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The machinery fault signal is a typical non-Gaussian and non-stationary process. The fault signal can be described by S U+03B1 S distribution model because of the presence of impulses. Time-frequency distribution is a useful tool to extract helpful information of the machinery fault signal. Various fractional lower order U+0028 FLO U+0029 time-frequency distribution methods have been proposed based on fractional lower order statistics, which include fractional lower order short time Fourier transform U+0028 FLO-STFT U+0029, fractional lower order Wigner-Ville distributions U+0028 FLO-WVDs U+0029, fractional lower order Cohen class time-frequency distributions U+0028 FLO-CDs U+0029, fractional lower order adaptive kernel time-frequency distributions U+0028 FLO-AKDs U+0029 and adaptive fractional lower order time-frequency auto-regressive moving average U+0028 FLO-TFARMA U+0029 model time-frequency representation method. The methods and the exiting methods based on second order statistics in S U+03B1 S distribution environments are compared, simulation results show that the new methods have better performances than the existing methods. The advantages and disadvantages of the improved time-frequency methods have been summarized. Last, the new methods are applied to analyze the outer race fault signals, the results illustrate their good performances.

Applications of fractional lower order time-frequency representation to machine bearing fault diagnosis