Identification of MDOF Non-Linear Uncoupled Dynamical Systems Using Hilbert Transform and Empirical Mode Decomposition Method

Abstract

A non-linear dynamical system identification method using Hilbert transform (HT) and empirical mode decomposition (EMD) is proposed. For a single-degree-of-freedom (SDOF) nonlinear system, the Hilbert transform identification method is good at identifying the instantaneous modal parameters (natural frequencies, damping characteristics and their dependencies on a vibration amplitude and frequency). For the multi-degree-of-freedom (MDOF) non-linear uncoupled dynamical systems, the EMD method is attempting for the decomposition of response signals into a collection of mono-components signals, termed intrinsic mode functions (IMFs). Considering the IMFs admit a well-behaved Hilbert transform, the HT identification method has been applied for the identification of nonlinear properties. The numerical simulation of a 2-dof shear-beam building model with nonlinear stiffness illustrated the proposed technique.