parameters to the updated model parameters can be quantified. Furthermore, the original ASMC method, which was developed by the authors, is extended for model class selection based on the set of generated Markov chain samples. To demonstrate the effectiveness of the proposed framework, multi-setup ambient vibration tests on a busy footbridge were conducted for measuring the accelerations at some pre-selected measurement points. The most probable modal and model parameters of the footbridge were identified together with the associated uncertainties by the proposed framework.