矩阵构造对奇异值分解信号处理效果的影响

Influence of Matrix Creation Way on Signal Processing Effect of Singular Value Decomposition

一维信号一般可以构造两种矩阵,第一种矩阵是通过对信号的连续截断来构造的,第二种则为重构吸引子矩阵.文中从理论上证明了在这两种矩阵方式下,奇异值分解都可以将信号表示为一系列分量信号的线性叠加,但是第一种矩阵获得的分量信号是彼此正交的,而第二种矩阵获得的分量信号则不具有正交性.两种矩阵的结构都可以利用分量信号信息量的变化趋势来合理地确定.对一个铣削力信号的处理结果表明,第一种矩阵分离出了机床主轴旋转基频完整的时域波形,分辨出了两个频率很接近的信号分量,发现了信号中隐含的调幅现象;而第二种矩阵则揭示了切削过程中由于材料颗粒不均匀和间隙而产生的对刀具的微弱冲击现象.

Generally, two kinds of matrices can be created by a one-dimension signal. The first one is always created by the continuous interception of signal, while the second one is a reconstruction attractor matrix. It is proved that a signal can be decomposed into the linear superposition of a series of component signals by singular value decomposition （SVD） using these two kinds of matrices. However, the component signals obtained by the first kind of matrix are orthogonal with each other, while those obtained by the second one are correlative with each other. The structure of both kinds of matrices can be rationally determined by the variation trend of information quantity of component signals. The processing results of a milling force signal show that, by using the first kind of matrix, the complete fundamental waveform of main spindle of miller is isolated, two component signals with close frequency are distinguished, and the phenomenon of amplitude modulation hidden in signal is also extracted; while by using the second one, the faint shock to cutter due to the uneven granule and rift in workpiece material is revealed.