局部放电灰度图像模式识别与分形压缩方法应用研究
|
摘要
绝缘内部局部放电被广泛认为是导致电气设备绝缘劣化的重要因素，与高电压电气设备运行的安全性和可靠性具有密切联系。局部放电在线监测系统中的放电类型自动识别，能够及时发现绝缘内部局部缺陷及放电发展程度，防止事故发生。针对局部放电模式自动识别的需要，作者系统地研究了局部放电灰度图像自动识别中的基本理论和实现方法：
(1)根据变压器局部放电在线监测的要求，设计了放电模型和实验方法，并通过模型实验获得了大量放电样本数据，为构造局部放电灰度图像和采用BPNN进行识别作好准备；
(2)研究了局部放电灰度图像的构造方法以及降维构造32×32灰度和矩阵的方法；在用人工神经网络对局部放电进行模式识别时，分析了BP网络的优缺点，对典型BP网络的结构和学习训练算法提出了改进，采用带有偏差单元的递归神经网络作为模式分类器；采用32×32灰度和矩阵进行BPNN识别结果表明这种方法是有效的。
(3)研究了局部放电灰度图像的四叉树分形图像压缩方法，通过仿真实验证明采用本文算法能够获得一定的图像压缩比，在局部放电灰度图像压缩应用中显示了良好的压缩效果，进一步研究了局部放电解码图像的识别结果与原始图像之结果的差异程度，研究结果初步表明该方法应用于局部放电模式自动识别系统中是有效的；
(4)研究了基于局部放电解码图像的BPNN识别方法及，通过分析对解码图像的识别效果，验证了设计的系统模式识别方案的有效性，同时表明该方案能够满足实地局部放电模式自动识别和远程数据通讯及自动识别的需要。
以上研究表明，提出的局部放电识别特征集与分形图像压缩方法，能够有效地应用于局部放电模式自动识别，并获得了良好的识别效果。
Partial discharge (PD) inside insulation is considered as one major cause of insulation degradation in electrical equipment and attached importance to the safety and reliability of running electrical equipment. Auto-recognition to discharge types in on-line PD monitoring system could be used to find out internal partial defects and the relevant discharge development degree in time,and then prevents equipment from the coming faults. According to the requirements to PD pattern auto-recognition,this paper studies systematically the basic theories and realizable methods for auto-recognition of PD gray intensity image:
(1) In the requirement of on-line PD monitoring for transformer,several discharge models are designed and the relevant experiment methods projected. With discharge model tests,a lot of discharge sample data is acquired. On the base of systematical research on recognition for PD gray intensity image,this paper puts forward two kinds of fractal features,the 2nd generalized dimensions of original PD images and fractal dimensions of high gray intensity PD images,and then the relevant extraction methods. Meantime,moments and correlative statistical features are studied for recognition of PD gray intensity images. Moreover,it's the first time to put forward and study the method to use recognition feature set consisting of above three kinds of features for auto-recognition of PD pattern.
(2) When applying the artificial neural network to recognize the PD patterns,merits and defects of BPNN wa:> researched,the structure .. learning arithmetic and training arithmetic were improved,and recursion NN with windage cell was designed. Aim at the problem of NN input choice,a new way which use a B Sk and Ku to generate input vector was brought forward. From the results of comparison with data array input method,it showed that the former has better effect and simplified the NN structure and shortened the learning time.
(3) This paper studies the method of quadtree partitioning fractal image compression (FIC) for PD gray intensity image. The simulation test results show that determinate compression ratio is achieved by the algorithm
proposed in this paper. Furthermore,good compression effectivity is presented in application to compression of PD gray intensity images. According to the research on difference degree between computational values of fractal features extracted from decoded PD images and that from original images,it is shown elementarily that the proposed method is effective for application in PD pattern auto-recognition system.
(4) This paper brings forward PD pattern auto-recognition project based on the above recognition features and fractal compression of PD gray intensity images and designs the classifier with back-propagation neural network (BPNN). The comparatively high recognition correctness probability is achieved in classification to original PD images. According to furthermore researches on recognition of decoded PD images,it is testified and meanwhile shown that the designed project for PD pattern auto-recognition is effective and can meet requirements for PD pattern auto-recognition in field and PD data telecommunication and remote auto-recognition.
The above research results show that the proposed PD recognition features set and FIC method,can be effectively used for PD pattern recognition and good recognition results are achieved.
(1)根据变压器局部放电在线监测的要求，设计了放电模型和实验方法，并通过模型实验获得了大量放电样本数据，为构造局部放电灰度图像和采用BPNN进行识别作好准备；
(2)研究了局部放电灰度图像的构造方法以及降维构造32×32灰度和矩阵的方法；在用人工神经网络对局部放电进行模式识别时，分析了BP网络的优缺点，对典型BP网络的结构和学习训练算法提出了改进，采用带有偏差单元的递归神经网络作为模式分类器；采用32×32灰度和矩阵进行BPNN识别结果表明这种方法是有效的。
(3)研究了局部放电灰度图像的四叉树分形图像压缩方法，通过仿真实验证明采用本文算法能够获得一定的图像压缩比，在局部放电灰度图像压缩应用中显示了良好的压缩效果，进一步研究了局部放电解码图像的识别结果与原始图像之结果的差异程度，研究结果初步表明该方法应用于局部放电模式自动识别系统中是有效的；
(4)研究了基于局部放电解码图像的BPNN识别方法及，通过分析对解码图像的识别效果，验证了设计的系统模式识别方案的有效性，同时表明该方案能够满足实地局部放电模式自动识别和远程数据通讯及自动识别的需要。
以上研究表明，提出的局部放电识别特征集与分形图像压缩方法，能够有效地应用于局部放电模式自动识别，并获得了良好的识别效果。
Partial discharge (PD) inside insulation is considered as one major cause of insulation degradation in electrical equipment and attached importance to the safety and reliability of running electrical equipment. Auto-recognition to discharge types in on-line PD monitoring system could be used to find out internal partial defects and the relevant discharge development degree in time,and then prevents equipment from the coming faults. According to the requirements to PD pattern auto-recognition,this paper studies systematically the basic theories and realizable methods for auto-recognition of PD gray intensity image:
(1) In the requirement of on-line PD monitoring for transformer,several discharge models are designed and the relevant experiment methods projected. With discharge model tests,a lot of discharge sample data is acquired. On the base of systematical research on recognition for PD gray intensity image,this paper puts forward two kinds of fractal features,the 2nd generalized dimensions of original PD images and fractal dimensions of high gray intensity PD images,and then the relevant extraction methods. Meantime,moments and correlative statistical features are studied for recognition of PD gray intensity images. Moreover,it's the first time to put forward and study the method to use recognition feature set consisting of above three kinds of features for auto-recognition of PD pattern.
(2) When applying the artificial neural network to recognize the PD patterns,merits and defects of BPNN wa:> researched,the structure .. learning arithmetic and training arithmetic were improved,and recursion NN with windage cell was designed. Aim at the problem of NN input choice,a new way which use a B Sk and Ku to generate input vector was brought forward. From the results of comparison with data array input method,it showed that the former has better effect and simplified the NN structure and shortened the learning time.
(3) This paper studies the method of quadtree partitioning fractal image compression (FIC) for PD gray intensity image. The simulation test results show that determinate compression ratio is achieved by the algorithm
proposed in this paper. Furthermore,good compression effectivity is presented in application to compression of PD gray intensity images. According to the research on difference degree between computational values of fractal features extracted from decoded PD images and that from original images,it is shown elementarily that the proposed method is effective for application in PD pattern auto-recognition system.
(4) This paper brings forward PD pattern auto-recognition project based on the above recognition features and fractal compression of PD gray intensity images and designs the classifier with back-propagation neural network (BPNN). The comparatively high recognition correctness probability is achieved in classification to original PD images. According to furthermore researches on recognition of decoded PD images,it is testified and meanwhile shown that the designed project for PD pattern auto-recognition is effective and can meet requirements for PD pattern auto-recognition in field and PD data telecommunication and remote auto-recognition.
The above research results show that the proposed PD recognition features set and FIC method,can be effectively used for PD pattern recognition and good recognition results are achieved.
引文
[1] 朱德恒，严璋主编．高电压绝缘．第1版．北京：清华大学出版社．1992年2月
[2] [苏]库钦斯基著，徐永禧，胡维新译，高压电气设备局部放电，第1版，北京：水利电力出版社，1984年6月
[3] 葛景滂，邱昌容主编：局部放电测量，第1版，北京：机械工业出版社，1984年6月
[4] 朱德恒，谈克雄主编，电绝缘诊断技术，第1版，北京：中国电力出版社，1999年4月
[5] A. Lapp and H.-G. Kranz. "The Use of the CIGRE Data Format for PD Diagnosis Applications". IEEE Trans. on Dielectrics and Electrical Insulation. Vol.7 No. 1. Feb. 2000. pp102-112
[6] Marek Florkowski. "Wavelet Denoisiong of Partial Discharge Images". Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials. June 21-26, 2000, Xi'an, China. Pp459-462
[7] H.Borsi. "A PD Measuring and Evaluation System Based on Digital Signal Processing". IEEE Trans. on Dielectrics and Electrical Insulation. Vol.7 No. 1. Feb. 2000. Pp21-29
[8] R.Schifani, R.Candela. A New Algorithm for Mixed Weibull Analysis Of Partial Discharge Amplitude Distriburions. IEEE Trans On Dielectrics and Electrical Insulation,VOL.6 No.2,1999.
[9] Jean Jacquelin. Inference of Sampling on Weibull Representation. IEEE Transaction on Dielectrics and Electrical Insulation, Vol.3, No.6, December 1996.
[10] G.C.Montanari. Optimum Estimators for the Weibull Distribution from Censored Test Data. IEEE Transaction on Dielectrics and Electrical Insulation, Vol.5, No.2, December 1998.
[11] A.Contin, G.Rabach. PD Analysis of Rotating ac Machines. IEEE Transaction on Electrical Insulation, Vol.28, No.6, December 1993.
[12] Jean Jacquelin. Inference of Sampling on Weibull Parameter Estimation. IEEE Transaction on Dielectrics and Electrical Insulation, Vol.3, No.6, December 1996.
[13] R. Candela, G. Mirelli, R. Schifani. "PD Recognition by Means of Statistical and Fractal Parameters and a Neural Network". IEEE Trans. on Dielectrics and Electrical Insulation. Vol.7 No. 1. Feb. 2000. pp87-94
[14] 李新，局部放电在线监测的信号重构和模式识别方法的研究，重庆大学博士论文，1999年7月
[15] 文志英编著．分形几何的数学基础．第1版．上海：上海科技教育出版社．2000年12月
[16] 杨展如编著．分形物理学．第1版．上海：上海科技教育出版社．1996年9月
[17] 王东生，曹磊编著．混沌、分形及其应用．第1版．合肥：中国科学技术大学出版社．1995年6月
[18] 刘式达，刘式适编著．分维和分形引论．第1版．北京：气象出版社．1993年9月
[19] 谢和平，薛秀谦编著．分形应用中的数学基础与方法．第1版．北京：科学出版社．1997年3月
[20] Paul Meakin著．分形、标度及远离平衡态的增长(影印本)．第1版．北京：清华大学出版社．2000年6月
[21] 伯努瓦．B．曼德布罗特著．陈守吉，凌复华译．大自然的分形几何学(最新修订本)．第1版．上海：上海远东出版社．1998年12月
[22] 李后强，汪富泉．“分形理论及其在分子科学中的应用”．第1版．北京：科学出版社．1993年12月
[23] Nirupam Sarker and B. B. Chaudhuri. "An efficient differential box-counting approach to compute
fractal dimension of image". IEEE Trans. on systems, man, and cybernetics. Vol. 24. No. 1. Jan. 1994. pp115-120
[24] 1版．上海：王士同编著．模糊系统、模糊神经网络及应用程序设计．第上海科学技术文献出版社．1998年12月
[25] Amira A.Mazroua. R.Bartnikas M.M.A.Salama."Neural Network System using the Multi layer Perception technique for the Recognition of PD Pulse Shapes due to Cavities and Electrical Trees" IEEE Transaction on Power Delivery. Vol. 10 No. 1 Jan. 1995
[26] L.satish and Walter. S.Zengl."Artificial Neural Networks for Recognition of 3-d Partial Discharge Patterns" IEEE Transaction on DEl. Vol1
[27] Armin Schnettler, Michael Kurrat. "Partial Discharge Diagnosis Using Artificial Neural Network". 8th International Symposium on High Voltage Engineering, Ylkohama, Japan. Aug. 23-27, 1993 .pp.57-60
[28] B.T. Phung, T. R. Blackburn and R. E. James. "A Neural Network for Discharge Recognition Based on Integrated and Statistical Parameters". 8th International Symposium on High Voltage Engineering, Ylkohama, Japan. Aug. 23-27, 1993. Pp61-64
[29] C. Chang and Q. Su. "Partial Discharge Source Identification Using SOFM and MLP Neural Networks". Proceedings of the 1st International Conference aon Insulation Conditiion Monitoring of Electrical Plant. Wuhan. China. Sep. 24-26. 2000. Pp190-195
[30] Guangning Wu, Xiongwei Jiang and Hengkun Xie. "A Neural Network Used for PD Pattern Recognition with Genetic Algorithm". Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials. June 21-26, 2000, Xi'an, China. Pp.451-454
[31] 庄楚强，吴亚森编．应用数理统计基础．第1版．广州：华南理工大学出版社．1992年11月
[32] 袁曾任主编．人工神经网络及其应用．第1版．北京：清华大学出版社．南宁：广西科学技术出版社．1999年10月
[33] 王永骥，涂健．神经元网络控制．第1版．北京：机械工业出版社．1998年2月
[34] 王士同编著．模糊系统、模糊神经网络及应用程序设计．第1版．上海：上海科学技术文献出版社．1998年12月
[35] 赵振宇，徐用懋．模糊理论和神经网络的应用基础．第1版．北京：清华大学出版社．南宁：广西科学技术出版社．1996年6月
[36] 戴葵编著．神经网络实现技术．第1版．长沙：国防科技大学出版社．1998年7月
[37] 黄凤岗，宋克欧编著．模式识别．第1版．哈尔滨：哈尔滨工程大学出版社．1998年3月
[38] 吴乐男编著．数据压缩．第1版．北京：电子工业出版社．2000年6月
[39] 边肇祺，张学工等编著．模式识别．第2版．北京：清华大学出版社．2000年1月
[40] 阮秋琦编著．数字图像处理学．第1版．北京：电子工业出版社．2001年1月
[41] 吴乐男编著．数据压缩．第1版．北京：电子工业出版社．2000年6月
[42] 李在铭等编著．数字图像处理压缩与识别技术．第1版．成都：电子科技大学出版社．2000年11月
[43] Jiang Lei, Zhu Deheng, Li Fuqi, Tan Kexiongm Qin Gangli, Jin Xianhe, Wang Changchang, T. C. Cheng. "Partial Discharge Pattern Recognition of Insulation Models of Power Transformers". Proceedings of the 6th International Conference on Properties and Applications of Dielectric
Materials. June 21-26, 2000, Xi'an, China. Pp129-132
[44] Kai Gao, Kexiong, Fuqi Li, Jing Huang. "Simulation Study on Discharge Recognition by Using Fractal Features". Proceedings of the Asian Conference of Electrical Insulation Diagnosis '99. Cheongju, Korea. Nov. 18-23, 1999.
[45] G. Nell and K. M. Curtis. "Shape Recognition Using Fractal Dimension". Pattern Recognition. Vol. 30. No.12. 1997. pp1957-1969
[46] M Hoof, R. Patsch. "Pulse-Sequence Analysis: A New Method for Investigation the Physics of PD-induced aging", IEE Proc.-Sci. Meas. Technol., Col.142, No.1, January 1995. Pp95-101
[47] 王汇源编著．数字图像通信原理与技术．第1版．北京：国防工业出版社．2000年9月．
[48] 王财胜．神经网络在大型电力变压器运行状态监测中的应用研究．重庆大学工学硕士论文．重庆．1997年6月
[49] 马波，裘正定．“图象分形编码研究现状”．信号处理．第15卷第3期．1999年9月．pp212-219
[50] 高凯，谈克雄，李福祺，吴成琦．“基于神经元网络的发电机定子模型线棒放电模式识别的研究”．中国电机工程学报．第19卷第10期．1999年10月．Pp64-71．
[51] 姜磊，朱德恒，李福祺，谈克雄，覃刚力，金显贺，王昌长，T.C.Tang.“基于人工神经网络绝缘模型放电模式识别的研究”．中国电机工程学报．第21卷第1期．2001年1月．Pp21-24
[52] Jiang Lei, Zhu Deheng, Li Fuqi, Tan Kexiongm Qin Gangli, Jin Xianhe, Wang Changchang, T. C. Cheng. "Partial Discharge Pattern Recognition of Insulation Models of Power Transformers". Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials. June 21-26, 2000, Xi'an, China. Pp129-132
[53] G. Neil and K. M. Curtis. "Shape Recognition Using Fractal Dimension". Pattern Recognition. Vol. 30. No.12. 1997. pp1957-1969
[2] [苏]库钦斯基著，徐永禧，胡维新译，高压电气设备局部放电，第1版，北京：水利电力出版社，1984年6月
[3] 葛景滂，邱昌容主编：局部放电测量，第1版，北京：机械工业出版社，1984年6月
[4] 朱德恒，谈克雄主编，电绝缘诊断技术，第1版，北京：中国电力出版社，1999年4月
[5] A. Lapp and H.-G. Kranz. "The Use of the CIGRE Data Format for PD Diagnosis Applications". IEEE Trans. on Dielectrics and Electrical Insulation. Vol.7 No. 1. Feb. 2000. pp102-112
[6] Marek Florkowski. "Wavelet Denoisiong of Partial Discharge Images". Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials. June 21-26, 2000, Xi'an, China. Pp459-462
[7] H.Borsi. "A PD Measuring and Evaluation System Based on Digital Signal Processing". IEEE Trans. on Dielectrics and Electrical Insulation. Vol.7 No. 1. Feb. 2000. Pp21-29
[8] R.Schifani, R.Candela. A New Algorithm for Mixed Weibull Analysis Of Partial Discharge Amplitude Distriburions. IEEE Trans On Dielectrics and Electrical Insulation,VOL.6 No.2,1999.
[9] Jean Jacquelin. Inference of Sampling on Weibull Representation. IEEE Transaction on Dielectrics and Electrical Insulation, Vol.3, No.6, December 1996.
[10] G.C.Montanari. Optimum Estimators for the Weibull Distribution from Censored Test Data. IEEE Transaction on Dielectrics and Electrical Insulation, Vol.5, No.2, December 1998.
[11] A.Contin, G.Rabach. PD Analysis of Rotating ac Machines. IEEE Transaction on Electrical Insulation, Vol.28, No.6, December 1993.
[12] Jean Jacquelin. Inference of Sampling on Weibull Parameter Estimation. IEEE Transaction on Dielectrics and Electrical Insulation, Vol.3, No.6, December 1996.
[13] R. Candela, G. Mirelli, R. Schifani. "PD Recognition by Means of Statistical and Fractal Parameters and a Neural Network". IEEE Trans. on Dielectrics and Electrical Insulation. Vol.7 No. 1. Feb. 2000. pp87-94
[14] 李新，局部放电在线监测的信号重构和模式识别方法的研究，重庆大学博士论文，1999年7月
[15] 文志英编著．分形几何的数学基础．第1版．上海：上海科技教育出版社．2000年12月
[16] 杨展如编著．分形物理学．第1版．上海：上海科技教育出版社．1996年9月
[17] 王东生，曹磊编著．混沌、分形及其应用．第1版．合肥：中国科学技术大学出版社．1995年6月
[18] 刘式达，刘式适编著．分维和分形引论．第1版．北京：气象出版社．1993年9月
[19] 谢和平，薛秀谦编著．分形应用中的数学基础与方法．第1版．北京：科学出版社．1997年3月
[20] Paul Meakin著．分形、标度及远离平衡态的增长(影印本)．第1版．北京：清华大学出版社．2000年6月
[21] 伯努瓦．B．曼德布罗特著．陈守吉，凌复华译．大自然的分形几何学(最新修订本)．第1版．上海：上海远东出版社．1998年12月
[22] 李后强，汪富泉．“分形理论及其在分子科学中的应用”．第1版．北京：科学出版社．1993年12月
[23] Nirupam Sarker and B. B. Chaudhuri. "An efficient differential box-counting approach to compute
fractal dimension of image". IEEE Trans. on systems, man, and cybernetics. Vol. 24. No. 1. Jan. 1994. pp115-120
[24] 1版．上海：王士同编著．模糊系统、模糊神经网络及应用程序设计．第上海科学技术文献出版社．1998年12月
[25] Amira A.Mazroua. R.Bartnikas M.M.A.Salama."Neural Network System using the Multi layer Perception technique for the Recognition of PD Pulse Shapes due to Cavities and Electrical Trees" IEEE Transaction on Power Delivery. Vol. 10 No. 1 Jan. 1995
[26] L.satish and Walter. S.Zengl."Artificial Neural Networks for Recognition of 3-d Partial Discharge Patterns" IEEE Transaction on DEl. Vol1
[27] Armin Schnettler, Michael Kurrat. "Partial Discharge Diagnosis Using Artificial Neural Network". 8th International Symposium on High Voltage Engineering, Ylkohama, Japan. Aug. 23-27, 1993 .pp.57-60
[28] B.T. Phung, T. R. Blackburn and R. E. James. "A Neural Network for Discharge Recognition Based on Integrated and Statistical Parameters". 8th International Symposium on High Voltage Engineering, Ylkohama, Japan. Aug. 23-27, 1993. Pp61-64
[29] C. Chang and Q. Su. "Partial Discharge Source Identification Using SOFM and MLP Neural Networks". Proceedings of the 1st International Conference aon Insulation Conditiion Monitoring of Electrical Plant. Wuhan. China. Sep. 24-26. 2000. Pp190-195
[30] Guangning Wu, Xiongwei Jiang and Hengkun Xie. "A Neural Network Used for PD Pattern Recognition with Genetic Algorithm". Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials. June 21-26, 2000, Xi'an, China. Pp.451-454
[31] 庄楚强，吴亚森编．应用数理统计基础．第1版．广州：华南理工大学出版社．1992年11月
[32] 袁曾任主编．人工神经网络及其应用．第1版．北京：清华大学出版社．南宁：广西科学技术出版社．1999年10月
[33] 王永骥，涂健．神经元网络控制．第1版．北京：机械工业出版社．1998年2月
[34] 王士同编著．模糊系统、模糊神经网络及应用程序设计．第1版．上海：上海科学技术文献出版社．1998年12月
[35] 赵振宇，徐用懋．模糊理论和神经网络的应用基础．第1版．北京：清华大学出版社．南宁：广西科学技术出版社．1996年6月
[36] 戴葵编著．神经网络实现技术．第1版．长沙：国防科技大学出版社．1998年7月
[37] 黄凤岗，宋克欧编著．模式识别．第1版．哈尔滨：哈尔滨工程大学出版社．1998年3月
[38] 吴乐男编著．数据压缩．第1版．北京：电子工业出版社．2000年6月
[39] 边肇祺，张学工等编著．模式识别．第2版．北京：清华大学出版社．2000年1月
[40] 阮秋琦编著．数字图像处理学．第1版．北京：电子工业出版社．2001年1月
[41] 吴乐男编著．数据压缩．第1版．北京：电子工业出版社．2000年6月
[42] 李在铭等编著．数字图像处理压缩与识别技术．第1版．成都：电子科技大学出版社．2000年11月
[43] Jiang Lei, Zhu Deheng, Li Fuqi, Tan Kexiongm Qin Gangli, Jin Xianhe, Wang Changchang, T. C. Cheng. "Partial Discharge Pattern Recognition of Insulation Models of Power Transformers". Proceedings of the 6th International Conference on Properties and Applications of Dielectric
Materials. June 21-26, 2000, Xi'an, China. Pp129-132
[44] Kai Gao, Kexiong, Fuqi Li, Jing Huang. "Simulation Study on Discharge Recognition by Using Fractal Features". Proceedings of the Asian Conference of Electrical Insulation Diagnosis '99. Cheongju, Korea. Nov. 18-23, 1999.
[45] G. Nell and K. M. Curtis. "Shape Recognition Using Fractal Dimension". Pattern Recognition. Vol. 30. No.12. 1997. pp1957-1969
[46] M Hoof, R. Patsch. "Pulse-Sequence Analysis: A New Method for Investigation the Physics of PD-induced aging", IEE Proc.-Sci. Meas. Technol., Col.142, No.1, January 1995. Pp95-101
[47] 王汇源编著．数字图像通信原理与技术．第1版．北京：国防工业出版社．2000年9月．
[48] 王财胜．神经网络在大型电力变压器运行状态监测中的应用研究．重庆大学工学硕士论文．重庆．1997年6月
[49] 马波，裘正定．“图象分形编码研究现状”．信号处理．第15卷第3期．1999年9月．pp212-219
[50] 高凯，谈克雄，李福祺，吴成琦．“基于神经元网络的发电机定子模型线棒放电模式识别的研究”．中国电机工程学报．第19卷第10期．1999年10月．Pp64-71．
[51] 姜磊，朱德恒，李福祺，谈克雄，覃刚力，金显贺，王昌长，T.C.Tang.“基于人工神经网络绝缘模型放电模式识别的研究”．中国电机工程学报．第21卷第1期．2001年1月．Pp21-24
[52] Jiang Lei, Zhu Deheng, Li Fuqi, Tan Kexiongm Qin Gangli, Jin Xianhe, Wang Changchang, T. C. Cheng. "Partial Discharge Pattern Recognition of Insulation Models of Power Transformers". Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials. June 21-26, 2000, Xi'an, China. Pp129-132
[53] G. Neil and K. M. Curtis. "Shape Recognition Using Fractal Dimension". Pattern Recognition. Vol. 30. No.12. 1997. pp1957-1969