Nonlinear MDOF system characterization and identi cation using the Hilbert-Huang transform

The Hilbert transform is one of the most successful approaches to tracking the varying nature of vibration of a large class of nonlinear systems thanks to the extraction of backbone curves from experimental data. Because signals with multiple frequency components do not admit a well-behaved Hilbert transform, it is inherently limited to the analysis of single-degree-of-freedom systems. In this study, the joint application of the complexification-averaging method and the empirical mode decomposition enables us to develop a new technique, the slow-flow model identification method. Through numerical and experimental applications, we demonstrate that the proposed method is adequate for characterizing and identifying multi-degree-offreedom nonlinear systems

The slow-flow method of identification in nonlinear structural dynamics

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-flowmodel identification method, which is demonstrated using numerical examples

Nonlinear MDOF System Characterization and Identification using the Hilbert- Huang Transform: Experimental Demonstration

The Hilbert transform is one of the most successful approaches to tracking the varying nature of vibration of a large class of nonlinear systems, thanks to the extraction of backbone curves from experimental data. Because signals with multiple frequency components do not admit a well-behaved Hilbert transform, this transform is inherently limited to the analysis of single-degree-of-freedom systems; this shortcoming is potentially overcome by the Hilbert-Huang transform (HHT). In this study, the joint application of the complexification-averaging method and the HHT enables us to develop a new technique, the slow-flow model identification method. Through an experimental application, we demonstrate that the proposed method is adequate for characterizing and identifying multi-degreeof-freedom nonlinear systems