Correspondence between intrinsic mode functions and slow flows

Young S. Lee, Stylianos Tsakirtzis, Alexander F Vakakis, Lawrence Bergman, D. Michael McFarland

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

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.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
Pages661-670
Number of pages10
EditionPART A
DOIs
StatePublished - Jun 25 2010
Event2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009 - San Diego, CA, United States
Duration: Aug 30 2009Sep 2 2009

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
NumberPART A
Volume1

Other

Other2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009
CountryUnited States
CitySan Diego, CA
Period8/30/099/2/09

Fingerprint

Intrinsic Mode Function
Time series
Correspondence
Decomposition
Decompose
Nonlinear System Identification
Nonlinear systems
Nonlinear Oscillator
Identification (control systems)
Coupled Oscillators
Analyticity
Physics
Time Domain
Degree of freedom
Sensors
Equivalence
Sensor
Demonstrate

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Electrical and Electronic Engineering

Cite this

Lee, Y. S., Tsakirtzis, S., Vakakis, A. F., Bergman, L., & McFarland, D. M. (2010). Correspondence between intrinsic mode functions and slow flows. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009 (PART A ed., pp. 661-670). (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; Vol. 1, No. PART A). https://doi.org/10.1115/DETC2009-87588

Correspondence between intrinsic mode functions and slow flows. / Lee, Young S.; Tsakirtzis, Stylianos; Vakakis, Alexander F; Bergman, Lawrence; McFarland, D. Michael.

Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A. ed. 2010. p. 661-670 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; Vol. 1, No. PART A).

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

Lee, YS, Tsakirtzis, S, Vakakis, AF, Bergman, L & McFarland, DM 2010, Correspondence between intrinsic mode functions and slow flows. in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A edn, Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009, no. PART A, vol. 1, pp. 661-670, 2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009, San Diego, CA, United States, 8/30/09. https://doi.org/10.1115/DETC2009-87588
Lee YS, Tsakirtzis S, Vakakis AF, Bergman L, McFarland DM. Correspondence between intrinsic mode functions and slow flows. In Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A ed. 2010. p. 661-670. (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; PART A). https://doi.org/10.1115/DETC2009-87588
Lee, Young S. ; Tsakirtzis, Stylianos ; Vakakis, Alexander F ; Bergman, Lawrence ; McFarland, D. Michael. / Correspondence between intrinsic mode functions and slow flows. Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009. PART A. ed. 2010. pp. 661-670 (Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009; PART A).
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