带有余弦函数的三维混沌弱信号检测系统及电路实现
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摘要
从理论上分析了二维Duffing弱信号检测系统变量输出在混沌和周期态之间交替转换。发现一种新的三维混沌弱信号检测系统生成规则,以生成4种检测系统之一的三维Liu-cos混沌系统为例,采用傅里叶变换等方法从理论上验证了新生成的三维混沌弱信号检测系统输出信号具有广域收敛性,解决了二维Duffing混沌弱信号检测系统不能广域检测和输出信号不收敛问题;新设计的三维Liu-cos混沌弱信号检测电路空中声波实验显示可抗低频声波干扰,检测性能优于二维Duffing混沌电路和新设计的Duffing+滤波器电路,水中实验显示三维Liu-cos混沌弱信号检测电路可抗高频水声干扰,可检测波形畸变的水声信号。
The output wave changes between periodic and chaotic state of the variable in the two dimensional Duffing chaotic weak signal detection system were analysed. A new rule to generate the three dimensional chaotic weak signal detection system was discoveried. Making the three-dimensional Liu-cos chaotic weak signal detection system generated by above the rule as one of the four detection systems for an example,the wide convergence of the output signals of the threedimensional chaotic weak signal detection system generated by the rule was verified by using the Fourier transform theoretical. The problems for the signal can not be detection in the wide area and can not be convergence by the two dimensional Duffing chaotic weak signal detection system were solved. The experiments in air showed that the low-frequency acoustic interference can be overcome by the new designed three-dimensional Liu-cos chaotic weak signal detection circuit.The detection performances of desigened three-dimensional Liu-cos chaotic weak signal detection circuit are better than the two dimensional Duffing circuit as well as the new designed Duffing and Filter circuits. The experiments in water showed that the high frequency acoustic interference can be overcome and the distorted acoustic signal can be detected by the threedimensional Liu-cos chaotic weak signal detection circuit.
The output wave changes between periodic and chaotic state of the variable in the two dimensional Duffing chaotic weak signal detection system were analysed. A new rule to generate the three dimensional chaotic weak signal detection system was discoveried. Making the three-dimensional Liu-cos chaotic weak signal detection system generated by above the rule as one of the four detection systems for an example,the wide convergence of the output signals of the threedimensional chaotic weak signal detection system generated by the rule was verified by using the Fourier transform theoretical. The problems for the signal can not be detection in the wide area and can not be convergence by the two dimensional Duffing chaotic weak signal detection system were solved. The experiments in air showed that the low-frequency acoustic interference can be overcome by the new designed three-dimensional Liu-cos chaotic weak signal detection circuit.The detection performances of desigened three-dimensional Liu-cos chaotic weak signal detection circuit are better than the two dimensional Duffing circuit as well as the new designed Duffing and Filter circuits. The experiments in water showed that the high frequency acoustic interference can be overcome and the distorted acoustic signal can be detected by the threedimensional Liu-cos chaotic weak signal detection circuit.
引文
[1]赖志慧,冷永刚,孙建桥等.基于Duffing振子的变尺度微弱特征信号检测方法研究[J].物理学报,2012,61(5):050503.Lai Z H,Leng Y G,Sun J Q,et al. Weak characteristic signal detection based on scale transformation of Duffing oscillator[J]. Acta Phys Sin,2012,61(5):050503.
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[7]孟玲玲,宋艳君,王晓东.基于变形Lorenz系统微弱周期信号频率检测新方法[J].计量学报,2013,34(5):480-485.Meng L L,Song Y J,Wang X D. New Method of Weak Periodic Signal Frequency Detection Based on a Deformable Lorenz System[J]. Acta Metrologica Sinica,2013,34(5):480-485.
[8]王梦蛟,曾以成,谢常清,等. Chen系统在微弱信号检测中的应用[J].物理学报,2012,18:52-56.Wang M J,Zeng Y C,Xie C Q,et al. Application of Chen's system to detecting weak harmonic signals[J].Acta Phys Sin,2012,61(18):180502.
[9]刘剑鸣,杨霞,高跃龙,等.类Liu系统在水声微弱信号检测中的应用研究[J].物理学报,2016,65(7):070501.Liu J M,Yang X,Gao Y L,et al. Application of similar Liu system in underwater weak signal detection[J]. Acta Physica Sinica,2016,65(7):070501.
[10]刘剑鸣,杨霞,宋菲菲,等.五种新混沌弱信号检测系统设计[J].计量学报,2016. 37(9):525-530.Liu J M,Yang X,Song F F,et al. The Design of Five New Chaotic Systems on Weak Signal Detection[J].Acta Metrologica Sinica,2016,37(5):525-530.
[11]刘剑鸣,习敬伟. Liu-cos混沌系统在声波弱信号检测中的应用[J].计量学报,2018,39(3):386-39.Liu J M,Xi J W. Liu-cos Chaotic System and Its Application in Acoustic Weak Signal Detection[J]. Acta Metrologica Sinica,2018,39(3):386-391.
[2]冯俊,徐伟,顾仁财等.有界噪声与谐和激励联合作用下Duffing-Rayleigh振子的Melnikov混沌[J].物理学报,2011,60(9):090507.Feng J,Xu W,Gu R C,et al. Melnikov chaos in DuffingRayleigh oscillator subjected to combined bounded noise and harmonic excitations[J]. Acta Phys Sin,2011,60(9):090507.
[3]时培明.孙彦龙.韩东颖.基于双耦合混沌振子变尺度微弱信号检测方法研究[J].计量学报,2016,37(3):310-31.Shi P M,Sun Y L,Han D Y. Study on Variable Scale Weak Signal Detection Method Based on Two Coupled Chaotic Oscillator[J]. Acta Metrologica Sinica,2016,37(3):310-313.
[4]范剑,赵文礼,王万强.基于Duffing振子的微弱周期信号混沌检测性能研究[J].物理学报,2013,62(18):18050.Fan J,Zhao W L,Wang W Q. Study on the weak sinusoidal signal detection property using Duffing chaos system[J]. Acta Phys Sin,2013,62(18):180502.
[5]何文平,封国林,高新全等.准周期外力驱动下Lorenz系统的动力学行为[J].物理学报,2006,55(6):3179.He W P,Feng G L,Gao X Q,et al. Dynamics of the Lorenz system under quasiperiodic driving[J]. Acta Phys Sin,2006,55(6):3175-317.
[6]孟玲玲,宋艳君,王晓东.基于变形Lorenz系统和李雅普诺夫指数的微弱周期信号检测[J].计量学报,2012,33(6):559-564.Meng L L,Song Y J,Wang X D. Weak Periodic Signal Detection Based on a Deformable Lorenz Detection System and the Maximum Lyapunov Exponent[J]. Acta Metrologica Sinica,2012,33(6):559-564.
[7]孟玲玲,宋艳君,王晓东.基于变形Lorenz系统微弱周期信号频率检测新方法[J].计量学报,2013,34(5):480-485.Meng L L,Song Y J,Wang X D. New Method of Weak Periodic Signal Frequency Detection Based on a Deformable Lorenz System[J]. Acta Metrologica Sinica,2013,34(5):480-485.
[8]王梦蛟,曾以成,谢常清,等. Chen系统在微弱信号检测中的应用[J].物理学报,2012,18:52-56.Wang M J,Zeng Y C,Xie C Q,et al. Application of Chen's system to detecting weak harmonic signals[J].Acta Phys Sin,2012,61(18):180502.
[9]刘剑鸣,杨霞,高跃龙,等.类Liu系统在水声微弱信号检测中的应用研究[J].物理学报,2016,65(7):070501.Liu J M,Yang X,Gao Y L,et al. Application of similar Liu system in underwater weak signal detection[J]. Acta Physica Sinica,2016,65(7):070501.
[10]刘剑鸣,杨霞,宋菲菲,等.五种新混沌弱信号检测系统设计[J].计量学报,2016. 37(9):525-530.Liu J M,Yang X,Song F F,et al. The Design of Five New Chaotic Systems on Weak Signal Detection[J].Acta Metrologica Sinica,2016,37(5):525-530.
[11]刘剑鸣,习敬伟. Liu-cos混沌系统在声波弱信号检测中的应用[J].计量学报,2018,39(3):386-39.Liu J M,Xi J W. Liu-cos Chaotic System and Its Application in Acoustic Weak Signal Detection[J]. Acta Metrologica Sinica,2018,39(3):386-391.