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微弱谐波信号的灵敏检测具有重要的实际应用意义, 本文利用受控Chen系统来实现强噪声背景下的这种检测. 因动力系统可分解为慢变系统与快变系统的叠加, 这里用平均法对检测系统进行处理得到慢变系统, 并获取使系统由周期轨道突变为稳定平衡点的检测参数临界值. 通过调节检测参数, 观测系统状态变量的变化可判断待测信号是否存在. 仿真结果表明, 此方法可以准确检测出强噪声背景下的微弱谐波信号. 与目前其他基于混沌振子的检测方法相比, 该方案对噪声具有更强的免疫性, 而且可通过理论分析得出检测参数阈值的准确范围, 有利于在相关领域推广应用.The detection of weak harmonic signals has important practical value. In this paper, the detection of weak harmonic signals in strong noise is realized with the controlled Chen's system. Dynamics can be divided into slowly varying dynamics and fast varying dynamics, so a slowly varying dynamics is obtained by an averaging method. The critical values of detection parameters are determined, which lead to a sudden change of system dynamical behavior from periodic orbit to stable equilibrium point. Weak harmonic signals can be detected by adjusting the detection parameters and observing the change of system variables. Simulation results show that weak harmonic signals in strong noise can be detected accurately with this system. Compared with existing detection methods with chaotic oscillator, this method is of stronger immunity to noise, and the accurate range of parameter threshold can be obtained through theoretical analysis, which enables its popularization and application in relevant fields.
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Keywords:
- Chen's system /
- weak harmonic signal /
- signal detection /
- averaging method
[1] Wang G Y, Tao G L, Chen X, Lin J Y 1997 J. Sci. Instru. 18 209 (in Chinese) [王冠宇, 陶国良, 陈行, 林建亚 1997 仪器仪表学报 18 209]
[2] Li Y, Yang B J 2003 Chin. Sci. Bull. 48 19 (in Chinese) [李月, 杨宝俊 2003 科学通报 48 19]
[3] Li Y, Lu P, Yang B J, Zhao X P 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李月, 路朋, 杨宝俊, 赵雪平 2006 物理学报 55 1672]
[4] Chen L, Wang D S 2007 Acta Phys. Sin. 56 5098 (in Chinese) [谌龙, 王德石 2007 物理学报 56 5098]
[5] Chen Z, Zeng Y C, Fu Z J 2008 Acta Phys. Sin. 57 46 (in Chinese) [陈争, 曾以成, 付志坚 2008 物理学报 57 46]
[6] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 140 (in Chinese) [行鸿彦, 金天力 2010 物理学报 59 140]
[7] Xu Y C, Yang C L, Qu X D 2010 Chin. Phys. B 19 030516
[8] Jia H Y, Chen Z Q, Ye F 2011 Acta Phys. Sin. 60 010203 (in Chinese) [贾红艳, 陈增强, 叶菲 2011 物理学报 60 010203]
[9] Feng C W, Cai L, Kang Q, Zhang L S 2011 Acta Phys. Sin. 60 030503 (in Chinese) [冯朝文, 蔡理, 康强, 张立森 2011 物理学报 60 030503]
[10] Lorenz E N 1963 J. Atmos. Sci. 20 130
[11] Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[12] Liu C X, Liu L, Liu K 2004 Chaos, Soliton and Fractals 22 1031
[13] Tang L R, Li J, Fan B, Zhai M Y 2009 Acta Phys. Sin. 58 785 (in Chinese) [唐良瑞,李静,樊冰,翟明岳 2009 物理学报 58 785]
[14] Yu F, Wang C H, Yin J W, Xu H 2012 Acta Phys. Sin. 61 020506 (in Chinese) [余飞, 王春华, 尹晋文, 徐浩 2012 物理学报 61 020506]
[15] Ueta T, Chen G R 2000 Int. J. Bifur. Chaos 10 1917
[16] Li Y, Yang B J 2004 Introduction of Detection Methods with Chaotic Oscillator (1st Ed.) (Beijing: Publishing House of Electronics Industry) pp49-51 (in Chinese) [李月, 杨宝俊 2004 混沌振子检测引论 (第1版) (北京: 电子工业出版社) 第49-51页]
[17] Lima R, Pettini M 1990 Phys. Rev. A 41 726
[18] Chacón R, Bejarano J D 1993 Phys. Rev. Lett. 71 3103
[19] Soong C Y, Huang W T, Lin F P, Tzeng P Y 2004 Phys. Rev. E 70 0162111
[20] Choe C U, Hohne K, Benner H, Kivshar Y S 2005 Phys. Rev. E 72 0362061
[21] Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 0105091 (in Chinese) [王梦蛟, 曾以成, 陈光辉, 贺娟 2011 物理学报 60 0105091]
[22] Liu Y Z, Chen L Q 2001 Nonlinear Vibrations (1st Ed.) (Beijing: High Education Press) pp73-82 (in Chinese) [刘延柱, 陈立群 2001 非线性振动 (第1版) (北京: 高等教育出版社) 第73-82页]
[23] Kivshar Yu S, Rodelsperger F, Benner H 1994 Phys. Rev. E 49 319
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[1] Wang G Y, Tao G L, Chen X, Lin J Y 1997 J. Sci. Instru. 18 209 (in Chinese) [王冠宇, 陶国良, 陈行, 林建亚 1997 仪器仪表学报 18 209]
[2] Li Y, Yang B J 2003 Chin. Sci. Bull. 48 19 (in Chinese) [李月, 杨宝俊 2003 科学通报 48 19]
[3] Li Y, Lu P, Yang B J, Zhao X P 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李月, 路朋, 杨宝俊, 赵雪平 2006 物理学报 55 1672]
[4] Chen L, Wang D S 2007 Acta Phys. Sin. 56 5098 (in Chinese) [谌龙, 王德石 2007 物理学报 56 5098]
[5] Chen Z, Zeng Y C, Fu Z J 2008 Acta Phys. Sin. 57 46 (in Chinese) [陈争, 曾以成, 付志坚 2008 物理学报 57 46]
[6] Xing H Y, Jin T L 2010 Acta Phys. Sin. 59 140 (in Chinese) [行鸿彦, 金天力 2010 物理学报 59 140]
[7] Xu Y C, Yang C L, Qu X D 2010 Chin. Phys. B 19 030516
[8] Jia H Y, Chen Z Q, Ye F 2011 Acta Phys. Sin. 60 010203 (in Chinese) [贾红艳, 陈增强, 叶菲 2011 物理学报 60 010203]
[9] Feng C W, Cai L, Kang Q, Zhang L S 2011 Acta Phys. Sin. 60 030503 (in Chinese) [冯朝文, 蔡理, 康强, 张立森 2011 物理学报 60 030503]
[10] Lorenz E N 1963 J. Atmos. Sci. 20 130
[11] Chen G, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[12] Liu C X, Liu L, Liu K 2004 Chaos, Soliton and Fractals 22 1031
[13] Tang L R, Li J, Fan B, Zhai M Y 2009 Acta Phys. Sin. 58 785 (in Chinese) [唐良瑞,李静,樊冰,翟明岳 2009 物理学报 58 785]
[14] Yu F, Wang C H, Yin J W, Xu H 2012 Acta Phys. Sin. 61 020506 (in Chinese) [余飞, 王春华, 尹晋文, 徐浩 2012 物理学报 61 020506]
[15] Ueta T, Chen G R 2000 Int. J. Bifur. Chaos 10 1917
[16] Li Y, Yang B J 2004 Introduction of Detection Methods with Chaotic Oscillator (1st Ed.) (Beijing: Publishing House of Electronics Industry) pp49-51 (in Chinese) [李月, 杨宝俊 2004 混沌振子检测引论 (第1版) (北京: 电子工业出版社) 第49-51页]
[17] Lima R, Pettini M 1990 Phys. Rev. A 41 726
[18] Chacón R, Bejarano J D 1993 Phys. Rev. Lett. 71 3103
[19] Soong C Y, Huang W T, Lin F P, Tzeng P Y 2004 Phys. Rev. E 70 0162111
[20] Choe C U, Hohne K, Benner H, Kivshar Y S 2005 Phys. Rev. E 72 0362061
[21] Wang M J, Zeng Y C, Chen G H, He J 2011 Acta Phys. Sin. 60 0105091 (in Chinese) [王梦蛟, 曾以成, 陈光辉, 贺娟 2011 物理学报 60 0105091]
[22] Liu Y Z, Chen L Q 2001 Nonlinear Vibrations (1st Ed.) (Beijing: High Education Press) pp73-82 (in Chinese) [刘延柱, 陈立群 2001 非线性振动 (第1版) (北京: 高等教育出版社) 第73-82页]
[23] Kivshar Yu S, Rodelsperger F, Benner H 1994 Phys. Rev. E 49 319
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