基于二次样条小波细节信号峰值的有效奇异值确定

赵学智;向可;叶邦彦;陈统坚

振动与冲击 ›› 2010, Vol. 29 ›› Issue (11) : 6-12.

PDF(2888 KB)
PDF(2888 KB)
振动与冲击 ›› 2010, Vol. 29 ›› Issue (11) : 6-12.
论文

基于二次样条小波细节信号峰值的有效奇异值确定

  • 赵学智;向可;叶邦彦;陈统坚
作者信息 +

Determination of Effective Singular Values Based on the Peak of Detail Signal of Quadratic Spline Wavelet

  • ZHAO Xue-zhi; XIANG Ke; YE Bang-yan;
    CHEN Tong-jian
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文章历史 +

摘要



摘研究了Hankel矩阵方式下交流分量、直流分量和噪声的奇异值分布特点,指出当矩阵阶数足够大时,代表这三个分量的奇异值在总奇异值向量中将被作为单独的坐标被分离开,而其衔接点处存在突变。提出利用二次样条小波对奇异值向量进行变换,并根据其细节信号的峰值位置来确定有效奇异值。研究结果表明,当细节信号的最大峰值位于第二个坐标时,表明原始信号中存在较大直流分量,此时根据第二最大峰值可确定全部有效奇异值,否则就根据最大峰值位置确定有效奇异值。信号处理实例证实了此方法的准确性。利用此法有效地分离出了轴承振动信号中的调制特征,进而据此准确地判断了轴承滚道的损伤情况。


Abstract

The characteristics of singular values of alternating current, direct current and noise components when Hankel matrix is used in singular value decomposition (SVD) are studied respectively. It’s pointed out that if the order of matrix is big enough, the singular values representing these three components will be isolated as independent coordinates in the total singular value vector, and there are sudden changes in the joints of these coordinates. It’s proposed that this total singular value vector be processed by quadratic spline wavelet transform, and then the effective singular values can be determined by the peak position of wavelet detail signal. The studying results show that if the maximum peak happened in the second coordinates, then it means that a major direct current component is existed in the original signal and under this circumstance the number of effective singular values will be determined by the second maximum peak position, otherwise the number of effective singular values is determined by the maximum peak position. Signal processing examples demonstrate the effectiveness of this method, and the processing result for the vibration signal of bearing shows that a modulated signal is isolated successfully from the strong background noise and the injuring state of roll track of this bearing is diagnosed reliably according to this modulated signal.

关键词

奇异值分解 / 二次样条小波 / 峰值位置 / 有效奇异值 / 轴承振动

Key words

singular value decomposition / quadratic spline wavelet / peak position / effective singular value / bearing vibration

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导出引用
赵学智;向可;叶邦彦;陈统坚. 基于二次样条小波细节信号峰值的有效奇异值确定[J]. 振动与冲击, 2010, 29(11): 6-12
ZHAO Xue-zhi;XIANG Ke;YE Bang-yan;CHEN Tong-jian. Determination of Effective Singular Values Based on the Peak of Detail Signal of Quadratic Spline Wavelet[J]. Journal of Vibration and Shock, 2010, 29(11): 6-12

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