Abstract
Multi-wavelet has many excellent properties that single wavelet cannot satisfy simultaneously, such as symmetry, orthogonality, compact support and high vanishing moments etc. It contains several scaling functions and wavelet functions, which can make it match different characteristics of analyzed signal. Therefore, it is always used in bearing fault diagnosis. However, multi-wavelet is multi-dimensional and vibration signal is one-dimensional, so the 1-D vibration signal should be preprocessed before being decomposed with multi-wavelet. It means that the initial data need to be converted to r-dimensional data, and then is input to a tower algorithm. If preprocessing is done, multi-wavelet properties will be destroyed. Due to balanced multi-wavelet has unique properties, the preprocessing can be omitted. In this paper, a balanced multi-wavelet called CL4BAL is designed through balancing original CL4 multi-wavelet and is applied in the vibration signal processing. Comparing the frequency band index after decomposition and reconstruction of CL4BAL and CL4 multi-wavelet, it can be proved that CL4BAL is much better than that of CL4 multi-wavelet in bearing fault diagnosis.
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