The slow-flow method of identification in nonlinear structural dynamics

Abstract

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition. The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, we attempt to provide the missing link, showing the relationship between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system described by slowly-varying amplitudes and phases is obtained. These variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a nonlinear system identification method, termed the slow-flow model identification method, which is demonstrated using numerical examples.

Detection and identification of nonlinearities by amplitude and frequency modulation analysis

“…However, the use of HHT for nonlinear system identification is still in its early stage [14][15][16][17]. Tasks of nonlinear system identification include (1) detection of the existence and spatial locations of nonlinearities, (2) determination of the types, orders, and functional forms, and (3) identification of system parameters.…”

Empirical Mode Decomposition in the Reduced-Order Modeling of Aeroelastic Systems

“…In several earlier papers, the authors demonstrated a relationship between Intrinsic Mode Functions (IMFs), derived from the Empirical Mode Decomposition (EMD), and the slow-flow model of a strongly nonlinear dynamical system 1,2,3 . This naturally led to the development of the Slow Flow Model Identification (SFMI) method for strongly nonlinear systems, in which the physical parameters of such systems could be identified from experimental data.…”