Recognization of signal singularity based on Hermitian wavelet transform

The signal in the nature of singularity is always caused by mechanical fault of equipment. It is important to recognize the singularity correctly for mechanical fault diagnosis. The complex Hermitian wavelet is constructed based on the first and the second derivatives of the Gaussian function to detect signal singularities. There are two advantages of using Hermitian wavelet: First, the complex Hermitian wavelet has a real Fourier transform that will not mix the signal phase with its filter phase; Second, the real part and the imagine part of Hermitian wavelet have less oscillation than Morlet wavelet, so that the convolution operation can be process with fewer number of data points and the signal singularity will not be smeared. The time-scale amplitude plot and phase plot based on Hermitian wavelet are presented to detect signal singularities. A successful application has been obtained in impact rub fault diagnosis of large air compressor gearbox.