基于Duffing振子的弱正弦信号检测方法研究

摘要

数值仿真发现,通过设置Duffing振子初值和参考信号初相使其满足一定关系,Duffing振子从大周期态向混沌态的转变(正向相变),比较其从混沌态向大周期态的转变(逆向相变),对周期策动力的幅值体现出了更稳健的敏感性.据此,提出了一种利用Duffing振子逆向相变实现弱正弦信号检测的方法,分析了其可行性,并通过仿真与传统的检测方法进行了对比.数据表明,相同条件下,所提检测方法具有更高的检测精度.此外,根据相空间分布特点,提出了一种相轨迹运动状态的判别方法.该判别方法计算量小,并具有较好的实时性,通过仿真验证了该方法的正确性.%It is found in numerical simulations that Duffing oscillator state transition from big-cycle motion to chaotic motion has more robust sensitivity to the amplitude of the forced periodic term than the transition from chaotic motion to big-cycle motion, as long as the reference signal initial phase and the Duffing oscillator initial value are matched.On this basis,a new weak sinusoidal signal detection scheme is advanced, whose feasibility is then analyzed.The advanced scheme shows higher detection capability by comparing with traditional methods.Besides, considering the characteristics of the Duffing oscillator phase space, a new Duffing oscillator motion state judging method is proposed, which features good real-time performance and low computational complexity, and is verified with simulations.