Physics-based foundation for empirical mode decomposition

Lee, YS; Tsakirtzis, S; Vakakis, AF; Bergman, LA; McFarland, DM

dc.contributor.author	Lee, YS	en
dc.contributor.author	Tsakirtzis, S	en
dc.contributor.author	Vakakis, AF	en
dc.contributor.author	Bergman, LA	en
dc.contributor.author	McFarland, DM	en
dc.date.accessioned	2014-03-01T01:31:40Z
dc.date.available	2014-03-01T01:31:40Z
dc.date.issued	2009	en
dc.identifier.issn	0001-1452	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19871
dc.subject	Empirical Mode Decomposition	en
dc.subject.classification	Engineering, Aerospace	en
dc.subject.other	Analyticity	en
dc.subject.other	Empirical Mode Decomposition	en
dc.subject.other	Flow analysis	en
dc.subject.other	Flow model	en
dc.subject.other	Intrinsic Mode functions	en
dc.subject.other	Mathematical expressions	en
dc.subject.other	Oscillatory mode	en
dc.subject.other	Physics-based	en
dc.subject.other	Slow dynamics	en
dc.subject.other	Slow flow	en
dc.subject.other	Structural systems	en
dc.subject.other	Theoretical foundations	en
dc.subject.other	Dynamical systems	en
dc.subject.other	Functions	en
dc.subject.other	Nonlinear dynamical systems	en
dc.subject.other	Signal analysis	en
dc.subject.other	Structures (built objects)	en
dc.subject.other	Time series	en
dc.subject.other	Vibrations (mechanical)	en
dc.subject.other	Decomposition	en
dc.title	Physics-based foundation for empirical mode decomposition	en
heal.type	journalArticle	en
heal.identifier.primary	10.2514/1.43207	en
heal.identifier.secondary	http://dx.doi.org/10.2514/1.43207	en
heal.language	English	en
heal.publicationDate	2009	en
heal.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. Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc.	en
heal.publisher	AMER INST AERONAUT ASTRONAUT	en
heal.journalName	AIAA Journal	en
dc.identifier.doi	10.2514/1.43207	en
dc.identifier.isi	ISI:000272503800014	en
dc.identifier.volume	47	en
dc.identifier.issue	12	en
dc.identifier.spage	2938	en
dc.identifier.epage	2963	en