基于奇异值能量谱的Morlet小波尺度优化

Optimization of Morlet wavelet scale based on energy spectrum of singular values

针对尺度对Morlet小波变换结果具有决定性影响的问题,提出一种奇异值能量谱方法,实现Morlet小波尺度的优化并提取故障特征。首先采用Shannon熵的方法优化Morlet小波中心频率与带宽参数,针对Shannon熵计算结果中无明确极小值点的情况,通过比较不同参数下的小波变换结果,得到了最优小波参数。然后,根据实际频率与尺度的对应关系,选择有效尺度范围进行连续Morlet小波变换。最后,将每一尺度下的小波系数进行奇异值分解并计算奇异值能量谱,通过选择能量谱峰值来确定最优尺度参数,实现对故障特征的提取。对仿真信号和实际轴承信号的分析表明,此方法克服了以往方法的缺点,在低信噪比时具有良好的故障特征提取效果。

Aiming at the fact that the scale has a tremendous impact on results of Morlet wavelet transformation,a method based on energy spectrum of singular values was proposed to optimize Morlet wavelet scale and extract fault features. Firstly,Shannon entropy was used to optimize the central frequency and bandwidth parameter of Morlet wavelet.Aiming at the situation that there was no minimum value in calculation results of Shannon entropy,Morlet wavelet decomposition results with different parameters were compared to obtain the optimal wavelet parameters. Then,the effective scale ranges were chosen to do Morlet wavelet transformation according to the relationship between practical frequencies and wavelet scale parameters. Finally,the wavelet coefficients under each scale were decomposed into singular values and the energy spectrum of singular values was calculated. The optimal scale was obtained by choosing the peak values in energy spectrum,and then the faults feature were extracted. The experimental results and simulation ones of rolling bearing signals showed that the proposed method overcomes disadvantages of previous methods and has a good effect on fault feature extraction when the signal-to-noise ratio（ SNR） is low.