Fractional Order Frequency Weighted Energy Operator and its Application in Bearing Fault Diagnosis

In order to solve the problem that it is difficult to extract the fault features of rolling bearings under strong noise, a new feature enhancement method named fractional order frequency weighted energy operator (FFWEO) is proposed. Firstly, Fourier transform is used to transform the signal from time domain to frequency domain to obtain the amplitude function and phase function. Secondly, set the variation range and step size of differential order, perform fractional differential processing on the amplitude function of the signal in the frequency domain according to the time domain differential property of Fourier transform, combine the amplitude function with the phase function, and then use the inverse Fourier transform to obtain the modified signal. Thirdly, Hilbert transform is applied to differential signals of different orders to obtain envelope signals. The envelope kurtosis index is used to select the best differential order, and the envelope spectrum is obtained from differential signals to determine the bearing fault mode. The experimental results show that the method can effectively extract the fault features of rolling bearings under the strong noise background.