Cepstrum-based operational modal analysis: regeneration of frequency response functions

This paper discusses the regeneration of frequency response functions (FRFs) based on a previously-proposed cepstrum-based operational modal analysis (OMA) technique. OMA differs from experimental modal analysis (EMA) in that it seeks to determine a structure's dynamic characteristics from response-only measurements, without precise knowledge of excitation forces. Response measurements, however, comprise both excitation and transmission path effects, which must be separated before the structural properties can be determined. The method employed in this paper achieves source-path separation with the cepstrum, which is able to deal with 'frequentially smooth' (not just frequentially white) inputs. After separation, the poles and zeros of the transfer function can be obtained by curve-fitting the transfer path cepstrum. But the FRF regenerated from these poles and zeros corresponds to a truncated model of the system, covering only a limited frequency range. The out-of-band poles and zeros affect the magnitude and phase of the in-band FRFs, and this distortion must be corrected in the FRF regeneration process. This paper focuses on that correction using data from a steel beam experiment. To do this, an 'equalisation curve' is used, based on a comparison of the regenerated FRF with a 'reference FRF', found with EMA or FEM techniques. The paper proposes a polynomial-fit approach to obtain the equalisation curves, resulting in excellent agreement between measured and OMA-regenerated FRFs. The techniques outlined in the paper have a number of potential applications, particularly in the fault diagnostics and structural health monitoring fields, where damage is often detectable by changes in the structure's FRFs.