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A time-domain nonlinear system identification method based on multiscale dynamic partitions

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Abstract

Based on a theoretical foundation for empirical mode decomposition, which dictates the correspondence between the analytical and empirical slow-flow analyses, we develop a time-domain nonlinear system identification (NSI) technique. This NSI method is based on multiscale dynamic partitions and direct analysis of measured time series, and makes no presumptions regarding the type and strength of the system nonlinearity. Hence, the method is expected to be applicable to broad classes of applications involving time-variant/time-invariant, linear/nonlinear, and smooth/non-smooth dynamical systems. The method leads to nonparametric reduced order models of simple form; i.e., in the form of coupled or uncoupled oscillators with time-varying or time-invariant coefficients forced by nonhomogeneous terms representing nonlinear modal interactions. Key to our method is a slow/fast partition of transient dynamics which leads to the identification of the basic fast frequencies of the dynamics, and the subsequent development of slow-flow models governing the essential dynamics of the system. We provide examples of application of the NSI method by analyzing strongly nonlinear modal interactions in two dynamical systems with essentially nonlinear attachments.

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Authors and Affiliations

  1. Mechanical and Aerospace Engineering, New Mexico State University, PO Box 30001, MSC 3450, Las Cruces, NM, 88003, USA

    Young S. Lee

  2. School of Applied Mathematical and Physical Sciences, National Technical University of Athens, P.O. Box 64042, Zografos, Athens, 157 10, Greece

    Stylianos Tsakirtzis

  3. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green St., Urbana, IL, 61801, USA

    Alexander F. Vakakis

  4. Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 104 S., Wright St., Urbana, IL, 61801, USA

    Lawrence A. Bergman & D. Michael McFarland

Authors
  1. Young S. Lee
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  2. Stylianos Tsakirtzis
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  3. Alexander F. Vakakis
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  4. Lawrence A. Bergman
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  5. D. Michael McFarland
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Correspondence to Young S. Lee.

Additional information

This work was supported in part by the US Air Force Office of Scientific Research through Grant Number FA9550-07-1-0335.

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Lee, Y.S., Tsakirtzis, S., Vakakis, A.F. et al. A time-domain nonlinear system identification method based on multiscale dynamic partitions. Meccanica 46, 625–649 (2011). https://doi.org/10.1007/s11012-010-9327-7

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  • DOI: https://doi.org/10.1007/s11012-010-9327-7

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