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. A new 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 spectral correlation function, as demonstrated in a recent PhD thesis by Hanson. Another method is represented by a MIMO version of the mean differential cepstrum, first suggested by Antoni at ISMA2000, but further developed in a recent PhD thesis by Chia. This suffers from noise problems, but these may possibly be solved by using the random decrement for smoothing prior to analysis. An example using random decrement to extract the forcing function in a SIMO situation is presented to strengthen the proposition.
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