Abstract
A least square method based on data fitting is proposed to construct a new lifting wavelet, together with the nonlinear idea and redundant algorithm, the adaptive redundant lifting transform based on fitting is firstly stated in this paper. By variable combination selections of basis function, sample number and dimension of basis function, a total of nine wavelets with different characteristics are constructed, which are respectively adopted to perform redundant lifting wavelet transforms on low-frequency approximate signals at each layer. Then the normalized lP norms of the new node-signal obtained through decomposition are calculated to adaptively determine the optimal wavelet for the decomposed approximate signal. Next, the original signal is taken for subsection power spectrum analysis to choose the node-signal for single branch reconstruction and demodulation. Experiment signals and engineering signals are respectively used to verify the above method and the results show that bearing faults can be diagnosed more effectively by the method presented here than by both spectrum analysis and demodulation analysis. Meanwhile, compared with the symmetrical wavelets constructed with Lagrange interpolation algorithm, the asymmetrical wavelets constructed based on data fitting are more suitable in feature extraction of fault signal of roller bearings.
Highlights
IntroductionRoller bearings are among the most commonly used components in modern production facilities
Roller bearings are among the most commonly used components in modern production facilities.Breakdowns caused by running wear and inappropriate operation will lead to huge economic losses for enterprises, but potentially to serious casualties
Based on the existing theoretical and applied research on lifting algorithms, the adaptive redundant lifting wavelet transform based on data fitting is proposed here and the paper is organized as follows: in Section 2, a new way to construct lifting wavelets with variable characteristics based on the least square method of data fitting is introduced, and the adaptive redundant lifting wavelet analysis is presented as well
Summary
Roller bearings are among the most commonly used components in modern production facilities. Though the linear phase of filters can be ensured by the symmetry of wavelets to avoid or minimize the phase distortion during signal processing, there is still a problem: how to flexibly and construct wavelets with a lifting algorithm to implement the idea of obtaining wavelets with desired characteristics through the design of the lifting operator, while realizing effective feature extraction of various complicated practical signals, which has been a major difficulty to be resolved. Based on the existing theoretical and applied research on lifting algorithms, the adaptive redundant lifting wavelet transform based on data fitting is proposed here and the paper is organized as follows: in Section 2, a new way to construct lifting wavelets with variable characteristics based on the least square method of data fitting is introduced, and the adaptive redundant lifting wavelet analysis is presented as well.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
