Cepstrum-based operational modal analysis revisited: A discussion on pole-zero models and the regeneration of frequency response functions

摘要

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.