TY - JOUR
T1 - Current efforts towards a non-linear system identification methodology of broad applicability
AU - Vakakis, A. F.
AU - Bergman, L. A.
AU - McFarland, D. M.
AU - Lee, Y. S.
AU - Kurt, M.
N1 - Funding Information:
This work was supported in part by the U.S. Air ForceOffice of Scientific Research [grant number FA9550-07-1-0335] and by the U.S. National Science Foundation [grants number CMMI-0927995 and CMMI-0928062].
PY - 2011/11
Y1 - 2011/11
N2 - 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.
AB - 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.
KW - Empirical mode decomposition
KW - Frequency-energy plot
KW - Intrinsic modal oscillator
KW - Nonlinear system identification
KW - Vibro-impact dynamics
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U2 - 10.1177/0954406211417217
DO - 10.1177/0954406211417217
M3 - Review article
AN - SCOPUS:81255143199
VL - 225
SP - 2497
EP - 2515
JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science
SN - 0954-4062
IS - 11
ER -