Cepstrum-based operational modal analysis revisited: A discussion on pole–zero models and the regeneration of frequency response functions. (15th October 2016) - Smith, Wade A.; Randall, Robert B.
Abstract: Operational modal analysis (OMA) seeks to determine a structure׳s dynamic characteristics from response-only measurements, which comprise both excitation and transmission path effects. The cepstrum has been used successfully in a number of applications to separate these source and path effects, after which the poles and zeros of the transfer function can be obtained via a curve-fitting process. The contributions from the individual poles and zeros can then be added (in log magnitude) to regenerate the frequency response function (FRF). Cepstrum-based OMA was originally developed in the 1980s and 90s, but there have been a number of recent developments that warrant discussion and explanation, and this is the basis of the present paper, which focusses on the FRF regeneration process and on a number of broader points explaining FRFs from a pole–zero perspective. The FRF regenerated from identified poles and zeros is subject to magnitude distortion from the effects of truncation, i.e., from the residual effects of out-of-band poles and zeros. As long as a reference FRF is available – for example from conventional experimental modal analysis or from a finite element model – this distortion can be corrected for using a magnitude equalisation curve. This paper discusses the nature of this equalisation curve, and gives recommendations on how best to obtain it. Other topics covered in the discussion are: the required distribution of poles and zeros for the successful regeneration of FRFs; node points and weak modes in a pole–zero model; the differences in pole–zero distribution between receptance, mobility and accelerance FRF forms; and, how to deal with the very low frequency region when regenerating FRFs. Special consideration is given to the identification of zeros – often masked by noise in response measurements – using transmissibility estimation. It is hoped that the discussion will assist in the application of cepstrum-based OMA methods and will lead to improved understanding of the FRF regeneration process and of frequency response functions more broadly. Highlights: We outline a number of new developments in cepstrum OMA. The regeneration of FRFs from poles and zeros is thoroughly explained. We show how to correct for magnitude distortion from the truncation of poles and zeros. We discuss node points, weak modes and other topics in a pole–zero model context. The identification of zeros using transmissibility is discussed.