Analysis of energy leakage characteristics of dual-tree complex wavelet packet transform and its application on gear fault diagnosis

Abstract: The gear is the key component of rotating machinery, so a fault in the gear will directly affect the condition of the whole machine's operation. It was difficult to extract the fault feature information effectively from the vibration signals of a faulty gear. In the field of fault diagnosis, envelope demodulation was one of the most common signal processing methods. However, a filtering process was required before envelope demodulation. The parameters of a filter were determined by experience, and that has a great influence on the results of signal processing. The discrete wavelet packet transform has a larger energy leakage of frequency band, which obviously affected the results of the envelope demodulation. It is necessary to have a method with a lower energy leakage of the frequency band before envelope demodulation. The dual tree complex wavelet packet transform (DT-CWPT) was a new signal processing method that had many good qualities. Because the energy leakage of the frequency band was smaller when the signal was decomposed by a dual tree complex wavelet packet transform, the dual tree complex wavelet packet transform was used to extract the fault feature information in the field of fault diagnosis. In this paper, first, according to the characteristics of Gaussian white noise, whose frequency was full of the whole frequency band, Gaussian white noise was decomposed by a dual-tree complex wavelet packet transform, and the parts with energy leakage were regarded as a theoretical part band beyond the range of the frequency components. Then the lower energy leakage characteristic of dual tree complex wavelet packet transform was verified by a quantitative analysis method of frequency band energy leakage. A dual tree complex wavelet packet transform has an advantage in the pretreatment of envelope demodulation compared with the method of discrete wavelet packet transform. Secondly, the signal was decomposed layer-by-layer by a dual tree complex wavelet packet transform, and the kurtogram based on a dual tree complex wavelet packet transform could be obtained by computing the spectral kurtosis of every layer's components. According to the standard of maximum kurtosis, the layer of decomposition and the component about the signal can be chosen automatically and accurately. The best layer of the dual tree complex wavelet packet decomposition was the layer of the maximum kurtosis and the component which had the maximum kurtosis was the best component of decomposition. Finally, the vibration signal of the engineering was processed by the method of spectral kurtosis based on a dual tree complex wavelet packet transform, the best decomposition layer and component could be chosen, and the fault feature information was extracted effectively by a Hilbert envelope demodulation, where the feasibility and effectiveness of the method were verified. The research will provide a reference for extracting the fault feature information of a gearbox fault diagnosis in rotating machinery.