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Physics-based foundation for empirical mode decomposition

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National Technical University of Athens   

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Physics-based foundation for empirical mode decomposition (EN)
McFarland, DM (EN)
Tsakirtzis, S (EN)
Vakakis, AF (EN)
Bergman, LA (EN)
Lee, YS (EN)
journalArticle (EN)
2014-03-01T01:31:40Z
2009 (EN)
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. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. (EN)
Engineering, Aerospace (EN)
Empirical Mode Decomposition (EN)
Vibrations (mechanical) (EN)
Analyticity (EN)
Time series (EN)
Theoretical foundations (EN)
Functions (EN)
Decomposition (EN)
Slow flow (EN)
Nonlinear dynamical systems (EN)
Dynamical systems (EN)
Mathematical expressions (EN)
Physics-based (EN)
Structures (built objects) (EN)
Intrinsic Mode functions (EN)
Structural systems (EN)
Oscillatory mode (EN)
Flow model (EN)
Slow dynamics (EN)
Signal analysis (EN)
Flow analysis (EN)
AIAA Journal (EN)
English
AMER INST AERONAUT ASTRONAUT (EN)
National Technical University of Athens
Digital Library of National Technical University of Athens | Dspace@NTUA
Κεντρική Βιβλιοθήκη Ε.Μ.Π.
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