Physics-based foundation for empirical mode decomposition

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

Research output: Contribution to journalArticle

Abstract

We study the correspondence between analytical and empirical slow-flow analyses. 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 is a useful tool for decomposing the measured time series in terms of intrinsic mode functions, 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 intrinsic mode functions derived from empirical mode decomposition provides a physics-based theoretical foundation for empirical mode decomposition, which currently is performed formally in an ad hoc fashion. To demonstrate correspondence between analytical and empirical slow flows, we derive appropriate mathematical expressions governing the empirical slow flows and based on analyticity conditions. Several nonlinear dynamical systems are considered to demonstrate this correspondence, and the agreement between the analytical and empirical slow dynamics proves the assertion.

Original languageEnglish (US)
Pages (from-to)2938-2963
Number of pages26
JournalAIAA journal
Volume47
Issue number12
DOIs
StatePublished - Dec 1 2009

ASJC Scopus subject areas

  • Aerospace Engineering

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    Lee, Y. S., Tsakirtzis, S., Vakakis, A. F., Bergman, L. A., & McFarland, D. M. (2009). Physics-based foundation for empirical mode decomposition. AIAA journal, 47(12), 2938-2963. https://doi.org/10.2514/1.43207