McFarland, DMTsakirtzis, SVakakis, AFBergman, LALee, YSWe 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.http://hdl.handle.net/123456789/1987112472963ISI:0002725038000140001-1452293810.2514/1.43207engAMER INST AERONAUT ASTRONAUTAIAA JournalEmpirical Mode DecompositionVibrations (mechanical)AnalyticityTime seriesTheoretical foundationsFunctionsDecompositionSlow flowNonlinear dynamical systemsDynamical systemsMathematical expressionsPhysics-basedStructures (built objects)Intrinsic Mode functionsStructural systemsOscillatory modeFlow modelSlow dynamicsSignal analysisFlow analysisPhysics-based foundation for empirical mode decompositionjournalArticle2009Δημοσίευση σε περιοδικόPublication in journalΑεροδιαστημική μηχανικήAerospace Engineeringisi - Engineering, Aerospace includes resources concerned with astronautics, aeronautics, aerospace, and aviation. Topics covered include the design and construction of aircraft, space vehicles, missiles, satellites, instrumentation, and power units, as well as the launch, flight, and guidance of crafts in the earth's atmosphere or in space. Resources in this category draw from many fields, including mechanics and mechanical engineering, automation, instrumentation, and materials science.Επιστημονικό άρθροScientific articleΕθνικό Μετσόβιο ΠολυτεχνείοGreek Aggregator OpenArchives.gr | National Documentation Centre (EKT)other