Application of Double Tree Complex Wavelet Packet and Adaptive Permutation Entropy in Bearing Fault Diagnosis
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摘要: 针对滚动轴承信号存在大量噪声、故障特征难以提取，而双树复小波包可减少有用信息的丢失，提出双树复小波包与排列熵结合的轴承故障诊断方法。首先经双树复小波包与排列熵结合对不同层数的分量计算平均排列熵值，确定最佳分解层数；其次采用峭度值作为指标对加噪信号选取分解后的最佳分量；最后对最佳分量进行包络分析提取故障特征频率。双树复小波包与排列熵相结合确定最佳层数方法，避免了对原始信号的过分解和欠分解，从而有效应提取到故障特征。Abstract: Aiming at the fact that rolling bearing signal has a lot of noise and its fault features are difficult to extract, and the dual-tree complex wavelet packet (DCWP) can reduce the loss of useful information, a fault diagnosis method combining DCWP and permutation entropy (PE) is proposed in this paper. Firstly, the average permutation entropy of the components of different layers is calculated by combining DCWP and PE, and the optimal number of layers is determined. Secondly, the kurtosis value is used as the index to select the optimal component after decomposition of the noise signal. Finally, the optimal component is analyzed by envelope analysis to extract the fault characteristic frequency. The combination of DCWP and PE to determine the best number of layers avoids the over-decomposition and under-decomposition of the original signal and can effectively extract the fault features of rolling bearings.
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图 1 双树复小波包2层分解与重构
Figure 1. Dual-tree complex wavelet packet 2-level decomposition and reconstruction
图 3 仿真信号时域波形及包络谱
Figure 3. Time-domain waveform and envelope spectrum of the simulated signal
图 6 双树复小波包2层分解波形及频谱图
Figure 6. Waveform and frequency spectrum of dual-tree complex wavelet packet 2-level decomposition
图 8 故障原始信号时域波形及包络谱
Figure 8. Time-domain waveform and envelope spectrum of raw fault signals
图 9 加噪故障信号时域波形及包络谱
Figure 9. Time-domain waveform and envelope spectrum of noisy fault signals
表 1 不同层数平均排列熵值
Table 1. Average permutation entropy values for different levels
分解层数 2 3 4 5 平均排列熵值 0.478 0 0.481 8 0.509 1 0.486 3 
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表 2 各分量峭度值
Table 2. Kurtosis values of each component
分量 a1 a2 a3 a4 峭度 16.18 11.49 15.22 9.71
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表 3 不同层数平均排列熵值
Table 3. Average permutation entropy values for different levels
分解层数 2 3 4 5 6 平均排列熵值 0.657 0 0.549 5 0.521 0 0.585 6 0.575 1
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