A time-domain nonlinear system identification method based on multiscale dynamic partitions |
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Authors: | Young S. Lee Stylianos Tsakirtzis Alexander F. Vakakis Lawrence A. Bergman D. Michael McFarland |
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Affiliation: | 1.Mechanical and Aerospace Engineering,New Mexico State University,Las Cruces,USA;2.School of Applied Mathematical and Physical Sciences,National Technical University of Athens,Athens,Greece;3.Department of Mechanical Science and Engineering,University of Illinois at Urbana-Champaign,Urbana,USA;4.Department of Aerospace Engineering,University of Illinois at Urbana-Champaign,Urbana,USA |
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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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