Fast Bayesian FFT Method for Ambient Modal Identification with Separated Modes
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 137, Issue 3
Abstract
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.
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Acknowledgments
The data from the super-tall building example was obtained through Collaborative Research Project (UNSPECIFIEDURN 05/81d) with Ove Arup and Partners Hong Kong Ltd., whose support is gratefully acknowledged. The author would like to thank Dr. Alex To, Associate at OAP, for logistics help on the field test of super-tall buildings. The author would also like to thank Dr. Kohler for providing the UCLA Factor Building data and generous assistance during the process. Constructive comments from anonymous reviewers are gratefully acknowledged.
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Published In
Journal of Engineering Mechanics
Volume 137 • Issue 3 • March 2011
Pages: 214 - 226
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Nov 6, 2009
Accepted: Jul 29, 2010
Published online: Feb 15, 2011
Published in print: Mar 1, 2011
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