Use of the cepstrum to remove selected discrete frequency components from a time signal R.B. Randall, N. Sawalhi School of Mechanical and Manufacturing Engineering, University of New South Wales, Sydney 2052 ABSTRACT In machine diagnostics there are a number of tools for separating discrete frequency components from random and cyclostationary components. This is the basis of separating gear (deterministic) from bearing (second order cyclostationary) signals for example. Time synchronous averaging (TSA) requires a separate operation, including resampling, to be carried out for each periodic frequency, and the method cannot be used for discrete frequency sidebands, or partial bandwidth spectra. Self adaptive noise cancellation (SANC) and discrete/random separation (DRS) remove all discrete frequencies, whether harmonics or sidebands, and it is not possible to decide if some should be left. The method proposed here uses the cepstrum to localise discrete frequency components, which manifest themselves as harmonic or sideband families. Selected families can be removed in the cepstrum, leaving any it might be desirable to retain, and generating a notch filter that is flexible enough to allow for small speed fluctuations, or even narrow band noise peaks that sometimes result from slight random modulation of periodic signals. Normally, to edit the cepstrum and return to the time domain, it is necessary to use the complex cepstrum, but the latter requires the phase signal to be unwrapped. This is not possible for response signals containing discrete frequencies and noise, where the phase is not continuous. The procedure proposed here uses the real cepstrum to localise and edit the log amplitude of the original signal, removing the unwanted discrete frequency components, and then combines the edited amplitude with the original phase spectrum to return to the time domain. The paper shows how this technique can be used to remove discrete frequency components from signals measured on two machines with a faulty bearing, and then perform envelope analysis on the residual signal to diagnose the bearing fault. One is a gear test rig for which the discrete frequencies are harmonics of the shaft speed and gearmesh frequency, and the other a bladed disc test rig for which the discrete frequencies are harmonics of the shaft speed and bladepass frequency. Envelope analysis can be done on both full bandwidth and partial (zoom) bandwidth signals, the latter to save on computation, and restrict the amount of discrete frequency components to be removed, since the signal envelope is independent of frequency shifts. 1. Introduction Signal processing used for condition monitoring purposes is usually concerned with separating various signal components from each other, so as to identify changes in any one of them. This has to be done blind, since measured responses are a sum of components from a multitude of sources, and include deterministic (discrete frequency at constant speed), stationary random, and cyclostationary random components. The latter are typically produced by modulation of random signals by discrete frequencies, and are often produced by rotating and reciprocating machines. T. Proulx (ed.), Rotating Machinery, Structural Health Monitoring, Shock and Vibration, Volume 5, Conference Proceedings of the Society for Experimental Mechanics Series 8, DOI 10.1007/978-1-4419-9428-8_38, © The Society for Experimental Mechanics, Inc. 2011 451
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