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为了进一步提高微弱信号的检测能力,在更低信噪比环境下提取微弱信号的特征信息,提出采用分数阶Duffing系统实现微弱周期信号检测。基于常规Duffing-Holmes数学模型,通过加入分数阶微分算子引入了分数阶Duffing方程数学模型,利用变量代换对该模型进行改进可实现任意频率的微弱周期信号检测。研究分析系统阻尼比参数变化对系统非线性动力学特性的影响,给出了最佳阻尼比参数范围;研究了微分阶次与系统临界混沌阈值变化关系,得出微分阶次与系统临界混沌阈值成反比关系的结论。分别在高斯白噪声及色噪声背景下对微弱信号进行检测与识别,大量仿真结果表明,分数阶Duffing系统检测微弱信号的最低信噪比门限值比整数阶Duffing系统降低了10 dB,提高了检测微弱信号能力。
In order to further improve the detection ability of weak signals, we extract the feature information of weak signals in a lower signal-to-noise ratio environment and propose a fractional Duffing system to detect weak periodic signals. Based on the classical Duffing-Holmes mathematical model, the fractional order differential operator is introduced into the mathematical model of fractional Duffing equation. The variable substitution is used to improve the model to detect the weak periodic signal at any frequency. The influence of the change of system damping ratio on the nonlinear dynamic characteristics of the system is analyzed and the optimum range of damping ratio parameters is given. The relationship between the differential order and the critical chaos threshold of the system is studied, and the relationship between the differential order and the system critical chaos threshold The inverse relationship between the conclusion. Weak signals are detected and identified in the background of Gaussian white noise and color noise respectively. A large number of simulation results show that the minimum signal-to-noise ratio threshold of fractional-order Duffing system for detecting weak signals is 10 dB lower than that of the integer order Duffing system, Detection of weak signal capabilities.