组合电器局部放电超高频信号数学模型构建和模式识别研究
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摘要
气体绝缘组合电器(Gas Insulated Substation,简称GIS)具有占地面积小、运行安全可靠、维护工作量少、检修周期长等一系列优点,在电力系统得到了广泛的应用。然而,GIS内部不可避免的绝缘缺陷会逐步扩展并导致故障发生,最常见的电气故障特征是在绝缘完全击穿或闪络前发生局部放电(Partial Discharge,简称PD)。研究表明,采用超高频(Ultra-high frequency,简称UHF)法对GIS PD信号检测,可以避开常规电气测试方法中难以避开的电晕放电等干扰,从而有效发现GIS内部存在的绝缘缺陷。GIS中常见的绝缘缺陷有金属突出物缺陷、自由金属微粒缺陷、绝缘子金属污染物缺陷、气隙缺陷等。因此,针对GIS内不同绝缘缺陷的PD所激发的超高频电磁波,深入研究GIS内UHF PD信号特征,分别建立相应的数学模型并进行模式识别的研究,对于认识GIS中放电信号的传输特性、指导GIS放电检测、掌握GIS的绝缘状况和缺陷类型,以及指导GIS的检修工作和保证GIS的安全可靠运行有着十分重要的意义。
     为此,本文在分析国内外GIS局部放电检测、数学模型构建和模式识别研究状况的基础上,深入研究了不同绝缘缺陷UHF PD信号波形特征,首次构建了GIS内UHF PD信号数学模型,并提出了一种适合UHF PD信号模式识别的新方法。其主要工作有:
     ①采用UHF法对GIS模拟装置内所设计的4种绝缘缺陷物理模型进行了大量的PD试验,获取了4种典型GIS缺陷的物理模型分别在不同尺寸规格下、置于不同位置处、在不同电压等级下的UHF PD信号波形,对GIS内不同绝缘缺陷UHF PD信号特征做了深入研究和系统分析;
     ②针对GIS内4种典型绝缘缺陷UHF PD信号特征,构建了GIS的UHF PD信号数学模型,给出了数学模型的参数值,并从拟合误差、能量分布和时频联合分析的角度证明了数学模型构建的正确性,最后将构建的数学模型应用于PD信号复小波去噪的理论仿真研究;
     ③根据二元树复小波变换优良平移时不变特性的特点,提出了一种基于二元树复小波变换的时频特征空间构造方法,通过伸缩和平移等运算功能对UHF PD信号进行多尺度细化分析,综合选用了UHF PD信号在各频带投影序列的能量、在各个尺度下的极大值和统计参量,完备地描述了UHF PD信号的特性,构造了完整的UHF PD信号特征空间,并根据已建立的GIS内4种典型缺陷UHF PD数学模型,对特征子集进行验证,进一步证明了所构造特征空间的正确性;
     ④深入研究流形学习中的LLE算法、ISOMAP算法、Laplacian Eigenmap算法、KPCA等,提出了基于流形学习的UHF PD特征空间降维方法,可保持降低维数空间后的原有信号特性最大限度不变,并使降维处理后的UHF PD信号能量特征子集、极大值特征子集、统计特征子集作为组合神经网络分类器成员分类器的输入量,识别效果达到最优。
Gas Insulated Substation (GIS) has developed very quickly and has been in use all over the world, its compact size, high reliability, low maintenance have made it an attractive option in many circumstance. However, operation experiences show that intrinsic defects in GIS still cause accidents though its high reliability. It is well known that insulation breakdown is often preceded by Partial discharge (PD) activities. GIS internal defects can be discovered in time with the interferences such as corona discharge from the power system using Ultra-high frequency (UHF) method. Several types of defects occur in GIS, such as protrusion fixed to the conductor, free particles, surface contamination on the insulator and electrode gap defects and so on. Therefore, the analysis of UHF PD pulse shape, establishment of UHF PD mathematical models and pattern recognition of UHF PD are very important and necessary to realize UHF PD transmission, detect UHF PD signals, estimate GIS insulation condition and types of defects and guide its maintenance.
     In this paper, UHF PD signals of typical insulated defects in GIS are deeply studied based on analyzing researches about PD detection in GIS, establishment of mathematical model and its pattern recognition home and abroad; secondly, mathematical models are established, analyzed and justified; lastly, a new method of PD pattern recognition are introduced. The main achievements are as follows,
     ①A plenty of PD data are sampled with artificial physical models of PD defect in laboratory in different condition, including different defect size or shape, different detector location, different voltage level and so on, and the same time, UHF PD signals are analyzed roundly;
     ②Mathematical models based on these defects are established, and the principles and methods of establishment are summarized. Furthermore, the parameters of mathematical models are given and the validity of PD mathematical model is proved by fitting error, power spectrum and time-frequency analysis. In the end, applications of the UHF PD mathematical models and complex wavelet transform for extracting the relevant signals from a white noise background are illustrated.
     ③A new method of feature extraction for UHF PD signals based on the dual-tree complex wavelet transform is proposed with its shift invariance. Furthermore, feature space of UHF PD signals are constructed by energy values, maximum of module and statistical parameters, which describes the characters of UHF signals very well. At last, the validity of feature space has been proved by UHF PD mathematical models in the simulation.
     ④A new method of dimension reduction for feature space of UHF PD signals based on manifold learning is proposed, and LLE algorithm, ISOMAP algorithm, Laplacian Eigenmap algorithm and KPCA condense data from the high-dimensional space to the low-dimensional space and maintain the structure of the original sample patterns greatly. The results show that the UHF PD pattern recognition is satisfied when the sub-space features of energy, maximum values and statistical parameters are used as the input of the combined NN.
引文
[1] 中华人民共和国国家标准. GB 2900 1920-1994. 电工术语:高压开关设备. 北京: 中国标准出版社, 1994
    [2] 邱毓昌. GIS 装置及其绝缘技术. 水利电力出版社. 1994.6
    [3] 苑舜. 高压开关设备状态监测与诊断技术. 北京. 机械工业出版社. 2001.2
    [4] 黎明, 黄维枢. SF6 气体及 SF6 气体绝缘变电站的运行. 水利电力出版社. 1993.12
    [5] D.Kopejtkova, T.Molony, S.kobayashi, and I.M.Welch. A Twenty-five Year Review of Experience with SF6 Gas Insulated Substations(GIS). CIGRE, Paris, France, 1992, 30th August-5th September: pp23~101
    [6] 小崎正光. 高电压与绝缘技术. 科学出版社. OHM 出版社. 2001.7
    [7] 罗学琛. 变电所使用 GIS 设备与常规设备的综合比较. 中国电力, 1996, Vol.29, No.4: pp24~26
    [8] 苏舜. GIS 内部放电监测方法的分析. 东北电力技术. 1997.7, No.7: pp7~11
    [9] 刘卫东, 金立军等. 日本 SF6 电器局部放电监测技术研究近况. 高电压技术, 2001, Vol.27, No.2: pp76~77
    [10] 许高峰. 全封闭组合电器局部放电信号内置传感检测和分形特征提取的研究. 重庆大学博士学位论文,2003.5
    [11] L.E.Lundgarrd, M.Runde, B.Skyberg. Acoustic Diagnosis of Gas Insulated Substations: A Theoretical and Experimental Basis. IEEE Transactions on Dielectrics and Electrical Insulation, 1990, Vol.5, No.4: pp1751~1758
    [12] E.Kimura, T.Harunami, N.Konma and K.Saito. Development of GIS Insulation Monitoring System Using External Antenna. 日新电机技报, 1993, Vol.38, No.3: pp30~37
    [13] A.G.Sellars, O.Farish, M.M. Peterson. UHF Detection of Leader Discharges in SF6. IEEE Transactions on Dielectrics and Electrical Insulation, 1995, Vol.2, No.1: pp143~154
    [14] A.Pedersen, G.C.Crichton and I.W.Mcallister. Partial Discharge Detection: Theoretical and Practical Aspects. IEE Proc.-Sci. Meas. Technol., 1995, Vol.142, No.1: pp29~36
    [15] W.Ziomek, E.Kuffel. Activity of Moving Metallic Particles in Prebreakdown State in GIS. IEEE Transactions on Dielectrics and Electrical Insulation, 1997, Vol.4, No.1: pp39~43
    [16] M.D.Judd, O.Farish, J.S.Pearson and B.F.Hampton. Dielectric Windows for UHF Partial Dischage Detection. IEEE Transactions on Dielectrics and Electrical Insulation, 2001, Vol.8, No.6: pp953~958
    [17] 冯昌远. GIS 的运行经验和现场经验. 高压电器, 2000,(1):49~53
    [18] W.Boeck etal. Diagnostic Methods for GIS Insulating Systems. CIGRE: 1992 Session, 30thAugust-5thSeptember, 15/23-01, Paris: pp151~182
    [19] K.S.Prakash, K.D.Srivastava and M.M.Morcos. Movement of Particles in Compressed SF6 GIS with Dielectric Coated Enclosure. IEEE Transactions on Dielectrics and Electrical Insulation, 1997.6, Vol.4, No.3: pp344~347
    [20] Ratnesh Kumar, R.S.Gorayan, B.P.Singh. Movement of Free Particle In A 3-Phase Gas Insulated System. The 12th International Symposium on High Voltage Engineering, Bangalore, India, August, 2001: pp449~452
    [21] L.E.Lundgarrd, M.Runde, B.Skyberg. Acoustic Diagnosis of Gas Insulated Substations: A Theoretical and Experimental Basis. IEEE Transactions on Dielectrics and Electrical Insulation, 1990, Vol.5, No.4: pp1751~1758
    [22] 梁曦东, 陈昌渔, 周远翔. 高电压工程. 清华大学出版社. 2003,9
    [23] L.Niemeyer, L.Ullrich and N.Wiegart. The Mechanism of Leader Breakdown in Electronegative Gases. Transactions on Electrical Insulation, Vol.24, No.2, April 1989
    [24] H.Hama, K.Inami. Stream to leader transition of surface discharges under impulse voltages in SF6 gas,8th ISH, 1993
    [25] I.D.Chalmers. Leader development in short point/plane gaps in compressed SF6. Proc IEE, 1984: pp131~159
    [26] 邱昌容, 王乃庆. 电工设备局部放电及其测试技术. 机械工业出版社, 1994
    [27] 葛景滂, 邱昌容. 局部放电测量. 机械工业出版社, 1984
    [28] 郝艳捧, 王国利, 谢恒堃等. 基于局部放电和超声波法研究大电机定子绝缘的老化特性. 电工技术学报, 2002, 17 (2): pp1~6
    [29] 王建生, 邱毓昌. 气体绝缘开关设备中局部放电的在线监测技术. 电工电能新技术. 2000.4, No.4: pp44~48
    [30] M. Piemontesi, L. Niemeyer. Sorption of SF6 and SF6 decomposition products by activated alumina and molecular sieve 13X. IEEE International Symposium on Electrical Insulation, Montreal, Quebec, Canada, 1996, Jun. 16-19: pp828~838
    [31] C. Beyer, H.Jenett and D. Klockow. Influence of reactive SFx gases on electrode surfaces after electrical discharges under SF6 atmosphere. IEEE Transactions on Dielectrics and Electrical Insulation, 2000.4, Vol.7, No.2: pp234~240
    [32] 姚唯建, 钟志铿. 气体分析法用于六氟化硫电气设备故障的检测. 广东电力, 1994, No.2: pp21~24
    [33] 赵旺初. 有关 SF6 电器标准问题的探讨. 黑龙江电力技术, 1996.2, Vol.18, No.1, Feb: pp8~12
    [34] Y. Qiu, E. Kuffel. Comparison of SF6/N2 and SF6/CO2 gas mixtures as alternatives to SF6 gas. IEEE Transactions on Dielectrics and Electrical Insulation, 1999.10, Vol.6, No.6: pp892~895
    [35] S.Okabe, T.Kawashima, H. Wada. Deterioration characteristics of insulation subjected to partial discharge in SF6 gas. IEEE Transmission and Distribution Conference and Exhibition: Asia Pacific. 2002.10, Vol.2: pp792~797
    [36] H. M. Heise, R. Kurte, P. Fischer, et al. Gas analysis by infrared spectroscopy as a tool for electrical fault diagnostics in SF6 insulated equipment. Fresenius' Journal of Analytical Chemistry. 1997.3, Vol.358, No.7-8: pp793~799
    [37] 国家标准 GB/T8905-1996 和 GB/T18867-2002, 国家标准局批发, 1996 和 2002
    [38] 国际电工委员会标准 IEC60480-2004, 中国电机工程学会高压专委会, 2004
    [39] 邵涛, 周文俊. 特高频法检测 GIS 局部放电的试验研究. 高电压技术. 2001.6, Vol.27, No.3: pp15~16
    [40] 朱周侠, 邱毓昌. GIS 局部放电的现场检测技术. 供用电. 2001.12, Vol.18, No.6:14~15
    [41] A.G.Sellars, O.Farish, M.M. Peterson. UHF Detection of Leader Discharges in SF6. IEEE Transactions on Dielectrics and Electrical Insulation, 1995.9, Vol.2, No.1: pp143~154
    [42] M.D.Judd, O.Farish, B.F.Hampton. The Excitation of UHF Signals by Partial Discharges in GIS. IEEE Transactions on Dielectrics and Electrical Insulation. 1996,Vol.3 No.2: pp213~228
    [43] G.Wanninger. Antennas as Coupling Devices for UHF Diagnostics in GIS. The 9th International Symposium on High Voltage Engineering, Austria, Europe, August, 1995: pp482~486
    [44] E.Colombo, W.Koltunowicz, M.Boldrin. Sensitivity Verification of the UHF System for PD detection in GIS. The 12th International Symposium on High Voltage Engineering, Bangalore, India, August, 2001: pp397~400
    [45] L.J.Jin, J.Q.Huang, W.D.Liu, J.L.Qian. Diagnosis of Partial Discharge in GIS based on UHF Sensing Technique. Proceedings of 2001 International Symposium on Electrical Insulating Materials, November, 2001, Himeji, Japan: pp251~253
    [46] Masatake Kawada, Zen-Ichiro Kawasaki and Kenji Matsu-ura. A New on-line Insulation Diagnostic Technique for Power Apparatus by Detecting Electromagnetic Signals Emitted frim PD. 1996 Asian International Conference on Dielectrics and Electrical Insulation, 4th Japan-China Conference on Electrical Insulation Diagnosis, Xi'an, China, October, 1996: pp325~328
    [47] Uwe Schichler, J?rg Gorablenkow. Experience with UHF PD Detection in GIS Substations. Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials, Xi’an, China, June, 2000: pp286~289
    [48] 唐炬. 组合电器局放在线监测外置传感器和复小波抑制干扰的研究. 重庆大学博士学位论文, 2004
    [49] Nicholas De Kock, Branko Coric and Ralf Pietsch, UHF PD Detection in Gas-insulated Switchgear—Suitability and Sensitivity of the UHF Method in Comparison with the IEC 270 Method, IEEE Electrical Insulation Magazine, 1996.2, Vol.12, No.6: pp20~26
    [50] CIGRE WG15.03, Diagnostic methods for GIS insulating system, Cigre, Paris, 1992.6: p15~23
    [51] M.D.Judd, O.farish and B.F.Hampton. Broadband Couplers for UHF detection of Partial Discharge in Gas-insulated Substations, IEE Proc-Sci. Meas.Technol, 1995.6, Vol.142, No.3: pp237~243
    [52] 覃剑, 王昌长等. 特高频在电力设备局部放电在线监测中的应用, 电网技术, 1997.6, Vol.21, No.6: pp33~36
    [53] 李智敏. 超高频法检测 GIS 局部放电的研究, 西安交通大学博士学位论文, 1999.7
    [54] 邱毓昌. 用超高频法对 GIS 绝缘进行在线监测. 高压电器, 1997.5, Vol.33, No.4: pp36~40
    [55] Kurrer R, et al. Antenna theory of flat sensors for partial discharge detection at ultra-high frequencies in GIS, 9th ISH on High Voltage Engineering, Graz, 1995.2: pp5615~5619
    [56] 韩小莲. GIS 局部放电检测系统的研究. 西安交通大学博士学位论文, 1995.7
    [57] 王建生, 邱毓昌, 吴向华, 孙晓滨. 用于 GIS 局部放电检测的超高频传感器频率响应特性. 中国电机工程学报, 2000.8, Vol.20, No.8: pp42~45
    [58] 张鸣超, 王建生, 邱毓昌. GIS 中局部放电产生的超高频电磁波及其测量. 高电压技术, 1998.3, Vol.24, No.2: pp22~25
    [59] 刘卫东, 黄瑜珑, 王剑锋, 钱家骊. GIS 局部放电特高频在线检测和定位. 高压电器, 1999.2, Vol.35, No.1: pp11~15
    [60] 王晓蓉, 杨敏中. 电力设备局部放电测量中抗干扰研究的现状和展望, 电网技术, 2000.6, Vol.24, No.6: pp42~45
    [61] 孙才新, 李新, 杨永明. 从白噪声中提取局部放电信号的小波变换方法的研究, 电工技术学报, 1999.6, Vol.14, No.3: pp47~50
    [62] 高宁, 朱德恒等. 变压器局部放电在在线监测信号中的电磁干扰及抑制, 电工电能新技术, 1999.4, Vol.26, No.2: pp23~27
    [63] P. Osvath, W. Zaengl, and H. I. Weber. Measurement of Partial Discharge: Problems and How They Can be Solved with Flexible Measuring Systems. Tettex Instruments Bulletin SEV/VSE 76 (1985) 19, ISSN 036-1321
    [64] L.Satish, B.Nazneen. Wavelet-based Denoising of Partial Discharge Signals Buried in Excessive Noise and Interference. IEEE Trans. Dielect. Elect. Insul., 2003, Vol.10: pp354~367
    [65] X. Ma, C. Zhou, and I.J. Kemp. Automated Wavelet Selection and Thresholding for PDDetection. IEEE Electr. Insul. Mag., 2002, Vol.18, No.2: pp37~45
    [66] X. Ma, C. Zhou, and I.J. Kemp. Interpretation of Wavelet Analysis and Its Application in Partial Discharge Detection. IEEE Trans. Dielect. Elect. Insul., 2002, Vol.9, No.3: pp446~457
    [67] A.Lapp. and H.-G. Kranz. The Use of the CIGRE Data Format for PD Diagnosis Applications. IEEE Trans. on Dielectrics and Electrical Insulation. 2000.2, Vol.7, No.1: pp102~112
    [68] N. C. Sahoo, M. M. A. Salama. Trends in Partial Discharge Pattern Classification: A Survey. IEEE Trans. on Dielectrics and Electrical Insulation. 2005.4, Vol.12, No.2: pp248~264
    [69] R. Bartnikas. Note on Multichannel Corona Pulse-height Analysis. IEEE Trans. Electr. Insul., 1973, Vol. 8: pp2~5
    [70] A. Kelen. The Functional Testing of HV Generator Stator Insulation. Proc. CIGRE, Paris, 1976, Paper 15-03
    [71] I. C. Bapt, Bui Ai, and C. Mayoux. Coronal Frequency Analysisin Artificial Cavities in Epoxy Resins. Conf. Electr. Insul. Dielectr. Phenomena, NAS/NRC, Washington, D.C., 1974, pp282~288
    [72] Hucker and H.-G. Kranz. Requirements of Automated PD Diagnosis Systems for Fault Identification in Noisy Conditions. IEEE Trans. Dielectr. Electr. Insul., 1995, Vol.2: pp544~556
    [73] H. G. Kranz. Diagnosis of Partial Discharge Signals Using Neural Networks and Minimum Distance Classification. IEEE Trans. Electr. Insul., 1993, Vol.28: pp1016~1024
    [74] E. Gulski and A. Krivda. Neural Networks as a Tool for Recognition of Partial Discharges. IEEE Trans. Electr. Insul. 1993, Vol.28: pp984~1001
    [75] R. E. James and B. T. Phung. Development of Computer-based Measurements and their Application to PD Pattern Analysis. IEEE Trans. on Dielectrics and Electrical Insulation. 1995, Vol.2: pp838~856
    [76] M. K. A. Rahman, R. Arora and S. C. Srivastava. Partial Discharge Classification Using Principal Component Transformation. IEE Proc., Part A, 2000, Vol.147: pp7~13
    [77] E. M. Lalitha and L. Satish. Wavelet Analysis for Classification of Multi-source PD Patterns. IEEE Trans. on Dielectr. Electr. Insul., 2000, Vol.7: pp40~47
    [78] E. Gulski. Discharge Pattern Recognition in High Voltage Equipment. IEE Proc. Sci., Meas. Technol., 1995, Vol.142: pp51~61
    [79] M Hoof, R. Patsch. Pulse-Sequence Analysis: A New Method for Investigation the Physics of PD-induced Aging. IEE Proc.-Sci. Meas. Technol., Vol.142, No.1, January 1995: pp95~101
    [80] M. Hoof and R. Patsch. Characteristics of Partial Discharge Pulse Sequences during Electrical Treeing in Polyethylene. 9th International Symposium on High Voltage Engineering, Graz, Austria. 1995. Paper 5606
    [81] Martin Hoof, Bernd Freisleben and Rainer Patsch. PD Source Identification with Novel Discharge Parameters using Counterpropagation Neural Networks. IEEE Transactions on Dielectrics and Electrical Insulation, Vol.4, No.1, Feb. 1997: pp17~32
    [82] Amira A. Mazroua. Discrimination Between PD Pulse Shapes Using Different Neural Network Paradigms. IEEE Transactions on Electrical Insulation. Vol.1 No.6. Dec. 1994: pp1119~1131
    [83] Zhenyuan Wang, Deheng Zhu, Kexiong Tan, Fuqi Li. PD Monitor System for Power Generators. IEEE Transactions on Electrical Insulation. Vol.5, No.6, Dec. 1998: pp850~856
    [84] 郑重, 谈克雄, 高凯. 局部放电脉冲波形特征分析. 高电压技术. 1999, 25(4): 15~17
    [85] Zheng Zhong, Tan Kexiong. Partial Discharge Recognition Based on Pulse Waveform Using Time Domain Data Compression Method. Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials, June 21-26, 2000, Xi’an, China. pp483~486
    [86] M. Cacciari, A. Contin, G. Rabach and G. C. Montanari. An Approach to Partial Discharge Investigation by Height Distribution Analysis. IEE Proc. Sci., Meas. Technol., 1995, Vol.142: pp102~108
    [87] M. Cacciari, A. Contin and G. C. Montanari. Use of a Mixed Weibull Distribution for the Identification of PD Phenomena. IEEE Trans. on Dielectr. Electr. Insul., 1995, Vol.2: pp1166~1179
    [88] R. Bartnikas, Editor. Engineering Dielectrics, Vol. IIB, Measurement Techniques, STP 926, ASTM, Philadelphia, 1987
    [89] L. Satish and W. S. Zaengl. Can Fractal Features be Used for Recogniztion 3-D Partial Discharge Patterns. IEEE Trans. on Dielectrics and Electrical Insulation. Vol.2, No.3, June 1995: pp352~359
    [90] A. Krivda, E. Gulski, L. Satish and W. S. Zaengl. The Use of Fractal Features for Recognition of 3-D Discharge Patterns. IEEE Transactions on Dielectrics and Electrical Insulation. Vol.2, No.5, Oct. 1995: pp889~892
    [91] R. Candela, G. Mirelli, R. Schifani. PD Recognition by Means of Statistical and Fractal Parameters and a Neural Network. IEEE Transactions. on Dielectrics and Electrical Insulation. Vol.7, No.1, Feb. 2000: pp87~94
    [92] 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
    [93] 高凯, 谈克雄, 李福祺, 吴成琦. 基于散点集分形特征的局部放电模式识别研究. 中国电机工程学报, 2002, vol.22, No.5: pp22~26
    [94] 李剑, 孙才新等. 局部放电灰度图象分维数的研究. 中国电机工程学报, 2002, vol.22, No.8:pp123~127
    [95] 张晓星, 唐炬, 孙才新, 周倩等. 基于多重分形维数的 GIS 局部放电模式识别. 仪器仪表学报, 2007, vol.28, No.4: pp597~602
    [96] 淡文刚. 小波变换应用于大型电力变压器局部放电模式识别的研究. 中国电力科学研究院博士学位论文, 2000.9
    [97] J. Jin, C.S. Chang, C.Chang. Classification of Partial Discharge Events in Gas-insulated Substations Using Wavelet Packet Transform and Neural Network Approaches. IEE Proc.-Sci. Meas. Technol., Vol.153, No.2, March 2006: pp55~63
    [98] 孙才新, 李新, 李俭. 小波与分形理论的互补性及其在局部放电模式识别中的应用研究. 中国电机工程学报, 2001, 21(12): pp73~76
    [99] 成永红, 谢小军, 蒋雁. 基于小波提取的超宽频带局部放电信号分形分析. 西安交通大学学报, 2002 , Vol.36, No.6: pp551~554
    [100] 张晓星. 组合电器局部放电非线性鉴别特征提取与模式识别方法研究. 重庆大学博士论文, 2006 年 12 月
    [101] J. B. Tenenbaum, V. D. Silva and K. C. Langford. A Global Geometric Framework for Nonlinear Dimensionality Reduction. Science, 2000, Vol.290, No.22: pp2319~2323
    [102] S. T. Roweis and L. K. Saul. Nonlinear Dimensionality Reduction by Locally Linear Embedding. Science, 2000, Vol.290, No.22: pp2323~2326
    [103] Zhang Z.Y. , Zha H. Y. Principal manifolds and nonlinear dimensionalty reduction via tangent space alignment. SIAM Journal of Scientific Computing, 2004, 26(1): pp313~338
    [104] M. Belkin, P. Niyogi. Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. NIPS 15, 2001
    [105] 谈克雄, 李福祺. 局部放电识别用的几种人工神经网络. 高电压技术, 1996, 22(4): pp3~7
    [106] 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
    [107] 李剑. 局部放电灰度图象识别特征提取与分形压缩方法的研究. 重庆大学博士学位论文, 2001.12
    [108] Kai Gao, Kexiong Tan, Fuqi Li. PD Pattern Recognition for Stator Bar Models with Six Kinds of Characteristic Vectors using BP Networks. IEEE Transactions on Dielectrics and Electrical Insulation, 2002, Vol.9, No.3: pp381~389
    [109] Monica Bianchini et al. Learning without Local Minima in Radial Basis Function Networks. IEEE Neural Networks, 1995, Vol.6, No.3: pp749~755
    [110] Chen S. et al. Recursive hybrid algorithm for non-linear system identification using Radial Basis Function Networks. INT.J.Control, 1992, Vol.55, No.5: pp1051~1070
    [111] 张桂才, 史铁林等. 高阶统计量与 RBF 网络结合用于齿轮故障分类. 中国机械工程, 1999, Vol.10, No.11: pp1250~1252
    [112] G. Baudat, F. Anouar. Generalized discriminant analysis using a kernel approach. Neural Computation, 2000, 12: pp2385~2404
    [113] Duchene J, Leclercq S. An optimal transformation for discriminant and principal component analysis. IEEE Trans. On PAMI, 1988, 10(6): pp978~983
    [114] Guangning Wu, Xiongwei Jiang, 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: pp451~454
    [115] 蒋雄伟, 王振华, 谢恒堏. 基于遗传算法的神经网络在局部放电模式识别中的应用. 西安交通大学学报, 1999, Vol.33, No.12: pp1~4
    [116] D.Wenzel, H.Borsi, E.Gockenbach. A New Approach for Partial Discharge Recognition on Transformers on-site by means of Genetic Algorithms. Conference Record of the 1996 IEEE International Symposium on Electric Insulation, Montreal, Quebec, Canada, 1996, June16-19: pp57~60
    [117] 张寒, 文习山, 邓维. 小生境遗传算法的模糊识别在局放中的应用. 高电压技术, 2005, Vol.31, No.6: pp15~18
    [118] C. Chang and Q. Su. Partial Discharge Source Identification Using SOFM and MLP Neural Networks. Proceedings of the 1st ICMEP. Wuhan, China. Sep. 24-26. 2000: pp190~195
    [119] Sylvain Sardy. Minimax threshold for denoising complex signals with waveshrink. IEEE Trans. Signal Processing, 2000, Vol. 48: pp1023~1028
    [120] L.科恩(白居宪译). 时-频分析: 理论与应用. 西安: 西安交通大学出版社, 1998.3
    [121] Haibo He, Shijie Cheng, Youbing Zhang et al. Analysis of reflection of signal transmitted in low-voltage powerline with complex wavelet. IEEE Transactions on Power Delivery, 2004, 19(1): pp86~91
    [122] 陈祥训, 淡文刚. 一种生成双正交紧支复小波的 Lifting 方法. 中国电机工程学报, 2001, 21(5): pp34~38
    [123] Peter Werle, Asghar Akbari, Hossein Borsi and Ernst Gockenbach. Enhanced Online PD Evaluation on Power Transformers Using Wavelet Techniques and Frequency Rejection Filter for Noise Suppression. IEEE Int. Sym. Electrical Insulation. April. 2002: pp195~198
    [124] Stephane Mallat. A Wavelet Tour of Signal Processing(Second Edition). Academic Press, 1999
    [125] E.P.Simoncelli, W.T.Freeman, E.H.Adelson, D.J.Heeger. Shiftable multiscale transforms. IEEE Trans. Inform. Theory, 1992, 38: pp587~607
    [126] J. Liang, T. W. Parks. A translation invariant wavelet representation algorithm with applications. IEEE Trans. Signal Processing, Feb.1996,44(2): pp225~232
    [127] J. Liang and T. W. Parks. A two-dimensional translation invariant wavelet representation and its applications. Proc. Int. Conf. On Image Processing, Austin, TX, Nov.1994: pp66~70
    [128] N.G. Kingsbury. The dual-tree complex wavelet transform: a new efficient tool for image restoration and enhancement. Proc. European Signal Processing Conference, EUSIPCO 98, Rhodes, 1998: pp319~322
    [129] J. F. A. Magarey, N.G. Kingsbury. Motion estimation using a complex-valued wavelet transform. IEEE Trans. on Signal Processing, 1998, 46(4): pp1069~84
    [130] N. Kingsbury. Image processing with complex wavelets, Phil. Tran. R. Soc. Lond. A, 1999, 357: pp2543~2560
    [131] N. Kingsbury. Complex wavelets for shift invariant analysis and filtering of signals, 110 Appli. Comput. Harmon. Anal., 2001, 10(3): pp234~253
    [132] 张晓文, 杨煜普, 许晓鸣. 基于小波变换的特征构造与选择. 计算机工程与应用, 2003, 19: pp25~28
    [133] Lawrence K, Roweis S. An introduction to locally linear embedding. Technical Report, Gatsby Computational Neuroscience Unit, UCL, 2001
    [134] J.B. Tenenbaum, V. Silva, J.C. Langford. A global geometric framework for nonlinear dimensionality reduction. Science, 2000, 290: 2319~2323
    [135] He Xiaofei. Laplacian Eigenmap for Image Retrieval. Computer Science Department, University of Chicago, 2002
    [136] Sung K-K, Poggio T. Example-based learning for view-based human face detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1998, 20(1): pp39~51