Cyclostationarity and the cepstrum for operational modal analysis of MIMO systems—Part II: Obtaining scaled mode shapes through finite element model updating

This paper presents a new technique for scaling mode shapes, obtained from cepstrum-based operational modal analysis (OMA) techniques, such as that described in the companion paper, using finite element model updating. This OMA technique estimated frequency response functions (FRFs) between a cyclostationary input and response measurements. If the input is frequentially white, the resulting FRFs can be obtained up to an overall scaling constant using the in-band poles and zeros identified in the OMA process and employing the response autospectrum as a reference to correct for the effect of out of band modes. In this way, the mode shapes would be scaled correctly relative to each other but would still have arbitrary overall magnitude. If the input is not white, then no reference is available to correct FRF regenerated from in-band poles and zeros, and so these FRFs will exhibit both an overall slope resulting from the effect of out-of-band poles and zeros, and an arbitrary magnitude. This overall slope will differ between measurement locations so even the relative scaling between the mode shapes will be lost. This paper describes a simple technique for recovering both the relative and overall scaling of the FRFs, and hence the mode shapes, based on finite element model updating.