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.