nonlinear system identification, Hilbert-Huang transform, complexification-averaging, slow flow
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. 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, we attempt to provide the missing link, showing the relationship between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system described by slowly-varying amplitudes and phases is obtained. These 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 nonlinear system identification method, termed the slow-flowmodel identification method, which is demonstrated using numerical examples.
Disciplines :
Physics Mechanical engineering
Author, co-author :
Kerschen, Gaëtan ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Vakakis, Alexander F.; School of Applied Mathematical and Physical Sciences, National Technical University of Athens
Lee, Young.S; Department of Aerospace Engineering, University of Illinois, Urbana, Illinois
McFarland, D. Michael; Department of Aerospace Engineering, University of Illinois, Urbana, Illinois
Bergman, Lawrence A.; Department of Aerospace Engineering, University of Illinois, Urbana, Illinois
Language :
English
Title :
The slow-flow method of identification in nonlinear structural dynamics
Publication date :
2007
Event name :
Smart Str. and Mat. & Nondestructive Eval. and Health Mon.
Event place :
San Diego, United States
Audience :
International
Main work title :
Smart Str. and Mat. & Nondestructive Eval. and Health Mon., San Diego, 2007
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