基于SVD的奇异性信号检测原理及其应用

PRINCIPLE OF SINGULARITY DETECTION BASED ON SVD AND ITS APPLICATION

研究了Hankel矩阵方式下SVD的信号分解原理,证明了利用SVD可将原始信号分解为一系列分量信号的简单线性叠加。发现在Hankel矩阵方式下,从第二个SVD分量开始的各分量具有奇异性检测能力。指出与小波相比,SVD的奇异性检测具有两个特点,一是各分量的消失矩阶数逐次增加,第n个SVD分量具有n-1阶消失矩,因而各分量可以检测出具有不同奇异性指数的奇异点;二是所有SVD分量中指示奇异点位置的脉冲宽度始终保持不变,而且这个宽度由所构造的Hankel矩阵的列数决定。最后将这一方法应用于铣削力信号中的奇异性检测,揭示了由于刀具磨损或者工件材料颗粒不均匀和间隙而产生的对刀具的微弱冲击现象。

The signal decomposition principle of Hankel matrix based on singular value decomposition(SVD) is studied.It's proved that an original signal can be decomposed into a linear superposition of a series of component signals using Hankel matrix based on SVD.It's discovered that starting from the second SVD component signal,the singularity in the original signal can be detected by these SVD component signals.Compared with wavelet transformation,SVD method have two characteristics for singularity detection,the one is that the vanishing moment of SVD component signals is increased progressively and the n'th SVD component signal has the n-1'th order vanishing moment,so that singular points with different Lip index can also be detected using SVD component signals,the other is that the width of the impulse indicating the position of singular point will keep the same in all SVD component signals and this width is determined by the column number of Hankel matrix.This method is used to detect the singularity hidden in a milling force signal,and the faint shock to cutter,which might be caused by tool wear or uneven granule and rift in workpiece material,is revealed.