Variable scale-convex-peak method for weak signal detection

A variable scale-convex-peak method is constructed to identify the frequency of weak harmonic signal. The key of this method is to find a set of optimal identification coefficients to make the transition of dynamic behavior topologically persistent. By the stochastic Melnikov method, the lower bound of the chaotic threshold continuous function is obtained in the mean-square sense. The intermediate value theorem is applied to detect the optimal identification coefficients. For the designated identification system, there is a valuable co-frequency-convex-peak in bifurcation diagram, which indicates the state transition of chaos-period-chaos. With the change of the weak signal amplitude and external noise intensity in a certain range, the convex peak phenomenon is still maintained, which leads to the identification of frequency. Furthermore, the proposition of the existence of reversible scaling transformation is introduced to detect the frequency of the harmonic signal in engineering. The feasibility of constructing the hardware and software platforms of the variable scale-convex-peak method is verified by the experimental results of circuit design and the results of early fault diagnosis of actual bearings, respectively.

Automated summary

This study introduces a variable scale-convex-peak method for identifying the frequency of weak harmonic signals. By finding optimal identification coefficients and utilizing the stochastic Melnikov method, the method is able to identify the frequency while ensuring dynamic behavior transition persistence. Through analyzing the bifurcation diagram and introducing reversible scaling transformation, the feasibility of frequency detection in engineering is validated.