Assessing uncertainty in fast Bayesian modal identification based on seismic structural responses

Modal identification is an important step to evaluate the basic modal properties of structures using measured data. In this process, the existence of modeling error and measurement noise will inevitably lead to uncertainty in modal identification. A Bayesian framework was established to determine the optimal values of modal parameters efficiently based on the structural response under earthquake excitations. In this paper, in the same framework, a new method is presented to determine the analytical formulation for carrying out uncertainty evaluation of modal parameters utilizing seismic structural responses. Based on Bayes’ Theorem, the covariance matrix can be calculated based on the Hessian matrix determined using the negative log-likelihood function (NLLF). In this work, for determining the Hessian matrix, a series of formulations were derived analytically. Simulated data of a six-story building were generated to investigate the new formulations. The noise effects on the posterior uncertainty were investigated. After the verification, applications were carried out using the data in a shaking table test model under laboratory conditions and a real building from a field test. The modal properties and their uncertainty obtained by the proposed method were studied under different earthquake excitations.