Fast Bayesian FFT method for ambient modal identification with separated modes

Bayesian identification approach views modal identification as an inference problem where probability is used as a measure for the relative plausibility of outcomes given a model of the system and measured data. In the context of ambient vibration, A Bayesian modal identification theory using the Fast Fourier Transform of ambient time history data has been developed previously. The method provides a rigorous way for obtaining the modal properties as well as their uncertainties by operating in the frequency domain. In typical applications, the modal parameters are 'globally identifiable' and the posterior distribution can be well approximated by a Gaussian PDF, which is completely characterized by the most probable value and the covariance matrix. Computation of latter quantities, however, can be prohibitive in realistic applications. In particular, the posterior distribution is a non-trivial ill-conditioned nonlinear function of the modal parameters; the determination of the most probable value requires solving a multi-dimensional numerical optimization whose dimension grows with the number of measured channels. This paper presents a fast method for computing the posterior most probable values and covariance matrix, focusing on well-separated modes. The proposed method is illustrated using field data with a moderate to a large number of measured channels. The proposed algorithm allows Bayesian modal identification to be performed quickly, therefore making its application feasible in practical situations.