Fast Bayesian modal identification with known seismic excitations

Fast and accurate identification of structural modal parameters after an earthquake is crucial for assessing structural conditions and facilitating repair. With the development of modern earthquake observation techniques, the recorded ground motion can be leveraged as extra input information for modal identification, enabling the experimental modal analysis applicable. This study develops a Bayesian modal identification algorithm that aims at estimating the most probable value (MPV) of modal parameters and their identification uncertainty. Incorporating the recorded seismic input, the algorithm utilizes with the structural equation of motion in the frequency domain to formulate the likelihood function and adopts a constrained Laplace method for Bayesian posterior approximation of modal parameters. With the aid of complex matrix calculus, an iterative scheme is developed, allowing a fast search of the MPV of modal parameters and an analytical evaluation of the posterior covariance matrix. The performance of the proposed algorithm is validated by examples with synthetic, laboratory and field data, respectively. In addition, its effectiveness on predicting structural responses under a future earthquake is illustrated, showing its potential for various downstream applications in seismic structural health monitoring.