Free vibration-based system identification using temporal cross-correlations

Yasutaka Narazaki, Vedhus Hoskere, Billie F. Spencer

Research output: Contribution to journalArticlepeer-review


Free vibration measurements provide useful information in performing modal identification of civil infrastructure. Free vibration tests have been carried out frequently, because of the simple implementation and the availability of well-established pre/postprocessing techniques. In particular, the eigensystem realization algorithm (ERA) can be used with free vibration data to extract modal information in a straightforward and automatic manner. However, using free vibration data with the ERA is often problematic for civil infrastructure, because of the significant noise in the measurements caused primarily by small vibration amplitudes and higher structural damping. To address this problem, a method for generating ERA input is proposed that reduces the effect of noise in measured free vibration data. The proposed method is an extension of the natural excitation technique developed for stationary random vibration signals. The natural excitation technique method is adjusted to accommodate free vibration data by replacing the cross-correlations of stationary random processes with the temporal cross-correlations of free vibration signals. Then, an approach to reduce the noise effect in the temporal cross-correlations is proposed based on linear superposition of the cross power spectrum densities of overlapping data segments. Finally, results of the ERA using the proposed approach are compared with the corresponding results from directly applying ERA to the free vibration data. The comparisons using numerical and field test data show that the proposed method outperforms the conventional approach, especially for the modes whose amplitudes are small in the measured free vibration signals.

Original languageEnglish (US)
Article numbere2207
JournalStructural Control and Health Monitoring
Issue number8
StatePublished - Aug 2018


  • eigensystem realization algorithm (ERA)
  • free vibration
  • natural excitation technique (NExT)
  • noise reduction
  • optimization
  • system identification

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Mechanics of Materials


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