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。
Abstract
Acccording to the fact that the scale has a tremendous impact on the result of Morlet wavelet transform, a method based on energy spectrum of singular value is proposed to optimize Morlet wavelet scale and extract fault feature. Firstly, Shannon entropy is used to optimize the central frequency and bandwidth parameter of the Morlet wavelet. According to the situation that there is no clear minimum value in the calculation result of Shannon entropy, Morlet wavelet decomposition results with different parameters are compared to obtain the optimal wavelet parameter. Then, the effective scale ranges are chosen to do Morlet wavelet transform according to the relationship between practical frequency and wavelet scale parameter. Finally, the wavelet coefficients at each scale are decomposed into singular values and the energy spectrum of singular value is calculated. The optimal scale is obtained by choosing the maximum in energy spectrum, and then the fault feature can be extracted. The experimental results and analysis results of rolling bearing signals show that the proposed method overcomes the disadvantages of previous methods and has good effect in fault feature extraction when signal-to-noise ratio(SNR) is low.
关键词
Morlet小波 /
Shannon熵 /
奇异值能量谱 /
特征提取。
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Key words
Morlet wavelet /
Shannon entropy /
Energy spectrum of singular value /
Feature extraction.
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