A survey of the application of the cepstrum to structural modal analysis

The cepstrum has a very long history, since the first paper was published in 1963, two years before the publication of the FFT algorithm. The first application was to the determination of echo delay time, but it was quickly applied to speech analysis for two reasons. Firstly, it was able to detect voiced speech, and measure the voice pitch, and secondly it was able to separate the forcing and transfer function components in speech signals. These two properties apply equally to machine vibration signals, and the cepstrum can be used to detect and remove periodic discrete frequency components (harmonics and modulation sidebands) from the spectrum (and corresponding time signals) and also to extract the modal properties of a structure in the presence of the forcing function. This paper describes the development of these applications to structural modal analysis over many years, primarily to operational modal analysis (OMA), where the modal information is extracted from response signals, often with the structure in its normal operating environment. The cepstrum extracts the modal information in terms of pole/zero models, and requires compensation for the effects of unmeasured out-of-band modes, by an equalisation process, and overall scaling to obtain scaled mode shapes. Steady advances to achieve this have been made over the years. A recent development that has revolutionised the application has been the ability to edit stationary and slowly varying non-stationary signals using the real cepstrum (which does not contain the phase information of the original signals) but regenerating time signals by combining the edited amplitude spectra with the original phase spectra (with negligible error). There are currently two ways in which this can be used in operational modal analysis: