Current efforts towards a non-linear system identification methodology of broad applicability

A. F. Vakakis, L. A. Bergman, D. M. McFarland, Y. S. Lee, M. Kurt

Research output: Contribution to journalReview articlepeer-review


A review of current efforts towards developing a non-linear system identification (NSI) methodology of broad applicability [1-4] is provided in this article. NSI possess distinct challenges, since, even the task of identifying a set of (linearized) modal matrices modified ('perturbed') by non-linear corrections might be an oversimplification of the problem. In that context, the integration of diverse analytical, computational, and post-processing methods, such as slow flow constructions, empirical mode decompositions, and wavelet/Hilbert transforms to formulate a methodology that holds promise of broad availability, especially to systems with non-smooth non-linearities such as clearances, dry friction and vibro-impacts is proposed. In particular, the proposed methodology accounts for the fact that, typically, non-linear systems are energy- and initial condition-dependent, and has both global and local components. In the global aspect of NSI, the dynamics is represented in a frequency-energy plot (FEP), whereas in the local aspect of the methodology, sets of intrinsic modal oscillators are constructed to model specific non-linear transitions on the FEP. The similarity of the proposed methodology to linear experimental modal analysis is discussed, open questions are outlined, and some applications providing a first demonstration of the discussed concepts and techniques are provided.

Original languageEnglish (US)
Pages (from-to)2497-2515
Number of pages19
JournalProceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
Issue number11
StatePublished - Nov 2011
Externally publishedYes


  • Empirical mode decomposition
  • Frequency-energy plot
  • Intrinsic modal oscillator
  • Nonlinear system identification
  • Vibro-impact dynamics

ASJC Scopus subject areas

  • Mechanical Engineering


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