A Hilbert‐Huang transform based identification method for general linear time‐varying systems and weakly nonlinear systems

Abstract

AbstractThis paper proposes an identification method for general linear time‐varying (LTV) MDOF systems and weakly nonlinear systems based on the Hilbert‐Huang Transform (HHT)[1]. The proposed method uses Empirical mode decomposition (EMD) to decompose the response signals of systems into intrinsic mode functions (IMFs) and residues, and then analyzes the IMFs and the residues by Hilbert transform (HT) to obtain the analytical IMFs and analytical residues. After that, the above signals are synthesized to form new response signals and new analytical response signals. Finally, the new synthesized signals are used to identify the stiffness and damping coefficients of the systems. Three types of variation: smooth, abrupt and periodical variations are considered in the numerical simulations of LTV chainlike[2] and nonchainlike systems as well as weakly nonlinear systems such as Duffing oscillators and Van der Pol oscillators with white noise added in the system responses to demonstrate the effectiveness, accuracy and robustness of the proposed method. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)