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Correspondence Between Intrinsic Mode Functions and Slow Flows

[+] Author Affiliations
Young S. Lee

New Mexico State University, Las Cruces, NM

Stylianos Tsakirtzis

National Technical University of Athens, Athens, Greece

Alexander F. Vakakis, Lawrence A. Bergman, D. Michael McFarland

University of Illinois at Urbana-Champaign, Urbana, IL

Paper No. DETC2009-87588, pp. 661-670; 10 pages
doi:10.1115/DETC2009-87588
From:
  • ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 1: 22nd Biennial Conference on Mechanical Vibration and Noise, Parts A and B
  • San Diego, California, USA, August 30–September 2, 2009
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4898-2 | eISBN: 978-0-7918-3856-3
  • Copyright © 2009 by ASME

abstract

We study the correspondence between analytical and empirical slow-flow analyses, which will form a basis for a time-domain nonparametric nonlinear system identification method. Given a sufficiently dense set of sensors, measured time series recorded throughout a mechanical or structural system contains all information regarding the dynamics of that system. Empirical mode decomposition (EMD) is a useful tool for decomposing the measured time series in terms of intrinsic mode functions (IMFs), which are oscillatory modes embedded in the data that fully reproduce the time series. The equivalence of responses of the analytical slow-flow models and the dominant IMFs derived from EMD provides a physics-based theoretical foundation for EMD, which currently is performed formally, in an ad hoc fashion. First deriving appropriate mathematical expressions governing the empirical slow flows and based on analyticity conditions, we demonstrate only close correspondence between analytical and empirical slow flows in a physical system that can be modeled as a two-degree-of-freedom strongly nonlinear coupled oscillators.

Copyright © 2009 by ASME

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