双势阱Duffing-van der Pol振子微弱信号检测统计量构造

为解决双势阱Duffing-van der Pol振子同频微弱信号定量检测问题,分析发现了Poincare截面能明显区分系统不同状态的现象,构建了基于Poincare截面的检测统计量,并以此为基础设计了信号检测的有效实现方法。首先对Poincare截面进行数值计算得到系统关于策动力幅值的分岔点图,其次对不同状态下各幅值对应分布点做方差统计构建检测统计量。不同状态的检测统计量分布区间不同,按照统计值落入的区间即可判断信号有无。仿真实验给出了不同策动力角频率下检测统计量的临界值和检测区间,并通过与相平面检测结果的对比验证了该检测方法的可行性,为微弱信号定量检测提供了参考。

Construction of weak signal detection statistics with double-well Duffing-van der Pol oscillator

In order to solve the problem of co-frequency weak signals quantitative detection with the double-well Duffing-van der Pol oscillator, it is found that the Poincare section can clearly distinguish the different states of the system. The detection statistics based on the Poincare section is constructed, and based on that, an effective method of signal detection is designed. Firstly, the Poincare section is numerical calculated, and the bifurcation diagram about the driving signal amplitude is obtained. Then, the detection statistics are constructed by calculating the variance of the amplitude distribution points in different states. Distribution intervals of detection statistics in different states are different, thus the signal can be judged according to the interval in which the statistical value falls. Through the simulation experiments, the critical statistics and detection intervals of the detection statistics under different angular frequencies are given, and the feasibility of this detection method is proved by comparing with the phase plane detection results. The results provide references for quantitative detection of weak signals.