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Cepstral Methods of Operational Modal Analysis

Signal Processing

  1. Robert B. Randall

Published Online: 15 SEP 2009

DOI: 10.1002/9780470061626.shm045

Encyclopedia of Structural Health Monitoring

Encyclopedia of Structural Health Monitoring

How to Cite

Randall, R. B. 2009. Cepstral Methods of Operational Modal Analysis. Encyclopedia of Structural Health Monitoring. .

Author Information

  1. University of New South Wales, School of Mechanical and Manufacturing Engineering, Sydney, NSW, Australia

Publication History

  1. Published Online: 15 SEP 2009


The cepstrum is the inverse Fourier transform of the logarithmic spectrum. For SIMO (single input, multiple output) systems, the cepstrum of each output signal is the sum of the cepstra of the forcing function and the system properties. Where the input log spectrum is reasonably smooth and flat (impulsive or broadband random), the input is concentrated in the low part of the cepstrum and the high part can be curve fitted for the system poles and zeros. For minimum-phase systems, the complex cepstrum can be derived from response autospectra only. The so-called differential cepstrum has the advantage that it can be calculated from a time signal directly and also that its mathematical formulation allows the poles and zeros to be obtained using methods designed for fitting impulse response functions. For excitation by a series of (say burst random) pulses, the “mean differential cepstrum” gives a more accurate result. For MIMO (multiple input, multiple output) systems, which virtually always apply in practice, two approaches are currently being investigated: blind source separation to separate the response to one of the inputs (thus SIMO) and a matrix decomposition analogous to the mean differential cepstrum. The advantage of the cepstral techniques is the potential for obtaining scaled mode shapes because of obtaining zeros as well as poles.


  • cepstrum;
  • complex cepstrum;
  • differential cepstrum;
  • mean differential cepstrum;
  • operational modal analysis;
  • structural dynamics