THE DIRECTIONAL CHOI–WILLIAMS DISTRIBUTION FOR THE ANALYSIS OF ROTOR-VIBRATION SIGNALS

The accurate analysis of time-varying signals is an essential pre-request for the fault diagnosis and hence safe operation of rotating machines. The Wigner distribution (WD) is probably most widely used among the Cohenʹs class in order to describe how the spectral content of a signal changes over time. However, the basic nature of such signals causes significant interfering cross-terms, which do not permit a straightforward interpretation of the energy distribution. A new signal processing technique, the directional Choi–Williams distribution (dCWD), is proposed to account for complex-valued time-varying signals, which represent the planar motion of rotating machinery at each instant of time. Using the dCWD, not only are the cross-terms minimised but also the interference terms between the forward and backward harmonic components are avoided by transforming complex signals into the forward and backward pass analytic signals. Therefore, the dCWD produces a much lower level of the interference terms than the WD and hence leads to a much clear understanding of the dynamic behaviour of rotors under rotating conditions. The effectiveness of the dCWD is demonstrated by comparing it with the WD and Choi–Williams distribution through some numerical examples and an application to experimental signals.