Updated Cepstral Methods for Operational Modal Analysis

Abstract

Cepstral methods of modal analysis offer two advantages with respect to conventional methods. The first is that they give both poles and zeros of the transfer function, and thus most of the information about the relative scaling of the residues of adjacent modes. Fully scaled modes can be obtained using a minimum of extraneous information, which can be provided for example by a finite element (FE) model of the structure, which does not have to be very accurate. The other advantage is that for single input, multiple output (SIMO) systems, the cepstrum of the responses is the sum of the cepstra of the forcing and transfer functions, and provided the spectrum of the force is reasonably smooth (on a log scale) the corresponding cepstrum is very short and the higher quefrency part of the cepstrum is completely dominated by the transfer function and can be curve-fitted for its poles and zeros. This is a much weaker restriction than the assumption of most techniques that the excitation is white. The above properties of the cepstrum apply only to SIMO systems and in the normal MIMO situation one possibility is to separate the responses to a single input at each measurement point. The methods available for this include blind source separation (BSS) techniques, for convolutively mixed systems. An exciting possibility is where there is just one second order cyclostationary source with a particular cyclic frequency such as with a diesel railcar. The responses to this single source can be separated in the cepstrum of the spectral correlation function. A very recent development is the possibility of performing editing of time signals using the real cepstrum instead of the complex cepstrum. The latter contains all information about the phase, but only if it can be unwrapped to a continuous function of frequency, and this is not possible for stationary forcing or response functions. For many applications, the original phase can be combined with the edited amplitude information from the real cepstrum, even for general stationary responses.