基于二分递推SVD的信号奇异性位置精确检测

 提出利用信号构造行数为2的矩阵,在奇异值分解后保留小奇异值对应的分量,并取大奇异值所对应的分量信号重复构造相同矩阵进行奇异值分解,从而将原始信号分解为一组分量信号.这种分量信号具有二阶消失矩,可实现对原始信号中Lipschitz指数为0和1的奇异性的位置精确检测,其检测脉宽小,且在同一层分量中指示奇异点位置的模极大值和奇异点处的突变量、转折斜率具有正比线性关系.此法克服了小波变换检测结果的位置偏移和脉冲宽大的缺陷,在对铣削力信号的处理中,准确地检测出了其中的微弱冲击.

Accurate Detection of Signal Singularity Position Based on Dichotomizing Recursion SVD

It is proposed that a matrix with row number 2 is created by original signal and is processed by singular value decomposition(SVD),the component signal corresponding to the small singular value is retained,while the one corresponding to the big singular value is continuously used to create the same matrix to be continuously processed by SVD,by this way original signal can be decomposed into a group of component signals,which have the second order vanishing moment and can detect the accurate position of singularity with Lipschitz index 0 and 1 in original signal.Furthermore,the width of their detection impulse is small,and the modulus maxima in the component signals of the same level are proportional to the quantity of sudden change and the turning slope in the singular point.The defects of wavelet singularity detection,i.e.the deviation of singularity position and big width of detection impulse,are overcome and the faint impacts in the milling force signal are accurately detected by this method.