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

Abstract

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.