System identification of linear structures based on Hilbert-Huang spectral analysis. Part 2: Complex modes

Jann N. Yang, Ying Lei, Shuwen Pan, Norden Huang

Research output: Contribution to journalArticlepeer-review

169 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)1533-1554
Number of pages22
JournalEarthquake Engineering and Structural Dynamics
Volume32
Issue number10
DOIs
StatePublished - Aug 2003

Keywords

  • Complex modes
  • Data analysis
  • Hilbert transform
  • Hilbert-Huang spectral analysis
  • Linear structures
  • System identification

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