An innovative Bayesian system identification method using autoregressive model

This paper proposes an innovative Bayesian method for system identification based on autoregressive (AR) model. The dynamics of a structure is first modeled by an AR model. Due to measurement noise and modeling errors in practical problems, it is important to quantify uncertainties of the model. The posterior PDF of the parameters of the AR model is then formulated following Bayes’ theorem. New formulations of the most probable values (MPVs) and the posterior uncertainties of the AR model parameters are derived in closed form. It is shown that the model of a vibrating structure can be transformed to an AR model, so the modal parameters of the structure can be extracted from the parameter matrices of the AR model. For assessing the posterior uncertainties of the modal parameters, original analytical formulations are derived to propagate the uncertainties of AR model parameters to the modal parameters. The proposed method is verified by measured ambient vibration data of a 20-story building. Working directly on the measured accelerations, the proposed method can make use of the original information in the data to identify all modal parameters of interest together with corresponding uncertainties in a few minutes. The contribution of this paper is that the algebraically involved derivation is resolved to develop new formulations for the MPVs and associated uncertainties, reveal the complicated relationship between the uncertainties of modal parameters and those of AR model parameters, and provide a mathematically manageable algorithm for efficient practical applications.