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

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)625-649
Number of pages25
Issue number4
StatePublished - Aug 2011


  • Complexification-averaging technique
  • Empirical mode decomposition
  • Intrinsic modal Oscillator
  • Intrinsic mode function
  • Nonlinear system identification
  • Slow flow model

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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