ORBi: Kerschen Gaëtan - Toward a fundamental understanding of the Hilbert-Huang Transform in nonlinear dynamics

Reference : Toward a fundamental understanding of the Hilbert-Huang Transform in nonlinear dynamics


	Document type :	Scientific journals : Article
	Discipline(s) :	Engineering, computing & technology : Electrical & electronics engineering Engineering, computing & technology : Multidisciplinary, general & others Engineering, computing & technology : Mechanical engineering
	To cite this reference:	http://hdl.handle.net/2268/18265

Title :	Toward a fundamental understanding of the Hilbert-Huang Transform in nonlinear dynamics
Language :	English
Author, co-author :	Kerschen, Gaëtan [Université de Liège - ULg > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux >]
	Vakakis, Alexander F. [National Technical University of Athens > Department of Mechanical and Industrial Engineering > > >]
	Lee, Y. S. [University of Illinois at Urbana-Champaign > Department of Aerospace Engineering > > >]
	MacFarland, D. M. [University of Illinois at Urbana-Champaign > Department of Aerospace Engineering > > >]
	Bergman, L. A. [University of Illinois at Urbana-Champaign > Department of Aerospace Engineering > > >]
Publication date :	2008
Journal title :	Journal of Vibration & Control
Publisher :	SAGE Publications
Special issue title :	Special issue celebrating the 60th of Prof. G. Vestroni
Pages :	77-105
Peer reviewed :	Yes (verified by ORBi)
Audience :	International
ISSN :	1077-5463
Keywords :	[en] Nonlinear system identification, ; Hilbert-Huang transform ; empirical mode decomposition
	[fr] slow-flow dynamics Journal
Abstract :	[en] 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.
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/2268/18265
DOI :	10.1177/1077546307079381

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