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Time-frequency moments, eyelets, and machine faults

It has been shown that often the onset of developing faults in machines is clearly manifest in the time-frequency plane before any problems are noted by conventional methods such as the power spectrum. In this paper we explore a particular feature of some faulting machines, wherein a single vibration frequency briefly and intermittently appears as 'eyelets' in the time-frequency plane. We show that abrupt phase shifts in a tone, or equivalently sudden, rapid changes in the amplitude, cause a transient increase in the instantaneous spectral moments, particularly the instantaneous bandwidth and the instantaneous kurtosis, and cause eyelets in time-frequency similar to those seen in real machine vibrations.