Avariable 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 beh...Avariable 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 chaosperiod-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.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11872253, 11602151, 11790282)the Natural Science Foundation for Outstanding Young Researcher in Hebei Province of China(Grant No. A2017210177)+2 种基金the Natural Science Foundation in Hebei Province of China (Grant No. A2019421005)the Hundred Excellent Innovative Talents in Hebei Province (Grant No. SLRC2019037)the Basic Research Team Special Support Projects (Grant No. 311008)。
文摘Avariable 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 chaosperiod-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.
