基于Duffing振子检测频率未知微弱信号的新方法
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摘要
针对现有混沌振子难以检测频率未知微弱信号这一难点,提出利用Duffing振子输出值的方差峰值结合遗传算法检测淹没在强噪声背景中频率未知微弱信号的一种新方法。从分析混沌系统结构参数的阈值入手,讨论了周期策动力的频率、初始相位和噪声对系统运行状态的影响;研究系统输出值方差与系统状态的对应关系,探讨待测信号频率以及与周期策动力之间相位差对状态变量方差和状态转换时间的影响。由此,提出采用具有相位偏移的Duffing振子阵列覆盖全相位,并结合遗传算法,优化求解不同频率输入信号下系统输出值方差的极值,以此得到待测信号频率的方法。该方法解决了现有混沌振子类检测方法必须已知信号频率的限制。实验结果证明了本方法能准确、快速地检测待测信号频率。新方法的状态判定简便、检测精度高、更为灵活、适应性强,为微弱信号的检测提供了新的手段。
In order to detect weak signal with unknown frequency,this paper presents a novel method for detecting the unknown frequency signal by combining the variance peak value of the Duffing oscillator and genetic algorithm( GA). Firstly,the impact of periodic driving signal with different frequencies,initial phase angle and noise on the system operating state are analyzed. Second,the corresponding relationship between the system output variance and the system running state is studied. The effect of the test signal frequency,as well as the phase difference between the periodic driving signal and the test signal on the state variables variance and the state transition time are discussed. Finally,the new method is proposed,which using a number of Duffing oscillators with different initial phases to cover all phase signal detection. Moreover,the proposed method combines with genetic algorithm to obtain the detected signal frequency by optimizing the calculation of peak value of system output varaince under different input frequency signals. This method resolves the limitation of existing weak signal detection method based on the chaotic oscillator,in which the signal frequency needs to be known. Experimental results show that the method can accurately and flexibly detect the frequency of the test signal and has strong adaptability. This workt provides a novel approach for the weak signal detection.
In order to detect weak signal with unknown frequency,this paper presents a novel method for detecting the unknown frequency signal by combining the variance peak value of the Duffing oscillator and genetic algorithm( GA). Firstly,the impact of periodic driving signal with different frequencies,initial phase angle and noise on the system operating state are analyzed. Second,the corresponding relationship between the system output variance and the system running state is studied. The effect of the test signal frequency,as well as the phase difference between the periodic driving signal and the test signal on the state variables variance and the state transition time are discussed. Finally,the new method is proposed,which using a number of Duffing oscillators with different initial phases to cover all phase signal detection. Moreover,the proposed method combines with genetic algorithm to obtain the detected signal frequency by optimizing the calculation of peak value of system output varaince under different input frequency signals. This method resolves the limitation of existing weak signal detection method based on the chaotic oscillator,in which the signal frequency needs to be known. Experimental results show that the method can accurately and flexibly detect the frequency of the test signal and has strong adaptability. This workt provides a novel approach for the weak signal detection.
引文
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[11]李月,祁放,张铭,等.微弱正弦信号的一种新的混沌检测系统[J].仪器仪表学报,2004,25(增刊1):19-20.LI Y,QI F,Zh ANG M,et al.The detection of weak sine signals using special chaotic system[J].Chinese Journal of Scientific Instrument,2004,25(Suppl.1):19-20.
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[13]RASHTCHI V,NOURAZAR M.A multiprocessor Nios II implementation of Duffing oscillator array for weak signal detection[J].Journal of Circuits Systems and Computers,2014,23(4):3-21.
[14]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):50501-050501.LIU H B,WU D W,JIN W,et al.Study on weak signal detection method with Duffing oscillators[J].Acta Physica Sinica,2013,62(5):050501.
[15]丛超,李秀坤,宋扬.一种基于新型间歇混沌振子的舰船线谱检测方法[J].物理学报,2014,63(6):168-179.CONG CH,LI X K,SONG Y.A method of detecting line spectrum of ship-radiated noise using a new intermittent chaotic oscillator[J].Acta Physica Sinica,2014,63(6):168-179.
[16]聂春燕,石要武.基于互相关检测和混沌理论的弱信号检测方法研究[J].仪器仪表学报,2001,22(1):32-35.NIE CH Y,SHI Y W.The reaserch of weak signal detection based on cross-orrelation and chaos theory[J].Chinese Journal of Scientific Instrument,2001,22(1):32-35.
[17]杨东升,李乐,杨珺,等.基于双耦合混沌振子的未知频率弱信号检测[J].东北大学学报:自然科学版,2012,33(9):1226-1230.YANG D SH,LI L,YANG J,et al.Detection of the weak signal with unknown frequency based on the coupled chaos oscillator[J].Journal of Northeastern University:Natural Science,2012,33(9):1226-1230.
[18]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):60-68.LAI ZH H,LENG Y G,SUN J Q,et al.Weak characteristic signal detection based on scale transformation of Duffing oscillator[J].Acta Physica Sinica,2012,61(5):60-68.
[19]刘海波,吴德伟,戴传金,等.基于Duffing振子的弱正弦信号检测方法研究[J].电子学报,2013,41(1):8-12.LIU H B,WU D W,DAI CH J,et al.A new weak sinusoidal signal detection method based on Duffing oscillators[J].Acta Electronica Sinica,2013,41(1):8-12.
[20]ZHAO Z,WANG F L,JIA M X,et al.Intermittentchaos-and-cepstrum-analysis-based early fault detection on shuttle valve of hydraulic tube tester[J].IEEE Transactions on Industrial Electronics,2009,56(7):2764-2770.
[21]WANG G Y,HE S L.A quantitative study on detection and estimation of weak signals by using chaotic Duffing oscillators[J].IEEE Transactions on Circuits and Systems I-Regular Papers,2003,50(7):945-953.
[22]陈志光,李亚安,陈晓.基于Hilbert变换及间歇混沌的水声微弱信号检测方法研究[J].物理学报,2015,64(20):69-76.CHEN ZH G,LI Y AN,CHEN X.Underwater acoustic weak signal detection based on Hilbert transform and intermittent chaos[J].Acta Physica Sinica,2015,64(20):69-76.
[23]牛德智,陈长兴,班斐,等.Duffing振子微弱信号检测盲区消除及检测统计量构造[J].物理学报,2015,64(6):060503.NIU D ZH,CHEN CH X,BAN F,et al.Blind angle elimination method in weak signal detection with Duffing oscillator and construction of detection statistics[J].Acta Physica Sinica,2015,64(6):060503.
[24]陈果.基于遗传算法的支持向量机时间序列预测模型优化[J].仪器仪表学报,2006,27(9):1080-1084.CHEN G.Optimizing of support vector machine time series forecasting model parameters based on genetic algorithms[J].Chinese Journal of Scientific Instrument,2006,27(9):1080-1084.
[25]官伯林,贾建援,朱应敏.基于自适应遗传算法的三轴光电跟踪策略[J].仪器仪表学报,2012,33(8):1758-1764.GUAN B L,JIA J Y,ZHU Y M.Tracking strategy of three-axis photoelectric tracking system based on adaptive genetic algorithm[J].Chinese Journal of Scientific Instrument,2012,33(8):1758-1764.
[2]樊养余,李利品,党瑞荣.基于随机共振的任意大频率微弱信号检测方法研究[J].仪器仪表学报,2013,34(3):566-572.FAN Y Y,LI L P,DANG R R.Study on high frequency weak signal detection method based on stochastic resonance[J].Chinese Journal of Scientific Instrument,2013,34(3):566-572.
[3]胡颖,丁天怀,王鹏.多路微小平面线圈信号检测系统的设计与实现[J].仪器仪表学报,2012,34(2):326-331.HU Y,DING T H,WANG P.Design and implementation of multi-channel signal detection system for small planar coils[J].Chinese Journal of Scientific Instrument,2012,34(2):326-331.
[4]郭静波,谭博,蔡雄.基于反相双峰指数模型的微弱瞬态极低频信号的估计与检测[J].仪器仪表学报,2015,36(8):1682-1691.GUO J B,TAN B,CAI X.Estimation and detection of the weak transient ELF signal based on the phase inverting double-peak exponential model[J].Chinese Journal of Scientific Instrument,2015,36(8):1682-1691.
[5]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,2015,36(12):2657-2665.SUN W J,RUI G SH,Zh ANG S,et al.Research on steadiness chaotic detection model based on the selfexcited oscillatory system[J].Chinese Journal of Scientific Instrument,2015,36(12):2657-2665.
[6]VAHEDI H,GHAREHPETIAN G B,KARRARI M,Application of Duffing oscillators for passive islanding detection of inverter-based distributed generation units[J].IEEE Transactions on Power Delivery,2012,27(4):1973-1983.
[7]WANG G,CHEN D,LIN J,et al.The application of chaotic oscillators to weak signal detection[J].IEEE Transactions on Industrial Electronics,1999,46(2):440-444.
[8]路鹏,钟时,谭力.微弱正弦信号的互相关—混沌系统合成检测技术[J].仪器仪表学报,2004,25(增刊1):21-22.LU P,ZHONG SH,TAN L.Detection technique of weak sine signal via cross-correlation and chaotic system[J].Chinese Journal of Scientific Instrument,2004,25(Suppl.1):21-22.
[9]王一清,宋爱国,黄惟一,等.一种用于混沌信号去噪的循环相关算法[J].仪器仪表学报,2005,26(4):403-406.WANG Y M,SONG AI G,HUANG W Y,et al.A round correlation algorithm used to separate chaotic signal from noise background[J].Chinese Journal of Scientific Instrument,2005,26(4):403-406.
[10]王清亮,基于符号序列信息熵混沌特性的微弱信号检测[J].仪器仪表学报,2009,30(12):2491-2496.WANG Q L.Weak signal identification based on chaoticnature of symbol-sequence entropy[J].Chinese Journal of Scientific Instrument,2009,30(12):2491-2496.
[11]李月,祁放,张铭,等.微弱正弦信号的一种新的混沌检测系统[J].仪器仪表学报,2004,25(增刊1):19-20.LI Y,QI F,Zh ANG M,et al.The detection of weak sine signals using special chaotic system[J].Chinese Journal of Scientific Instrument,2004,25(Suppl.1):19-20.
[12]王永生,姜文志,赵建军,等.一种Duffing弱信号检测新方法及仿真研究[J].物理学报,2008,57(4):2053-2059.WANG Y SH,JIANG W ZH,ZHAO J J,et al.A new method of weak signal detection using Duffing oscillator and its simulation research[J].Acta Physica Sinica,2008,57(4):2053-2059.
[13]RASHTCHI V,NOURAZAR M.A multiprocessor Nios II implementation of Duffing oscillator array for weak signal detection[J].Journal of Circuits Systems and Computers,2014,23(4):3-21.
[14]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):50501-050501.LIU H B,WU D W,JIN W,et al.Study on weak signal detection method with Duffing oscillators[J].Acta Physica Sinica,2013,62(5):050501.
[15]丛超,李秀坤,宋扬.一种基于新型间歇混沌振子的舰船线谱检测方法[J].物理学报,2014,63(6):168-179.CONG CH,LI X K,SONG Y.A method of detecting line spectrum of ship-radiated noise using a new intermittent chaotic oscillator[J].Acta Physica Sinica,2014,63(6):168-179.
[16]聂春燕,石要武.基于互相关检测和混沌理论的弱信号检测方法研究[J].仪器仪表学报,2001,22(1):32-35.NIE CH Y,SHI Y W.The reaserch of weak signal detection based on cross-orrelation and chaos theory[J].Chinese Journal of Scientific Instrument,2001,22(1):32-35.
[17]杨东升,李乐,杨珺,等.基于双耦合混沌振子的未知频率弱信号检测[J].东北大学学报:自然科学版,2012,33(9):1226-1230.YANG D SH,LI L,YANG J,et al.Detection of the weak signal with unknown frequency based on the coupled chaos oscillator[J].Journal of Northeastern University:Natural Science,2012,33(9):1226-1230.
[18]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):60-68.LAI ZH H,LENG Y G,SUN J Q,et al.Weak characteristic signal detection based on scale transformation of Duffing oscillator[J].Acta Physica Sinica,2012,61(5):60-68.
[19]刘海波,吴德伟,戴传金,等.基于Duffing振子的弱正弦信号检测方法研究[J].电子学报,2013,41(1):8-12.LIU H B,WU D W,DAI CH J,et al.A new weak sinusoidal signal detection method based on Duffing oscillators[J].Acta Electronica Sinica,2013,41(1):8-12.
[20]ZHAO Z,WANG F L,JIA M X,et al.Intermittentchaos-and-cepstrum-analysis-based early fault detection on shuttle valve of hydraulic tube tester[J].IEEE Transactions on Industrial Electronics,2009,56(7):2764-2770.
[21]WANG G Y,HE S L.A quantitative study on detection and estimation of weak signals by using chaotic Duffing oscillators[J].IEEE Transactions on Circuits and Systems I-Regular Papers,2003,50(7):945-953.
[22]陈志光,李亚安,陈晓.基于Hilbert变换及间歇混沌的水声微弱信号检测方法研究[J].物理学报,2015,64(20):69-76.CHEN ZH G,LI Y AN,CHEN X.Underwater acoustic weak signal detection based on Hilbert transform and intermittent chaos[J].Acta Physica Sinica,2015,64(20):69-76.
[23]牛德智,陈长兴,班斐,等.Duffing振子微弱信号检测盲区消除及检测统计量构造[J].物理学报,2015,64(6):060503.NIU D ZH,CHEN CH X,BAN F,et al.Blind angle elimination method in weak signal detection with Duffing oscillator and construction of detection statistics[J].Acta Physica Sinica,2015,64(6):060503.
[24]陈果.基于遗传算法的支持向量机时间序列预测模型优化[J].仪器仪表学报,2006,27(9):1080-1084.CHEN G.Optimizing of support vector machine time series forecasting model parameters based on genetic algorithms[J].Chinese Journal of Scientific Instrument,2006,27(9):1080-1084.
[25]官伯林,贾建援,朱应敏.基于自适应遗传算法的三轴光电跟踪策略[J].仪器仪表学报,2012,33(8):1758-1764.GUAN B L,JIA J Y,ZHU Y M.Tracking strategy of three-axis photoelectric tracking system based on adaptive genetic algorithm[J].Chinese Journal of Scientific Instrument,2012,33(8):1758-1764.