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

G. Kerschen, A. F. Vakakis, Y. S. Lee, D. M. McFarland, L. A. Bergman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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. 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-flow model identification method, which is demonstrated using numerical examples.

Original languageEnglish (US)
Title of host publicationIMAC-XXIV
Subtitle of host publicationConference and Exposition on Structural Dynamics - Looking Forward: Technologies for IMAC
StatePublished - 2006
Event24th Conference and Exposition on Structural Dynamics 2006, IMAC-XXIV - St Louis, MI, United States
Duration: Jan 30 2006Feb 2 2006

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Other

Other24th Conference and Exposition on Structural Dynamics 2006, IMAC-XXIV
Country/TerritoryUnited States
CitySt Louis, MI
Period1/30/062/2/06

ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mechanics
  • Mechanical Engineering

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