Abstract: Aiming at the automatic detection on arc welding stability,this paper proposed the theory of weak periodic and multi-channel signals with normal repetition rate. Through a scientific mathematical deduction,an equation has been put forward,which can sufficiently demonstrate the dynamic characteristics of the repetition rate of periodic signal. To overcome the problems brought in by scattered signals during actual sampling, this paper has introduced a method by subdividing a signal point into countless micro points which normally distribute in a multidimensional signal space. Therefore,an important parameter of the equation,the generalized actual area could be reasonably calculated,through which the whole equation could be accurately solved. 104 times of arc welding electric signals were conducted as samples. Based on the probabilistic neural network(PNN), the samples has been trained and tested,which show that the dynamic characteristics drawn through the above-mentioned theory are closely related to the stability of CO₂ arc welding,and thereby the automatic detection can be realized.