Time-Varying Linear and Nonlinear Structural Identification with Analytical Mode Decomposition and Hilbert Transform
Publication: Journal of Structural Engineering
Volume 139, Issue 12
Abstract
Analytical mode decomposition (AMD) of a time series concerning any preselected bisecting frequency with Hilbert transform has been developed for closely spaced multicomponent signal decomposition. For this class of structures, it is often challenging, if not impossible, to apply empirical mode decomposition. In this study, the instantaneous structural frequencies are directly derived from the decomposed modal responses for systems with single and multiple degrees of freedom with both free and force vibrations, based on AMD combined with Hilbert transform analysis. The results show that the slow varying component of the instantaneous frequency of the signal is approximately equal to the instantaneous frequency of the systems for slowly time varying linear or weakly nonlinear structures. Both numerical simulations and experimental tests show that the proposed method is capable of tracking the frequency variations with high accuracy for time varying linear structures or weakly nonlinear structures.
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Acknowledgments
Financial support to complete this study was provided in part by the National Science Foundation under Award No. CMMI0409420. The second author wishes to thank the National Science Foundation of China for providing additional support under Grants No. 51078357 and No. 51208165.
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Published In
Journal of Structural Engineering
Volume 139 • Issue 12 • December 2013
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Dec 29, 2011
Accepted: Feb 25, 2013
Published online: Feb 27, 2013
Published in print: Dec 1, 2013
Discussion open until: Jan 30, 2014
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