A global-local approach to nonlinear system identification: A review

Abstract

We present the basic components of a time-domain nonlinear system identification (NSI) method with a promise of applicability to a broad class of smooth and non-smooth dynamical systems. The proposed NSI method is based on the close correspondence between analytical and empirical slow-flow dynamics, and relies on the direct analysis of measured time series without any a priori assumptions on the system dynamics; i.e. it is purely an output-based approach. The central assumption of the methodology is that the measured time series can be decomposed in terms of a finite number of oscillating components that are in the form of ‘fast’ monochromatic oscillations modulated by ‘slow’ amplitudes. The empirical slow-flow model of the dynamics is obtained from empirical mode decomposition (EMD), and its correspondence to the analytical slow-flow model establishes a local nonlinear interaction model (NIM). A NIM consists of a set of intrinsic modal oscillators (IMOs) that can reproduce the measured time series over different time scales and can account for (even strongly) nonlinear modal interactions. Hence, it represents a local model of the dynamics, identifying specific nonlinear transitions. An IMO, whose response can reproduce the corresponding intrinsic mode function acquired from EMD analysis, represents the dynamical characteristics of the system under certain initial or parameter conditions (i.e. local aspects). By collecting energy-dependent frequency behaviors from all identified IMOs, a frequency-energy plot (in the modal space) can be constructed, which depicts global features of the dynamical system. This represents a global model of the dynamics. We demonstrate the efficacy of the outlined global–local NSI method with two-degree-of-freedom dynamical systems—one smooth, and the other non-smooth. Copyright © 2010 John Wiley & Sons, Ltd.