Dense framelets with two generators and their application in mechanical fault diagnosis

•We propose a new family of dense framelets with high symmetry and regularity.•We construct symmetric framelets with vanishing moments and good shift-invariance.•The proposed framelets have greatly high vibration signal denoising performance.•The proposed framelets are superior to other typical wavelets in fault diagnosis.

Wavelet analysis has been widely applied to mechanical fault diagnosis. Aiming at the problems of current wavelet basis, such as low time–frequency sampling, asymmetry and poor shift-invariance, this paper develops a new family of dense framelets with two generators and some desirable properties. To perform the corresponding framelet transform, three-channel iterated filterbank should be used, where the first and the third channel is decimated while the second channel is undecimated. This arrangement is very helpful for extracting the fault feature of the mid and low frequency band signal components and obtaining some symmetric framelets. To obtain framelets with high symmetry and a specified number of vanishing moments, B-spline and maximally flat linear FIR filter are, respectively, used to design filterbank. Three symmetric framelets and one framelets with symmetric low-pass filter and high-pass filter are constructed. Compared with the higher density framelets and orthonormal wavelets, the proposed framelets have better shift-invariance and denoising performance. Finally, the proposed framelets are applied to fault diagnosis of two gearboxes. The results show that the proposed framelets can be effectively applied to mechanical fault diagnosis and is superior to other commonly-used framelets/wavelets.