Application of VMD-SVD in Underdetermined Source Number Estimation of Mechanical Fault Signals
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摘要: 针对在观测信号数目小于机械故障振动信号源数目的欠定情况下, 源信号的个数难以估计的问题, 提出一种变分模态分解(Variational mode decomposition, VMD)和奇异值分解(Singular value decomposition, SVD)相结合的盲源数目估计方法。首先利用VMD对振动信号进行分解, 得到若干本征模态函数分量(Intrinsic mode function, IMF), 然后对IMF进行重新组合得到多维观测信号的协方差矩阵, 最后依据奇异值分解的结果来对信号源数目进行最终确定。仿真信号分析验证了该方法的有效性, 将该方法运用到轴承复合故障振动信号中, 分析结果表明, 该方法能够实现欠定情况下源数目的可靠估计。Abstract: To solve the problem that it is difficult to estimate the number of source signals when the number of observed signals is less than the number of vibration signal sources for mechanical faults, a blind source number estimation method based on variational mode decomposition (VMD) and singular value decomposition (SVD) was proposed in this paper. Firstly, VMD was used to decompose the original vibration signal to obtain several intrinsic mode function (IMF). Then, IMF was recombined to obtain the covariance matrix of multidimensional observation signals. Finally, the number of signal sources was determined according to the result of singular value decomposition. Simulation signal analysis verifies the effectiveness of the method. And the method is also applied to the vibration signals of the bearing composite faults, and the analysis results show that the method can achieve reliable estimation of the number of sources under underdetermined conditions.
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表 1 第一路信号不同K值所对应的中心频率
K1 中心频率/Hz IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 2 463 2 231 3 365 1 456 2 283 4 363 1 448 2 235 2 944 5 356 1 300 1 596 2 247 2 953 6 356 1 294 1 590 2 239 2 909 3 775 
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表 2 第二路信号不同K值所对应的中心频率
K2 中心频率/Hz IMF1 IMF2 IMF3 IMF4 IMF5 IMF6 IMF7 2 1 201 1 753 4 470 1 196 1 716 2 183 5 469 1 196 1 715 2 180 3 821 6 459 1 154 1 462 1 754 2 192 3 823 7 459 1 154 1 461 1 752 2 181 3 002 3 846
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表 3 奇异值分解相关结果
名称 σ1 σ2 σ3 σ4 σ5 σ6 σ7 σ8 σ9 特征值 0.360 5 0.280 1 0.235 3 0.141 3 0.090 9 0.061 8 0.042 1 0.036 1 0.029 8 邻近比 1.287 0 1.190 4 1.665 3 1.554 5 1.470 9 1.468 0 1.166 2 1.211 4
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