与被测材料无关的电涡流传感器基础理论与实现方法研究
|
摘要
为消除被测材料电磁特性对电涡流传感器输出的影响、提高传感器的灵敏度和线性范围,本文以电涡流传感器基本理论、时谐电磁场理论和有限元建模理论为基础,研究了被测材料电磁特性和传感器线圈阻抗之间的关系,提出通过矢量投影方法和幅值/相位混合调制思想消除被测材料电磁特性对传感器输出的影响;同时研究了探头结构及其几何参数与线圈阻抗的关系,从而得出探头结构及其几何参数和线圈阻抗的关系,并以此指导探头结构的优化设计。
本文主要对以下几个方面进行了深入研究:
1.线圈阻抗理论计算方法的研究
根据研究需要建立了磁性/非磁性被测体下线圈阻抗的理论求解模型,从理论上推导了磁性被测体下线圈的阻抗积分表达式,在利用贝赛尔级数将阻抗积分表达式展开成级数表达式后利用Mathematic~(TM)得到了线圈阻抗值。
2.线圈阻抗数值计算方法研究
根据电涡流传感器的几何特征和边界条件,结合有限元建模理论,建立了电涡流传感器的2D和3D数值计算模型,根据电磁场时谐分析结果得到了线圈阻抗值的数值计算方法,并获得线圈阻抗值。
3.与被测材料无关的电涡流传感器基础理论研究
提出同时获取线圈电阻和感抗两个信号,通过矢量投影法消除被测材料电磁特性对传感器输出的影响;采用有限元法和试验法验证了提出的方法的正确性和可行性;根据验证结论提出了对传感器进行非线性校正的方法。
4.与被测材料无关的电涡流传感器功能电路的设计与仿真
在验证的基础上,根据提出的消除被测材料电磁特性对传感器输出影响的方法和非线性校正方法,采用幅值/相位混合调制的设计思想,利用Multisim对功能电路进行设计与仿真。
5.功能电路的功能测试试验研究
根据电路设计的特点和关键器件的性能特征,在protel DXP中进行布局和布线;制板和元器件焊接后对PCB电路进行调试。利用调试好的电路板搭建了实验平台并对电路功能进行了测试。
6.探头线圈结构及其几何参数对传感器性能影响研究
通过理论推导和有限元法从线圈形状及其几何参数和铁氧体磁芯及其几何参数两个角度研究了探头线圈结构及其几何参数对传感器阻抗与检测距离的关系曲线的影响。
以上研究不仅消除了被测材料电磁特性对传感器输出的影响,而且对线圈阻抗的研究也从非磁性被测体发展到磁性被测体;从线圈阻抗的角度探索探头结构及其几何参数对传感器性能的影响,使研究结果对探头结构的优化更具指导意义。
本文的创新点概括如下:
1.建立了磁性/非磁性被测体下传感器线圈阻抗的统一计算模型
电涡流传感器测量中被测量的变化通过线圈阻抗的变化来体现,因此线圈阻抗是传感器测量中的重要物理量。而目前关于线圈阻抗的研究主要针对非磁性被测体,对磁性被测体下线圈阻抗计算方法的研究较少。文中建立了磁性/非磁性被测体下传感器线圈阻抗的统一计算数学模型和有限元分析模型。通过数学模型详细推导了磁性/非磁性被测体下线圈阻抗的积分表达式,并针对线圈阻抗积分表达式的特点,提出采用贝塞尔级数展开并截取空气边界的方法获取线圈阻抗的理论计算值;通过有限元分析模型得到了传感器的磁场分布、被测体中的涡流分布和线圈阻抗值。该项研究使关于线圈阻抗计算方法的研究从非磁性被测体向磁性被测体拓展,进一步完善了涡流检测理论。
2.提出消除被测体电磁特性对传感器输出影响的方法
根据磁场能量守恒定理和对不同电磁特性被测体对传感器输出影响的研究,得出在相同检测距离、不同被测体下线圈电阻和感抗之间存在线性关系,据此提出采用矢量投影法消除传感器测量中被测体电磁特性影响的方法;通过试验法和有限元仿真方法验证了该方法的可行性和正确性;最后通过线圈阻抗幅值/相位混合调制思想实现了传感器输出和被测材料无关的功能。
3.通过线圈阻抗研究探头结构及其几何参数和传感器性能之间的关系
在被测参数一定的情况下,线圈阻抗变化不仅直接体现了探头结构及其参数的变化,而且阻抗变化趋势也体现了传感器性能的好坏。目前关于这方面的研究主要是通过探头结构及线圈参数对传感器的磁场分布的影响进行,而关于线圈磁场分布的理论推导存在大量假设,实验测量较困难且仪器昂贵,测量不便。与此相比,线圈阻抗的计算和测量更为方便和准确。因此提出通过线圈阻抗确定探头结构及其几何参数对传感器性能的影响关系。
Aimed at eliminating the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor and improving the sensor's performances, this thesis focuses on studying the relationship between the electromagnetic properties of measured material and the coil impedance; presents the approach that the coil impedance vectors are projected onto the projection plane and the amplitude/phase mixed modulation approach to eliminate the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor. In addition, this thesis also researches the influences of the probe structure and its geometric parameters on the coil impedance, which are helpful to optimize the probe and improve the sensor's performances.
To sum up, the following works are carried out:
1. Research on the theoretical computational method to the coil impedance
The theoretical computational model of eddy current sensor with the non-magneticand magnetic measured material is constructed, the coil impedance integral expression is deduced, and the coil impedance value is obtained by the Bessel series expansion using software package Mathematic?.
2. Research on the numerical computation method to the coil impedance
Based on the geometric characteristics and boundary conditions of eddy currentsensor, 2D and 3D finite element models of eddy current sensor are built, respectively. The coil current is obtained by the time-harmonic electromagnetic analysis, and the coil impedance value is got according to the coil current obtained before.
3. Fundamental theory for material-independent eddy current sensor
The approach that the coil impedance vectors are projected onto the projection plane is presented to eliminate the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor by extracting two signals: coil resistance signal and inductance signal; the effectivity and feasibility of the approach above is validated by finite element method and experiment method. Meanwhile, the nonlinear errors compensation approaches are presented according to the validated conclusions.
4. The functional circuit design and simulation of material-independent eddy current sensor
According to the validation conclusions and the presented approach eliminating the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor, the amplitude/phase mixed modulation approach are adopted to design, the designed circuit is simulated in software package Multisim, and the functional circuit and the fitting function method is used to compensate the nonlinear errors.
5. The experiment on the functional circuit
Based on the characteristics of designed circuit and the properties of key components, the layout and wiring of PCB is performed in software package Protel DXP; The circuit is debugged after the components are welded; The experiment platform is constructed and the function of the circuit is experimented.
6. Research on the influence of the probe structures and its geometric parameters on the sensor's performances
The influences of the probe structure and its geometric parameters on the coil impedance are investigated in terms of coil shape and its geometric parameters, the ferrite core and its geometric parameters by the theoretical deduction and finite element method. The influences of them on the sensor's performances are determined further.
The researches above can eliminate the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor, as well as result in that the study on coil impedance from the nonmagnetic measured material to the magnetic one, that the conclusions on the influence of the probe structure and its geometric parameters arrived from the coil impedance is more effective to instruct the design of probe than those from the magnetic flux distribution.
The originalities in this thesis can be summarized as follows:
1. The computational models of coil impedance under a magnetic and nonmagnetic measured material are built
The measurand of eddy current testing is embodied by the change of coil impedance. Therefore, the coil impedance is a very important physical quantity in eddy current testing. However, the present studies mainly focus on the nonmagnetic measured material, and the researches on the coil impedance under the magnetic one are limited. The mathematical model of coil impedance and finite element model under a magnetic and nonmagnetic measured material are built, respectively. Based on the mathematical model, the integral expression of coil impedance under the magnetic and nonmagnetic measured material is deduced in detail. To obtain the coil impedance value conveniently, the integral expression of coil impedance is expanded as the Bessel series and the air domain is truncated, and the impedance value is obtained by Mathematic~(TM). Based on the finite element model, the magnetic flux distribution of sensor, the eddy current distribution in measured and the coil impedance value are computed, respectively. The above research develops the research on the coil impedance computational methods from the nonmagnetic measured material to the magnetic one, which promotes the eddy current testing theory perfect.
2. The approach to eliminate the influence of the electromagnetic properties of measured material on the output voltage of sensor is presented.
According to the energy conservation principle and the conclusions arrived from the analysis to the change of coil impedance under different measured material, the phenomenon that the coil resistance and inductance under different materials and the same measurement distance is linear is discovered. Therefore, the approach that the coil impedance vectors are projected onto the projection plane is put forward to eliminate the influence of the electromagnetic properties of measured material on the output voltage of sensor, and finite element method and experiment method validate the above approach is feasible and effective. Finally, the amplitude/phase mixed modulation approach is used to design the functional circuit.
3. The relationships between the probe structure, geometric parameters and the sensor's performances are investigated in terms of coil impedance.
When the measurand is constant, the changes of the probe structure and its geometric parameters not only show the changes of coil impedance, but also affect the sensor's performances. The present studies mainly pay attention to the influence of the probe structure and its geometric parameters on the electromagnetic field distribution of eddy current sensor. However, there are many hypotheses in the theoretical deduction about the electromagnetic field distribution, it is difficult and inaccurate to measure the electromagnetic field distribution. In addition, the instrument measuring the electromagnetic field distribution is expansive. Compared with the electromagnetic field distribution, the computation and measurement to the coil impedance is more accurate and convenient. Hence, the conclusions arrived from the influences of the probe structure and its geometric parameters on the sensor's performances are more effective to instruct the design of probe and improve the sensor's performances.
本文主要对以下几个方面进行了深入研究:
1.线圈阻抗理论计算方法的研究
根据研究需要建立了磁性/非磁性被测体下线圈阻抗的理论求解模型,从理论上推导了磁性被测体下线圈的阻抗积分表达式,在利用贝赛尔级数将阻抗积分表达式展开成级数表达式后利用Mathematic~(TM)得到了线圈阻抗值。
2.线圈阻抗数值计算方法研究
根据电涡流传感器的几何特征和边界条件,结合有限元建模理论,建立了电涡流传感器的2D和3D数值计算模型,根据电磁场时谐分析结果得到了线圈阻抗值的数值计算方法,并获得线圈阻抗值。
3.与被测材料无关的电涡流传感器基础理论研究
提出同时获取线圈电阻和感抗两个信号,通过矢量投影法消除被测材料电磁特性对传感器输出的影响;采用有限元法和试验法验证了提出的方法的正确性和可行性;根据验证结论提出了对传感器进行非线性校正的方法。
4.与被测材料无关的电涡流传感器功能电路的设计与仿真
在验证的基础上,根据提出的消除被测材料电磁特性对传感器输出影响的方法和非线性校正方法,采用幅值/相位混合调制的设计思想,利用Multisim对功能电路进行设计与仿真。
5.功能电路的功能测试试验研究
根据电路设计的特点和关键器件的性能特征,在protel DXP中进行布局和布线;制板和元器件焊接后对PCB电路进行调试。利用调试好的电路板搭建了实验平台并对电路功能进行了测试。
6.探头线圈结构及其几何参数对传感器性能影响研究
通过理论推导和有限元法从线圈形状及其几何参数和铁氧体磁芯及其几何参数两个角度研究了探头线圈结构及其几何参数对传感器阻抗与检测距离的关系曲线的影响。
以上研究不仅消除了被测材料电磁特性对传感器输出的影响,而且对线圈阻抗的研究也从非磁性被测体发展到磁性被测体;从线圈阻抗的角度探索探头结构及其几何参数对传感器性能的影响,使研究结果对探头结构的优化更具指导意义。
本文的创新点概括如下:
1.建立了磁性/非磁性被测体下传感器线圈阻抗的统一计算模型
电涡流传感器测量中被测量的变化通过线圈阻抗的变化来体现,因此线圈阻抗是传感器测量中的重要物理量。而目前关于线圈阻抗的研究主要针对非磁性被测体,对磁性被测体下线圈阻抗计算方法的研究较少。文中建立了磁性/非磁性被测体下传感器线圈阻抗的统一计算数学模型和有限元分析模型。通过数学模型详细推导了磁性/非磁性被测体下线圈阻抗的积分表达式,并针对线圈阻抗积分表达式的特点,提出采用贝塞尔级数展开并截取空气边界的方法获取线圈阻抗的理论计算值;通过有限元分析模型得到了传感器的磁场分布、被测体中的涡流分布和线圈阻抗值。该项研究使关于线圈阻抗计算方法的研究从非磁性被测体向磁性被测体拓展,进一步完善了涡流检测理论。
2.提出消除被测体电磁特性对传感器输出影响的方法
根据磁场能量守恒定理和对不同电磁特性被测体对传感器输出影响的研究,得出在相同检测距离、不同被测体下线圈电阻和感抗之间存在线性关系,据此提出采用矢量投影法消除传感器测量中被测体电磁特性影响的方法;通过试验法和有限元仿真方法验证了该方法的可行性和正确性;最后通过线圈阻抗幅值/相位混合调制思想实现了传感器输出和被测材料无关的功能。
3.通过线圈阻抗研究探头结构及其几何参数和传感器性能之间的关系
在被测参数一定的情况下,线圈阻抗变化不仅直接体现了探头结构及其参数的变化,而且阻抗变化趋势也体现了传感器性能的好坏。目前关于这方面的研究主要是通过探头结构及线圈参数对传感器的磁场分布的影响进行,而关于线圈磁场分布的理论推导存在大量假设,实验测量较困难且仪器昂贵,测量不便。与此相比,线圈阻抗的计算和测量更为方便和准确。因此提出通过线圈阻抗确定探头结构及其几何参数对传感器性能的影响关系。
Aimed at eliminating the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor and improving the sensor's performances, this thesis focuses on studying the relationship between the electromagnetic properties of measured material and the coil impedance; presents the approach that the coil impedance vectors are projected onto the projection plane and the amplitude/phase mixed modulation approach to eliminate the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor. In addition, this thesis also researches the influences of the probe structure and its geometric parameters on the coil impedance, which are helpful to optimize the probe and improve the sensor's performances.
To sum up, the following works are carried out:
1. Research on the theoretical computational method to the coil impedance
The theoretical computational model of eddy current sensor with the non-magneticand magnetic measured material is constructed, the coil impedance integral expression is deduced, and the coil impedance value is obtained by the Bessel series expansion using software package Mathematic?.
2. Research on the numerical computation method to the coil impedance
Based on the geometric characteristics and boundary conditions of eddy currentsensor, 2D and 3D finite element models of eddy current sensor are built, respectively. The coil current is obtained by the time-harmonic electromagnetic analysis, and the coil impedance value is got according to the coil current obtained before.
3. Fundamental theory for material-independent eddy current sensor
The approach that the coil impedance vectors are projected onto the projection plane is presented to eliminate the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor by extracting two signals: coil resistance signal and inductance signal; the effectivity and feasibility of the approach above is validated by finite element method and experiment method. Meanwhile, the nonlinear errors compensation approaches are presented according to the validated conclusions.
4. The functional circuit design and simulation of material-independent eddy current sensor
According to the validation conclusions and the presented approach eliminating the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor, the amplitude/phase mixed modulation approach are adopted to design, the designed circuit is simulated in software package Multisim, and the functional circuit and the fitting function method is used to compensate the nonlinear errors.
5. The experiment on the functional circuit
Based on the characteristics of designed circuit and the properties of key components, the layout and wiring of PCB is performed in software package Protel DXP; The circuit is debugged after the components are welded; The experiment platform is constructed and the function of the circuit is experimented.
6. Research on the influence of the probe structures and its geometric parameters on the sensor's performances
The influences of the probe structure and its geometric parameters on the coil impedance are investigated in terms of coil shape and its geometric parameters, the ferrite core and its geometric parameters by the theoretical deduction and finite element method. The influences of them on the sensor's performances are determined further.
The researches above can eliminate the influence of the electromagnetic properties of measured material on the output voltage of eddy current sensor, as well as result in that the study on coil impedance from the nonmagnetic measured material to the magnetic one, that the conclusions on the influence of the probe structure and its geometric parameters arrived from the coil impedance is more effective to instruct the design of probe than those from the magnetic flux distribution.
The originalities in this thesis can be summarized as follows:
1. The computational models of coil impedance under a magnetic and nonmagnetic measured material are built
The measurand of eddy current testing is embodied by the change of coil impedance. Therefore, the coil impedance is a very important physical quantity in eddy current testing. However, the present studies mainly focus on the nonmagnetic measured material, and the researches on the coil impedance under the magnetic one are limited. The mathematical model of coil impedance and finite element model under a magnetic and nonmagnetic measured material are built, respectively. Based on the mathematical model, the integral expression of coil impedance under the magnetic and nonmagnetic measured material is deduced in detail. To obtain the coil impedance value conveniently, the integral expression of coil impedance is expanded as the Bessel series and the air domain is truncated, and the impedance value is obtained by Mathematic~(TM). Based on the finite element model, the magnetic flux distribution of sensor, the eddy current distribution in measured and the coil impedance value are computed, respectively. The above research develops the research on the coil impedance computational methods from the nonmagnetic measured material to the magnetic one, which promotes the eddy current testing theory perfect.
2. The approach to eliminate the influence of the electromagnetic properties of measured material on the output voltage of sensor is presented.
According to the energy conservation principle and the conclusions arrived from the analysis to the change of coil impedance under different measured material, the phenomenon that the coil resistance and inductance under different materials and the same measurement distance is linear is discovered. Therefore, the approach that the coil impedance vectors are projected onto the projection plane is put forward to eliminate the influence of the electromagnetic properties of measured material on the output voltage of sensor, and finite element method and experiment method validate the above approach is feasible and effective. Finally, the amplitude/phase mixed modulation approach is used to design the functional circuit.
3. The relationships between the probe structure, geometric parameters and the sensor's performances are investigated in terms of coil impedance.
When the measurand is constant, the changes of the probe structure and its geometric parameters not only show the changes of coil impedance, but also affect the sensor's performances. The present studies mainly pay attention to the influence of the probe structure and its geometric parameters on the electromagnetic field distribution of eddy current sensor. However, there are many hypotheses in the theoretical deduction about the electromagnetic field distribution, it is difficult and inaccurate to measure the electromagnetic field distribution. In addition, the instrument measuring the electromagnetic field distribution is expansive. Compared with the electromagnetic field distribution, the computation and measurement to the coil impedance is more accurate and convenient. Hence, the conclusions arrived from the influences of the probe structure and its geometric parameters on the sensor's performances are more effective to instruct the design of probe and improve the sensor's performances.
引文
[1]何金田.传感器技术(上、下册)[M].哈尔滨:哈尔滨工业大学出版社.2004:1-10.
[2]何希才,薛永毅,姜余祥.传感器技术及应用[M].北京:北京航空航天大学出版社.2005:1-15.
[3]美国无损检测学会.美国无损检测手册(电磁卷)[M].世界图书出版社.1996:1-296.
[4]Tai Ch.Ch.,Rose J.H,Moulder J.C.Thickness and conductivity of metallic layers from pulsed eddy-current measurement[J].Review of Scientific Instruments.1996.67(11):3965 - 3972.
[5]Hamasaki Y,Ide T.Fabrication of multi-layer eddy current micro sensors for non-destructive inspection of small diameter pipes[C].Proceedings of the 8th IEEE Workshop on Micro Electro Mechanical Systems,Amsterdam(Netherlands),29 Jan.-2 Feb.1995:232-237.
[6]黄平捷,吴昭同,严仍春.多层厚度电涡流检测阻抗模型仿真及验证[J].仪器仪表学报.2004.25(4):24-28.
[7]黄平捷,侯迪波,周泽魁.多层导电结构缺陷电涡流扫描检测信号预处理技术研究[J].传感技术学报.2006.19(1):222-227.
[8]黄卡玛,赵翔.电磁场中的逆问题及应用[M].北京:科学出版社.2005:1-58.
[9]杨涛,付宜利,马玉林等.铣削颤振特征提取的小波包和主成分分析方法[J].哈尔滨工业大学学报.2001.33(6):758-762.
[10]Tian G.Y,Sophian A,Taylor D,et.al.Wavelet-based PCA defect classification and quantification for pulsed eddy current NDT[J].IEE Proc.-Sci.Meas.Technol..2005.152(4):141-148.
[11]吴今培.基于核函数的主成分分析及应用[J].系统工程.2005.23(2):117-120.
[12]Zhu X.L,Zhang X.D,Ding Z.Zh,et.al.Adaptive Nonlinear PCA Algorithms for Blind Source Separation Without Prewhitening[J].IEEE Transactions on Circuits and Systems.2006.53(3):745-753.
[13]Xie X.D,Lain K.M.Gabor-Based Kernel PCA With Doubly Nonlinear Mapping for Face Recognition With a Single Face Image[J].IEEE Transactions on Image Processing.2006.15(9):2481-2492.
[14]夏庆观,路红,陈桂.基于小波神经网络的零件图像特征提取和识别[J].仪器仪表学报.2005.26(8):611-613.
[15]韩琦,康戈文.基于小波变换的带钢表面缺陷分形特征研究[J].自动化技术与应用.2006.25(3):4-6.
[16]Wang X.A Novel Signal Feature Extraction Method Based on Wavelet Analysis[C].Proceedings of the 6th World Congress on Intelligent Control and Automation,June 21-23,Dalian,China.2006:4967-1971.
[17]Li L.Q,Tsukada K,Liu Zh.Fusion of Multi-Frequency Eddy Current Signals by Using Wavelet Analysis Method[C].Proceedings of the Fifth International Conference on Information Fusion.2002:108-113.
[18]Acharyya M,De R.K,Du K.K.Extraction of Features Using M-Band Wavelet Packet Frame and Their Neuro-Fuzzy Evaluation for Multitexture Segmentation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.2003.25(12):1639-1644.
[19]Li D.Q,Pedrycz W,Nicolino J.P.Fuzzy Wavelet Packet Based Feature Extraction Method and Its Application to Biomedical Signal Classification[J].IEEE Transactions on Biomedical Engineering.2005.52(6):1132-1139.
[20]Stefanos K.G,Michael E.Z,Stavrakakis G.S.Classification of Washing Machines Vibration Signals Using Discrete Wavelet Analysis for Feature Extraction[J].IEEE Transactions on Instrumentation and Measurement.2002.51(3):497-508.
[21]Li Sh.T,Liao Ch,Kwok T.J.Wavelet-Based Feature Extraction for Microarray Data Classification[C].Proceedings of 2006 International Joint Conference on Neural Networks Sheraton Vancouver Wall Centre Hotel,Vancouver,BC,Canada,July 16-21.2006:5028-5033.
[22]Li Yue,Udpa L,Udpa S.S.Three-Dimensional Defect Reconstruction From Eddy-Current NDE Signals Using a Genetic Local Search Algorithm[J].IEEE Transactions on Magnetics.2004.40(2):410-417.
[23]Tomasz Ch,Masato E,Ryszard S,et.al.Natural Crack Recognition Using Inverse Neural Model and Multi-Frequency Eddy Current Method[J].IEEE Transactions on Magnetics.2001.37(4):2797-2799.
[24]Yoshiaki N,Toshiyuki T,Tetsuya U,et.al.Identification of Multiple Cracks from Eddy-Current Testing Signals with Noise Sources by Image Processing and Inverse Analysis[J].IEEE Transactions on Magnetics.2004.40(2):1112-1115.
[25]Grimberg R,Udpa L,Savin A.2D Eddy Current Sensor Array[J].NDT&E International.39(2006):264-271.
[26]陈祥林,丁天怀,黄毅平.新型接近式柔性电涡流阵列传感器系统[J].机械工程学报. 2006.26(8):150-153.
[27]Tomasz C,Masato E,Ryszard S.Neural Network Models of Eddy Current Multi-Frequency System for Nondestructive Testing[J].IEEE Transactions on Magnetics.2000.36(4):1724-1727.
[28]Yang B.F,Luo F.L,Cao X.H,et.al.Array Pulsed Eddy Current Imaging System Used to Detect Corrosion[J].Chinese Journal of Mechanical Engineering.2005.18(2):196-198.
[29]Clauzon T,Thollon F,Nicolas A.Flaws Characterization with Pulsed Eddy Currents NDT[J].IEEE Transactions on Magnetics.1999.35(3):1873-1876.
[30]Kreutzbruck M.V,Allweins K,Ruhl T,et.al.Defect Detection and Classification using a SQUID based Multiple Frequency Eddy Current NDE System[J].IEEE Transactions on Applied Superconductivity.2001.11(1):1032-1037.
[31]Tian G.Y,Sophian A,Taylor D,et.al.Multiple Sensors on Pulsed Eddy-Current Detection for 3-D Subsurface Crack Assessment[J].IEEE Sensors Journal.2005.5(1):90-96.
[32]X.Jian,S.Dixon.Enhancement of EMAT and eddy current using a ferrite back-plate[J].Sensors and Actuators.A.136(2007):132-136
[33]徐平,罗飞路,张玉华.基于脉冲涡流检测技术的缺陷定量检测研究[J].计量测试与检定.2006.16(2):6-10.
[34]时振堂,陈德智.涡流检测信号小波除噪与缺陷特征提取[J].无损检测.2003.25(9):472-477.
[35]庄弘炜,马逸尘,张志斌等.涡流检测中识别缺陷形状的一种新方法[J].应用数学和力学.2005.26(11):1380-1386.
[36]Dodd C.V,Deeds W.E.Analytical solutions to eddy-current probe-coil problems[J].Journal ofApplied Physics,39(6),1968,2829-2837.
[37]Luquire J.W,Deeds W.E,Dodd C.V.Alternating current distribution between planar conductors [J].Journal of Applied Physics,1970,41(10):3983-3991.
[38]Garcia.A,Carrasco J.A,Soto J.F,et al.A Method for Calculating the Magnetic Field Produced by A Coil of Any Shape[J].Sensors and Actuators:A.91(2001):230-232.
[39]Fava J.O,Marta C.R.Calculation and Simulation of Impedance Diagrams of Planar Rectangular Spiral Coils for Eddy Current Testing[J].NDT & E International.39(2006):414-424.
[40]Ditchburn R.J,Burke S.K.Planar Rectangular Spiral Coils in Eddy-Current Non-Destructive Inspection[J].NDT & E International.38(2005):690-700.
[41]Theodoros P.T,Epameinondas E.K.Impedance Evaluation of Rectangular Coils for Eddy Current Testing of Planar Media[J].NDT & E international.35(2002):407-414.
[42]雷银照.时谐电磁场解析方法[M].北京:科学出版社.2000:120-194.
[43]Mayergoyz I.Boundary Integral Equations of Minimum Order for the Calculation of Three-dimensional Eddy Current Problems[J].IEEE Transactions on Magnetics.1982.18(2):536 -539.
[44]Jenkins S.A,Bowler J.R.Calculations of the Flaw Signal Generated by A Differential Eddy Current Probe[J].NDT & E International.1997.30(3 ):829-835.
[45]Bahramgiri M,Barkcshli K.Non-Destructive Testing of Cracks Using Eddy Currents and a Generalized Regression Neural Network(GRNN)[C].IEEE Antennas and Propagation Society International Symposium.2003:239-242.
[46]John B.Eddy-Current Inversion for the Determination of Crack Geometry[C].IEE Colloquium on New Applications in Modelling and Inversion Techniques for Non-Destructive Testing.London.UK.1999:1-4.
[47]Juillard J,Barmon B.D,Berthiau G.Simple Analytical Three-Dimensional Eddy-Current Model [J].IEEE Transactions on Magnetics.2000.36(1):258-266.
[48]Páivó J,Lesselier D.Calculation of Eddy Current Testing Probe Signal With Global Approximation[J].IEEE Transactions on Magnetics.2006.42(4):1419-1422.
[49]Bowler J.R,Harfield N.Thin-Skin Eddy-Current Interaction with Semielliptical and Epicyclic Cracks[J].IEEE Transactions on Magnetics.2000.36(1 ):281-291.
[50]Lee H.B,Kim D.H.Impedance Calculation for a Plate with Crack in Eddy Current NDT Using 3D Indirect BIEM[J].IEEE Transactions on Magnetics.2000.36(5):3131-3133.
[51]Theodoros T,Epameinondas K.Series expansions in eddy current nondestructive evaluation models[J].Journal of Material Processing Technology.2005.161(1-2):343-347.
[52]雷银照,马信山.涡流线圈的阻抗计算[J].电工技术学报.1996.11(1):17-20.
[53]Ma Ch.F.A Finite-Element Approximation of a Quasi- Magnetostatic 3D Eddy Current Model by Fractional-Step A-φ Scheme[J].Mathematical and Computer Modelling.39(2004):567-580.
[54]Morozov M,Rubinacci G,Tamburrino A,et.al.Numerical Models of Volumetric Insulating Cracks in Eddy-Current Testing With Experimental Validation[J].IEEE Transactions on Magnetics.2006.42(5):1568-1576.
[55]Mihalache O,Grimberg R,Radu E,et.al.Finite Element Numerical Simulation for Eddy Current Transducer with Orthogonal Coils[J].Sensors and Actuators A:Physical.1997.59(1-3): 213-218.
[56] Bermudez A, Bull6n J, Pena F, et.al. A Numerical Method for Transient Simulation of Metallurgical Compound Electrodes [J]. Finite Elem. Anal. Des.. 39(2003): 283-299.
[57] Liu Ch.P, Lin T.K. Study of Eddy Current Power Loss from Outer-Winding Coils of a Magnetic Position Sensor [J]. Journal of Magnetism and Magnetic Materials. 209(2000): 201-204.
[58] Bermudez A, Rodriguez R, Salgado P. A Finite Element Method with Lagrange Multipliers for Low-frequency Harmonic Maxwell Equations [J]. SIAM J. Numer. Anal. 40(2002): 1823-1848.
[59] Bermridez A, Rodriguez R, Salgado P. Modelling and numerical treatment of boundary data in an eddy currents problem [J]. C. R. Acad. Sci.Paris. 335(2002): 633-638.
[60] Hashizume H, Yamada Y, Miya K, et.al. Numerical and Experimental Analysis of Eddy Current Testing for A tube with cracks [J]. IEEE Transactions on Magnetics. 28(2005): 1469-1472.
[61] Bermudez A, Rodriguez R, Salgado P. Numerical analysis of the electric field formulation of an eddy current problem [J]. Numerical Analysis. 337(2003): 359-364.
[62] Bermudez A, Rodriguez R, Salgado P, et.al. Numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via Lagrange multipliers [J].Mathematics of Computation. 74(2005): 123-151.
[63] Ludwig R, Dai X. W. Numerical and Analytical Modeling of Pulsed Eddy Currents in a Conducting Half-space [J]. IEEE Transactions on Magnetics. 1990. 26(1): 299-307.
[64] Dai X.W, Ludwig R, Palanisamy R. Numerical Simulation of Pulsed Eddy-Current Nondestructive Testing Phenomena [J]. IEEE Transactions on Magnetics. 1990. 26(6):3089-3093.
[65] Patel U, Rodger D. Finite Element Modelling Of Pulsed Eddy Currents For Nondestructive Testing [J]. IEEE Transactions on Magnetics. 1996. 32(3): 1593-1596.
[66] Wilde J, Lai Y.Q. Design optimization of an eddy current sensor using the finite-elements method [J]. Microelectronics Reliability. 43(2003): 345-349.
[67] Tanaka M, Tsuboi H. Finite Element Model of Natural Crack in Eddy Current Testing Problem [J]. IEEE Transactions on Magnetics. 2001. 37(5): 3125-3128.
[68] Noritaka Yusa, Stephane Perrin, Kazue Mizuno, et.al. Numerical modeling of general cracks from the viewpoint of eddy current simulations[J] .NDT&E International. 40 (2007): 577-583.
[69] Gabriel P, Bogdan C.C, Florea I, et.al. Nonlinear FEM-BEM Formulation and Model-Free Inversion Procedure for Reconstruction of Cracks Using Pulse Eddy Currents [J]. IEEE Transactions on Magnetics. 2002. 38(2): 1241-1244.
[70]Takahashi Y,Wakao S.Large-Scale Analysis of Eddy-Current Problems by the Hybrid Finite Element-Boundary Element Method Combined With the Fast Multipole Method[J].IEEE Transactions on Magnetics.2006.42(4):671-674.
[71]Viana S.A,Rodger D,Lai H.C.Application of the Local Radial Point Interpolation Method to Solve Eddy-Current Problems[J].IEEE Transactions on Magnetics.2006.42(4):591-594.
[72]王春兰,张钢,董鲁宁等.电涡流传感器的有限元仿真研究与分析[J].传感器与微系统.2006.25(2):41-44.
[73]周丹丽,赵辉,刘伟文.电涡流传感器建模与仿真分析[J].传感器技术.2005.24(5):28-30.
[74]蒋齐密,张新访,刘土光.电涡流检测系统的参数设置依据[J].无损检测.2001.23(3):100-103.
[75]蒋齐密,张新访,刘土光.电涡流检测系统仿真分析的前处理技术[J].计算机仿真.2001.18(1):46-49.
[76]蒋齐密,张新访,刘土光.电涡流检测系统中的电磁场仿真[J].计算机仿真.2000.17(5):36-39.
[77]贾永平,丁天怀,王鹏.曲面体间隙电涡流检测的有限元分析[J].传感技术学报.2005.18(2):221-224.
[78]周丹丽,赵辉,刘伟文等.基于三维有限元的电涡流传感器参数的仿真研究[J].计算机测量与控制.2005.13(6):618-620.
[79]Tian G.Y,Zhao Z.X,Baines R.W.The Research of Inhomogeneity in Eddy Current Sensors[J].Sensors and Actuators:A.69(1998):148-151.
[80]单成祥.传感器理论与设计基础及其应用[M].北京:国防工业出版社.1999:1-228.
[81]曲民兴,司家屯.电磁无损检测与数值计算(第三讲)--涡流检测探头信号的有限元预估[J].无损检测.1994.16(6):172-177.
[82]Theodoros P.T,Epameinondas E.K.Impedance Evaluation of Rectangular Coils for Eddy Current Testing of Planar Media[J].NDT & E international.35(2002):407-414.
[83]Ditchburn R.J,Burke S.K.Planar Rectangular Spiral Coils in Eddy-Current Non-Destructive Inspection[J].NDT & E International.38(2005):690-700.
[84]Buvat F,Pichenot G,Premel D,et al.Eddy-Current Modeling of Ferrite-Cored Probes[C].Proceedings of AIP Conference.760(2005):463-470.
[85]Sabbagh H.A.A Model of Eddy-Current Probes with Ferrite Cores[J].IEEE Transactions on Magnetics.1987.23(3):1888-1904.
[86]Burke S.K.A Semi-empirical Model for Eddy-Current NDE Using Ferrite-Cored Probes[J].Nondestructive Testing and Evaluation.1992.6(5):267-277.
[87]黄浩,陆继明,毛承雄等.Rogowski线圈结构参数仿真研究[J].电力系统及其自动化学报.3(2004):72-75.
[88]王军平,王安,樊文侠.电涡流传感器线圈参数对传感器性能的影响[J].自动化仪表.2001.22(12):22-24.
[89]黄小秋,丁天怀,付志斌.简化目标函数的电涡流传感器线圈参数优化设计法[J].传感器技术.11(2000):3-5.
[90]许德章.电涡流传感器信号调理电路的设计[J].自动化仪表.1998.19(6):37-39.
[9l]邵爱霞。赵辉,刘伟文.定频调幅式电涡流传感器电路及其在防水数显卡尺中的应用[J].计算机测量与控制.2005.13(5):508-510.
[92]张珍明,劳奇成,李平等.电感式传感器信号处理模块的研制[J].计量技术.9(1999):11-13.
[93]邵爱霞,赵辉,刘伟文.基于MSP430的定频调幅式电涡流传感器位移测量系统[J].计量技术.4(2005):29-31.
[94]贾智伟,刘红飞,李应红.传感器信号的非线性补偿[J].传感器技术.2002.21(5):30-32.
[95]刘清.传感器模糊神经网络非线性误差补偿的研究[J].自动化仪表.2006.27(3):11-14.
[96]蒋小燕,徐大诚.基于BP神经网络的压力传感器非线性校正方法[J].苏州大学学报(自然科学版.2005.21(4):54-58.
[97]芦俊,陈俊杰,颜景平.基于遗传算法的传感器系统的非线性校正[J].仪表技术与传感器.6(2001):38-40.
[98]王生铁,王志和,傅闯.铂电阻温度传感器非线性校正的新方法[J].仪表技术与传感器.2(2000):40-42.
[99]Ricken W.L.Optimisation of Parameters of an Eddy Current Sensor Used for a Displacement Measurement[J].Technisches Messen..2004.71(9):460-465.
[100]方秋华,茅佩,田新启.电涡流传感器温度漂移的自动补偿[J].仪器仪表学报.1997.18(2):198-201.
[101]Li Q.P,Ding F.Novel Displacement Eddy Current Sensor with Temperature Compensation for Electrohydranlic Valves[J].Sensors and Actuators:A.122(2005):83-87.
[102]肖茂森,原思聪,钟春生等.PIC单片机芯片在电涡流传感器温度补偿中的应用[J].工业,计量.2005.15(1):16-18.
[103]Yann L.B.3-D Finite-Element Analysis of Eddy-Current Evaluation of Curved Plates[J]. IEEE Transactions on Magnetics.2002.38(2):1161-1164.
[104]Sophian A,Tian G.Y,Taylor D,et.al.Design of a Pulsed Eddy Current Sensor for Detection of Defects in Aircraft Lap-joints[J].Sensors and Actuators:A.101(2002):92-98.
[105]徐志刚,张栋,傅国如.飞机机翼与机身连接螺栓裂纹分析[J].腐蚀科学与防护技术.2005.17(4):286-287.
[106]Maeda N,Yamaguchi A,Sugibayashi T,et.al.Degradation Detection of Material Used in Nuclear Power Plant Components Applying Probe-type Eddy Current Sensor - Part 2 Detection of Fatigue and Irradiation Embrittlement in Low Alloy Steel for Reactor Pressure Vessel[J].Journal of the Japanese Society for Non-Destructive Inspection.1997.46(2):127-133.
[107]Joubert P.Y,Bihan Y.L,Placko D.Localization of defects in steam generator tubes using a multi-coil eddy current probe dedicated to high speed inspection[J].NDT & E International.2002.35(1):53-59.
[108]徐可君,江龙平.航空燃气涡轮发动机工作叶片疲劳与寿命[J].航空制造技术.6(1998):20-22.
[109]张明恩,薛世峰,张治坤.航空燃气涡轮发动机状态监控和技术诊断导论[J].沈阳航空工业学院学报.1994.28(4):82-88.
[110]Song S.J,Shin Y.K.Eddy Current Flaw Characterization in Tubes by Neural Networks and Finite Element Modeling[J].NDT&E International.33(2000):233-243.
[111]Hur D.H,Lee D.H,Choi M.S,et.al.Discrimination Method of Through-Wall Cracks in Steam Generator Tubes using Eddy Current Signals[J].NDT&E International.39(2006):361-366.
[112]金涛,阙沛文,陶正苏.小波神经网络在海底石油管道漏磁缺陷检测中的应用[J].石油大学学报(自然科学版).2005.29(3):83-87.
[113]徐小力,梁福平,许宝杰等.旋转机械状态监测及预测技术的发展与研究[J].建筑机械技术与管理.7(2003):20-24.
[114]李博,翁莹,佟海云.电涡流传感器在汽轮发电机组的应用及标定[J].宝钢科技.2005.31(5):36-38.
[115]F.Vachera,F.Alvesb,C.Gilles-Pascauda.Eddy current nondestructive testing with giant magneto-impedance sensor[J].NDT&E International.40(2007):439-442.
[116]孙建民,杨清梅.传感器技术[M].北京:清华大学出版社,北京交通大学出版社.2005:1-109.
[117]陈行禄,吴志鹤.传感器原理[M].北京:航空工业出版社.1987:1-153.
[118]游凤荷,陈丹,牛龙江.涡流三维磁场测量及实际渗透深度建模[J].仪器仪表学报.2002. 23(4):431-434.
[119]杜平安,甘娥忠,于亚婷.有限元法--原理、建模及应用[M].北京:国防工业出版社.2004:1-272.
[120]Thomas G.K,Madabushi V.K.The Application of Finite Element Method Analysis to Eddy Current Nondestructive Evaluation[J].IEEE Transactions on Magnetics.1979.15(6):1956-1960.
[121]胡之兴.电机电磁场的分析与计算(修订本)[M].北京:机械工业出版社.1989:1-234.
[122]邵惠民.数学物理方法[M].北京:科学出版社.2005:44-325.
[123]Vyroubal D.Impedance of the Eddy-Current Displacement Probe:the Transformer Model[J].IEEE Transactions on Instrumentation and Measurement,2004.53(2):384-391.
[124]全泽松.电磁场理论[M].成都:电子科技大学出版社.1995:1-30.
[125]南京工学院数学教研组编.数学物理方程与特殊函数[M].北京:高等教育出版社.1990:101-126.
[126]张韵华.Mathematic符号计算系统实用教程[M].合肥:中国科学技术大学出版社.1998:1-141.
[127]于亚婷,杜平安,王振伟.有限元法应用现状研究[J].机械设计.2005.22(3):6-9.
[128]Li J.Ch.Optimal Error Estimates of Mixed Finite Element Methods for A Fourth-Order Nonlinear Elliptic Problem[J].Journal of Mathematical Analysis and Applications.2007.334(1):183-195.
[129]Lynn K.M,Isobe D.Structural Collapse Analysis of Framed Structures under Impact Loads using ASI-Gauss Finite Element Method[J].International Journal of Impact Engineering.2007.34(9):1500-1516.
[130]Byon S.M,Kim H.S,Lee Y.Investigation of the Size Effect on Crack Propagation using Finite Element Method and Strain Gradient Plasticity[J].Journal of Materials Processing Technology.2007.191(1-3):193-197.
[128]Toparli M,Sen F,Culha O,et.al.Thermal Stress Analysis of HVOF Sprayed WC-Co/NiA1Multilayer Coatings on Stainless Steel Substrate using Finite Element Methods[J].Journal of Materials Processing Technology.2007.190(1-3):26-32.
[132]Kujime T,Tane M,Hyun S.K,et.al.Three-Dimensional Image-Based Modeling of Lotus-Type Porous Carbon Steel and Simulation of Its Mechanical Behavior by Finite Element Method[J].Materials Science and Engineering:A.2007(460-461):220-226.
[133]Shin D.S,Lee K,Kim D.Biomechanical Study of Lumbar Spine with Dynamic Stabilization Device using Finite Element Method[J].Computer-Aided Design.2007.39(7):559-567.
[134]Tber M.H,Talibi M.E.A Finite Element Method for Hydraulic Conductivity Identification in a Seawater Intrusion Problem[J].Computers & Geosciences.2007.33(7):860-874.
[135]Park K.S,VanTyne Ch.J,Moon Y.H.Process Analysis of Multistage Forging by using Finite Element Method[J].Journal of Materials Processing Technology.2007(187-188):586-590.
[136]Ma Ch.F,Wang D.Sh.Finite Element Analysis of An A-ψ Method for Time-Dependent Maxwell's Equations based on Explicit-Magnetic-Field Scheme[J].Applied Mathematics and Computation.2007.190(2):1273-1283.
[137]Zhang H.W,Rong Ch.B,Du X.B,et.al.Investigation on the Coercivity and Remanence of Single-Phase Nanocrystalline Permanent Magnets by Micromagnetic Finite-Element Method [J].Journal of Magnetism and Magnetic Materials.2004.278(I-2):127-137.
[138]Liu G.Nan C.W,Cai N,et.al.Calculations of Giant Magnetoelectric Effect in Multiferroic Composites of Rare-Earth-Iron Alloys and PZT by Finite Element Method[J].International Journal of Solids and Structures.2004.41(16-17):4423-4434.
[139]吕英华.计算电磁学的数值方法[M].北京:清华大学出版社.2006:1-481.
[140]杜平安.建立有限元模型的基本原则[J].机械与电子.2001(4):40-42.
[141]博弈创作室.APDL参数化有限元分析技术及其应用实例[M].北京:中国水利水电出版社2005:1-115.
[142]小飒工作室.最新经典ANSYS及Workbench教程[M].北京:电子工业出版社.2004:564-615
[143]Yann L.B.Study on the Transformer Equivalent Circuit of Eddy Current Nondestructive Evaluation[J].NDT&E International.36(2003):297-302.
[144]张秀敏,苑津莎,崔翔.用棱边与节点有限元耦合的E-E-ψ法计算三维涡流场[J].中国电机工程学报.2003.21(3):70-74.
[145]王泽忠,王炳革,卢斌先等.三维开域涡流场A-V位有限元与边界元耦合分析方法[J].中国电机工程学报.2000.20(5):1-4.
[146]雷银照,马信山.三维探伤涡流场的研究与线圈阻抗计算[J].电机工程学报.1996.16(5):289-294.
[147]袁建生,宗伟.计算三维涡流场的三分量边界元法[J].中国电机工程学报.1999.19(5):27-29.
[148]梁晋文,陈林才,何贡.误差理论与数据处理[M].中国计量出版社.2001:95-135.
[149]中国材料实用手册编委会.工程材料实用手册(1,2,3,4)[M].中国标准出版社.1988: 815-420,5-385,9-368,581-867.
[150]张志涌.精通MATLAB 6.5版[M].北京:北京航空航天大学出版社.2003:1-265.
[151]周剑平.精通Origin7.0[M].北京:北京航空航天大学出版社.2004:1-135.
[152]段九州.振荡电路实用设计手册[M].沈阳:辽宁科学技术出版社.2002:1-21.
[153]郭荣祥,周惠潮。常用电子元件及典型应用[M].北京:电子工业出版社.2005:104-194.
[154]黑天彻.电子元器件应用技术[M].北京:科学出版社.2006:179-203.
[155]朱达斌,张宝玉,李亦群等.高速运算放大器应用技术[J].电子技术应用.1998(4):68-70.
[156]森荣二.LC滤波器设计与制作[M].北京:科学出版社.2006:49-59.
[157]李学厚.负载接地的单支运放电压--电流变换器[J].大连水产学院学报.1997.12(4):45-48.
[158]稻叶保.模拟技术应用技巧101例[M].北京:科学出版社.2004:65-170.
[159]张伟.电路设计与制板--Protel DXP入门与提高[M].北京:人民邮电出版社.2003:20-243.
[160]倪泽峰,江中华.电路设计与制板--Protel DXP典型实例[M].北京:人民邮电出版社.2003:87-348.
[161]Capobianco T.E,Splett J.D,Iyer H.K.Eddy Current Sensitivity as a Function of Coil Construction Parameters[J].Research in Nondestructive Evaluation.1990.2(3):169-186.
[162]张宝裕,刘恒基.磁场的产生[M].北京:机械工业出版社.1987:1-116.
[163][日]大森丰明编.刘代琦,梁宇青译.磁性材料手册[M].北京:机械工业出版社.1985:183-335.
[2]何希才,薛永毅,姜余祥.传感器技术及应用[M].北京:北京航空航天大学出版社.2005:1-15.
[3]美国无损检测学会.美国无损检测手册(电磁卷)[M].世界图书出版社.1996:1-296.
[4]Tai Ch.Ch.,Rose J.H,Moulder J.C.Thickness and conductivity of metallic layers from pulsed eddy-current measurement[J].Review of Scientific Instruments.1996.67(11):3965 - 3972.
[5]Hamasaki Y,Ide T.Fabrication of multi-layer eddy current micro sensors for non-destructive inspection of small diameter pipes[C].Proceedings of the 8th IEEE Workshop on Micro Electro Mechanical Systems,Amsterdam(Netherlands),29 Jan.-2 Feb.1995:232-237.
[6]黄平捷,吴昭同,严仍春.多层厚度电涡流检测阻抗模型仿真及验证[J].仪器仪表学报.2004.25(4):24-28.
[7]黄平捷,侯迪波,周泽魁.多层导电结构缺陷电涡流扫描检测信号预处理技术研究[J].传感技术学报.2006.19(1):222-227.
[8]黄卡玛,赵翔.电磁场中的逆问题及应用[M].北京:科学出版社.2005:1-58.
[9]杨涛,付宜利,马玉林等.铣削颤振特征提取的小波包和主成分分析方法[J].哈尔滨工业大学学报.2001.33(6):758-762.
[10]Tian G.Y,Sophian A,Taylor D,et.al.Wavelet-based PCA defect classification and quantification for pulsed eddy current NDT[J].IEE Proc.-Sci.Meas.Technol..2005.152(4):141-148.
[11]吴今培.基于核函数的主成分分析及应用[J].系统工程.2005.23(2):117-120.
[12]Zhu X.L,Zhang X.D,Ding Z.Zh,et.al.Adaptive Nonlinear PCA Algorithms for Blind Source Separation Without Prewhitening[J].IEEE Transactions on Circuits and Systems.2006.53(3):745-753.
[13]Xie X.D,Lain K.M.Gabor-Based Kernel PCA With Doubly Nonlinear Mapping for Face Recognition With a Single Face Image[J].IEEE Transactions on Image Processing.2006.15(9):2481-2492.
[14]夏庆观,路红,陈桂.基于小波神经网络的零件图像特征提取和识别[J].仪器仪表学报.2005.26(8):611-613.
[15]韩琦,康戈文.基于小波变换的带钢表面缺陷分形特征研究[J].自动化技术与应用.2006.25(3):4-6.
[16]Wang X.A Novel Signal Feature Extraction Method Based on Wavelet Analysis[C].Proceedings of the 6th World Congress on Intelligent Control and Automation,June 21-23,Dalian,China.2006:4967-1971.
[17]Li L.Q,Tsukada K,Liu Zh.Fusion of Multi-Frequency Eddy Current Signals by Using Wavelet Analysis Method[C].Proceedings of the Fifth International Conference on Information Fusion.2002:108-113.
[18]Acharyya M,De R.K,Du K.K.Extraction of Features Using M-Band Wavelet Packet Frame and Their Neuro-Fuzzy Evaluation for Multitexture Segmentation[J].IEEE Transactions on Pattern Analysis and Machine Intelligence.2003.25(12):1639-1644.
[19]Li D.Q,Pedrycz W,Nicolino J.P.Fuzzy Wavelet Packet Based Feature Extraction Method and Its Application to Biomedical Signal Classification[J].IEEE Transactions on Biomedical Engineering.2005.52(6):1132-1139.
[20]Stefanos K.G,Michael E.Z,Stavrakakis G.S.Classification of Washing Machines Vibration Signals Using Discrete Wavelet Analysis for Feature Extraction[J].IEEE Transactions on Instrumentation and Measurement.2002.51(3):497-508.
[21]Li Sh.T,Liao Ch,Kwok T.J.Wavelet-Based Feature Extraction for Microarray Data Classification[C].Proceedings of 2006 International Joint Conference on Neural Networks Sheraton Vancouver Wall Centre Hotel,Vancouver,BC,Canada,July 16-21.2006:5028-5033.
[22]Li Yue,Udpa L,Udpa S.S.Three-Dimensional Defect Reconstruction From Eddy-Current NDE Signals Using a Genetic Local Search Algorithm[J].IEEE Transactions on Magnetics.2004.40(2):410-417.
[23]Tomasz Ch,Masato E,Ryszard S,et.al.Natural Crack Recognition Using Inverse Neural Model and Multi-Frequency Eddy Current Method[J].IEEE Transactions on Magnetics.2001.37(4):2797-2799.
[24]Yoshiaki N,Toshiyuki T,Tetsuya U,et.al.Identification of Multiple Cracks from Eddy-Current Testing Signals with Noise Sources by Image Processing and Inverse Analysis[J].IEEE Transactions on Magnetics.2004.40(2):1112-1115.
[25]Grimberg R,Udpa L,Savin A.2D Eddy Current Sensor Array[J].NDT&E International.39(2006):264-271.
[26]陈祥林,丁天怀,黄毅平.新型接近式柔性电涡流阵列传感器系统[J].机械工程学报. 2006.26(8):150-153.
[27]Tomasz C,Masato E,Ryszard S.Neural Network Models of Eddy Current Multi-Frequency System for Nondestructive Testing[J].IEEE Transactions on Magnetics.2000.36(4):1724-1727.
[28]Yang B.F,Luo F.L,Cao X.H,et.al.Array Pulsed Eddy Current Imaging System Used to Detect Corrosion[J].Chinese Journal of Mechanical Engineering.2005.18(2):196-198.
[29]Clauzon T,Thollon F,Nicolas A.Flaws Characterization with Pulsed Eddy Currents NDT[J].IEEE Transactions on Magnetics.1999.35(3):1873-1876.
[30]Kreutzbruck M.V,Allweins K,Ruhl T,et.al.Defect Detection and Classification using a SQUID based Multiple Frequency Eddy Current NDE System[J].IEEE Transactions on Applied Superconductivity.2001.11(1):1032-1037.
[31]Tian G.Y,Sophian A,Taylor D,et.al.Multiple Sensors on Pulsed Eddy-Current Detection for 3-D Subsurface Crack Assessment[J].IEEE Sensors Journal.2005.5(1):90-96.
[32]X.Jian,S.Dixon.Enhancement of EMAT and eddy current using a ferrite back-plate[J].Sensors and Actuators.A.136(2007):132-136
[33]徐平,罗飞路,张玉华.基于脉冲涡流检测技术的缺陷定量检测研究[J].计量测试与检定.2006.16(2):6-10.
[34]时振堂,陈德智.涡流检测信号小波除噪与缺陷特征提取[J].无损检测.2003.25(9):472-477.
[35]庄弘炜,马逸尘,张志斌等.涡流检测中识别缺陷形状的一种新方法[J].应用数学和力学.2005.26(11):1380-1386.
[36]Dodd C.V,Deeds W.E.Analytical solutions to eddy-current probe-coil problems[J].Journal ofApplied Physics,39(6),1968,2829-2837.
[37]Luquire J.W,Deeds W.E,Dodd C.V.Alternating current distribution between planar conductors [J].Journal of Applied Physics,1970,41(10):3983-3991.
[38]Garcia.A,Carrasco J.A,Soto J.F,et al.A Method for Calculating the Magnetic Field Produced by A Coil of Any Shape[J].Sensors and Actuators:A.91(2001):230-232.
[39]Fava J.O,Marta C.R.Calculation and Simulation of Impedance Diagrams of Planar Rectangular Spiral Coils for Eddy Current Testing[J].NDT & E International.39(2006):414-424.
[40]Ditchburn R.J,Burke S.K.Planar Rectangular Spiral Coils in Eddy-Current Non-Destructive Inspection[J].NDT & E International.38(2005):690-700.
[41]Theodoros P.T,Epameinondas E.K.Impedance Evaluation of Rectangular Coils for Eddy Current Testing of Planar Media[J].NDT & E international.35(2002):407-414.
[42]雷银照.时谐电磁场解析方法[M].北京:科学出版社.2000:120-194.
[43]Mayergoyz I.Boundary Integral Equations of Minimum Order for the Calculation of Three-dimensional Eddy Current Problems[J].IEEE Transactions on Magnetics.1982.18(2):536 -539.
[44]Jenkins S.A,Bowler J.R.Calculations of the Flaw Signal Generated by A Differential Eddy Current Probe[J].NDT & E International.1997.30(3 ):829-835.
[45]Bahramgiri M,Barkcshli K.Non-Destructive Testing of Cracks Using Eddy Currents and a Generalized Regression Neural Network(GRNN)[C].IEEE Antennas and Propagation Society International Symposium.2003:239-242.
[46]John B.Eddy-Current Inversion for the Determination of Crack Geometry[C].IEE Colloquium on New Applications in Modelling and Inversion Techniques for Non-Destructive Testing.London.UK.1999:1-4.
[47]Juillard J,Barmon B.D,Berthiau G.Simple Analytical Three-Dimensional Eddy-Current Model [J].IEEE Transactions on Magnetics.2000.36(1):258-266.
[48]Páivó J,Lesselier D.Calculation of Eddy Current Testing Probe Signal With Global Approximation[J].IEEE Transactions on Magnetics.2006.42(4):1419-1422.
[49]Bowler J.R,Harfield N.Thin-Skin Eddy-Current Interaction with Semielliptical and Epicyclic Cracks[J].IEEE Transactions on Magnetics.2000.36(1 ):281-291.
[50]Lee H.B,Kim D.H.Impedance Calculation for a Plate with Crack in Eddy Current NDT Using 3D Indirect BIEM[J].IEEE Transactions on Magnetics.2000.36(5):3131-3133.
[51]Theodoros T,Epameinondas K.Series expansions in eddy current nondestructive evaluation models[J].Journal of Material Processing Technology.2005.161(1-2):343-347.
[52]雷银照,马信山.涡流线圈的阻抗计算[J].电工技术学报.1996.11(1):17-20.
[53]Ma Ch.F.A Finite-Element Approximation of a Quasi- Magnetostatic 3D Eddy Current Model by Fractional-Step A-φ Scheme[J].Mathematical and Computer Modelling.39(2004):567-580.
[54]Morozov M,Rubinacci G,Tamburrino A,et.al.Numerical Models of Volumetric Insulating Cracks in Eddy-Current Testing With Experimental Validation[J].IEEE Transactions on Magnetics.2006.42(5):1568-1576.
[55]Mihalache O,Grimberg R,Radu E,et.al.Finite Element Numerical Simulation for Eddy Current Transducer with Orthogonal Coils[J].Sensors and Actuators A:Physical.1997.59(1-3): 213-218.
[56] Bermudez A, Bull6n J, Pena F, et.al. A Numerical Method for Transient Simulation of Metallurgical Compound Electrodes [J]. Finite Elem. Anal. Des.. 39(2003): 283-299.
[57] Liu Ch.P, Lin T.K. Study of Eddy Current Power Loss from Outer-Winding Coils of a Magnetic Position Sensor [J]. Journal of Magnetism and Magnetic Materials. 209(2000): 201-204.
[58] Bermudez A, Rodriguez R, Salgado P. A Finite Element Method with Lagrange Multipliers for Low-frequency Harmonic Maxwell Equations [J]. SIAM J. Numer. Anal. 40(2002): 1823-1848.
[59] Bermridez A, Rodriguez R, Salgado P. Modelling and numerical treatment of boundary data in an eddy currents problem [J]. C. R. Acad. Sci.Paris. 335(2002): 633-638.
[60] Hashizume H, Yamada Y, Miya K, et.al. Numerical and Experimental Analysis of Eddy Current Testing for A tube with cracks [J]. IEEE Transactions on Magnetics. 28(2005): 1469-1472.
[61] Bermudez A, Rodriguez R, Salgado P. Numerical analysis of the electric field formulation of an eddy current problem [J]. Numerical Analysis. 337(2003): 359-364.
[62] Bermudez A, Rodriguez R, Salgado P, et.al. Numerical treatment of realistic boundary conditions for the eddy current problem in an electrode via Lagrange multipliers [J].Mathematics of Computation. 74(2005): 123-151.
[63] Ludwig R, Dai X. W. Numerical and Analytical Modeling of Pulsed Eddy Currents in a Conducting Half-space [J]. IEEE Transactions on Magnetics. 1990. 26(1): 299-307.
[64] Dai X.W, Ludwig R, Palanisamy R. Numerical Simulation of Pulsed Eddy-Current Nondestructive Testing Phenomena [J]. IEEE Transactions on Magnetics. 1990. 26(6):3089-3093.
[65] Patel U, Rodger D. Finite Element Modelling Of Pulsed Eddy Currents For Nondestructive Testing [J]. IEEE Transactions on Magnetics. 1996. 32(3): 1593-1596.
[66] Wilde J, Lai Y.Q. Design optimization of an eddy current sensor using the finite-elements method [J]. Microelectronics Reliability. 43(2003): 345-349.
[67] Tanaka M, Tsuboi H. Finite Element Model of Natural Crack in Eddy Current Testing Problem [J]. IEEE Transactions on Magnetics. 2001. 37(5): 3125-3128.
[68] Noritaka Yusa, Stephane Perrin, Kazue Mizuno, et.al. Numerical modeling of general cracks from the viewpoint of eddy current simulations[J] .NDT&E International. 40 (2007): 577-583.
[69] Gabriel P, Bogdan C.C, Florea I, et.al. Nonlinear FEM-BEM Formulation and Model-Free Inversion Procedure for Reconstruction of Cracks Using Pulse Eddy Currents [J]. IEEE Transactions on Magnetics. 2002. 38(2): 1241-1244.
[70]Takahashi Y,Wakao S.Large-Scale Analysis of Eddy-Current Problems by the Hybrid Finite Element-Boundary Element Method Combined With the Fast Multipole Method[J].IEEE Transactions on Magnetics.2006.42(4):671-674.
[71]Viana S.A,Rodger D,Lai H.C.Application of the Local Radial Point Interpolation Method to Solve Eddy-Current Problems[J].IEEE Transactions on Magnetics.2006.42(4):591-594.
[72]王春兰,张钢,董鲁宁等.电涡流传感器的有限元仿真研究与分析[J].传感器与微系统.2006.25(2):41-44.
[73]周丹丽,赵辉,刘伟文.电涡流传感器建模与仿真分析[J].传感器技术.2005.24(5):28-30.
[74]蒋齐密,张新访,刘土光.电涡流检测系统的参数设置依据[J].无损检测.2001.23(3):100-103.
[75]蒋齐密,张新访,刘土光.电涡流检测系统仿真分析的前处理技术[J].计算机仿真.2001.18(1):46-49.
[76]蒋齐密,张新访,刘土光.电涡流检测系统中的电磁场仿真[J].计算机仿真.2000.17(5):36-39.
[77]贾永平,丁天怀,王鹏.曲面体间隙电涡流检测的有限元分析[J].传感技术学报.2005.18(2):221-224.
[78]周丹丽,赵辉,刘伟文等.基于三维有限元的电涡流传感器参数的仿真研究[J].计算机测量与控制.2005.13(6):618-620.
[79]Tian G.Y,Zhao Z.X,Baines R.W.The Research of Inhomogeneity in Eddy Current Sensors[J].Sensors and Actuators:A.69(1998):148-151.
[80]单成祥.传感器理论与设计基础及其应用[M].北京:国防工业出版社.1999:1-228.
[81]曲民兴,司家屯.电磁无损检测与数值计算(第三讲)--涡流检测探头信号的有限元预估[J].无损检测.1994.16(6):172-177.
[82]Theodoros P.T,Epameinondas E.K.Impedance Evaluation of Rectangular Coils for Eddy Current Testing of Planar Media[J].NDT & E international.35(2002):407-414.
[83]Ditchburn R.J,Burke S.K.Planar Rectangular Spiral Coils in Eddy-Current Non-Destructive Inspection[J].NDT & E International.38(2005):690-700.
[84]Buvat F,Pichenot G,Premel D,et al.Eddy-Current Modeling of Ferrite-Cored Probes[C].Proceedings of AIP Conference.760(2005):463-470.
[85]Sabbagh H.A.A Model of Eddy-Current Probes with Ferrite Cores[J].IEEE Transactions on Magnetics.1987.23(3):1888-1904.
[86]Burke S.K.A Semi-empirical Model for Eddy-Current NDE Using Ferrite-Cored Probes[J].Nondestructive Testing and Evaluation.1992.6(5):267-277.
[87]黄浩,陆继明,毛承雄等.Rogowski线圈结构参数仿真研究[J].电力系统及其自动化学报.3(2004):72-75.
[88]王军平,王安,樊文侠.电涡流传感器线圈参数对传感器性能的影响[J].自动化仪表.2001.22(12):22-24.
[89]黄小秋,丁天怀,付志斌.简化目标函数的电涡流传感器线圈参数优化设计法[J].传感器技术.11(2000):3-5.
[90]许德章.电涡流传感器信号调理电路的设计[J].自动化仪表.1998.19(6):37-39.
[9l]邵爱霞。赵辉,刘伟文.定频调幅式电涡流传感器电路及其在防水数显卡尺中的应用[J].计算机测量与控制.2005.13(5):508-510.
[92]张珍明,劳奇成,李平等.电感式传感器信号处理模块的研制[J].计量技术.9(1999):11-13.
[93]邵爱霞,赵辉,刘伟文.基于MSP430的定频调幅式电涡流传感器位移测量系统[J].计量技术.4(2005):29-31.
[94]贾智伟,刘红飞,李应红.传感器信号的非线性补偿[J].传感器技术.2002.21(5):30-32.
[95]刘清.传感器模糊神经网络非线性误差补偿的研究[J].自动化仪表.2006.27(3):11-14.
[96]蒋小燕,徐大诚.基于BP神经网络的压力传感器非线性校正方法[J].苏州大学学报(自然科学版.2005.21(4):54-58.
[97]芦俊,陈俊杰,颜景平.基于遗传算法的传感器系统的非线性校正[J].仪表技术与传感器.6(2001):38-40.
[98]王生铁,王志和,傅闯.铂电阻温度传感器非线性校正的新方法[J].仪表技术与传感器.2(2000):40-42.
[99]Ricken W.L.Optimisation of Parameters of an Eddy Current Sensor Used for a Displacement Measurement[J].Technisches Messen..2004.71(9):460-465.
[100]方秋华,茅佩,田新启.电涡流传感器温度漂移的自动补偿[J].仪器仪表学报.1997.18(2):198-201.
[101]Li Q.P,Ding F.Novel Displacement Eddy Current Sensor with Temperature Compensation for Electrohydranlic Valves[J].Sensors and Actuators:A.122(2005):83-87.
[102]肖茂森,原思聪,钟春生等.PIC单片机芯片在电涡流传感器温度补偿中的应用[J].工业,计量.2005.15(1):16-18.
[103]Yann L.B.3-D Finite-Element Analysis of Eddy-Current Evaluation of Curved Plates[J]. IEEE Transactions on Magnetics.2002.38(2):1161-1164.
[104]Sophian A,Tian G.Y,Taylor D,et.al.Design of a Pulsed Eddy Current Sensor for Detection of Defects in Aircraft Lap-joints[J].Sensors and Actuators:A.101(2002):92-98.
[105]徐志刚,张栋,傅国如.飞机机翼与机身连接螺栓裂纹分析[J].腐蚀科学与防护技术.2005.17(4):286-287.
[106]Maeda N,Yamaguchi A,Sugibayashi T,et.al.Degradation Detection of Material Used in Nuclear Power Plant Components Applying Probe-type Eddy Current Sensor - Part 2 Detection of Fatigue and Irradiation Embrittlement in Low Alloy Steel for Reactor Pressure Vessel[J].Journal of the Japanese Society for Non-Destructive Inspection.1997.46(2):127-133.
[107]Joubert P.Y,Bihan Y.L,Placko D.Localization of defects in steam generator tubes using a multi-coil eddy current probe dedicated to high speed inspection[J].NDT & E International.2002.35(1):53-59.
[108]徐可君,江龙平.航空燃气涡轮发动机工作叶片疲劳与寿命[J].航空制造技术.6(1998):20-22.
[109]张明恩,薛世峰,张治坤.航空燃气涡轮发动机状态监控和技术诊断导论[J].沈阳航空工业学院学报.1994.28(4):82-88.
[110]Song S.J,Shin Y.K.Eddy Current Flaw Characterization in Tubes by Neural Networks and Finite Element Modeling[J].NDT&E International.33(2000):233-243.
[111]Hur D.H,Lee D.H,Choi M.S,et.al.Discrimination Method of Through-Wall Cracks in Steam Generator Tubes using Eddy Current Signals[J].NDT&E International.39(2006):361-366.
[112]金涛,阙沛文,陶正苏.小波神经网络在海底石油管道漏磁缺陷检测中的应用[J].石油大学学报(自然科学版).2005.29(3):83-87.
[113]徐小力,梁福平,许宝杰等.旋转机械状态监测及预测技术的发展与研究[J].建筑机械技术与管理.7(2003):20-24.
[114]李博,翁莹,佟海云.电涡流传感器在汽轮发电机组的应用及标定[J].宝钢科技.2005.31(5):36-38.
[115]F.Vachera,F.Alvesb,C.Gilles-Pascauda.Eddy current nondestructive testing with giant magneto-impedance sensor[J].NDT&E International.40(2007):439-442.
[116]孙建民,杨清梅.传感器技术[M].北京:清华大学出版社,北京交通大学出版社.2005:1-109.
[117]陈行禄,吴志鹤.传感器原理[M].北京:航空工业出版社.1987:1-153.
[118]游凤荷,陈丹,牛龙江.涡流三维磁场测量及实际渗透深度建模[J].仪器仪表学报.2002. 23(4):431-434.
[119]杜平安,甘娥忠,于亚婷.有限元法--原理、建模及应用[M].北京:国防工业出版社.2004:1-272.
[120]Thomas G.K,Madabushi V.K.The Application of Finite Element Method Analysis to Eddy Current Nondestructive Evaluation[J].IEEE Transactions on Magnetics.1979.15(6):1956-1960.
[121]胡之兴.电机电磁场的分析与计算(修订本)[M].北京:机械工业出版社.1989:1-234.
[122]邵惠民.数学物理方法[M].北京:科学出版社.2005:44-325.
[123]Vyroubal D.Impedance of the Eddy-Current Displacement Probe:the Transformer Model[J].IEEE Transactions on Instrumentation and Measurement,2004.53(2):384-391.
[124]全泽松.电磁场理论[M].成都:电子科技大学出版社.1995:1-30.
[125]南京工学院数学教研组编.数学物理方程与特殊函数[M].北京:高等教育出版社.1990:101-126.
[126]张韵华.Mathematic符号计算系统实用教程[M].合肥:中国科学技术大学出版社.1998:1-141.
[127]于亚婷,杜平安,王振伟.有限元法应用现状研究[J].机械设计.2005.22(3):6-9.
[128]Li J.Ch.Optimal Error Estimates of Mixed Finite Element Methods for A Fourth-Order Nonlinear Elliptic Problem[J].Journal of Mathematical Analysis and Applications.2007.334(1):183-195.
[129]Lynn K.M,Isobe D.Structural Collapse Analysis of Framed Structures under Impact Loads using ASI-Gauss Finite Element Method[J].International Journal of Impact Engineering.2007.34(9):1500-1516.
[130]Byon S.M,Kim H.S,Lee Y.Investigation of the Size Effect on Crack Propagation using Finite Element Method and Strain Gradient Plasticity[J].Journal of Materials Processing Technology.2007.191(1-3):193-197.
[128]Toparli M,Sen F,Culha O,et.al.Thermal Stress Analysis of HVOF Sprayed WC-Co/NiA1Multilayer Coatings on Stainless Steel Substrate using Finite Element Methods[J].Journal of Materials Processing Technology.2007.190(1-3):26-32.
[132]Kujime T,Tane M,Hyun S.K,et.al.Three-Dimensional Image-Based Modeling of Lotus-Type Porous Carbon Steel and Simulation of Its Mechanical Behavior by Finite Element Method[J].Materials Science and Engineering:A.2007(460-461):220-226.
[133]Shin D.S,Lee K,Kim D.Biomechanical Study of Lumbar Spine with Dynamic Stabilization Device using Finite Element Method[J].Computer-Aided Design.2007.39(7):559-567.
[134]Tber M.H,Talibi M.E.A Finite Element Method for Hydraulic Conductivity Identification in a Seawater Intrusion Problem[J].Computers & Geosciences.2007.33(7):860-874.
[135]Park K.S,VanTyne Ch.J,Moon Y.H.Process Analysis of Multistage Forging by using Finite Element Method[J].Journal of Materials Processing Technology.2007(187-188):586-590.
[136]Ma Ch.F,Wang D.Sh.Finite Element Analysis of An A-ψ Method for Time-Dependent Maxwell's Equations based on Explicit-Magnetic-Field Scheme[J].Applied Mathematics and Computation.2007.190(2):1273-1283.
[137]Zhang H.W,Rong Ch.B,Du X.B,et.al.Investigation on the Coercivity and Remanence of Single-Phase Nanocrystalline Permanent Magnets by Micromagnetic Finite-Element Method [J].Journal of Magnetism and Magnetic Materials.2004.278(I-2):127-137.
[138]Liu G.Nan C.W,Cai N,et.al.Calculations of Giant Magnetoelectric Effect in Multiferroic Composites of Rare-Earth-Iron Alloys and PZT by Finite Element Method[J].International Journal of Solids and Structures.2004.41(16-17):4423-4434.
[139]吕英华.计算电磁学的数值方法[M].北京:清华大学出版社.2006:1-481.
[140]杜平安.建立有限元模型的基本原则[J].机械与电子.2001(4):40-42.
[141]博弈创作室.APDL参数化有限元分析技术及其应用实例[M].北京:中国水利水电出版社2005:1-115.
[142]小飒工作室.最新经典ANSYS及Workbench教程[M].北京:电子工业出版社.2004:564-615
[143]Yann L.B.Study on the Transformer Equivalent Circuit of Eddy Current Nondestructive Evaluation[J].NDT&E International.36(2003):297-302.
[144]张秀敏,苑津莎,崔翔.用棱边与节点有限元耦合的E-E-ψ法计算三维涡流场[J].中国电机工程学报.2003.21(3):70-74.
[145]王泽忠,王炳革,卢斌先等.三维开域涡流场A-V位有限元与边界元耦合分析方法[J].中国电机工程学报.2000.20(5):1-4.
[146]雷银照,马信山.三维探伤涡流场的研究与线圈阻抗计算[J].电机工程学报.1996.16(5):289-294.
[147]袁建生,宗伟.计算三维涡流场的三分量边界元法[J].中国电机工程学报.1999.19(5):27-29.
[148]梁晋文,陈林才,何贡.误差理论与数据处理[M].中国计量出版社.2001:95-135.
[149]中国材料实用手册编委会.工程材料实用手册(1,2,3,4)[M].中国标准出版社.1988: 815-420,5-385,9-368,581-867.
[150]张志涌.精通MATLAB 6.5版[M].北京:北京航空航天大学出版社.2003:1-265.
[151]周剑平.精通Origin7.0[M].北京:北京航空航天大学出版社.2004:1-135.
[152]段九州.振荡电路实用设计手册[M].沈阳:辽宁科学技术出版社.2002:1-21.
[153]郭荣祥,周惠潮。常用电子元件及典型应用[M].北京:电子工业出版社.2005:104-194.
[154]黑天彻.电子元器件应用技术[M].北京:科学出版社.2006:179-203.
[155]朱达斌,张宝玉,李亦群等.高速运算放大器应用技术[J].电子技术应用.1998(4):68-70.
[156]森荣二.LC滤波器设计与制作[M].北京:科学出版社.2006:49-59.
[157]李学厚.负载接地的单支运放电压--电流变换器[J].大连水产学院学报.1997.12(4):45-48.
[158]稻叶保.模拟技术应用技巧101例[M].北京:科学出版社.2004:65-170.
[159]张伟.电路设计与制板--Protel DXP入门与提高[M].北京:人民邮电出版社.2003:20-243.
[160]倪泽峰,江中华.电路设计与制板--Protel DXP典型实例[M].北京:人民邮电出版社.2003:87-348.
[161]Capobianco T.E,Splett J.D,Iyer H.K.Eddy Current Sensitivity as a Function of Coil Construction Parameters[J].Research in Nondestructive Evaluation.1990.2(3):169-186.
[162]张宝裕,刘恒基.磁场的产生[M].北京:机械工业出版社.1987:1-116.
[163][日]大森丰明编.刘代琦,梁宇青译.磁性材料手册[M].北京:机械工业出版社.1985:183-335.