基于混沌理论的微弱周期信号检测
摘要
随着科学技术的迅猛发展,微弱信号的检测在雷达、故障诊断、系统辨识、通信等领域有着广泛的应用,所以一直都是国内外学者研究的热点。从强噪声背景中把微弱有效信号提取出来是现代信号处理学的一个重要内容,目前常用的时域和频域方法要求苛刻,在噪声强、待检信号弱的情况下,需要提高信噪比。由于混沌振子对噪声具有很强的免疫力而对小信号有极强的敏感性,所以与以往检测方法不同,解决了传统检测方法对噪声抑制不彻底的缺陷。
为了有效地实现噪声背景下微弱信号的提取,本文对Duffing混沌振子进行改进建模,利用混沌振子对噪声具有很强的免疫力而对小信号有极强的敏感性,通过调整系统参数使得振子对不同频率的信号进行检测。通过对混沌的基本特征、Duffing振子的带通滤波和高斯化特性分析,首先给出了基于Duffing振子检测微弱正弦信号的数学模型,通过改变周期摄动力γ的大小,观察相轨迹图像的变化,得到系统历经同宿轨道、分叉、混沌轨迹、临界周期轨迹和大尺度周期等的各种状态。在此基础上,通过改进Duffing方程的非线性恢复力项,构建新的微弱周期信号检测模型,通过Matlab仿真,观察其图形变化。研究结果表明,基于Duffing振子的信号检测方法对极微弱周期信号检测有其独到的优势,能够检测比目前常用的时域方法低很多的信噪比,提高了检测精度。
此项工作的研究是发展高新技术、探索及发现新的自然规律的重要手段,其在雷达、水声信号等实际信号的检测中有直接的应用,而且在未来的信号检测和处理工作中具有一定的理论意义与实际意义。
With the rapid development of science and technology, weak signal detection has been widely used in the fields of radar,fault diagnosis,system identification and communication,and it has always been the hot for domestic and foreign scholars. The extraction of weak signal under strong noise is a essential part of modern signal processing science. The commonly used frequency-domain and time-domain approaches in use nowadays has limitations, especially for weak signal detection under strong noise, the signal-noise ratio need further improvement. Because chaos oscillator is immune to noise and sensitive to weak signal, the detection method used in this paper is different from the traditional ones, overcoming the noise suppress problem.
In order to effectively extract weak signal from noisy background, this paper improve the Duffing Chaos Oscillator model, and utilize chaos oscillator’s characteristics, that the phase transition of it is extremely sensitive and immune to the interference signal with great noise and frequency different, to detect signal. Adjust the system parameter to detect signal with different frequency. Base on analysis of the chaos characteristics, band-pass filter and Gaussian characteristic, the mathematic model of Duffing oscillator for weak signal detecting is presented. By changing the magnitude of periodic perturbation, and observing image, the monoclinic orbit, furcation, chaos traction, critical periodic traction, large scale cycle of the system is derived. Construct a new weak periodic signal detection model by improving the nonlinear resilience term. Simulate using Matlab, and observe image changing. Results indicate that the advantage of Duffing oscillator method in weak periodic signal detection, and it is feasible for its frequency error rate is manageable.
The research is an important means of developing high and new technologies, exploring and discovering new laws of nature. It has immediate applications in the detection of real signal , such as radar signal and underwater acoustic signal. And it has certain theoretical meaning and useful value in signal detecting and processing in the future.
为了有效地实现噪声背景下微弱信号的提取,本文对Duffing混沌振子进行改进建模,利用混沌振子对噪声具有很强的免疫力而对小信号有极强的敏感性,通过调整系统参数使得振子对不同频率的信号进行检测。通过对混沌的基本特征、Duffing振子的带通滤波和高斯化特性分析,首先给出了基于Duffing振子检测微弱正弦信号的数学模型,通过改变周期摄动力γ的大小,观察相轨迹图像的变化,得到系统历经同宿轨道、分叉、混沌轨迹、临界周期轨迹和大尺度周期等的各种状态。在此基础上,通过改进Duffing方程的非线性恢复力项,构建新的微弱周期信号检测模型,通过Matlab仿真,观察其图形变化。研究结果表明,基于Duffing振子的信号检测方法对极微弱周期信号检测有其独到的优势,能够检测比目前常用的时域方法低很多的信噪比,提高了检测精度。
此项工作的研究是发展高新技术、探索及发现新的自然规律的重要手段,其在雷达、水声信号等实际信号的检测中有直接的应用,而且在未来的信号检测和处理工作中具有一定的理论意义与实际意义。
With the rapid development of science and technology, weak signal detection has been widely used in the fields of radar,fault diagnosis,system identification and communication,and it has always been the hot for domestic and foreign scholars. The extraction of weak signal under strong noise is a essential part of modern signal processing science. The commonly used frequency-domain and time-domain approaches in use nowadays has limitations, especially for weak signal detection under strong noise, the signal-noise ratio need further improvement. Because chaos oscillator is immune to noise and sensitive to weak signal, the detection method used in this paper is different from the traditional ones, overcoming the noise suppress problem.
In order to effectively extract weak signal from noisy background, this paper improve the Duffing Chaos Oscillator model, and utilize chaos oscillator’s characteristics, that the phase transition of it is extremely sensitive and immune to the interference signal with great noise and frequency different, to detect signal. Adjust the system parameter to detect signal with different frequency. Base on analysis of the chaos characteristics, band-pass filter and Gaussian characteristic, the mathematic model of Duffing oscillator for weak signal detecting is presented. By changing the magnitude of periodic perturbation, and observing image, the monoclinic orbit, furcation, chaos traction, critical periodic traction, large scale cycle of the system is derived. Construct a new weak periodic signal detection model by improving the nonlinear resilience term. Simulate using Matlab, and observe image changing. Results indicate that the advantage of Duffing oscillator method in weak periodic signal detection, and it is feasible for its frequency error rate is manageable.
The research is an important means of developing high and new technologies, exploring and discovering new laws of nature. It has immediate applications in the detection of real signal , such as radar signal and underwater acoustic signal. And it has certain theoretical meaning and useful value in signal detecting and processing in the future.
引文
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[25]张宾,李月,马海涛.微弱信号混沌检测临界阈值Lyapunov指数算法[J].地球物理学报,2003,18(4):748-751.
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[34]代慧,文元美,申利民等.Duffing振子微弱信号检测方法的分析比较[J].理论与研究,2008,(1):6-8.
[35]行鸿彦,徐伟.混沌背景中微弱信号检测的神经网络方法[J].物理学报,2007,7(56):3771-3775.
[36]江进朋,徐家品.振子微弱信号检测方法的应用研究[J].软件天地,2009,6:263-265.
[37]郝柏林.混沌——开创新科学[M].上海:上海译文出版社,1990:54-75.
[38]吴祥兴,陈忠.混沌学导论[M].上海:上海科学技术文献出版社,1996:131-142.
[39]郑松.一个新的超混沌系统的动力学分析[D].江苏:江苏大学,2008:12.
[40]李后强等著.分形理论的哲学发轫[M].四川:四川大学出版社,1993:12.
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[42]王冠宇,陶国良,陈行等.混沌振子在强噪声背景信号检测中的应用[J].仪器仪表学报,1997,18(2):209-212.
[43]赵淑清,郑薇.随机信号分析.哈尔滨工业大学出版社,1999,(6):93-94.
[44] Hu Gang.Stochastic forces and nonlinear systems.Shanghai:Shanghai Science&Technology Rdncation Press,1994.
[45] Parlitz U,Lauterborn W.Superstructure in the bifurcation set of the Buffing equation[J]. Phy. Lett.A,1987,107(8):351-355.
[46] Sang-YOON KIM . Bifurcation structure of the double-well buffing oscillation[J].International Journal of Modem PhysicsB,2000,14(17):1801-1812.
[47]李月.混沌振子检测引论[M].北京:工业出版社,2004:23-26.
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[53] Shang Qiufeng,Yin Chengqun,Li Shilin.Study on detection of weak simusoidal signal by using doffing oscilator[J].Zhongguo Dianji Gongcheng Xuebao,2005,(25):66-70.
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[2]卢侃.混沌学传奇[M].孙建化,译.上海翻译出版公司,1991:32-36.
[3] R.Forre.The henon attractor as a keystream generator[J].In Abstract of Eurocrypt,1991,91(6):76-81.
[4]李月,杨宝俊.混沌振子检测引论[M].北京:工业出版社,2004:15-21.
[5]郑松.一个新的超混沌系统的动力学分析、控制与同步研究[D].江苏:江苏大学,2008:10-35.
[6] Suykens J,Vandewalle J.Generation of n-double scrolls (n=1,2,3, 4)[J].IEEE Trans,Circuits Syst,1993,40(11):861-867.
[7]罗晓曙,覃少华.混沌和超混沌系统中的奇怪吸引子及其分析[J].广西物理,1998,19(4):10-14.
[8] Yalcin M E,Suykens J,Vandewalle J.Experimental confirmation of 3-and 5-scroll attractors from a generalized Chua’s circuit[J].IEEE Trans,Circuits Syst.2000,47(3):425-429.
[9]刘孝贤,王英龙,刘蓓.低阶混沌电路非线性动力学特性的实验研究[J].山东科学,2001,15(1):50-54.
[10]刘孝贤,王英龙,刘蓓.低阶混沌电路非线性动力学特性的数学模型与仿真[J].山东科学,2001,14(4):5-9.
[11]禹思敏,林清华,丘水生.四维系统中多涡卷混沌与超混沌吸引子的仿真研究[J].物理学报,2003,52(1):25-32.
[12]邓成良,肖慧娟.四维系统中多涡卷混沌吸引子及其同步的研究[J].电路与系统学报,2004,9(4):54-57.
[13]杨芳艳,混沌电路的理论分析[D].重庆:重庆邮电大学,2006:5.
[14]唐洁.超混沌系统设计及其性能分析[D].南京:南京航天航空大学,2007.
[15]肖慧娟,邓成良.多涡卷及超混沌吸引子的实验研究[J].通信技术,2007,6:50-51.
[16]刘扬正,姜长生.关联可切换超混沌系统的构建与特性分析[J].物理学报,2009,2(58):771-777.
[17]郑艳,王光义.一种新的超混沌扩频序列及其性能分析[J].杭州电子科技大学学报,2007,27(3):9-12.
[18]于波,胡国四,王中训.近似时滞超混沌系统的动力学特性分析[J].烟台大学学报,2009,22(4):255-258.
[19]戴逸松.微弱信号检测方法及仪器[M].北京:国防工业出版社,1994:34-36.
[20]袁坚.混沌理论及其在电子工程中的应用研究[D].成都:电子科技大学,1997:27-28.
[21] Birxd L,Pipenberg S L.Chaotic o scillator and complex mapping feed for war (CMFFNS) for signal deteetion in noisy environments[C]. IEEE Internation Jo int Conference on NeuralNetworks,New York:IEEE Press,1992:881-888.
[22] Dykman.M.I.High frequency stochastic resonance in periodically driven systems[J].Jetp Letters,1993,58:150-156.
[23]李月,杨宝俊.混沌振子检测引论[M].北京:工业出版社,2004.
[24]李月,杨宝俊,石要武.色噪声背景下微弱正弦信号的混沌检测[J].物理学报,2003,52(3):526-530.
[25]张宾,李月,马海涛.微弱信号混沌检测临界阈值Lyapunov指数算法[J].地球物理学报,2003,18(4):748-751.
[26]王冠宇,陶国良,陈行等.混沌振子在强噪声背景信号检测中的应用.仪器仪表学报,1997,18(2):209-212.
[27] Wang Guanyu,Dajun Chen,Jianya Li.Net al.The application of chaotic oscillators to weak signal detection.IEEE transactions on intustrial electronic,1999,46(2):440-444.
[28]聂春燕.混沌理论及基于特定混沌系统的微弱信号检测方法研究[D].吉林,吉林大学,2006:15.
[29]吕志民,徐金梧,翟绪圣.基于混沌振子的微弱特征信号检测原理及应用[J].河北工业大学学报,1998.
[30]何建华,杨宗凯,王殊.基于混沌和神经网络的弱信号探测[J].电子学报,1998.
[31]赵向阳,史百舟,刘君华.硅微谐振传感器微弱频率变化的提取新方法[J].2001.
[32]姜万录,吴胜强,张建成.Duffing振子的检测微弱信号的方法及区别[J].燕山大学报,2002,26(2):114-117.
[33]张淑清,吴月娥.混沌理论微弱信号检测方法的可行性分析[J].测控技术,2001,21(7):53-54.
[34]代慧,文元美,申利民等.Duffing振子微弱信号检测方法的分析比较[J].理论与研究,2008,(1):6-8.
[35]行鸿彦,徐伟.混沌背景中微弱信号检测的神经网络方法[J].物理学报,2007,7(56):3771-3775.
[36]江进朋,徐家品.振子微弱信号检测方法的应用研究[J].软件天地,2009,6:263-265.
[37]郝柏林.混沌——开创新科学[M].上海:上海译文出版社,1990:54-75.
[38]吴祥兴,陈忠.混沌学导论[M].上海:上海科学技术文献出版社,1996:131-142.
[39]郑松.一个新的超混沌系统的动力学分析[D].江苏:江苏大学,2008:12.
[40]李后强等著.分形理论的哲学发轫[M].四川:四川大学出版社,1993:12.
[41] Brown R,Chua L,Popp B.Is sensitive dependence on initial conditi ons natures sensory device [J].I nt.J.Bifurc.Chaos,1992,2(1):193-199.
[42]王冠宇,陶国良,陈行等.混沌振子在强噪声背景信号检测中的应用[J].仪器仪表学报,1997,18(2):209-212.
[43]赵淑清,郑薇.随机信号分析.哈尔滨工业大学出版社,1999,(6):93-94.
[44] Hu Gang.Stochastic forces and nonlinear systems.Shanghai:Shanghai Science&Technology Rdncation Press,1994.
[45] Parlitz U,Lauterborn W.Superstructure in the bifurcation set of the Buffing equation[J]. Phy. Lett.A,1987,107(8):351-355.
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