应用锁相环技术判别混沌相变的方法
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摘要
针对经典的李氏指数法(Lyapunov Exponential Method)等混沌相变判别方法复杂度高的问题,提出了一种应用锁相环技术判别混沌相变的新方法。首先,理论推导了混沌系统的解析特性,分析了系统在不同相态下含有的频率成分;然后,构建了针对混沌系统的数字锁相环模型,研究锁相环下混沌态和大周期态呈现的频率特性;最后,提出了一种基于锁相环技术的混沌相变判别新方法。仿真实验显示,相比于李氏指数法,所提方法判别速度快一个数量级,检测差错率为0时,性能提高近2 d B。新方法应用锁相环技术,简便易行,判别速度快,为混沌相变判别的工程应用提供了新的手段。
For the problem of high complexity of chaotic phase change method based on classical Lyapunov exponential method,a new method is proposed for discriminating chaotic phase transition by using phase-locked loop(PLL) technique. Firstly,the analytical characteristics of chaotic system are deduced,and the frequency components of the system are analyzed. Then,the digital PLL model for chaotic system is constructed to study the frequency characteristics of chaotic and large periodic states. Finally,the new chaotic phase change method based on PLL technology is proposed. The simulation results show that compared with the Lyapunov exponential method,the proposed method has a faster discriminant speed of one order of magnitude,and when the detection error rate is 0,the performance is improved by nearly 2 d B. The new method using the PLL technology is simple and easy to judge,and it provides a new distinguishing method for the engineering application of chaotic phase change.
For the problem of high complexity of chaotic phase change method based on classical Lyapunov exponential method,a new method is proposed for discriminating chaotic phase transition by using phase-locked loop(PLL) technique. Firstly,the analytical characteristics of chaotic system are deduced,and the frequency components of the system are analyzed. Then,the digital PLL model for chaotic system is constructed to study the frequency characteristics of chaotic and large periodic states. Finally,the new chaotic phase change method based on PLL technology is proposed. The simulation results show that compared with the Lyapunov exponential method,the proposed method has a faster discriminant speed of one order of magnitude,and when the detection error rate is 0,the performance is improved by nearly 2 d B. The new method using the PLL technology is simple and easy to judge,and it provides a new distinguishing method for the engineering application of chaotic phase change.
引文
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[15]杨红英,叶昊,王桂增,等.Duffing振子的Lyapunov指数与Floquet指数研究[J].仪器仪表学报,2008(5):927-932.YANG Hongying,YE Hao,WANG Guizeng,et al.Lyapunov exponent and Floquet index of Duffing oscillator[J].Journal of Instrumentation,2008(5):927-932.(in Chinese)
[16]魏恒东,甘露,李立萍.基于哈密顿量的Duffing振子微弱信号检测[J].电子科技大学学报,2012,41(2):203-207.WEI Hengdong,GAN Lu,LI Liping.Detection of weak signal of Duffing oscillator based on Hamiltonian[J].Journal of University of Electronic Science and Technology of China,2012,41(2):203-207.(in Chinese)
[17]许志鹏,崔琛,余剑.基于锁频环与锁相环相结合的载波跟踪技术[J].电讯技术,2012,52(4):558-561.XU Zhipeng,CUI Chen,YU Jian.Carrier tracking based on combination of FLL[J].Telecommunication Engineering,2012,52(4):558-561.(in Chinese)
[18]孙文军,芮国胜,张嵩,等.基于自激振荡系统的混沌稳健检测模型[J].仪器仪表学报,2015,38(12):2657-2665.SUN Wenjun,RUI Guosheng,ZHANG Song,et al.Chaotic robust detection model based on self-excited oscillation system[J].Journal of Instrumentation,2015,38(12):2657-2665.(in Chinese)
[19]朱来普,张陆勇,谢文凤,等.基于Duffing混沌振子的微弱信号检测研究[J].无线电工程,2012(1):17-20.ZHU Laipu,ZHANG Luyong,XIE Wenfeng,et al.The study of weak signal detection based on Duffing oscillator[J].Radio Engineering,2012(1):17-20.(in Chinese)
[2]徐艳春,杨春玲.高阶混沌振子的微弱信号频率检测新方法[J].哈尔滨工业大学学报,2010,42(3):446-450.XU Yangchun,YANG Chunling.A new method of weak signal frequency detection for high order Chaotic oscillator[J].Journal of Harbin Institute of Technology,2010,42(3):446-450.(in Chinese)
[3]TAJADDODIANFAR F,PISHKENARI H N,YAZDI M RH.Prediction of Chaos in electrostatically actuated arch micro-nano resonators:analytical approach[J].Communications in Nonlinear Science and Numerical Simulation,2016,30(1):182-195.
[4]PEINADO A,FUSTER-SABATER A.Generation of pseudorandom binary sequences by mean of linear feedback shift registers(LFSRS)with dynamic feedback[J].Mathematical and Computer Modelling,2013,11(57):2596-2604.
[5]PALACIOUS-LUENGAS L,DELGADO-GUTIERREZG,GRUZ-IRISSON M,et al.Digital noise produced by a non-discretized tent Chaotic map[J].Microelectronic Engineering,2013,112(1):264-268.
[6]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):170-177.FENG Jun,XU Wei,GU Rencai,et al.Melnikov Chaos of Duffing-Rayleigh oscillator under bounded noise and harmonic excitation[J].Journal of Physics,2011,60(9):170-177.(in Chinese)
[7]孙文军,芮国胜,王林,等.一种利用Duffing-Vanderpol振子估计弱信号相位的方法[J].电讯技术,2016,56(1):14-19.SUN Wenjun,RUI Guosheng,WANG Lin,et al.Estimation of weak signal phase by using Duffing-Vanderpo oscillator[J].Telecommunication Engineering,2016,56(1):14-19.(in Chinese)
[8]张雷,吴勇军.外共振耦合Duffing-van der Pol系统的首次穿越[J].力学学报,2012(2):437-442.ZHANG Lei,WU Yongjun.The first crossing of the external resonance coupled Duffing-van der Pol system[J].Journal of Mechanics,2012(2):437-442.(in Chinese)
[9]孙春艳,徐伟.含分数阶导数项的随机Duffing振子的稳态响应分析[J].振动工程学报,2015(3):374-380.SUN Chunyan,XU Wei.Steady-state response analysis of stochastic duffing oscillator with fractional derivative terms[J].Journal of Vibration Engineering,2015(3):374-380.(in Chinese)
[10]余耀,赵鹤鸣.非平稳噪声环境下的噪声功率谱估计方法[J].数据采集与处理,2012(4):486-489.YU Yao,ZHAO Heming.Noise power spectrum estimation method for non-stationary noise environment[J].Data Acquisition and Processing,2012(4):486-489.(in Chinese)
[11]李爽,李倩,李佼瑞.Duffing系统随机相位抑制混沌与随机共振并存现象的机理研究[J].物理学报,2015(10):71-77.LI Shuang,LI Qian,LI Jiaorui.Duffing system random phase suppression Chaos and stochastic resonance coexistence phenomenon mechanism[J].Journal of Physics,2015(10):71-77.(in Chinese)
[12]林敏,黄咏梅.双稳系统随机共振的能量输入机理[J].物理学报,2012(22):34-38.LING Min,LUANG Yongmei.The energy input mechanism of stochastic resonance of bistable systems[J].Journal of Physics,2012(22):34-38.(in Chinese)
[13]芮国胜,张洋,史特,等.基于卡尔曼增益的Duffing系统状态预测算法[J].宇航学报,2012(8):1144-1149.RUI Guosheng,ZHANG Yang,SHI Te,et al.State prediction algorithm of Duffing system based on Kalman gain[J].Journal of Astronautics,2012(8):1144-1149.(in Chinese)
[14]芮国胜,张洋,苗俊,等.联合增益递推的Duffing系统弱信号检测算法[J].电子学报,2012(6):1269-1273.RUI Guosheng,ZHANG Yang,MIAO Jun,et al.A weak signal detection method by Duffing system with the gain[J].Acta Electronica Sinica,2012(6):1269-1273.(in Chinese)
[15]杨红英,叶昊,王桂增,等.Duffing振子的Lyapunov指数与Floquet指数研究[J].仪器仪表学报,2008(5):927-932.YANG Hongying,YE Hao,WANG Guizeng,et al.Lyapunov exponent and Floquet index of Duffing oscillator[J].Journal of Instrumentation,2008(5):927-932.(in Chinese)
[16]魏恒东,甘露,李立萍.基于哈密顿量的Duffing振子微弱信号检测[J].电子科技大学学报,2012,41(2):203-207.WEI Hengdong,GAN Lu,LI Liping.Detection of weak signal of Duffing oscillator based on Hamiltonian[J].Journal of University of Electronic Science and Technology of China,2012,41(2):203-207.(in Chinese)
[17]许志鹏,崔琛,余剑.基于锁频环与锁相环相结合的载波跟踪技术[J].电讯技术,2012,52(4):558-561.XU Zhipeng,CUI Chen,YU Jian.Carrier tracking based on combination of FLL[J].Telecommunication Engineering,2012,52(4):558-561.(in Chinese)
[18]孙文军,芮国胜,张嵩,等.基于自激振荡系统的混沌稳健检测模型[J].仪器仪表学报,2015,38(12):2657-2665.SUN Wenjun,RUI Guosheng,ZHANG Song,et al.Chaotic robust detection model based on self-excited oscillation system[J].Journal of Instrumentation,2015,38(12):2657-2665.(in Chinese)
[19]朱来普,张陆勇,谢文凤,等.基于Duffing混沌振子的微弱信号检测研究[J].无线电工程,2012(1):17-20.ZHU Laipu,ZHANG Luyong,XIE Wenfeng,et al.The study of weak signal detection based on Duffing oscillator[J].Radio Engineering,2012(1):17-20.(in Chinese)