The slow-flow method of identification 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 publicationSensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2007
DOIs
StatePublished - 2007
EventSensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2007 - San Diego, CA, United States
Duration: Mar 19 2007Mar 22 2007

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
Volume6529 PART 1
ISSN (Print)0277-786X

Other

OtherSensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2007
CountryUnited States
CitySan Diego, CA
Period3/19/073/22/07

Keywords

  • Complexification-averaging
  • Hilbert-Huang transform
  • Nonlinear system identification
  • Slow flow

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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