Smoothing localized directional cyclic autocorrelation and application in oil-film instability analysis

In this paper, smoothing localized directional cyclic autocorrelation (SLDCA) is proposed as a novel time–frequency distribution to analyze the vibration signal of rotor-bearing system in oil-film instability. Based on the cyclostationarity of real-valued signal, directional cyclic autocorrelation (DCA) is defined for the complex-valued signal. In order to suppress the cross-term interferences, the DCA is localized and filtered with two-dimensional time–frequency window which allows the smoothing kernel function to adapt to the signal time–frequency-varying characteristics. And then the localized DCA is smoothed by the localized optimal radially Gaussian kernel and cascaded to produce the SLDCA with high time–frequency resolution and less susceptibility to cross-term interferences. The application of SLDCA in the oil-film instability analysis verifies that the SLDCA can not only precisely detect the instantaneous frequency information in the time–frequency distribution with high resolution and robustness to the noises and cross-terms, but also provide the phase coupling information of rotor instantaneous planar motion by which the directivity and shape of the planar motion can be determined.