模拟电路故障诊断研究
|
摘要
模拟电路故障诊断对电子系统的设计生产和使用维护起着至关重要的作用,但是由于模拟电路的自身难点,使模拟电路故障诊断成为困扰电路发展的瓶颈,模拟电路故障诊断研究成为电路研究领域十分迫切的重要课题。
为了增加模拟电路故障诊断技术的理论储备,促进模拟电路故障诊断应用技术的发展,本文结合国内外现有的模拟电路故障诊断方法,对模拟电路故障诊断的理论原理与诊断技术进行了系统深入的研究。针对模拟电路故障诊断的故障样本采集与处理、故障诊断的测试点优选、故障诊断方法及其与故障诊断相关的数学算法,提出了几种新的模拟电路系统分析与故障诊断方法,全文的主要工作与研究成果如下。
1.针对模拟电路的灰色系统特性,将基于灰色关联分析与灰熵分析的灰熵关联算法应用于模拟电路故障诊断领域,计算灰熵关联度以量化待诊断电路与故障状态之间的关联程度,仅需要少量样本和测试点即可准确完成模拟电路故障诊断。提出了基于灰熵关联算法的模拟电路测试点优选方法,使用灰熵关联度量化模拟电路的测试点与故障元件之间的关联程度,为选择模拟电路故障诊断的最佳测试点提供了数学模型,客观明确的描述了测试点在模拟电路故障诊断中的优劣。
2.提出了基于聚类算法与马氏距离算法的模拟电路故障诊断法,首先使用层次聚类算法或FCM聚类算法将模拟电路故障样本按照故障状态进行分类,根据各聚类中心建立故障字典,继而使用马氏距离算法完成模拟电路故障诊断。将聚类算法与马氏距离算法相结合进行模拟电路故障诊断,既能发挥聚类算法优秀的分类能力,也能发挥马氏距离算法优秀的距离计算能力,拓展了传统的故障字典法,诊断流程清晰流畅,诊断方法具有很好的实用性。
3.提出将模糊隶属函数转化为模拟电路故障度量化函数,建立了常用的故障度量化函数,提出了基于故障度量化函数与决策函数的模拟电路故障度量化算法,使用模拟电路故障度量化算法计算模拟电路的故障度指数,客观准确地评价了模拟电路的故障程度,实现了模拟电路系统的精确描述。使用基于隶属函数与决策函数的模糊算法进行模拟电路故障诊断,将待诊断电路与各电路状态的相似程度由模糊量转变为数字量,精确实现模拟电路故障诊断。
4.提出了基于重分类与支持向量机相结合的模拟电路故障诊断方法,研究了两种重分类方法,重新分类存在故障类重叠的故障样本,以提高模拟电路故障诊断的正确率。根据支持向量机的分类结果验证了重分类方法对降低故障诊断误诊率的有效性。
本文共6章,图41幅,表54个,参考文献115篇。
Fault diagnosis of analog circuits is very important in the process of electronic system design, production, using and maintain. Because there is much trouble in analog circuits, fault diagnosis of analog circuits already have been the restriction of circuit research. The research on fault diagnosis of analog circuits is an urgent subject in the circuit research field.
In order to develop fault diagnosis of analog circuits, increase the theory reserves of fault diagnosis of analog circuits, put the technology of fault diagnosis of analog circuits into use, this dissertation study theory and technology of fault diagnosis of analog circuits integrally. Theory and technology of fault diagnosis of analog circuits is summarized at home and abroad. This dissertation study every field of fault diagnosis of analog circuits including the collection and handling of fault samples, the selection of optimal test points, the method and algorithm of fault diagnosis of analog circuits. Several kinds of new method of system analysis and fault diagnosis are proposed. The major study and result of this dissertation are the following.
1. Grey entropy relational algorithm which come from the combination of grey relational analysis and grey entropy analysis is proposed to analyze and diagnose analog circuits because there is the character of grey system in analog circuits. Grey entropy relational degree is used to quantify the relationship between undiagnosed circuits and fault states. With the smaller samples and test points, grey entropy relational algorithm can ensure the accuracy of fault diagnosis of analog circuits. Grey entropy relational algorithm is proposed to select the optimal test points of analog circuits. Grey entropy relational degree is used to quantify the relationship between test points and fault components, grey entropy relational algorithm can ensure the objectivity of selecting the optimal test points.
2. A new method based on clustering algorithm and Mahalanobis distance algorithm is proposed to diagnose analog circuits. Fuzzy C-means (FCM) clustering algorithm and hierarchical clustering algorithm are used to analyze fault samples of analog circuits. After clustering analysis, fault samples are classified, fault dictionary is structured simultaneously. Mahalanobis distance algorithm and fault dictionary method are combined to finish fault diagnosis of analog circuits. This method can utilize the excellent classification ability of clustering algorithm and the excellent distance calculation ability of Mahal anobis distance algorithm. Traditional fault dictionary method is expanded. This method has the advantages of smooth process and practical applicability.
3. Fuzzy membership function is transformed to quantify the fault degree of analog circuits. Several common fault degree quantification function are set up. Fault degree quantification algorithm based on fault degree quantification function and decision function is proposed to calculate the fault index of analog circuits. Fault index of analog circuits can evaluate the fault degree of analog circuits objectively, describe analog circuit system accurately. Fuzzy algorithm based on membership function and decision function is used to diagnose analog circuits accurately. The similarity between undiagnosed circuits fault states is quantified by Fuzzy algorithm.
4. A new method based on reclassification and SVM is proposed to diagnose analog circuits. Two method of reclassification are studyed to reclassify fault samples of types overlap. The classification result of SVM prove that reclassification can increase the accuracy of fault diagnosis when there is overlap area in fault samples of different fault types.
This dissertation consists of6chapters, including41figures,54tables and115references.
为了增加模拟电路故障诊断技术的理论储备,促进模拟电路故障诊断应用技术的发展,本文结合国内外现有的模拟电路故障诊断方法,对模拟电路故障诊断的理论原理与诊断技术进行了系统深入的研究。针对模拟电路故障诊断的故障样本采集与处理、故障诊断的测试点优选、故障诊断方法及其与故障诊断相关的数学算法,提出了几种新的模拟电路系统分析与故障诊断方法,全文的主要工作与研究成果如下。
1.针对模拟电路的灰色系统特性,将基于灰色关联分析与灰熵分析的灰熵关联算法应用于模拟电路故障诊断领域,计算灰熵关联度以量化待诊断电路与故障状态之间的关联程度,仅需要少量样本和测试点即可准确完成模拟电路故障诊断。提出了基于灰熵关联算法的模拟电路测试点优选方法,使用灰熵关联度量化模拟电路的测试点与故障元件之间的关联程度,为选择模拟电路故障诊断的最佳测试点提供了数学模型,客观明确的描述了测试点在模拟电路故障诊断中的优劣。
2.提出了基于聚类算法与马氏距离算法的模拟电路故障诊断法,首先使用层次聚类算法或FCM聚类算法将模拟电路故障样本按照故障状态进行分类,根据各聚类中心建立故障字典,继而使用马氏距离算法完成模拟电路故障诊断。将聚类算法与马氏距离算法相结合进行模拟电路故障诊断,既能发挥聚类算法优秀的分类能力,也能发挥马氏距离算法优秀的距离计算能力,拓展了传统的故障字典法,诊断流程清晰流畅,诊断方法具有很好的实用性。
3.提出将模糊隶属函数转化为模拟电路故障度量化函数,建立了常用的故障度量化函数,提出了基于故障度量化函数与决策函数的模拟电路故障度量化算法,使用模拟电路故障度量化算法计算模拟电路的故障度指数,客观准确地评价了模拟电路的故障程度,实现了模拟电路系统的精确描述。使用基于隶属函数与决策函数的模糊算法进行模拟电路故障诊断,将待诊断电路与各电路状态的相似程度由模糊量转变为数字量,精确实现模拟电路故障诊断。
4.提出了基于重分类与支持向量机相结合的模拟电路故障诊断方法,研究了两种重分类方法,重新分类存在故障类重叠的故障样本,以提高模拟电路故障诊断的正确率。根据支持向量机的分类结果验证了重分类方法对降低故障诊断误诊率的有效性。
本文共6章,图41幅,表54个,参考文献115篇。
Fault diagnosis of analog circuits is very important in the process of electronic system design, production, using and maintain. Because there is much trouble in analog circuits, fault diagnosis of analog circuits already have been the restriction of circuit research. The research on fault diagnosis of analog circuits is an urgent subject in the circuit research field.
In order to develop fault diagnosis of analog circuits, increase the theory reserves of fault diagnosis of analog circuits, put the technology of fault diagnosis of analog circuits into use, this dissertation study theory and technology of fault diagnosis of analog circuits integrally. Theory and technology of fault diagnosis of analog circuits is summarized at home and abroad. This dissertation study every field of fault diagnosis of analog circuits including the collection and handling of fault samples, the selection of optimal test points, the method and algorithm of fault diagnosis of analog circuits. Several kinds of new method of system analysis and fault diagnosis are proposed. The major study and result of this dissertation are the following.
1. Grey entropy relational algorithm which come from the combination of grey relational analysis and grey entropy analysis is proposed to analyze and diagnose analog circuits because there is the character of grey system in analog circuits. Grey entropy relational degree is used to quantify the relationship between undiagnosed circuits and fault states. With the smaller samples and test points, grey entropy relational algorithm can ensure the accuracy of fault diagnosis of analog circuits. Grey entropy relational algorithm is proposed to select the optimal test points of analog circuits. Grey entropy relational degree is used to quantify the relationship between test points and fault components, grey entropy relational algorithm can ensure the objectivity of selecting the optimal test points.
2. A new method based on clustering algorithm and Mahalanobis distance algorithm is proposed to diagnose analog circuits. Fuzzy C-means (FCM) clustering algorithm and hierarchical clustering algorithm are used to analyze fault samples of analog circuits. After clustering analysis, fault samples are classified, fault dictionary is structured simultaneously. Mahalanobis distance algorithm and fault dictionary method are combined to finish fault diagnosis of analog circuits. This method can utilize the excellent classification ability of clustering algorithm and the excellent distance calculation ability of Mahal anobis distance algorithm. Traditional fault dictionary method is expanded. This method has the advantages of smooth process and practical applicability.
3. Fuzzy membership function is transformed to quantify the fault degree of analog circuits. Several common fault degree quantification function are set up. Fault degree quantification algorithm based on fault degree quantification function and decision function is proposed to calculate the fault index of analog circuits. Fault index of analog circuits can evaluate the fault degree of analog circuits objectively, describe analog circuit system accurately. Fuzzy algorithm based on membership function and decision function is used to diagnose analog circuits accurately. The similarity between undiagnosed circuits fault states is quantified by Fuzzy algorithm.
4. A new method based on reclassification and SVM is proposed to diagnose analog circuits. Two method of reclassification are studyed to reclassify fault samples of types overlap. The classification result of SVM prove that reclassification can increase the accuracy of fault diagnosis when there is overlap area in fault samples of different fault types.
This dissertation consists of6chapters, including41figures,54tables and115references.
引文
[1]Pease R A. Troubleshooting analog circuits [M]. USA, Boston, Butterworth-Heinemann, 1991:1-217.
[2]Jun Xu, Jianliang Li, Yong Jiang. Components Locating in PCB Fault Diagnosis Based on Infrared Thermal Imaging [C]. Second International Conference on Information and Computing Science, Britain, Manchester,2009,2:7-9.
[3]Maccanelli M, Halliday A, Bell B, et al. Practical application of automated fault diagnosis at the chip and board levels [C]. IEEE International Workshop on Defect and Fault Tolerance in VLSI System, USA, Dallas,1992,297-304.
[4]Alippi C, Catelani M, Fort A, et al. Automated selection of test frequencies for fault diagnosis in analog electronic circuits [J]. IEEE Transaction on Instrumentation and Measurement,2005,54 (3):1033-1044.
[5]Chung K H, Shepherd P R, Eberhardt F, et al. Hierarchical fault diagnosis of analog integrated circuits [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2001,48 (8):921-929.
[6]Ogg S, Lesage S, Jervis B W, et al. Multiple fault diagnosis in analogue circuits using time domain response features and multilayer perceptrons [J]. IEE Proceedings on Circuits, Devices and Systems,1998,145 (4):213-218.
[7]Brygilewicz V, Wojciechowski J. Time-domain fault diagnosis of analogue circuits in the presence of noise [J]. IEE Proceedings on Circuits, Devices and Systems,1998,145 (2): 125-131.
[8]Worsman M, Wong M W T, Lee Y S. Enhancing the fault diagnosis of linear analog circuit steady-state DC testing through the analysis of equivalent faults [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2003,50 (7):932-936.
[9]杨士元.模拟系统的故障诊断与可靠性设计[M].北京,清华大学出版社,2001,1-16.
[10]Chen Y. Experiment on fault location in large-scale analog circuits [J]. IEEE Transaction on Instrumentation and Measurement,1993,42 (1):30-34.
[11]Baoguang Yan, Qingguo Fan, Bernstein J B, et al. Reliability Simulation and Circuit-Failure Analysis in Analog and Mixed-Signal Applications [J]. IEEE Transaction on Device and Materials Reliability,2009,9 (3):339-347.
[12]Sun Xiubin, Chen Guangju, Xie Yongle. Test Point Selection for Analog Integrated Circuit [J]. Journal of Electronics and Information Technology,2004,26 (4):645-650.
[13]Vladimir N Vapnik. An Overview of Statistical Learning Theory [J]. IEEE Transactions On Neural Network,1999,10 (5):988-999.
[14]Decherchi S, Gastaldo P, Parodi M, et al. Low-complexity, linear circuit implementation of support vector machines training [J]. Electronics Letters,2008,44 (25):1478-1479.
[15]Anguita D, Ridella S, Rovetta S. Circuital implementation of support vector machines [J]. Electronics Letters,1998,34(16):1596-1597.
[16]Chih-Chung Chang, Chihjen Lin. LIBSVM:A library for support vector machines [EB/OL]. 2010, http://www.csie.ntu.edu.tw/-cjlin/libsvm.
[17]Slamani M, Kaminska B. Fault observability analysis of analog circuits in frequency domain [J]. IEEE Transactions on Circuits and Systems II:Analog and Digital Signal Processing,1996,43 (2):134-139.
[18]Malyshenko Yu V. Functional fault models for analog circuits [J]. IEEE Design & Test of Computers,1998,15 (2):80-85.
[19]Tadeusiewicz M, Halgas S, Korzybski M. An algorithm for soft-fault diagnosis of linear and nonlinear circuits [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2002,49 (11):1648-1653.
[20]Prasad V C. Equations of nonlinear analogue circuit for fault dictionary generation [J]. Electronics Letters,1990,26 (1):24-25.
[21]Chess B, Larrabee T. Creating small fault dictionaries [J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1999,18 (3):346-356.
[22]Pomeranz I, Reddy S M. On dictionary-based fault location in digital logic circuits [J]. IEEE Transactions on Computers,1997,46 (1):48-59.
[23]Hagas Stanisaw. Multiple soft fault diagnosis of nonlinear circuits using the fault dictionary approach [J]. Bulletin of the Polish Academy of Sciences:Technical Sciences,2008,56 (1): 53-57.
[24]张伟,许爱强,陈振林.模拟电路节点电压灵敏度权序列故障字典法[J].电子测量与仪器学报,2006,20(4)：46-49.
[25]陈圣俭,石志勇.可诊断容差模拟电路软故障的新故障字典法[J].电子学报,2000,28(2)：127-129.
[26]Aminian F, Aminian M, Collins H, et al. Analog fault diagnosis of actual circuits using neural network [J]. IEEE Transaction on Instrumentation and Measurement,2002,51 (3): 544-550.
[27]Lifen Yuan, Yigang He, Jiaoying Huang. A new neural-network-based fault diagnosis approach for analog circuits by using kurtosis and entropy as a preprocessor [J]. IEEE Transaction on Instrumentation and Measurement,2010,59 (3):586-595.
[28]张维强,徐晨,宋国乡.模拟电路故障诊断的小波包预处理神经网络改进算法[J].信号处理,2007,23(2)：204-209.
[29]Aminian M, Aminian F. Neural-network based analog-circuit fault diagnosis using wavelet transform as preprocessor [J]. IEEE Transactions on Circuits and Systems Ⅱ:Analog and Digital Signal Processing,2000,47 (2):151-156.
[30]王承,陈光(礻禹ju),谢永乐.小波-神经网络在模拟电路故障诊断中的应用[J].系统仿真学报,2005,17(8)：1936-1938.
[31]He Y, Tan Y, Sun Y. Wavelet neural network approach for fault diagnosis of analogue circuits [J]. IEE Proceedings on Circuits, Devices and Systems,2004,151 (4):379-384.
[32]Peng Wang, Shiyuan Yang. A New Diagnosis Approach for Handling Tolerance in Analog and Mixed-signal Circuits by Using Fuzzy Math [J]. IEEE Transactions on Circuits and Systems Part 1:Regular Papers,2005,52 (10):2118-2127.
[33]王鹏宇,黄智刚.模糊理论与神经网络结合对模拟电路进行分层故障诊断[J].电子测量技术,2002,1：7-9.
[34]曹荣敏,关静丽,张果.电子电路模糊神经网络故障诊断研究及仿真[J].计算机仿真,2005,22(11)：165-168.
[35]谢琳,李凡长.一类动态模糊机器学习算法研究[J].电子学报,2008,36(B12)：114-119.
[36]王继成.基于认知模拟的自适应机器学习算法研究[J].软件学报,2001,12(8)：1205-1211.
[37]Jen-Tzung Chien, Jung-Chun Chen. Recursive bayesian linear regression for adaptive classification [J]. IEEE Transactions on Signal Processing,2009,57 (2):565-575.
[38]Hearst M A, Dumais S T, Osman E, et al. Support vector machines [J]. IEEE Intelligent Systems and Their Applications,1998,13 (4):18-28.
[39]Mangasarian O L, Musicant D R. Successive overrelaxation for support vector machines [J]. IEEE Transactions on Neural Networks,1999,10 (5):1032-1037.
[40]Scholkopf B, Kah-Kay Sung, Burges C J C, et al. Comparing support vector machines with Gaussian kernels to radial basis function classifiers [J]. IEEE Transactions on Signal Processing,1997,45 (11):2758-2765.
[41]Chih-Wei Hsu, Chih-Jen Lin. A comparison of methods for multiclass support vector machines[J]. IEEE Transactions on Neural Network,2002,13 (2):415-425.
[42]Mattera D, Palmieri F, Haykin S. An explicit algorithm for training support vector machines [J]. IEEE Signal Processing Letters,1999,6 (9):243-245.
[43]Chih-Chung Chang, Chih-Wei Hsu, Chih-Jen Lin. The analysis of decomposition methods for support vector machines [J]. IEEE Transactions on Neural Networks,2000,11 (4): 1003-1008.
[44]Sebald D J, Bucklew J A. Support vector machines techniques for nonlinear equalization [J]. IEEE Transactions on Signal Processing,2000,48 (11):3217-3226.
[45]Chun-Fu Lin, Sheng-De Wang. Fuzzy support vector machines [J]. IEEE Transactions On Neural Network,2002,13 (2):464-471.
[46]El-Turky F, Perry E E. BLADES:an artificial intelligence approach to analog circuit design [J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1989, 8(6):680-692.
[47]王肃宁,杨士元,汪鹏.基于模式识别进行模拟电路故障诊断的方法[J].微电子学与计算机,2004,21(11)：113-116.
[48]李敏远,陈如清.一种基于模式识别的可控整流电路故障诊断方法[J].电工技术学报,2004,19(7)：53-58.
[49]吴洪兴,彭宇,彭喜元.基于支持向量机多分类方法的模拟电路故障诊断研究[J].电子测量与仪器学报,2007,21(4)：27-31.
[50]唐静远,师奕兵,张伟.基于支持向量机集成的模拟电路故障诊断[J].仪器仪表学报,2008,29(6)：1216-1220.
[51]宋国明,王厚军,刘红,等.基于提升小波变换和SVM的模拟电路故障诊断[J].电子测量与仪器学报,2010,24(1)：17-22.
[52]马晨光,胡昌华,骆功纯,等.粗糙集和支持向量机在复杂电路系统诊断中的应用[J].电光与控制,2009,16(3)：83-85,94.
[53]Pan Zhongliang, Chen Guangju. Neural network expert system approach for analog circuits fault diagnosis [J]电子科技大学学报,1997,26(4)：405-408.
[54]冯志红,林志贵,王炜.基于信息融合的模拟电路故障诊断方法分析[J].电子测量与仪器学报,2008,22(6)：47-53.
[55]Yanghong Tan, Yigang He, Chun Cui, et al. A Novel Method for Analog Fault Diagnosis Based on Neural Networks and Genetic Algorithms [J]. IEEE Transaction on Instrumentation and Measurement,2008,57 (11):2631-2639.
[56]于飞,田玲玲,刘喜梅,等.基于小波多分辨率分析和主元分析的电力电子电路故障诊断[J].华东理工大学学报：自然科学版,2006,32(9)：1113-1116,1125.
[57]周龙甫,师奕兵,李焱骏.容差条件下PSO算法诊断模拟电路单软故障方法[J].计算机辅助设计与图形学学报,2009,21(9)：1270-1274.
[58]Alippi C, Catelani M, Fort A, et al. SBT soft fault diagnosis in analog electronic circuits:a sensitivity-based approach by randomized algorithms [J]. IEEE Transaction on Instrumentation and Measurement,2002,51 (5):1116-1125.
[59]Jun Zhang, Chung H S, Lo A W, et al. Extended Ant Colony Optimization Algorithm for Power Electronic Circuit Design [J]. IEEE Transaction on Power Electronics,2009,24 (1): 147-162.
[60]Yuan F. Efficient sampled-data simulation method for transient analysis of nonlinear circuits [J]. IEE Proceedings on Circuits, Devices and Systems,2002,149 (2):105-111.
[61]Williams D F, Remley K A. Analytic sampling-circuit model [J]. IEEE Transactions on Microwave Theory and Techniques,2001,49 (6):1013-1019.
[62]Raahemi B, Opal A. Time domain sensitivity of linear circuits using sampled data simulation [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2000,47 (6):948-957.
[63]张屹,魏学业,蒋海峰.模拟电路故障诊断中故障重分类方法的研究[J].北京交通大学学报：自然科学版,2006,30(2)：53-56.
[64]Zhang Yi, Wei Xueye, Jiang Haifeng. One-class Classifier Based on SBT for Analog Circuit Fault Diagnosis [J]. Measurement,2008,41 (4):371-380.
[65]赵录怀,王曙鸿.使用MATLAB软件的符号电路分析[J].电气电子教学学报,2001,23(1)：85-87.
[66]Rutkowski J, Macura A. Multiple fault location in AC circuits [J]. IEE Proceedings G on Electronic Circuits & Systems,1986,133 (6):279-284.
[67]邓聚龙.灰色控制系统(第二版)[M].武汉,华中理工大学出版社,1997,1-498.
[68]Deng Julong. Introduction of grey system theory [J]. Journal of Grey System,1989,1 (1): 1-24.
[69]Kusiak A, Kurasek C. Data mining of printed-circuit board defects [J]. IEEE Transactions on Robotics and Automation,2001,17 (2):191-196.
[70]孙勇成,周献中,李桂芳.基于灰色关联分析的仿真模型验证及其改进[J].系统仿真学报,2005,17(3)：522-524.
[71]Lu Feng. Research on the Identification Coefficient of Relational Grade for Grey System [J]. System Engineering Theory and Practice,1997,17(6):49-54.
[72]宋久鹏,董大伟,高国安.基于层次分析法和灰色关联度的方案决策模型研究[J].西南交通大学学报,2002,37(4)：463466.
[73]Marrian C R K, Mack I A, Banks C, et al. Electronic neural net algorithm for maximum entropy solutions to ill-posed problems. II. Multiply connected electronic circuit implementation [J]. IEEE Transactions on Circuits and Systems,1990,37 (1):110-113
[74]Yang C Y, Chou J J. Entropy on Grey Relational Analysis [J]. Journal of Grey System,2001, 14 (4):313-320.
[75]张岐山,郭喜江,邓聚龙.灰关联熵分析方法[J].系统工程理论与实践,1996,8：7-11.
[76]Urszula Boryczka. Finding Groups in Data:Cluster Analysis with Ants [J]. Applied Soft Computing,2009,9(1):61-70.
[77]A J Scott, M Knott. A cluster analysis method for grouping means in the analysis of variance [J]. Biometrics,1974,30:507-512.
[78]Stapper C H. Correlation analysis of particle clusters on integrated circuit wafers [J]. IBM Journal of Research and Development,1987,31 (6):641-650.
[79]崔江,王友仁.模拟电路故障的一种聚类二叉树支持向量机诊断新方法[J].仪器仪表学报,2008,29(10)：2047-2051.
[80]彭刚,彭敏放,何怡刚.基于聚类模糊神经网络的非线性电路故障诊断[J].微电子学与计算机,2006,23(8)：1-3.
[81]Varghese K, Williams J, Towill D. Simplified ATPG and analog fault location via a clustering and separability technique [J]. IEEE Transactions on Circuits and Systems,1979, 26 (7):496-505.
[82]Maqbool O, Babri H A. Hierarchical clustering for software architecture recovery [J]. IEEE Transactions on Software Engineering,2007,33(11):759-780.
[83]Li X. Parallel algorithms for hierarchical clustering and cluster validity [J]. IEEE Transactions on Pattern Analysis and Machines Intelligence,1990,12(11):1088-1092.
[84]Rajasekaran S. Efficient parallel hierarchical clustering algorithms [J]. IEEE Transactions on Parallel and Distributed Systems,2005,16 (6):497-502.
[85]Aichholzer O, Aurenhammer F, Brandstatter B. Evolution strategy and hierarchical clustering [J]. IEEE Transactions on Magnetics,2002,38 (2-1):1041-1044.
[86]Krinidis S, Chatzis V. A robust fuzzy local information C-means clustering algorithm [J]. IEEE Transactions on Image Processing,2010,19 (5):1328-1337.
[87]牛强,夏士雄,周勇,等.改进的模糊C-均值聚类方法[J].电子科技大学学报,2007,36(6)：1257-1259,1272.
[88]张洪刚,刘刚FCM-VKNN聚类算法的研究[J].自动化学报,2002,28(4)：631-636.
[89]Yu Jian, Shao Chao, Lin Youfang, et al. Why m> 1 in the FCM algorithm [J]. Chinese of Journal Electronics,2005,14 (2):215-219.
[90]高新波,谢维信.模糊c-均值聚类算法中加权指数m的研究[J].电子学报,2000,28(4)：80-83.
[91]Gopalan A, Titus A H. A new wide range Euclidean distance circuit for neural network hardware implementations [J]. IEEE Transactions on Neural Networks,2003,14 (5): 1176-1186.
[92]R De Maesschalck, D Jouan-Rimbaud, D L Massart. The Mahalanobis distance [J]. Chemometrics and Intelligent Laboratory Systems,2000,50 (1):1-18.
[93]Ververidis D, Kotropoulos C. Gaussian mixture modeling by exploiting the Mahalanobis distance [J]. IEEE Transactions on Signal Processing,2008,56 (7-1):2797-2811.
[94]秦庆强,张晓安,李艾华,等.马氏距离在模拟电路硬故障检测中的应用研究[J].电子测量与仪器学报,2009,23(7)：4145.
[95]Papakostas D K, Hatzopoulos A, A. Impact of parameter covariance on fault detectability estimation of analogue and mixed-mode circuits [J]. IEE Proceedings on Circuits, Devices and Systems,2003,150 (5):434-438.
[96]Besson O, Bidon S, Tourneret JY. Covariance matrix estimation with heterogeneous samples [J]. IEEE Transactions on Signal Processing,2008,56(3):909-920.
[97]Masakazu Iwamura, Shinichiro Omachi, Hirotomo Aso. Estimation of true Mahalanobis distance from eigenvectors of sample covariance matrix [J]. Systems and Computers in Japan,2004,35 (9):30-38.
[98]Zadeh LA. Fuzzy sets [J]. Information and Control,1965,8 (3):338-353.
[99]Chen J J, Chen, C C, Tsao H W. Turnable membership function circuit for fuzzy control systems using CMOS technology [J]. Electronics Letters,1992,28 (22):2101-2103.
[100]李炜,黄心汉,陈曦.一种基于模式类特征空间统计分布的离散模糊隶属度函数模型[J].信号处理,2004,20(2)：170-173.
[101]刘贵喜,赵曙光,杨万海.基于T-S模糊模型的隶属度函数学习算法[J].西安电子科技大学学报,2000,27(5)：550-553.
[102]范春彦,韩晓明,王献峰.基于最大隶属度的目标威胁评估与排序法[J].系统工程与电子技术,2003,25(1)：47-67.
[103]Basterretxea K, Tarela J M, del Campo I. Digital Gaussian membership function circuit for neuro-fuzzy hardware [J]. Electronics Letters,2006,42 (1):44-46.
[104]Arnold Kaufmann, MM Gupta. Introduction to Fuzzy Arithmetic:Theory and Applications [J]. International Journal of Approximate Reasoning,1987,1 (1):141-146.
[105]Lo Schiavo A, Luciano A M. Powerful and flexible fuzzy algorithm for nonlinear dynamic system identification [J]. IEEE Transactions on Fuzzy Systems,2001,9 (6):828-835.
[106]Hollstein T, Halgamuge S K, Glesner M. Computer-aided design of fuzzy systems based on generic VHDL specifications [J]. IEEE Transactions on Fuzzy Systems,1996,4 (4): 403-417.
[107]Ascia G, Catania V, Ficili G, et al. A VLSI fuzzy expert system for real-time traffic control in ATM networks [J]. IEEE Transactions on Fuzzy Systems,1997,5(1):20-31.
[108]Hurdle J F. The synthesis of compact fuzzy neural circuits [J]. IEEE Transactions on Fuzzy Systems,1997,5(1):44-55.
[109]Chuen-Yau Chen, Yuan-Ta Hsieh, Bin-Da Liu. Circuit implementation of linguistic-hedge fuzzy logic controller in current-mode approach [J]. IEEE Transactions on Fuzzy Systems, 2003,11 (5):624-646.
[110]Baturone I, Sanchez-Solano S, Barriga A. Implementation of CMOS fuzzy controllers as mixed-signal integrated circuits [J]. IEEE Transactions on Fuzzy Systems,1997,5 (1):1-19.
[111]Kinnaird C D, Khotanzad A. Adaptive fuzzy process control of integrated circuit wire bonding [J]. IEEE Transactions on Electronics Packaging Manufacturing,1999,22 (3): 233-243.
[112]Matekovits L, Vecchi G, Bercigli M, et al. Synthetic-Functions Analysis of Large Aperture-Coupled Antennas [J]. IEEE Transactions on Antennas and Propagation,2009, 57(7):1936-1943.
[113]李盛德.因素状态的合成与综合函数的构造[J].辽宁工程技术大学学报：自然科学版,2001,20(5)：621-622.
[114]何清,李洪兴.综合函数与扩展原理[J].模糊系统与数学,1999,13(1)：89-93.
[115]阎礼祥,覃征.非线性群决策系统多模型模糊控制算法研究[J].电子学报,2004,32(11)：1907-1909.
[2]Jun Xu, Jianliang Li, Yong Jiang. Components Locating in PCB Fault Diagnosis Based on Infrared Thermal Imaging [C]. Second International Conference on Information and Computing Science, Britain, Manchester,2009,2:7-9.
[3]Maccanelli M, Halliday A, Bell B, et al. Practical application of automated fault diagnosis at the chip and board levels [C]. IEEE International Workshop on Defect and Fault Tolerance in VLSI System, USA, Dallas,1992,297-304.
[4]Alippi C, Catelani M, Fort A, et al. Automated selection of test frequencies for fault diagnosis in analog electronic circuits [J]. IEEE Transaction on Instrumentation and Measurement,2005,54 (3):1033-1044.
[5]Chung K H, Shepherd P R, Eberhardt F, et al. Hierarchical fault diagnosis of analog integrated circuits [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2001,48 (8):921-929.
[6]Ogg S, Lesage S, Jervis B W, et al. Multiple fault diagnosis in analogue circuits using time domain response features and multilayer perceptrons [J]. IEE Proceedings on Circuits, Devices and Systems,1998,145 (4):213-218.
[7]Brygilewicz V, Wojciechowski J. Time-domain fault diagnosis of analogue circuits in the presence of noise [J]. IEE Proceedings on Circuits, Devices and Systems,1998,145 (2): 125-131.
[8]Worsman M, Wong M W T, Lee Y S. Enhancing the fault diagnosis of linear analog circuit steady-state DC testing through the analysis of equivalent faults [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2003,50 (7):932-936.
[9]杨士元.模拟系统的故障诊断与可靠性设计[M].北京,清华大学出版社,2001,1-16.
[10]Chen Y. Experiment on fault location in large-scale analog circuits [J]. IEEE Transaction on Instrumentation and Measurement,1993,42 (1):30-34.
[11]Baoguang Yan, Qingguo Fan, Bernstein J B, et al. Reliability Simulation and Circuit-Failure Analysis in Analog and Mixed-Signal Applications [J]. IEEE Transaction on Device and Materials Reliability,2009,9 (3):339-347.
[12]Sun Xiubin, Chen Guangju, Xie Yongle. Test Point Selection for Analog Integrated Circuit [J]. Journal of Electronics and Information Technology,2004,26 (4):645-650.
[13]Vladimir N Vapnik. An Overview of Statistical Learning Theory [J]. IEEE Transactions On Neural Network,1999,10 (5):988-999.
[14]Decherchi S, Gastaldo P, Parodi M, et al. Low-complexity, linear circuit implementation of support vector machines training [J]. Electronics Letters,2008,44 (25):1478-1479.
[15]Anguita D, Ridella S, Rovetta S. Circuital implementation of support vector machines [J]. Electronics Letters,1998,34(16):1596-1597.
[16]Chih-Chung Chang, Chihjen Lin. LIBSVM:A library for support vector machines [EB/OL]. 2010, http://www.csie.ntu.edu.tw/-cjlin/libsvm.
[17]Slamani M, Kaminska B. Fault observability analysis of analog circuits in frequency domain [J]. IEEE Transactions on Circuits and Systems II:Analog and Digital Signal Processing,1996,43 (2):134-139.
[18]Malyshenko Yu V. Functional fault models for analog circuits [J]. IEEE Design & Test of Computers,1998,15 (2):80-85.
[19]Tadeusiewicz M, Halgas S, Korzybski M. An algorithm for soft-fault diagnosis of linear and nonlinear circuits [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2002,49 (11):1648-1653.
[20]Prasad V C. Equations of nonlinear analogue circuit for fault dictionary generation [J]. Electronics Letters,1990,26 (1):24-25.
[21]Chess B, Larrabee T. Creating small fault dictionaries [J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1999,18 (3):346-356.
[22]Pomeranz I, Reddy S M. On dictionary-based fault location in digital logic circuits [J]. IEEE Transactions on Computers,1997,46 (1):48-59.
[23]Hagas Stanisaw. Multiple soft fault diagnosis of nonlinear circuits using the fault dictionary approach [J]. Bulletin of the Polish Academy of Sciences:Technical Sciences,2008,56 (1): 53-57.
[24]张伟,许爱强,陈振林.模拟电路节点电压灵敏度权序列故障字典法[J].电子测量与仪器学报,2006,20(4)：46-49.
[25]陈圣俭,石志勇.可诊断容差模拟电路软故障的新故障字典法[J].电子学报,2000,28(2)：127-129.
[26]Aminian F, Aminian M, Collins H, et al. Analog fault diagnosis of actual circuits using neural network [J]. IEEE Transaction on Instrumentation and Measurement,2002,51 (3): 544-550.
[27]Lifen Yuan, Yigang He, Jiaoying Huang. A new neural-network-based fault diagnosis approach for analog circuits by using kurtosis and entropy as a preprocessor [J]. IEEE Transaction on Instrumentation and Measurement,2010,59 (3):586-595.
[28]张维强,徐晨,宋国乡.模拟电路故障诊断的小波包预处理神经网络改进算法[J].信号处理,2007,23(2)：204-209.
[29]Aminian M, Aminian F. Neural-network based analog-circuit fault diagnosis using wavelet transform as preprocessor [J]. IEEE Transactions on Circuits and Systems Ⅱ:Analog and Digital Signal Processing,2000,47 (2):151-156.
[30]王承,陈光(礻禹ju),谢永乐.小波-神经网络在模拟电路故障诊断中的应用[J].系统仿真学报,2005,17(8)：1936-1938.
[31]He Y, Tan Y, Sun Y. Wavelet neural network approach for fault diagnosis of analogue circuits [J]. IEE Proceedings on Circuits, Devices and Systems,2004,151 (4):379-384.
[32]Peng Wang, Shiyuan Yang. A New Diagnosis Approach for Handling Tolerance in Analog and Mixed-signal Circuits by Using Fuzzy Math [J]. IEEE Transactions on Circuits and Systems Part 1:Regular Papers,2005,52 (10):2118-2127.
[33]王鹏宇,黄智刚.模糊理论与神经网络结合对模拟电路进行分层故障诊断[J].电子测量技术,2002,1：7-9.
[34]曹荣敏,关静丽,张果.电子电路模糊神经网络故障诊断研究及仿真[J].计算机仿真,2005,22(11)：165-168.
[35]谢琳,李凡长.一类动态模糊机器学习算法研究[J].电子学报,2008,36(B12)：114-119.
[36]王继成.基于认知模拟的自适应机器学习算法研究[J].软件学报,2001,12(8)：1205-1211.
[37]Jen-Tzung Chien, Jung-Chun Chen. Recursive bayesian linear regression for adaptive classification [J]. IEEE Transactions on Signal Processing,2009,57 (2):565-575.
[38]Hearst M A, Dumais S T, Osman E, et al. Support vector machines [J]. IEEE Intelligent Systems and Their Applications,1998,13 (4):18-28.
[39]Mangasarian O L, Musicant D R. Successive overrelaxation for support vector machines [J]. IEEE Transactions on Neural Networks,1999,10 (5):1032-1037.
[40]Scholkopf B, Kah-Kay Sung, Burges C J C, et al. Comparing support vector machines with Gaussian kernels to radial basis function classifiers [J]. IEEE Transactions on Signal Processing,1997,45 (11):2758-2765.
[41]Chih-Wei Hsu, Chih-Jen Lin. A comparison of methods for multiclass support vector machines[J]. IEEE Transactions on Neural Network,2002,13 (2):415-425.
[42]Mattera D, Palmieri F, Haykin S. An explicit algorithm for training support vector machines [J]. IEEE Signal Processing Letters,1999,6 (9):243-245.
[43]Chih-Chung Chang, Chih-Wei Hsu, Chih-Jen Lin. The analysis of decomposition methods for support vector machines [J]. IEEE Transactions on Neural Networks,2000,11 (4): 1003-1008.
[44]Sebald D J, Bucklew J A. Support vector machines techniques for nonlinear equalization [J]. IEEE Transactions on Signal Processing,2000,48 (11):3217-3226.
[45]Chun-Fu Lin, Sheng-De Wang. Fuzzy support vector machines [J]. IEEE Transactions On Neural Network,2002,13 (2):464-471.
[46]El-Turky F, Perry E E. BLADES:an artificial intelligence approach to analog circuit design [J]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems,1989, 8(6):680-692.
[47]王肃宁,杨士元,汪鹏.基于模式识别进行模拟电路故障诊断的方法[J].微电子学与计算机,2004,21(11)：113-116.
[48]李敏远,陈如清.一种基于模式识别的可控整流电路故障诊断方法[J].电工技术学报,2004,19(7)：53-58.
[49]吴洪兴,彭宇,彭喜元.基于支持向量机多分类方法的模拟电路故障诊断研究[J].电子测量与仪器学报,2007,21(4)：27-31.
[50]唐静远,师奕兵,张伟.基于支持向量机集成的模拟电路故障诊断[J].仪器仪表学报,2008,29(6)：1216-1220.
[51]宋国明,王厚军,刘红,等.基于提升小波变换和SVM的模拟电路故障诊断[J].电子测量与仪器学报,2010,24(1)：17-22.
[52]马晨光,胡昌华,骆功纯,等.粗糙集和支持向量机在复杂电路系统诊断中的应用[J].电光与控制,2009,16(3)：83-85,94.
[53]Pan Zhongliang, Chen Guangju. Neural network expert system approach for analog circuits fault diagnosis [J]电子科技大学学报,1997,26(4)：405-408.
[54]冯志红,林志贵,王炜.基于信息融合的模拟电路故障诊断方法分析[J].电子测量与仪器学报,2008,22(6)：47-53.
[55]Yanghong Tan, Yigang He, Chun Cui, et al. A Novel Method for Analog Fault Diagnosis Based on Neural Networks and Genetic Algorithms [J]. IEEE Transaction on Instrumentation and Measurement,2008,57 (11):2631-2639.
[56]于飞,田玲玲,刘喜梅,等.基于小波多分辨率分析和主元分析的电力电子电路故障诊断[J].华东理工大学学报：自然科学版,2006,32(9)：1113-1116,1125.
[57]周龙甫,师奕兵,李焱骏.容差条件下PSO算法诊断模拟电路单软故障方法[J].计算机辅助设计与图形学学报,2009,21(9)：1270-1274.
[58]Alippi C, Catelani M, Fort A, et al. SBT soft fault diagnosis in analog electronic circuits:a sensitivity-based approach by randomized algorithms [J]. IEEE Transaction on Instrumentation and Measurement,2002,51 (5):1116-1125.
[59]Jun Zhang, Chung H S, Lo A W, et al. Extended Ant Colony Optimization Algorithm for Power Electronic Circuit Design [J]. IEEE Transaction on Power Electronics,2009,24 (1): 147-162.
[60]Yuan F. Efficient sampled-data simulation method for transient analysis of nonlinear circuits [J]. IEE Proceedings on Circuits, Devices and Systems,2002,149 (2):105-111.
[61]Williams D F, Remley K A. Analytic sampling-circuit model [J]. IEEE Transactions on Microwave Theory and Techniques,2001,49 (6):1013-1019.
[62]Raahemi B, Opal A. Time domain sensitivity of linear circuits using sampled data simulation [J]. IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2000,47 (6):948-957.
[63]张屹,魏学业,蒋海峰.模拟电路故障诊断中故障重分类方法的研究[J].北京交通大学学报：自然科学版,2006,30(2)：53-56.
[64]Zhang Yi, Wei Xueye, Jiang Haifeng. One-class Classifier Based on SBT for Analog Circuit Fault Diagnosis [J]. Measurement,2008,41 (4):371-380.
[65]赵录怀,王曙鸿.使用MATLAB软件的符号电路分析[J].电气电子教学学报,2001,23(1)：85-87.
[66]Rutkowski J, Macura A. Multiple fault location in AC circuits [J]. IEE Proceedings G on Electronic Circuits & Systems,1986,133 (6):279-284.
[67]邓聚龙.灰色控制系统(第二版)[M].武汉,华中理工大学出版社,1997,1-498.
[68]Deng Julong. Introduction of grey system theory [J]. Journal of Grey System,1989,1 (1): 1-24.
[69]Kusiak A, Kurasek C. Data mining of printed-circuit board defects [J]. IEEE Transactions on Robotics and Automation,2001,17 (2):191-196.
[70]孙勇成,周献中,李桂芳.基于灰色关联分析的仿真模型验证及其改进[J].系统仿真学报,2005,17(3)：522-524.
[71]Lu Feng. Research on the Identification Coefficient of Relational Grade for Grey System [J]. System Engineering Theory and Practice,1997,17(6):49-54.
[72]宋久鹏,董大伟,高国安.基于层次分析法和灰色关联度的方案决策模型研究[J].西南交通大学学报,2002,37(4)：463466.
[73]Marrian C R K, Mack I A, Banks C, et al. Electronic neural net algorithm for maximum entropy solutions to ill-posed problems. II. Multiply connected electronic circuit implementation [J]. IEEE Transactions on Circuits and Systems,1990,37 (1):110-113
[74]Yang C Y, Chou J J. Entropy on Grey Relational Analysis [J]. Journal of Grey System,2001, 14 (4):313-320.
[75]张岐山,郭喜江,邓聚龙.灰关联熵分析方法[J].系统工程理论与实践,1996,8：7-11.
[76]Urszula Boryczka. Finding Groups in Data:Cluster Analysis with Ants [J]. Applied Soft Computing,2009,9(1):61-70.
[77]A J Scott, M Knott. A cluster analysis method for grouping means in the analysis of variance [J]. Biometrics,1974,30:507-512.
[78]Stapper C H. Correlation analysis of particle clusters on integrated circuit wafers [J]. IBM Journal of Research and Development,1987,31 (6):641-650.
[79]崔江,王友仁.模拟电路故障的一种聚类二叉树支持向量机诊断新方法[J].仪器仪表学报,2008,29(10)：2047-2051.
[80]彭刚,彭敏放,何怡刚.基于聚类模糊神经网络的非线性电路故障诊断[J].微电子学与计算机,2006,23(8)：1-3.
[81]Varghese K, Williams J, Towill D. Simplified ATPG and analog fault location via a clustering and separability technique [J]. IEEE Transactions on Circuits and Systems,1979, 26 (7):496-505.
[82]Maqbool O, Babri H A. Hierarchical clustering for software architecture recovery [J]. IEEE Transactions on Software Engineering,2007,33(11):759-780.
[83]Li X. Parallel algorithms for hierarchical clustering and cluster validity [J]. IEEE Transactions on Pattern Analysis and Machines Intelligence,1990,12(11):1088-1092.
[84]Rajasekaran S. Efficient parallel hierarchical clustering algorithms [J]. IEEE Transactions on Parallel and Distributed Systems,2005,16 (6):497-502.
[85]Aichholzer O, Aurenhammer F, Brandstatter B. Evolution strategy and hierarchical clustering [J]. IEEE Transactions on Magnetics,2002,38 (2-1):1041-1044.
[86]Krinidis S, Chatzis V. A robust fuzzy local information C-means clustering algorithm [J]. IEEE Transactions on Image Processing,2010,19 (5):1328-1337.
[87]牛强,夏士雄,周勇,等.改进的模糊C-均值聚类方法[J].电子科技大学学报,2007,36(6)：1257-1259,1272.
[88]张洪刚,刘刚FCM-VKNN聚类算法的研究[J].自动化学报,2002,28(4)：631-636.
[89]Yu Jian, Shao Chao, Lin Youfang, et al. Why m> 1 in the FCM algorithm [J]. Chinese of Journal Electronics,2005,14 (2):215-219.
[90]高新波,谢维信.模糊c-均值聚类算法中加权指数m的研究[J].电子学报,2000,28(4)：80-83.
[91]Gopalan A, Titus A H. A new wide range Euclidean distance circuit for neural network hardware implementations [J]. IEEE Transactions on Neural Networks,2003,14 (5): 1176-1186.
[92]R De Maesschalck, D Jouan-Rimbaud, D L Massart. The Mahalanobis distance [J]. Chemometrics and Intelligent Laboratory Systems,2000,50 (1):1-18.
[93]Ververidis D, Kotropoulos C. Gaussian mixture modeling by exploiting the Mahalanobis distance [J]. IEEE Transactions on Signal Processing,2008,56 (7-1):2797-2811.
[94]秦庆强,张晓安,李艾华,等.马氏距离在模拟电路硬故障检测中的应用研究[J].电子测量与仪器学报,2009,23(7)：4145.
[95]Papakostas D K, Hatzopoulos A, A. Impact of parameter covariance on fault detectability estimation of analogue and mixed-mode circuits [J]. IEE Proceedings on Circuits, Devices and Systems,2003,150 (5):434-438.
[96]Besson O, Bidon S, Tourneret JY. Covariance matrix estimation with heterogeneous samples [J]. IEEE Transactions on Signal Processing,2008,56(3):909-920.
[97]Masakazu Iwamura, Shinichiro Omachi, Hirotomo Aso. Estimation of true Mahalanobis distance from eigenvectors of sample covariance matrix [J]. Systems and Computers in Japan,2004,35 (9):30-38.
[98]Zadeh LA. Fuzzy sets [J]. Information and Control,1965,8 (3):338-353.
[99]Chen J J, Chen, C C, Tsao H W. Turnable membership function circuit for fuzzy control systems using CMOS technology [J]. Electronics Letters,1992,28 (22):2101-2103.
[100]李炜,黄心汉,陈曦.一种基于模式类特征空间统计分布的离散模糊隶属度函数模型[J].信号处理,2004,20(2)：170-173.
[101]刘贵喜,赵曙光,杨万海.基于T-S模糊模型的隶属度函数学习算法[J].西安电子科技大学学报,2000,27(5)：550-553.
[102]范春彦,韩晓明,王献峰.基于最大隶属度的目标威胁评估与排序法[J].系统工程与电子技术,2003,25(1)：47-67.
[103]Basterretxea K, Tarela J M, del Campo I. Digital Gaussian membership function circuit for neuro-fuzzy hardware [J]. Electronics Letters,2006,42 (1):44-46.
[104]Arnold Kaufmann, MM Gupta. Introduction to Fuzzy Arithmetic:Theory and Applications [J]. International Journal of Approximate Reasoning,1987,1 (1):141-146.
[105]Lo Schiavo A, Luciano A M. Powerful and flexible fuzzy algorithm for nonlinear dynamic system identification [J]. IEEE Transactions on Fuzzy Systems,2001,9 (6):828-835.
[106]Hollstein T, Halgamuge S K, Glesner M. Computer-aided design of fuzzy systems based on generic VHDL specifications [J]. IEEE Transactions on Fuzzy Systems,1996,4 (4): 403-417.
[107]Ascia G, Catania V, Ficili G, et al. A VLSI fuzzy expert system for real-time traffic control in ATM networks [J]. IEEE Transactions on Fuzzy Systems,1997,5(1):20-31.
[108]Hurdle J F. The synthesis of compact fuzzy neural circuits [J]. IEEE Transactions on Fuzzy Systems,1997,5(1):44-55.
[109]Chuen-Yau Chen, Yuan-Ta Hsieh, Bin-Da Liu. Circuit implementation of linguistic-hedge fuzzy logic controller in current-mode approach [J]. IEEE Transactions on Fuzzy Systems, 2003,11 (5):624-646.
[110]Baturone I, Sanchez-Solano S, Barriga A. Implementation of CMOS fuzzy controllers as mixed-signal integrated circuits [J]. IEEE Transactions on Fuzzy Systems,1997,5 (1):1-19.
[111]Kinnaird C D, Khotanzad A. Adaptive fuzzy process control of integrated circuit wire bonding [J]. IEEE Transactions on Electronics Packaging Manufacturing,1999,22 (3): 233-243.
[112]Matekovits L, Vecchi G, Bercigli M, et al. Synthetic-Functions Analysis of Large Aperture-Coupled Antennas [J]. IEEE Transactions on Antennas and Propagation,2009, 57(7):1936-1943.
[113]李盛德.因素状态的合成与综合函数的构造[J].辽宁工程技术大学学报：自然科学版,2001,20(5)：621-622.
[114]何清,李洪兴.综合函数与扩展原理[J].模糊系统与数学,1999,13(1)：89-93.
[115]阎礼祥,覃征.非线性群决策系统多模型模糊控制算法研究[J].电子学报,2004,32(11)：1907-1909.