A global-local approach to nonlinear system identification

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

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

Abstract

We present the basic components of a time-domain nonlinear system identification (NSI) method with promise of applicability to a broad class of smooth and non-smooth dynamical systems. The proposed NSI method is based on the close correspondence between analytical and empirical slow-flow dynamics, and relies on direct analysis of measured time series without any a priori assumptions on the system dynamics. The central assumption is that the measured time series can be decomposed in terms of a finite number of oscillating components that are in the form of fast monochromatic oscillations modulated by slow amplitudes. The empirical slow-flow model of the dynamics is obtained from empirical mode decomposition, and its correspondence to the analytical slow-flow model establishes a local nonlinear interaction model (NIM). A NIM consists of a set of intrinsic modal oscillators (IMOs) that can reproduce the measured time series over different time scales and can account for (even strongly) nonlinear modal interactions. Hence, it represents a local model of the dynamics, identifying specific nonlinear transitions. By collecting energy-dependent frequency behaviors from all identified IMOs, a frequency-energy plot (in the modal space) can be constructed, which depicts global features of the dynamical system.

Original languageEnglish (US)
Title of host publicationModal Analysis Topics - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011
Pages513-524
Number of pages12
StatePublished - Jun 13 2011
Event29th IMAC, a Conference on Structural Dynamics, 2011 - Jacksonville, FL, United States
Duration: Jan 31 2011Feb 3 2011

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
Volume3
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652

Other

Other29th IMAC, a Conference on Structural Dynamics, 2011
CountryUnited States
CityJacksonville, FL
Period1/31/112/3/11

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ASJC Scopus subject areas

  • Engineering(all)
  • Computational Mechanics
  • Mechanical Engineering

Cite this

Lee, Y. S., Vakakis, A. F., McFarland, D. M., & Bergman, L. (2011). A global-local approach to nonlinear system identification. In Modal Analysis Topics - Proceedings of the 29th IMAC, a Conference on Structural Dynamics, 2011 (pp. 513-524). (Conference Proceedings of the Society for Experimental Mechanics Series; Vol. 3).