用于金属探测的混沌振子系统研究
|
摘要
金属探测器是一种金属检出设备,它利用电磁、射线等物理原理,对混合物品中的金属杂质或人体携带的金属物品(如铁、铜、不锈钢等)产生感应信号,从而达到报警剔除目的,起到保护生产设备、对食品医药等产品进行质量控制、保护人身安全等作用。本文主要研究对产品进行质量控制的金属探测器,要探测到混入食品、医药中微小金属颗粒,高灵敏度报警是关键,为了提高探测器的灵敏度,本文首次把混沌检测理论应用于金属探测领域,为金属探测领域提供了新的检测方法和技术。
就目前所查阅的资料,国内外尚无把混沌检测技术用于金属探测的报道,因此本课题是应用基础研究。混沌检测系统用于金属探测不是混沌检测系统和探测器探头机械的组合,而是充分结合金属探测的特点,研究出适合金属探测的混沌检测系统,特别能解决较高频率情况下混沌检测系统的阈值确定及状态判别、高频混沌检测电路、探测盲区等金属探测特有的技术问题。所创新的技术、改进的方法能为在其它方面的应用例如：管道探伤、电力系统的谐波分析、故障报警等奠定基础和提供思路。
另外,随着用户对产品质量的要求日益增加,国家对食品、医药等产品严把质量关,对产品的安全性监管力度加大,高灵敏度金属探测器市场将会十分广阔。如果研发出一种灵敏度高且成本低的金属探测器产品,可期具有一定经济效益。此外,实现核心技术的自主化,还能摆脱对国外产品的依赖,又具有相当的社会效益。本文的主要工作有以下几方面：
(1)本文首先在总结现有结论和方法的基础上,用Matlab编制了计算机软件程序。该软件可计算出不同半径、材质的金属小球(金属杂质)在通过平衡线圈式金属探测器时发出的微弱电压信号,其目的在于熟悉探测器探测金属杂质时,探头发出的微弱电压信号与金属小球的大小和材质等参数的量化关系,以及其与线圈的尺寸和空间位置、驱动系统电流的大小和频率等参数之间的量化关系。用程序计算了两个算例,得到的电压信号就是混沌检测系统要检测的信号,分析该信号的特点,可以确定对混沌检测系统的精度及频率等设计要求,为设计适合金属探测的混沌检测系统提供依据。
(2)在分析L-Y系统检测原理的基础上,建立了适合金属探测器高频检测的L-Y系统,用RHR算法推导了L-Y系统李雅普诺夫指数的计算方法,为准确判断系统状态提供了定量判据。在此基础上提出了一种改进的数值仿真模型,该模型把L-Y系统的状态方程和求解李雅普诺夫指数的状态方程合在一起,组成一个随机微分方程组,用Matlab的仿真工具箱Simulink构建了该模型,并用Simulink求解这个方程组。该模型可输出L-Y系统的数值解和系统相图,并可同步输出计入噪声影响时L-Y系统的李雅普诺夫指数。可用李雅普诺夫指数判断系统状态,克服了用相图法判断系统状态误差大等局限性,为确定L-Y系统的临界阈值和研究L-Y系统在噪声背景下的检测性能提供了定量判据。然后用该模型分析了L-Y系统的动力学行为、对微弱信号的敏感性及检测性能,仿真结果表明：L-Y系统是一个混沌系统,该系统对初始值非常敏感,当正弦信号的幅值稍微增加,系统就发生混沌态到大尺度周期态的临界相变,所以该系统可以进行较高频率下的微弱信号检测,并求取了信噪比,验证了该检测方法的可行性和有效性。
(3)针对已有Duffing混沌电路仅适用于低频情况的问题,提出一种改进的L-Y混沌检测电路,提出先积分后乘以角频率ω来设计电路的运算方式,克服了设计高频L-Y混沌电路时,高放大倍数造成的电路瞬间饱和问题,适当调整该电路的参数,可实现从低频到高频的微弱信号检测。使L-Y混沌电路用于高频微弱信号的检测得以实现,填补了该研究领域的空白。并对该电路中各个单元电路进行了详细的设计
(4)用电子工作平台软件(Multisim)对L-Y混沌电路进行了仿真分析,对该电路在较高频率下的动力学行为、对微弱信号的敏感性和检测性能进行了研究,仿真结果表明：该电路是一个混沌电路,对初始值非常敏感,当正弦信号的幅值稍微增加,电路就发生混沌态到大尺度周期态的临界相变,可进行较高频率下的微弱信号检测。通过加入热噪声,分析电路在噪声背景下检测微弱信号的能力,并求取了信噪比。对仿真结果进行分析发现：随着临界阈值精度的增加,也即检测精度的增加,信噪比越来越低的现象。另外,分析L-Y系统的电路结构可知,该电路是由两个低通滤波器串联而成,有滤除高频噪声的作用,通过对电路进行交流仿真,得到系统的幅频特性,分析其幅频特性发现,通过系统的总的噪声能量中,超过截止频率的高频噪声的能量所占的比例是非常小的,验证了该电路对高频噪声有很强的衰减作用,这种现象是Matlab等纯数值仿真难以发现的。
(5)提出双路混沌系统反相检测法,消除由被测信号和混沌系统内置信号的相位差引起的探测盲区,探讨了探测盲区存在的机理,建立了反相振子,用两个振子同时参与检测,可以互相取长补短,来消除探测盲区,用数值仿真模型验证了该方法的可行性。提出了另一种消除探测盲区的方法一自相关方法,讨论了该方法消除探测盲区的机理和去除噪声的原理,得出自相关方法具有消除探测盲区和滤除噪声双重作用的结论,提出了自相关技术和混沌检测技术联合使用的方法。
The metal detector is a metal detection equipment, which uses physical principles such as electromagnetic induction, to detect the induced signal from mixed goods or human-carrying metal material, and thus alarm. The detector on the assembly line can detect metal substance mixed in the raw materials, to protect production equipment or control quality of food, medicine and other products. This paper discusses the detectors for industrial production and product quality control. In order to improve the sensitivity of the detector, this paper will design a chaotic detection system for the metal detector which is high accuracy with reasonable structure and easy to operate to detect weak signals emitted by the metal detector probe.
There is no chaotic detection technology for metal detector reported, so the topic is the first of application and basic research. The chaotic detection system for the metal detector is not a system which is simply combined with the probe. According to the characteristics of the metal detector, an innovative chaotic detection system should be designed. Especially problems should be solved such as the higher frequency detection, the threshold determination, high frequency chaotic detection circuit and elimination of blind spot. This innovative technology can provide theories and ideas to other fields such as pipeline inspection, power system harmonic analysis and fault alarm
With the increasing requirements of the users to the product quality, and the national strict supervision on the safety of products, high sensitivity metal detector market will be very broad. Therefore, to develop a high sensitivity and low cost metal detector has considerable economic benefits. In addition, the core technology of autonomy to get rid of dependence on foreign products has considerable social benefits. The main work of this paper is summarized as follows:
(1) According to current conclusions and methods, this paper makes a computer software program by Matlab. The software can calculate the weak voltage signal from the probe, when different material metal particles (metal impurities) with different diameters, is passing through the balanced coil of the metal detector. Analysis of the characteristics of the signal can help to determine the accuracy and frequency of chaotic detection system. It provides the theoretical basis to design chaotic detection system for metal detection.
(2) Based on the principle of weak signal detection of L-Y chaotic system, a high frequency chaotic detection system for metal detection has been built. The Lyapunov characteristic exponents of the system have been obtained through the RHR algorithm. It can help to determine the state of the system accurately, and provides quantitative means to accurate discrimination of the system state. On this basis, this paper proposes an improved numerical simulation model. The model has been built by the simulation toolbox Simulink of Matlab. The model can output the L-Y system numerical solution, phase diagram and Lyapunov characteristic exponents simultaneously. The available Lyapunov characteristic exponents can judge the state of the system, and overcome the disadvantage of observing phase diagram to determine system state. This model is used to analyze the dynamic behavior, sensitivity to weak signals and detection performance to weak signals. Simulations show that L-Y is a chaotic system, which is very sensitive to the initial value. A slight increase of the amplitude of the sinusoidal signal can make the system change into to the large-scale periodic state from chaotic state. And then the signal-to-noise ratio is obtained. The feasibility and effectiveness are verified.
(3) In order to solve the problem that present Duffing chaotic circuit is only applicable to the low-frequency signal detection, this paper proposes an improved L-Y chaotic detection circuit. This circuit can solve the problem that the high magnification can cause instant saturation. If appropriate adjustments to the parameters of the circuit, it can detect the weak signal from low to high frequency. The detailed designs of each unit circuit have been finished.
(4) The L-Y chaotic circuit is built by the Electronic Work Platform software (Multisim). The dynamic behavior and the detection performance of weak signals of the circuit in the higher frequency have been analyzed. Simulation results show that:The circuit is a chaotic circuit, and it is very sensitive to the initial value. If slightly increase in the amplitude of the sinusoidal signal, the circuit will change into the large-scale periodic state from the chaotic state. If the thermal noise is added to the circuit, simulation results show that:with the increase of the accuracy of the critical threshold, the signal-to-noise ratio is becoming less and less. Additionally, from the analysis of L-Y circuit structure, it can be seen that the circuit is composed by two low pass filters in series, so it can filter out high frequency noise. This is verified by the amplitude-frequency characteristic curve which is outputted by the simulation. This phenomenon is hard to be discovered by the pure numerical simulation of the Matlab.
(5) This paper proposes dual chaotic system detection method to eliminate the blind spot. The causes why there is the blind spot have been discussed. In order to solve this problem, two chaotic systems are involved in the detection. The two systems can complement each other to eliminate the blind spot. Numerical simulation is used to verify the feasibility of the method. Another method to eliminate the blind spot detection-autocorrelation method, is discussed. The method can both eliminate the blind spot and filter noise. The autocorrelation method can be used together with chaotic detection technology.
就目前所查阅的资料,国内外尚无把混沌检测技术用于金属探测的报道,因此本课题是应用基础研究。混沌检测系统用于金属探测不是混沌检测系统和探测器探头机械的组合,而是充分结合金属探测的特点,研究出适合金属探测的混沌检测系统,特别能解决较高频率情况下混沌检测系统的阈值确定及状态判别、高频混沌检测电路、探测盲区等金属探测特有的技术问题。所创新的技术、改进的方法能为在其它方面的应用例如：管道探伤、电力系统的谐波分析、故障报警等奠定基础和提供思路。
另外,随着用户对产品质量的要求日益增加,国家对食品、医药等产品严把质量关,对产品的安全性监管力度加大,高灵敏度金属探测器市场将会十分广阔。如果研发出一种灵敏度高且成本低的金属探测器产品,可期具有一定经济效益。此外,实现核心技术的自主化,还能摆脱对国外产品的依赖,又具有相当的社会效益。本文的主要工作有以下几方面：
(1)本文首先在总结现有结论和方法的基础上,用Matlab编制了计算机软件程序。该软件可计算出不同半径、材质的金属小球(金属杂质)在通过平衡线圈式金属探测器时发出的微弱电压信号,其目的在于熟悉探测器探测金属杂质时,探头发出的微弱电压信号与金属小球的大小和材质等参数的量化关系,以及其与线圈的尺寸和空间位置、驱动系统电流的大小和频率等参数之间的量化关系。用程序计算了两个算例,得到的电压信号就是混沌检测系统要检测的信号,分析该信号的特点,可以确定对混沌检测系统的精度及频率等设计要求,为设计适合金属探测的混沌检测系统提供依据。
(2)在分析L-Y系统检测原理的基础上,建立了适合金属探测器高频检测的L-Y系统,用RHR算法推导了L-Y系统李雅普诺夫指数的计算方法,为准确判断系统状态提供了定量判据。在此基础上提出了一种改进的数值仿真模型,该模型把L-Y系统的状态方程和求解李雅普诺夫指数的状态方程合在一起,组成一个随机微分方程组,用Matlab的仿真工具箱Simulink构建了该模型,并用Simulink求解这个方程组。该模型可输出L-Y系统的数值解和系统相图,并可同步输出计入噪声影响时L-Y系统的李雅普诺夫指数。可用李雅普诺夫指数判断系统状态,克服了用相图法判断系统状态误差大等局限性,为确定L-Y系统的临界阈值和研究L-Y系统在噪声背景下的检测性能提供了定量判据。然后用该模型分析了L-Y系统的动力学行为、对微弱信号的敏感性及检测性能,仿真结果表明：L-Y系统是一个混沌系统,该系统对初始值非常敏感,当正弦信号的幅值稍微增加,系统就发生混沌态到大尺度周期态的临界相变,所以该系统可以进行较高频率下的微弱信号检测,并求取了信噪比,验证了该检测方法的可行性和有效性。
(3)针对已有Duffing混沌电路仅适用于低频情况的问题,提出一种改进的L-Y混沌检测电路,提出先积分后乘以角频率ω来设计电路的运算方式,克服了设计高频L-Y混沌电路时,高放大倍数造成的电路瞬间饱和问题,适当调整该电路的参数,可实现从低频到高频的微弱信号检测。使L-Y混沌电路用于高频微弱信号的检测得以实现,填补了该研究领域的空白。并对该电路中各个单元电路进行了详细的设计
(4)用电子工作平台软件(Multisim)对L-Y混沌电路进行了仿真分析,对该电路在较高频率下的动力学行为、对微弱信号的敏感性和检测性能进行了研究,仿真结果表明：该电路是一个混沌电路,对初始值非常敏感,当正弦信号的幅值稍微增加,电路就发生混沌态到大尺度周期态的临界相变,可进行较高频率下的微弱信号检测。通过加入热噪声,分析电路在噪声背景下检测微弱信号的能力,并求取了信噪比。对仿真结果进行分析发现：随着临界阈值精度的增加,也即检测精度的增加,信噪比越来越低的现象。另外,分析L-Y系统的电路结构可知,该电路是由两个低通滤波器串联而成,有滤除高频噪声的作用,通过对电路进行交流仿真,得到系统的幅频特性,分析其幅频特性发现,通过系统的总的噪声能量中,超过截止频率的高频噪声的能量所占的比例是非常小的,验证了该电路对高频噪声有很强的衰减作用,这种现象是Matlab等纯数值仿真难以发现的。
(5)提出双路混沌系统反相检测法,消除由被测信号和混沌系统内置信号的相位差引起的探测盲区,探讨了探测盲区存在的机理,建立了反相振子,用两个振子同时参与检测,可以互相取长补短,来消除探测盲区,用数值仿真模型验证了该方法的可行性。提出了另一种消除探测盲区的方法一自相关方法,讨论了该方法消除探测盲区的机理和去除噪声的原理,得出自相关方法具有消除探测盲区和滤除噪声双重作用的结论,提出了自相关技术和混沌检测技术联合使用的方法。
The metal detector is a metal detection equipment, which uses physical principles such as electromagnetic induction, to detect the induced signal from mixed goods or human-carrying metal material, and thus alarm. The detector on the assembly line can detect metal substance mixed in the raw materials, to protect production equipment or control quality of food, medicine and other products. This paper discusses the detectors for industrial production and product quality control. In order to improve the sensitivity of the detector, this paper will design a chaotic detection system for the metal detector which is high accuracy with reasonable structure and easy to operate to detect weak signals emitted by the metal detector probe.
There is no chaotic detection technology for metal detector reported, so the topic is the first of application and basic research. The chaotic detection system for the metal detector is not a system which is simply combined with the probe. According to the characteristics of the metal detector, an innovative chaotic detection system should be designed. Especially problems should be solved such as the higher frequency detection, the threshold determination, high frequency chaotic detection circuit and elimination of blind spot. This innovative technology can provide theories and ideas to other fields such as pipeline inspection, power system harmonic analysis and fault alarm
With the increasing requirements of the users to the product quality, and the national strict supervision on the safety of products, high sensitivity metal detector market will be very broad. Therefore, to develop a high sensitivity and low cost metal detector has considerable economic benefits. In addition, the core technology of autonomy to get rid of dependence on foreign products has considerable social benefits. The main work of this paper is summarized as follows:
(1) According to current conclusions and methods, this paper makes a computer software program by Matlab. The software can calculate the weak voltage signal from the probe, when different material metal particles (metal impurities) with different diameters, is passing through the balanced coil of the metal detector. Analysis of the characteristics of the signal can help to determine the accuracy and frequency of chaotic detection system. It provides the theoretical basis to design chaotic detection system for metal detection.
(2) Based on the principle of weak signal detection of L-Y chaotic system, a high frequency chaotic detection system for metal detection has been built. The Lyapunov characteristic exponents of the system have been obtained through the RHR algorithm. It can help to determine the state of the system accurately, and provides quantitative means to accurate discrimination of the system state. On this basis, this paper proposes an improved numerical simulation model. The model has been built by the simulation toolbox Simulink of Matlab. The model can output the L-Y system numerical solution, phase diagram and Lyapunov characteristic exponents simultaneously. The available Lyapunov characteristic exponents can judge the state of the system, and overcome the disadvantage of observing phase diagram to determine system state. This model is used to analyze the dynamic behavior, sensitivity to weak signals and detection performance to weak signals. Simulations show that L-Y is a chaotic system, which is very sensitive to the initial value. A slight increase of the amplitude of the sinusoidal signal can make the system change into to the large-scale periodic state from chaotic state. And then the signal-to-noise ratio is obtained. The feasibility and effectiveness are verified.
(3) In order to solve the problem that present Duffing chaotic circuit is only applicable to the low-frequency signal detection, this paper proposes an improved L-Y chaotic detection circuit. This circuit can solve the problem that the high magnification can cause instant saturation. If appropriate adjustments to the parameters of the circuit, it can detect the weak signal from low to high frequency. The detailed designs of each unit circuit have been finished.
(4) The L-Y chaotic circuit is built by the Electronic Work Platform software (Multisim). The dynamic behavior and the detection performance of weak signals of the circuit in the higher frequency have been analyzed. Simulation results show that:The circuit is a chaotic circuit, and it is very sensitive to the initial value. If slightly increase in the amplitude of the sinusoidal signal, the circuit will change into the large-scale periodic state from the chaotic state. If the thermal noise is added to the circuit, simulation results show that:with the increase of the accuracy of the critical threshold, the signal-to-noise ratio is becoming less and less. Additionally, from the analysis of L-Y circuit structure, it can be seen that the circuit is composed by two low pass filters in series, so it can filter out high frequency noise. This is verified by the amplitude-frequency characteristic curve which is outputted by the simulation. This phenomenon is hard to be discovered by the pure numerical simulation of the Matlab.
(5) This paper proposes dual chaotic system detection method to eliminate the blind spot. The causes why there is the blind spot have been discussed. In order to solve this problem, two chaotic systems are involved in the detection. The two systems can complement each other to eliminate the blind spot. Numerical simulation is used to verify the feasibility of the method. Another method to eliminate the blind spot detection-autocorrelation method, is discussed. The method can both eliminate the blind spot and filter noise. The autocorrelation method can be used together with chaotic detection technology.
引文
[1]K.Reber, M.Beller. A New Generation of Ultrasonic In-Line Tools for Detecting, Sizing and Locating Metal Loss and Cracks in Transmission Pipelines. IEEE Ultrasonics Symposium: 665-671,2002.
[2]刘慧娟.一种新型智能金属探测器.北方交通大学学报,2001,25(1)：95-99.
[3]王伟.金属探测器原理及其应用.矿冶.,1996,5(4)：78-84
[4]虞伟晨,蔡云升.食品中异物的在线检测和控制..食品工业,2002,(5)：33-35
[5]Peter.P Silvester. Sensitivity Maps for Metal Detector Design. IEEE Transactions on Geoscience and Remote Sensing, vol.34,No.3:788-792,May.1996.
[6]李秀山.金属感应探测线圈半径优化设计.传感器技术,2005,24(8)：51-53
[7]M.Brighten M.J.English. Calculation of Optimum Spacing For A Three Coil Axially Symmetric Metal Detector. Electronics Letters, vol.29, No.10:838-839,May.1993.
[8]H.Krueger, H.Ewald. Anvanced Signal Processing for Reduction of Alarm Rate of Metal Detector for Humanitarian Mine Clearance. IMTC2006, Italy:1452-1466, April 2006
[9]张鑫等Duffing振子检测微弱正弦信号的普遍性研究.计算机与数字工程.,2005,33(12)：71-73
[10]李月,杨宝俊.混沌振子检测引论.北京：电子工业出版社,2004.
[11]李月,杨宝俊.混沌振子系统(L-Y)与检测.北京：科学工业：出版社,2007.
[12]高金峰.非线性电路与混沌.北京：科学出版社,2005.
[13]刘宗华.混沌动力学基础及其应用.北京：高等教育出版社,2006.
[14]刘慧娟.一种数字式金属探测器的设计.仪器仪表学报.,2004,25(4)增刊：362-363
[15]梁莉,葛斌.基于鉴相原理的高性能金属探测仪的设计.大连大学学报.,2005,26(4)：15-18
[16]范丽珍,李树华.基于单片机的智能金属探测器的设计.内蒙古大学学报.,2006,37(2)：185-188
[17]王勤,梅松劲.基于intel 8DC196控制的智能金属探测仪.江南大学学报.,2003,2(1)：46-52
[18]卢森锴等.巨磁电阻效应及其研究进展.世界科技研究与发展.,2008,30(1)：84-88.
[19]陈晓晖.基于GMR磁传感器芯片的弱磁探伤电路.科技资讯.,2006,(20)：206-207
[20]Wallash.A, Magnetic Changes in GMR Head Caused by Electrostatic Discharge., IEEE Transactions on Magnetics., vol.34,No.4,:1519-1521,July.1998.
[21]刘慧娟等.一种基于电压和频率的金属探测方法.仪器仪表学报.,2006,27(7)：769-772
[22]张学勇,赵群,李义宝,唐震.一种金属探测器的设计.安徽建筑工业学院学报.,2007,15(3)：74-77.
[23]庞瑞帆,钟翔,胡泷等.双频金属探测器的研究..解放军理工大学学报：自然科学版,2001,2(2)：1-8.
[24]刘国亭,余晋岳.金属探测器的原理与应用[J].电子技术,1984,10(2)：25-29.
[25]周学才,李传芳.一种新型高稳定度金属探测器及保护系统.电测与仪表,1997,34(2)17-20.
[26]Hiroshi Nakane, Yoshio Sohara. A Method for Simultaneously Measuring Resistivity and Permeability with a Multiayer Solenoid Coil. IEEE Transactions on Instrumentation and Measurement, vol.39,No.1:32-37,February.1990.
[27]Yoshihiro Nonaka, Hiroshi Nakane. Simultaneous Measurement of the Resistivity and Permeability of film sample with a Double Coil. IEEE Transactions on Instrumentation and Measurement, vol.44,No.3,:679-682,June.1995.
[28]Sadao Yamazaki, Negishi, H. Nakane, and A Tanaka. Basic Analysis of a Metal Detector. IEEE Trans. Instrum. Meas., vol.51, No:810-814, Aug.2002.
[29]S. Yamazaki, T. Negishi, H. Nakane, and A. Tanaka, Simultaneous Measurement of Electric and Magnetic Properties of a Spherical Sample, IEEE Trans. Instrum. Meas., vol.45,No.2: 473-477, Apr.1996.
[30]雷银照.时谐电磁场的解析方法.北京：科学出版社,2000.
[31]高晋占.微弱信号检测.北京：清华大学出版社,2004
[32]吴正毅.测试技术与测试信号处理.北京：清华大学出版社,1991.
[33]刘俊,张斌珍.微弱信号检测技术.北京：电子工业出版社,2005.
[34]聂春燕,石要武.微弱正弦信号的时域处理方法研究.计量技术,2000,5：3-5
[35]侯楚,林熊萍,王德石.基于互相关与混沌理论相结合的水下目标信号检测.鱼雷技术,2006,14(5)：17-19
[36]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.仪器仪表学报,2004,25(4)：21-22
[37]赵吉祥,陈超婵,王欢等.微弱电信号检测方法回顾.中国计量学院学报,2009,20(3)：202-208
[38]户永清.基于取样积分技术的混沌检测法与微弱正弦信号检测.绵阳师范学院学报,2009,28(8)：34-38
[39]李月,徐凯,杨宝俊等.混沌振子系统周期解几何特征分析与微弱周期信号的定量检测.物理学报,2008,57(6)：3353-3358.
[40]ZHANG Siyi, GAO Hongxia, LI Yaan, et al. A new method for detecting line spectrum of ship-radiated noise using Duffing oscillator. Chinese Science Bulletin,2007,52(14):1906-1912.
[41]王冠宇等Duffing振子检测微弱信号方法的统计特性研究.电子学报.,1998,26
[42]李月等.纳伏级正弦信号的混沌检测方法的研究.通信学报.,2003,24(4)：26-30
[43]Li T Y, Yorke J A. Period Three Implies Chaos. Ameriean Mathematical Monthly,1975, 82(10):985-992
[44]Robert L Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley,1987: 48-53
[45]郝柏林.分岔、混沌、奇怪吸引子、湍流及其它一关于确定论系统中的内在随机性.物 理学进展,1983,3(3)：333-335
[46]郝柏林.从抛物线谈器一混沌动力学引论.上海：上海科技教育：出版社,1993(10)：38-44
[47]周凌云,王瑞丽等.非线性物理理论及应用.北京：北京大学：出版社,2000.
[48]梁福明,刘式适.自然科学中的混沌与分形.北京：北京大学：出版社,2003.
[49]刘宗华.混沌动力学基础及其应用.北京：高等教育：出版社,2006.
[50]刘曾荣.混沌的微扰判据.上海：上海科技教育：出版社,1994
[51]Pecora L M, Carroll T L. Synchronization in Chaotic Systems. Phys Rev Lett,1990,64(8): 821-825
[52]Louism P. Synchronization in Chaotic Systems..Physical Rev Lett,.64(.8):821-824,Aug. 1990
[53]陈琢,钱鸣奇等.混沌态电阻测量的研究.电子测量与仪器学报,2003,17(3)：46-51
[54]Kolumban G, Vizvari B, and Mogel A. Chaotic System:a Challenge for Measurement and Analysis[C]. In:IEEE Tech Conf, Belgium,1996:1396-1401
[55]Daolin Xu, zhiguang Li. Estimation of Periodic-like Motion of Chaotic Evolutions Using Detected Unstable Periodic Pattern. Pattern Recognition Letters,2002(23):245-252
[56]A.Venkatesan, S.Parthasarathy,Mlakshmanan. Occurrence of Multiple Period-doubling Route to Chaos in Peridically Pulsed Chaotic Dynamical Systems..Solutions and Fractals,2003,18: 891-898
[57]Yung Chiahsiao, Pi-Cheng Tung. Controlling Chaos for Nonautononmous Systems by Detecting Unstable Periodic Orbit.. Solutions and Fractals,2002(13):1043-1051
[58]Li Zhongnian, Huang Tao. A New Method of Measuring WDV Based on Chaos Theory. Electronics Letters, ICEMI 2007:125-128
[59]聂春燕,徐振忠.混沌系统在弱检测信号检测中的应用..传感器技术,
[60]姜万录,吴胜强Duffing振子的两种检测微弱信号的方法及区别.燕山大学学报,2002,26(2)：114-118
[61]姜万录等Duffing振子的两种检测微弱信号的方法及区别.燕山大学学报,2002,26(2)：114-118
[62]尚秋峰等Duffing振子微弱正弦信号检测方法研究.中国电机工程学报.,2005,25(2)：66-70
[63]葛晓慧等.利用Duffing振子估计多频信号参数.浙江大学学报.,2005,25(22)：71-73
[64]Li zuping, Dong Yuguo, Yao Peiyang. A Sensitive Cell Neuron Model Based on Chaos[C].Proceedings of ICSP2000:248-251
[65]Donald.I.Birx. Chaotic Oscillators and CMFFNS for Signal Detection in Noise Environments. IEEE International Joint Conference on Neural Networks,1992(22):881-888
[66]Satish TS, Bukkaptnama, Sounder Kumara RT, Akhlesh Lakhtakia. The Neighborhood Method and Its Coupling with the Wavelet Method for Signal Separation of Chaotic signal. Signal Processing,2002(82):1351-1374
[67]Dobrowiecki T P,Schoukens J, Practical choice in the FRF measurement in presence of nonlinear distortions.IEEE transactions on Instrumentation and Measurement,,2001,50(1): 2-7
[68]张鑫等Duffing振子检测微弱正弦信号的普遍性研究.计算机与数字工程.,2005,33(12)：71-73
[69]杨建红等Duffing振子信号探测故障电弧短路保护中的的应用.电力系统自动化.,2006,30(24)：69-72
[70]ZHANG Siyi, GAO Hongxia, LI Yaan, et al. A new method for detecting line spectrum of ship-radiated noise using Duffing oscillator. Chinese Science Bulletin,2007,52(14):1906-1912.
[71]王永生等Duffing混沌系统电路仿真研究.电路与系统学报,2008,13(2)：132-135
[72]王永生等.基于初值敏感性混沌弱信号检测的性能研究.电子器件,2007,30(5)：1651-1653
[73]M Franaszek, L. Fronzoni. Resonant Response and Its Scaling Property in Chaotic Systems Perturbed by Noise. IL Nuovo Cimento,1995,17(7):775-783.
[74]杨定新等.基于随机共振电路模拟的周期信号检测.电路与系统学报.,2004,9(6)：135-138
[75]刘秉正.非线性动力学与混沌基础..长春：东北师范大学出版社,1994.
[76]王平立,宋斌,王玲.混沌时间序列的Kolmogorov熵的应用研究.计算机工程与应用,2006(21)：162-164
[77]王树禾.微分方程模型与混沌.合肥：中国科学技术大学出版社,1999：441-442,489-491
[78]吕金虎,张锁春Lyapunov指数的数值计算方法.非线性动力学学报,2003,8(1)：84-92
[79]姜健飞.数值分析及其Matlab实验.北京：科学出版社,2004：150-152.
[80]薛定宇,陈阳泉.高等应用数学问题的Matlab求解.北京：清华大学出版社.2008：221-223.
[81]Rangarajan G, Habib S, and Ryne R D. Lyapunov Exponents without Rescaling and Reorthogonalization. Physical Review Letters, vol.80,3747-3750,1998
[82]张宾,李月,卢金Lyapunov特性指数用于混沌判据.吉林大学学报(信息科学版),2004,22(2):111-114. ZHANG Bin, LI Yue, LU Jin. Study of the Lyapunov characteristic
[83]刘丁,任海鹏,李虎明.基于Lyapunov指数的弱周期信号检测. 仪器仪表学报,2005,26(12)：1215-1218.
[84]高继坤,杨焕明.运算放大器应用分析.北京：北京理工大学出版社,1989：87-89
[85]李哲英,骆丽等.电子技术及其应用基础.北京：高等教育出版社,2003：51-53
[86]孔有林.集成运算放大器及其应用.北京：人民邮电出版社,1988：321-332
[87]钱国飞.集成运算放大器基本原理及应用.北京：清华大学出版社,1984：22.
[88]熊伟,侯传教等Mutisim7电路设计及仿真应用,上海：上海交通大学出版社,2005：71-72.
[89]从宏寿,程为群等Multisim8仿真与应用实例开发.北京：清华大学出版社,2007：22.
[2]刘慧娟.一种新型智能金属探测器.北方交通大学学报,2001,25(1)：95-99.
[3]王伟.金属探测器原理及其应用.矿冶.,1996,5(4)：78-84
[4]虞伟晨,蔡云升.食品中异物的在线检测和控制..食品工业,2002,(5)：33-35
[5]Peter.P Silvester. Sensitivity Maps for Metal Detector Design. IEEE Transactions on Geoscience and Remote Sensing, vol.34,No.3:788-792,May.1996.
[6]李秀山.金属感应探测线圈半径优化设计.传感器技术,2005,24(8)：51-53
[7]M.Brighten M.J.English. Calculation of Optimum Spacing For A Three Coil Axially Symmetric Metal Detector. Electronics Letters, vol.29, No.10:838-839,May.1993.
[8]H.Krueger, H.Ewald. Anvanced Signal Processing for Reduction of Alarm Rate of Metal Detector for Humanitarian Mine Clearance. IMTC2006, Italy:1452-1466, April 2006
[9]张鑫等Duffing振子检测微弱正弦信号的普遍性研究.计算机与数字工程.,2005,33(12)：71-73
[10]李月,杨宝俊.混沌振子检测引论.北京：电子工业出版社,2004.
[11]李月,杨宝俊.混沌振子系统(L-Y)与检测.北京：科学工业：出版社,2007.
[12]高金峰.非线性电路与混沌.北京：科学出版社,2005.
[13]刘宗华.混沌动力学基础及其应用.北京：高等教育出版社,2006.
[14]刘慧娟.一种数字式金属探测器的设计.仪器仪表学报.,2004,25(4)增刊：362-363
[15]梁莉,葛斌.基于鉴相原理的高性能金属探测仪的设计.大连大学学报.,2005,26(4)：15-18
[16]范丽珍,李树华.基于单片机的智能金属探测器的设计.内蒙古大学学报.,2006,37(2)：185-188
[17]王勤,梅松劲.基于intel 8DC196控制的智能金属探测仪.江南大学学报.,2003,2(1)：46-52
[18]卢森锴等.巨磁电阻效应及其研究进展.世界科技研究与发展.,2008,30(1)：84-88.
[19]陈晓晖.基于GMR磁传感器芯片的弱磁探伤电路.科技资讯.,2006,(20)：206-207
[20]Wallash.A, Magnetic Changes in GMR Head Caused by Electrostatic Discharge., IEEE Transactions on Magnetics., vol.34,No.4,:1519-1521,July.1998.
[21]刘慧娟等.一种基于电压和频率的金属探测方法.仪器仪表学报.,2006,27(7)：769-772
[22]张学勇,赵群,李义宝,唐震.一种金属探测器的设计.安徽建筑工业学院学报.,2007,15(3)：74-77.
[23]庞瑞帆,钟翔,胡泷等.双频金属探测器的研究..解放军理工大学学报：自然科学版,2001,2(2)：1-8.
[24]刘国亭,余晋岳.金属探测器的原理与应用[J].电子技术,1984,10(2)：25-29.
[25]周学才,李传芳.一种新型高稳定度金属探测器及保护系统.电测与仪表,1997,34(2)17-20.
[26]Hiroshi Nakane, Yoshio Sohara. A Method for Simultaneously Measuring Resistivity and Permeability with a Multiayer Solenoid Coil. IEEE Transactions on Instrumentation and Measurement, vol.39,No.1:32-37,February.1990.
[27]Yoshihiro Nonaka, Hiroshi Nakane. Simultaneous Measurement of the Resistivity and Permeability of film sample with a Double Coil. IEEE Transactions on Instrumentation and Measurement, vol.44,No.3,:679-682,June.1995.
[28]Sadao Yamazaki, Negishi, H. Nakane, and A Tanaka. Basic Analysis of a Metal Detector. IEEE Trans. Instrum. Meas., vol.51, No:810-814, Aug.2002.
[29]S. Yamazaki, T. Negishi, H. Nakane, and A. Tanaka, Simultaneous Measurement of Electric and Magnetic Properties of a Spherical Sample, IEEE Trans. Instrum. Meas., vol.45,No.2: 473-477, Apr.1996.
[30]雷银照.时谐电磁场的解析方法.北京：科学出版社,2000.
[31]高晋占.微弱信号检测.北京：清华大学出版社,2004
[32]吴正毅.测试技术与测试信号处理.北京：清华大学出版社,1991.
[33]刘俊,张斌珍.微弱信号检测技术.北京：电子工业出版社,2005.
[34]聂春燕,石要武.微弱正弦信号的时域处理方法研究.计量技术,2000,5：3-5
[35]侯楚,林熊萍,王德石.基于互相关与混沌理论相结合的水下目标信号检测.鱼雷技术,2006,14(5)：17-19
[36]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.仪器仪表学报,2004,25(4)：21-22
[37]赵吉祥,陈超婵,王欢等.微弱电信号检测方法回顾.中国计量学院学报,2009,20(3)：202-208
[38]户永清.基于取样积分技术的混沌检测法与微弱正弦信号检测.绵阳师范学院学报,2009,28(8)：34-38
[39]李月,徐凯,杨宝俊等.混沌振子系统周期解几何特征分析与微弱周期信号的定量检测.物理学报,2008,57(6)：3353-3358.
[40]ZHANG Siyi, GAO Hongxia, LI Yaan, et al. A new method for detecting line spectrum of ship-radiated noise using Duffing oscillator. Chinese Science Bulletin,2007,52(14):1906-1912.
[41]王冠宇等Duffing振子检测微弱信号方法的统计特性研究.电子学报.,1998,26
[42]李月等.纳伏级正弦信号的混沌检测方法的研究.通信学报.,2003,24(4)：26-30
[43]Li T Y, Yorke J A. Period Three Implies Chaos. Ameriean Mathematical Monthly,1975, 82(10):985-992
[44]Robert L Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley,1987: 48-53
[45]郝柏林.分岔、混沌、奇怪吸引子、湍流及其它一关于确定论系统中的内在随机性.物 理学进展,1983,3(3)：333-335
[46]郝柏林.从抛物线谈器一混沌动力学引论.上海：上海科技教育：出版社,1993(10)：38-44
[47]周凌云,王瑞丽等.非线性物理理论及应用.北京：北京大学：出版社,2000.
[48]梁福明,刘式适.自然科学中的混沌与分形.北京：北京大学：出版社,2003.
[49]刘宗华.混沌动力学基础及其应用.北京：高等教育：出版社,2006.
[50]刘曾荣.混沌的微扰判据.上海：上海科技教育：出版社,1994
[51]Pecora L M, Carroll T L. Synchronization in Chaotic Systems. Phys Rev Lett,1990,64(8): 821-825
[52]Louism P. Synchronization in Chaotic Systems..Physical Rev Lett,.64(.8):821-824,Aug. 1990
[53]陈琢,钱鸣奇等.混沌态电阻测量的研究.电子测量与仪器学报,2003,17(3)：46-51
[54]Kolumban G, Vizvari B, and Mogel A. Chaotic System:a Challenge for Measurement and Analysis[C]. In:IEEE Tech Conf, Belgium,1996:1396-1401
[55]Daolin Xu, zhiguang Li. Estimation of Periodic-like Motion of Chaotic Evolutions Using Detected Unstable Periodic Pattern. Pattern Recognition Letters,2002(23):245-252
[56]A.Venkatesan, S.Parthasarathy,Mlakshmanan. Occurrence of Multiple Period-doubling Route to Chaos in Peridically Pulsed Chaotic Dynamical Systems..Solutions and Fractals,2003,18: 891-898
[57]Yung Chiahsiao, Pi-Cheng Tung. Controlling Chaos for Nonautononmous Systems by Detecting Unstable Periodic Orbit.. Solutions and Fractals,2002(13):1043-1051
[58]Li Zhongnian, Huang Tao. A New Method of Measuring WDV Based on Chaos Theory. Electronics Letters, ICEMI 2007:125-128
[59]聂春燕,徐振忠.混沌系统在弱检测信号检测中的应用..传感器技术,
[60]姜万录,吴胜强Duffing振子的两种检测微弱信号的方法及区别.燕山大学学报,2002,26(2)：114-118
[61]姜万录等Duffing振子的两种检测微弱信号的方法及区别.燕山大学学报,2002,26(2)：114-118
[62]尚秋峰等Duffing振子微弱正弦信号检测方法研究.中国电机工程学报.,2005,25(2)：66-70
[63]葛晓慧等.利用Duffing振子估计多频信号参数.浙江大学学报.,2005,25(22)：71-73
[64]Li zuping, Dong Yuguo, Yao Peiyang. A Sensitive Cell Neuron Model Based on Chaos[C].Proceedings of ICSP2000:248-251
[65]Donald.I.Birx. Chaotic Oscillators and CMFFNS for Signal Detection in Noise Environments. IEEE International Joint Conference on Neural Networks,1992(22):881-888
[66]Satish TS, Bukkaptnama, Sounder Kumara RT, Akhlesh Lakhtakia. The Neighborhood Method and Its Coupling with the Wavelet Method for Signal Separation of Chaotic signal. Signal Processing,2002(82):1351-1374
[67]Dobrowiecki T P,Schoukens J, Practical choice in the FRF measurement in presence of nonlinear distortions.IEEE transactions on Instrumentation and Measurement,,2001,50(1): 2-7
[68]张鑫等Duffing振子检测微弱正弦信号的普遍性研究.计算机与数字工程.,2005,33(12)：71-73
[69]杨建红等Duffing振子信号探测故障电弧短路保护中的的应用.电力系统自动化.,2006,30(24)：69-72
[70]ZHANG Siyi, GAO Hongxia, LI Yaan, et al. A new method for detecting line spectrum of ship-radiated noise using Duffing oscillator. Chinese Science Bulletin,2007,52(14):1906-1912.
[71]王永生等Duffing混沌系统电路仿真研究.电路与系统学报,2008,13(2)：132-135
[72]王永生等.基于初值敏感性混沌弱信号检测的性能研究.电子器件,2007,30(5)：1651-1653
[73]M Franaszek, L. Fronzoni. Resonant Response and Its Scaling Property in Chaotic Systems Perturbed by Noise. IL Nuovo Cimento,1995,17(7):775-783.
[74]杨定新等.基于随机共振电路模拟的周期信号检测.电路与系统学报.,2004,9(6)：135-138
[75]刘秉正.非线性动力学与混沌基础..长春：东北师范大学出版社,1994.
[76]王平立,宋斌,王玲.混沌时间序列的Kolmogorov熵的应用研究.计算机工程与应用,2006(21)：162-164
[77]王树禾.微分方程模型与混沌.合肥：中国科学技术大学出版社,1999：441-442,489-491
[78]吕金虎,张锁春Lyapunov指数的数值计算方法.非线性动力学学报,2003,8(1)：84-92
[79]姜健飞.数值分析及其Matlab实验.北京：科学出版社,2004：150-152.
[80]薛定宇,陈阳泉.高等应用数学问题的Matlab求解.北京：清华大学出版社.2008：221-223.
[81]Rangarajan G, Habib S, and Ryne R D. Lyapunov Exponents without Rescaling and Reorthogonalization. Physical Review Letters, vol.80,3747-3750,1998
[82]张宾,李月,卢金Lyapunov特性指数用于混沌判据.吉林大学学报(信息科学版),2004,22(2):111-114. ZHANG Bin, LI Yue, LU Jin. Study of the Lyapunov characteristic
[83]刘丁,任海鹏,李虎明.基于Lyapunov指数的弱周期信号检测. 仪器仪表学报,2005,26(12)：1215-1218.
[84]高继坤,杨焕明.运算放大器应用分析.北京：北京理工大学出版社,1989：87-89
[85]李哲英,骆丽等.电子技术及其应用基础.北京：高等教育出版社,2003：51-53
[86]孔有林.集成运算放大器及其应用.北京：人民邮电出版社,1988：321-332
[87]钱国飞.集成运算放大器基本原理及应用.北京：清华大学出版社,1984：22.
[88]熊伟,侯传教等Mutisim7电路设计及仿真应用,上海：上海交通大学出版社,2005：71-72.
[89]从宏寿,程为群等Multisim8仿真与应用实例开发.北京：清华大学出版社,2007：22.