基于变形Lorenz混沌系统的微弱周期信号检测
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摘要
微弱周期信号混沌检测技术是混沌理论在信息科学应用中的一个重要分支，由于混沌检测系统具有对小信号的敏感性及对噪声的免疫性等特征，使得混沌系统在信号检测领域具有很好的发展前景，已取得了很大的进展。本文在Lorenz混沌系统的基础上，加入周期策动力信号形成一种变形的Lorenz混沌系统。具体内容如下：
利用广义哈密顿系统理论的梅尔尼科夫方法，证明了变形Lorenz系统具有Smale马蹄变换下的混沌。利用功率谱、Poincare截面、Lyapunov指数等分析方法，进一步仿真证明了变形Lorenz系统具有混沌系统的运动规律。
利用最大李雅普诺夫指数作为判断混沌系统由混沌态趋于类周期态变化的量化依据，自动的辨别混沌系统的临界态，更准确的判断微弱信号的存在。研究互相关检测与混沌检测相结合，实现强噪声背景下微弱周期信号幅值检测。通过这种方法能有效的检测出强噪声中的微弱周期信号。
借鉴平均法推导了变形Lorenz系统的近似周期解。将变形Lorenz系统与状态反馈控制方法相结合，将含有待检测信号的变形Lorenz系统从混沌态控制到类周期态，然后利用频谱分析的方法检测待检测信号的频率。说明了这种方法具有较高的检测精度。最后，对不同频率的微弱正弦信号和非正弦周期信号进行了频率检测，说明了此混沌系统的可行性和有效性。
在已知微弱正弦信号的频率基础上，研究变形Lorenz系统结合预置相位逼近法检测微弱正弦信号的相位。
将变形Lorenz混沌系统应用到电力系统间谐波检测中，检测噪声中微小间谐波的幅值、频率和相位。
Chaotic oscillator detection for weak periodic signal belongs to an importantapplication of Chaotic theory in information science, chaotic system is sensitive to weaksignals and immune to noise,which make chaos have good prospects and a great grogressin signal detection technique. In the paper,Based on Lorenz chaotic system, a deformableLorenz chaotic system is constructed by added cycle motive power signals.The followinggives the main work of this paper in detail.
The validity of Melnikov’s method in the generalized Hamilton proves thatdeformable Lorenz system has a deformation transformation in the sense of Smale chaos.The deformable Lorenz system is further proved that it has dynamical behavior,such aspower spectrum, Poincare mapping Lyapunov exponents pectrum.
The maximum Lyapunov exponent will be used to distinguish chaos state from classperiod state as the quantification basis.It can automatically identify the critical state ofchaotic systems and can more accurately determine the presence of weak signals.Thechaos detection combines with the cross-correlation detection method to achieve weakperiodic signals amplitude detection in strong noise.The method can effectively detectweak periodic signals in strong noise.
Approximate periodic solutions of the deformable Lorenz systems is deduced fromthe average method.Deformable Lorenz system and State feedback control are usedtogether to detect the frequency of weak signal.Deformable Lorenz system is controlled tocritical state from class periodic state to chaotic state.The method of spectrum analysis isused to measure the frequency of the detected signal.Simulation results show this methodhas higher detection precision.Finally,we detect the frequencies to different frequencyweak sine signals and non-sine periodic signals.Its results show that the chaotic system isfeasible and effective.
Based on the known the frequency of weak sine signals,the deformable Lorenzsystem and the presetting phase approximation method are used together to detect thephase of weak sine signals.
The deformable Lorenz chaotic system is applied to power system interharmonicsdetection.It can detect amplitude, frequency and phase of weak interharmonics in noise.
利用广义哈密顿系统理论的梅尔尼科夫方法，证明了变形Lorenz系统具有Smale马蹄变换下的混沌。利用功率谱、Poincare截面、Lyapunov指数等分析方法，进一步仿真证明了变形Lorenz系统具有混沌系统的运动规律。
利用最大李雅普诺夫指数作为判断混沌系统由混沌态趋于类周期态变化的量化依据，自动的辨别混沌系统的临界态，更准确的判断微弱信号的存在。研究互相关检测与混沌检测相结合，实现强噪声背景下微弱周期信号幅值检测。通过这种方法能有效的检测出强噪声中的微弱周期信号。
借鉴平均法推导了变形Lorenz系统的近似周期解。将变形Lorenz系统与状态反馈控制方法相结合，将含有待检测信号的变形Lorenz系统从混沌态控制到类周期态，然后利用频谱分析的方法检测待检测信号的频率。说明了这种方法具有较高的检测精度。最后，对不同频率的微弱正弦信号和非正弦周期信号进行了频率检测，说明了此混沌系统的可行性和有效性。
在已知微弱正弦信号的频率基础上，研究变形Lorenz系统结合预置相位逼近法检测微弱正弦信号的相位。
将变形Lorenz混沌系统应用到电力系统间谐波检测中，检测噪声中微小间谐波的幅值、频率和相位。
Chaotic oscillator detection for weak periodic signal belongs to an importantapplication of Chaotic theory in information science, chaotic system is sensitive to weaksignals and immune to noise,which make chaos have good prospects and a great grogressin signal detection technique. In the paper,Based on Lorenz chaotic system, a deformableLorenz chaotic system is constructed by added cycle motive power signals.The followinggives the main work of this paper in detail.
The validity of Melnikov’s method in the generalized Hamilton proves thatdeformable Lorenz system has a deformation transformation in the sense of Smale chaos.The deformable Lorenz system is further proved that it has dynamical behavior,such aspower spectrum, Poincare mapping Lyapunov exponents pectrum.
The maximum Lyapunov exponent will be used to distinguish chaos state from classperiod state as the quantification basis.It can automatically identify the critical state ofchaotic systems and can more accurately determine the presence of weak signals.Thechaos detection combines with the cross-correlation detection method to achieve weakperiodic signals amplitude detection in strong noise.The method can effectively detectweak periodic signals in strong noise.
Approximate periodic solutions of the deformable Lorenz systems is deduced fromthe average method.Deformable Lorenz system and State feedback control are usedtogether to detect the frequency of weak signal.Deformable Lorenz system is controlled tocritical state from class periodic state to chaotic state.The method of spectrum analysis isused to measure the frequency of the detected signal.Simulation results show this methodhas higher detection precision.Finally,we detect the frequencies to different frequencyweak sine signals and non-sine periodic signals.Its results show that the chaotic system isfeasible and effective.
Based on the known the frequency of weak sine signals,the deformable Lorenzsystem and the presetting phase approximation method are used together to detect thephase of weak sine signals.
The deformable Lorenz chaotic system is applied to power system interharmonicsdetection.It can detect amplitude, frequency and phase of weak interharmonics in noise.
引文
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[6]张浩然,侯楚林.基于混沌相平面变化的微弱信号检测[J].计算机测量与控制,2010,18(12):2718-2720.
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[8]兀旦晖.基于图像识别混沌的弱信号检测方法研究[J].计算机测量与控制,2010,18(2):320-322.
[9]吴勇峰,张世平,孙金玮.用相位差值判别Duffing振子相变的新方法[J].仪器仪表学报,2010,31(1):161-165.
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[13]王永生,姜文志,赵建军,等.一种Duffing弱信号检测新方法及仿真分析[J].物理学报,2008,57(4):2053-2059.
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[17] Hu N Q, Wen X S. The application of duffing oscillator in characteristic signal detection of earlyfault[J]. Journal of sound and Vibration,2003,268(5):917-931.
[18] Wen Q, Wang S X.., Zhu K Y. The application og chaotic oscillator to digital watermarkingdetection[J]. IEEE International Conference on Network&Signal Processing,2003,2:1513-1516.
[19] Zambrano S, Allaria E, Brugioni S, et al. Numerical and experimental exploration of phasecontrol of chaos[J]. American Institute of Physics,2006,16:013111.
[20] Lepik ü, Hein H. On response of nonlinear oscillators with random frequency ofexcitation[J].Journal of Sound and Vibration,2005,288:175-292.
[21] Lepikü, Hein H. Response of nonlinear oscillators with random frequency ofexcitation,revisited[J]. Journal of Sound and Vibration,2007,301:1040-1049.
[22] Li Y, Yang B J, Badal J, et al. Chaotic system detection of weak seismic signals[J]. GeophysicalJournal International,2009,178(3):1493-1522.
[23] Wang J X. A method of weak signal detection based on duffing oscillator[J]. IEEE InternationalConference on Network&IC4E’10,2010,18(3):387-390.
[24] Liu X C, Liu X L. Weak signal detection research based on doffing oscillator used for downholecommunication[J]. Journal of Computer,2011,6(2):359-367.
[25]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,1998,26(10):33-37.
[26]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,1998,27(4):13-17.
[27]张淑清,姜万录,王玉田.强噪声中弱信号检测的混沌方法及超声系统的实现[J].电子测量与仪器学报,2001,15(2):11-14.
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