扩展型Vanderpol振子的微弱信号检测的研究
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摘要
微弱信号检测系统中,信号被强噪音湮没的情况及其普遍。针对这一问题提出了基于扩展型Vanderpol振子下微弱信号的定量检测方法。主要研究扩展型的Vanderpol振子的稳定性,通过李雅普诺夫指数判别系统在临界状态和大周期状态的位置,从而达到检测待测信号的提取并检测待测信号的相位和幅度;通过Melnikov方法分析,对电气设备索道的谐波信号检测,估算该微弱待测信号的相位、频率。仿真结果表明,改进的Vanderpol振子系统信噪比显著提高了70%,改进算法实现微弱信号的高精度和高灵敏的幅度和相位检测,具有较高的免疫能力和强抗噪比。
Signal annihilation by strong noise in weak signal detection system and its prevalence. In order to solve this problem, a quantitative detection method for the weak signal of the extended vanderpol oscillator is proposed. The stability of the extended vanderpol oscillator is studied. By using Lyapunov exponent to judge the position of the system in the critical state and the large period state, the test of the extraction of the signal and the detection of the phase and amplitude of the signal are achieved. Based on the analysis of melnikov method, the phase and frequency of the weak signal are estimated by detecting the harmonic signal of the cableway of electrical equipment. The simulation results show that the improved signal-to-noise ratio(SNR) of the vanderpol vibration system is improved significantly. The improved algorithm achieves high accuracy and high sensitive amplitude and phase detection of weak signals, it has a high immune ability and a strong anti-noise ratio.
Signal annihilation by strong noise in weak signal detection system and its prevalence. In order to solve this problem, a quantitative detection method for the weak signal of the extended vanderpol oscillator is proposed. The stability of the extended vanderpol oscillator is studied. By using Lyapunov exponent to judge the position of the system in the critical state and the large period state, the test of the extraction of the signal and the detection of the phase and amplitude of the signal are achieved. Based on the analysis of melnikov method, the phase and frequency of the weak signal are estimated by detecting the harmonic signal of the cableway of electrical equipment. The simulation results show that the improved signal-to-noise ratio(SNR) of the vanderpol vibration system is improved significantly. The improved algorithm achieves high accuracy and high sensitive amplitude and phase detection of weak signals, it has a high immune ability and a strong anti-noise ratio.
引文
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[2] 曹满婷,宋菲菲.Duffing混沌微弱信号检测系统分析及电路实现[J].自动化仪表,2017,38(1):77-80.CAO M T,SONG F F.Analysis and circuit implementation of the Duffing chaotic weak signal detection system[J].Journal of Process Automation Instrumentation,2017,38(1):77-80.
[3] 陈维,孟晨,崔少辉,等.混沌测量仿真中的噪声模型研究[J].系统仿真学报,2012,24(10):2079-2082.CHEN W, MENG CH,CUI SH H,et al. Noise model in chaos measurement simulation[J].Journal of System Simulation,2012,24(10):2079-2082.
[4] 姜烁,徐艳春, 刘宇龙,等.改进高阶Vanderpol振子在微弱信号检测中的应用[J].电讯技术,2017,57(6):678-684.JIAN SH, XU Y CH, LIU Y L,et al. Application of improved higher order vanderpol oscillator in weak signal detection[J].Journal of Telecommunication Engineering,2017,57(6):678-684.
[5] 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):14-18.SUN W J,RUI G SH,WANG L, et al.Estimation of weak signal phase by using Duffing-Vanderpol oscillator[J],Journal of Telecommunication Engineering,2016,56(1):14-18.
[6] PLATAS GARZA M A,SERNA J A.Polynomial implementation of the Taylor Fourier transform for harmonic analysis[J].IEEE Transactions on Instrumentation and Measurement,2014,63(12):2846-2854.
[7] 李月,杨宝俊,林红波,等.基于特定混沌系统微弱谐波信号频率检测的理论分析与仿真[J].物理学报,2005,54(5):1994-1999.LI Y,YANG B J,LIN H B, et al.Theoretical analysis and simulation of weak harmonic signal frequency detection based on special chaotic system[J].Journal of Physics,2005,54(5):1994-1999.
[8] 李楠,李秀坤,刘彩虹.对称Alpha稳定分布噪声下的Duffing振子检测方法[J].船舶力学,2017,21(1):90-98.LI N,LI X K,LIU C H.Detection method of the Duffing oscillator under symmetric Alpha-stable noise[J].Journal of Ship Mechanics,2017,21(1):90-98.
[9] 王震,孙卫,蔺小林.多自由度Vanderpol振子极限环计算[J].计算机工程与应用,2012,48(13):230-233.WANG ZH,SUN W,LIAN X L.Computing for limit cycle of Vanderpol oscillator with multi degree of freedom[J].Computer Engineering and Applications,2012,48(13):230-233.
[10] AN G J,REN X,ZHANG S W.Adaptive bistable stochastic resonance aided spectrum sensing[J].IEEE Transactions on Wireless Communication,2014,3(7):4014-4024.
[11] LANDAUER R.Reversible computing and physical magne-tometer[J].Physics Today,2014,45(3):100-103.
[12] 自强,陈长征,谷艳玲,等.基于混沌和取样积分技术的大型风电增速箱早期故障诊断[J].振动与冲击,2013,32(9):113-117.ZI Q,CHEN CH ZH,GU Y L, et al.Early fault diagnosis of large wind power growth box based on chaos and sampling integral technology[J].Journal of Vibration and Shock,2013,32(9):113-117.
[13] 刘海波,吴德伟,金伟,等.Duffing振子微弱信号检测方法研究[J].物理学报,2013,62(5):42-47.LIU H B,WU D W,JIN W, et al.Research on weak signal detection method of Duffing oscillator[J].Journalof Physics,2013,62(5):42-47.
[14] 田晶晶,李世武,苏建,等.基于经验模态分解的载货汽车载荷动态检测策略研究[J].振动与冲击,2013,32(4):173-178.TIAN J J,LI SH W,SU J, et al.Research on dynamic load detection strategy of truck based on empirical mode decomposition[J].Journal of Vibration and Shock,2013,32(4):173-178.
[15] 徐一红,祝长生,赵耀培,等.基于稀疏分解和混沌理论的微弱信号检测[J].电讯技术,2015,55(11):1194-1199.XU Y H,ZHU CH SH,ZHAO Y P, et al.Weak signal detection based on sparse decomposition and chaotic theory[J].Journal of Telecommunication Engineering,2015,55(11):1194-1199.
[16] COELHO L S,GUERRA F A,BATISTELA N J.Multi-objective cuckoo search algorithm based on Duffing’s oscillator applied to Jiles-Atherton vector hysteresis parameters estimation[J].IEEE Transactions on Magnetics,2013,49(5):1745-1748.