Fractional-Order Smoothed Pseudo Wigner-Ville Distribution and its Applications in Machinery Fault Diagnosis

lower time-frequency resolution is caused by Smoothed pseudo Wigner-Ville distribution (SPWVD) in suppressing cross-terms interference, which limits its application in the processing of the non-stationary vibration signals. This paper proposes a novel fractional-order smoothed pseudo Wigner-Ville distribution (FrSPWVD) to solve the above problem. The details about step of the calculation are as follows: the appropriate fractional order of original signals are determined firstly; then fractional order Fourier transform transforms the original signals in the most appropriate fractional domain, and transformed signals are analyzed by SPWVD; lastly, parameters of original signals are accurately extracted according to the corresponding appropriate fractional order and fractional frequency of signals. By analyzing the signals in the most appropriate fractional domain, the proposed time-frequency distribution can obtain the time-frequency representation with much higher resolution compared to the classical SPWVD. Simulation results and fault diagnosis cases show the efficiency of the proposed method.