Construction of a symmetrical shifl-invariant fractional overcomplete wavelet and its application in bearing fault diagnosis

This article introduces the design of symmetrical approximately shift-invariant fractional overcomplete wavelet transforms. First, a design scheme for the symmetrical low-pass filter with minimum-length was proposed, and then the corresponding highpass filters with approximately shift-invariant properties were constructed via Toeplitz matrix factorization, which has a lower computational complexity than other methods. In addition, fractional overcomplete wavelet transforms could he designed with higher vanishing moments through the method proposed. Subsequently, a bearing fault diagnosis scheme was proposed using the symmetrical shiftinvariant fractional overcomplete wavelet transforms. Experimental results show that the bearing faults can be detected effectively using the symmetrical shift-invariant fractional overcomplete wavelet transforms.