Toward a fundamental understanding of the Hilbert-Huang transform in nonlinear structural dynamics

Kerschen, G; Vakakis, AF; Lee, YS; McFarland, DM; Bergman, LA

dc.contributor.author	Kerschen, G	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Lee, YS	en
dc.contributor.author	McFarland, DM	en
dc.contributor.author	Bergman, LA	en
dc.date.accessioned	2014-03-01T01:29:22Z
dc.date.available	2014-03-01T01:29:22Z
dc.date.issued	2008	en
dc.identifier.issn	1077-5463	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19249
dc.subject	Empirical mode decomposition	en
dc.subject	Hilbert-Huang transform	en
dc.subject	Nonlinear system identification	en
dc.subject	Slow-flow dynamics	en
dc.subject.classification	Acoustics	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.classification	Mechanics	en
dc.subject.other	Hilbert spaces	en
dc.subject.other	Nonlinear equations	en
dc.subject.other	Nonlinear systems	en
dc.subject.other	Parameter estimation	en
dc.subject.other	Signal processing	en
dc.subject.other	Empirical mode decomposition (EMD)	en
dc.subject.other	Fast dynamics	en
dc.subject.other	Hilbert-Huang transform	en
dc.subject.other	Nonstationary signals	en
dc.subject.other	Slow-flow dynamics	en
dc.subject.other	Structural dynamics	en
dc.title	Toward a fundamental understanding of the Hilbert-Huang transform in nonlinear structural dynamics	en
heal.type	journalArticle	en
heal.identifier.primary	10.1177/1077546307079381	en
heal.identifier.secondary	http://dx.doi.org/10.1177/1077546307079381	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition (EMD). The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, an attempt is made to provide the missing theoretical link, showing the relationship between the EMD and the slow-flow equations of a system. The slow-flow reduced-order model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique in order to derive a dynamical system described by slowly-varying amplitudes and phases. These slow-flow variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a novel nonlinear system identification method, termed the slow-flow model identification (SFMI) method. Through numerical and experimental application examples, we demonstrate that the proposed method is effective for characterization and parameter estimation of multi-degree-of-freedom nonlinear systems. © 2008 SAGE Publications Los Angeles.	en
heal.publisher	SAGE PUBLICATIONS LTD	en
heal.journalName	JVC/Journal of Vibration and Control	en
dc.identifier.doi	10.1177/1077546307079381	en
dc.identifier.isi	ISI:000252947600005	en
dc.identifier.volume	14	en
dc.identifier.issue	1-2	en
dc.identifier.spage	77	en
dc.identifier.epage	105	en