Fast Bayesian FFT Method for Ambient Modal Identification with Separated Modes

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

211 Scopus Citations
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  • Siu-Kui Au


Original languageEnglish
Pages (from-to)214 - 226
Journal / PublicationJournal of Engineering Mechanics - ASCE
Issue number3
Publication statusPublished - 2011


Previously a Bayesian theory for modal identification using the fast Fourier transform (FFT) of ambient data was formulated. That method provides a rigorous way for obtaining modal properties as well as their uncertainties by operating in the frequency domain. This allows a natural partition of information according to frequencies so that well-separated modes can be identified independently. Determining the posterior most probable modal parameters and their covariance matrix, however, requires solving a numerical optimization problem. The dimension of this problem grows with the number of measured channels; and its objective function involves the inverse of an ill-conditioned matrix, which makes the approach impractical for realistic applications. This paper analyzes the mathematical structure of the problem and develops efficient methods for computations, focusing on well-separated modes. A method is developed that allows fast computation of the posterior most probable values and covariance matrix. The analysis reveals a scientific definition of signal-to-noise ratio that governs the behavior of the solution in a characteristic manner. Asymptotic behavior of the modal identification problem is investigated for high signal-to-noise ratios. The proposed method is applied to modal identification of two field buildings. Using the proposed algorithm, Bayesian modal identification can now be performed in a few seconds even for a moderate to large number of measurement channels. DOI: 10.1061/(ASCE)EM.1943-7889.0000213. (C) 2011 American Society of Civil Engineers.

Research Area(s)

  • Bayesian analysis, Field tests, Modal analysis, Spectral analysis