A global-local approach to nonlinear system identification

We present the basic components of a time-domain nonlinear system identification (NSI) method with 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 direct analysis of measured time series without any a priori assumptions on the system dynamics. The central assumption 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, 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. 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.