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System identification of linear structures based on Hilbert–Huang spectral analysis. Part 2: Complex modes
Author(s) -
Yang Jann N.,
Lei Ying,
Pan Shuwen,
Huang Norden
Publication year - 2003
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.288
Subject(s) - eigenvalues and eigenvectors , impulse response , hilbert–huang transform , modal , normal mode , modal analysis using fem , modal analysis , vibration , mathematics , linear system , mathematical analysis , intermittency , frequency response , modal testing , algorithm , control theory (sociology) , computer science , acoustics , physics , engineering , white noise , turbulence , chemistry , quantum mechanics , thermodynamics , statistics , polymer chemistry , electrical engineering , artificial intelligence , control (management)
A method, based on the Hilbert–Huang spectral analysis, has been proposed by the authors to identify linear structures in which normal modes exist (i.e., real eigenvalues and eigenvectors). Frequently, all the eigenvalues and eigenvectors of linear structures are complex. In this paper, the method is extended further to identify general linear structures with complex modes using the free vibration response data polluted by noise. Measured response signals are first decomposed into modal responses using the method of Empirical Mode Decomposition with intermittency criteria. Each modal response contains the contribution of a complex conjugate pair of modes with a unique frequency and a damping ratio. Then, each modal response is decomposed in the frequency–time domain to yield instantaneous phase angle and amplitude using the Hilbert transform. Based on a single measurement of the impulse response time history at one appropriate location, the complex eigenvalues of the linear structure can be identified using a simple analysis procedure. When the response time histories are measured at all locations, the proposed methodology is capable of identifying the complex mode shapes as well as the mass, damping and stiffness matrices of the structure. The effectiveness and accuracy of the method presented are illustrated through numerical simulations. It is demonstrated that dynamic characteristics of linear structures with complex modes can be identified effectively using the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.