^{1}and Heung-Fai Lam

^{2}

^{1}Research Institute of Structural Engineering and Disaster Reduction, College of Civil Engineering, Tongji University, Shanghai, China

^{2}Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong, China

This paper presents a novel Bayesian operational method with emphasis on practical applications. The mathematical model of the dynamic system is first constructed using the modal parameters (i.e., modal frequencies, modal damping ratios, mode shapes and modal initial conditions). Conditional on the measured accelerations, the posterior probability density function (PDF) of the modal parameters is then derived following Bayes theorem. Bayesian modal analysis is thus to identify the posterior PDF. Because the posterior PDF cannot be analytically normalized, Markov chain Monte Carlo (MCMC) is applied to sample from the posterior PDF. Considering that the number of uncertain parameters to be identified is large, modal component sampling is developed. The idea is that instead of directly sampling from the posterior PDF, sampling is iterated among the PDFs of different modal components that consist of modal parameters of each mode. The efficiency of the proposed method is illustrated on a full-scale structure. The identified modal parameters reveal interesting dynamic behaviors of the structure and they are helpful for structural health monitoring.