电力系统过电压识别方法及混合过电压分解方法研究
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摘要
随着智能电网技术的迅速发展,多个国家与地区已将智能电网的建设纳入到电网的规划之中。我国已将智能电网提升为国家战略,国家电网公司也提出要建设以特高压电网为骨干网架,各级电网协调发展,具有信息化、自动化、互动化特征的“坚强智能电网”。智能电网的一个主要特征就是自愈电网,自愈电网能够进行连续不断的实时自我评估以预测电网可能出现的问题,发现已经存在的或正在发展的问题,并立即采取措施加以控制或纠正,以确保电网的可靠性、安全性、电能质量和效率。过电压是电力系统中开关操作、雷电以及故障的直接反映,对系统的安全运行具有很大的威胁,且随着电压等级的不断提高,过电压对系统设备有着更强的危害性。为了提高系统运行的可靠性及稳定性,开展电力系统过电压的在线监测与识别研究,对于保障电网安全运行具有十分重大的现实意义和指导意义。目前已有较多的过电压在线监测录波设备挂网运行,但是准确有效的过电压识别方法仍有待解决的研究难点。
本文构建了一个完整的过电压识别系统,该系统能够对金属性接地、分频铁磁谐振、工频铁磁谐振、高频铁磁谐振、合闸空载线路、合闸电容器组、雷电、弧光接地、单相接地等几种过电压类型进行有效识别区分。同时针对工频过电压识别难点与混合过电压问题,在单一类型识别系统的基础上,本文分别通过工频过电压识别子系统与混合过电压分解识别子系统对其进行了进一步的分类识别。
单一类型过电压识别系统采用S变换作为信号处理及分析算法,对8种过电压类型进行了分析,在该部分识别系统中,本文将三种在电压特征上具有高度相似性的基频铁磁谐振、单相接地以及3种断线引起的工频电压升高,合并为一类工频过电压。通过对几种过电压主要特征的分析,本文设计提出了6种基于时频特征的特征量。
通过对大量实测过电压信号进行特征计算,并对各种特征量的量值分布范围进行统计分析,采用模糊专家系统,结合支持向量机技术,构建了一套面向现场实际应用的、完整的过电压初步识别系统。
针对工频铁磁谐振、单相接地故障以及3种断线故障引起的在波形上高度相似的工频过电压,本文从典型故障电路计算入手,详细推导了几种工频过电压的电压电流解析表达式,通过综合对比其三相电压电流特征,有效的对断线故障进行了识别。同时,提出了一种基于系统零序相位的识别判据,成功的解决了称为“虚幻接地”的工频铁磁谐振过电压与单相接地过电压之间的识别难点。
通过大量实测过电压信号数据分析与对比,本文首次对混合过电压信号分解以及分类识别方法问题进行了研究。初步对混合过电压类型进行了探讨,在此基础上,以过电压类型识别为研究目标,研究了基于阻尼正弦原子库与匹配追踪算法的混合过电压原子分解方法。针对该算法原子库过于庞大以及分解计算量过大的问题,引入快速傅里叶变换、遗传算法与粒子群算法,对该算法的计算速度进行了优化。通过实测数据的检测,发现了两种在实际应用中有可能出现的分解错误,针对这两种分解错误,分别提出了一种基于短时傅里叶变换与希尔伯特变换的时域分段搜索算法和双原子分解算法,提高了分解精度与准确性。在原子分解的基础上,采用分形理论,构建了一个完整的混合过电压在线识别子系统,经实测数据检验,该系统能够有效的对混合过电压进行类型分解与识别应用。
在从不同研究层面结合多种算法,对不同类型过电压进行有效识别的方法与技术的研究基础上,本文将单一过电压识别系统、工频过电压识别系统以及混合过电压分解识别系统三部分,有机的结合起来构成一套完整的,具有现场实用价值的过电压综合识别体系。
In recent years, the smart grid technologies is developmented rapidly, a lot of countries and regions in the world have taken the construction of smart grid into their planning. China also has been upgrading the constricution of smart grid as the national strategy. State grid corporation of china proposes to build the“Strong and smart grid”based on the UHV power grid, which has the features of information, automation, and interactive. One of the main features of smart grid is the self-healing, which can continuously carry out on-line self-evaluation to predict the problems the grid may meet, discover existing faults, and immediately take control to ensure the reliability, safety and efficiency of the grid. The over-voltage caused by switching, lightning or system faults affects the security and stability of the power system. And it will become more dangerous to the system equipment with the increasing of voltage level. In order to improve the saftiy and staibility of power system, the research of over-voltage online monitoring and identification is ver important and has great practical significance for the protection of the safe operation of power grid. At present, a lot of over-voltage online monitoring equipment and waveform recorder have been put into field operation. However, accurate and effective over-voltage identification methold is still a problem need to be solved.
In this paper, a whole complete over-voltage identification system is built, which has ability to identify and classify the metallic grounding, sub-frequency ferroresonance, power frequency over-voltage, high frequency ferroresonance, switching line, switching capators, lightning, arc grounding over-voltage. Meanwhile, aiming at the problem of power frequency over-voltage and mixed over-voltage identification, two recognition subsystems are built out.
The main single-type identification system adopts the S-transform as the signals time-frequency analysis and feature extration algorithm, identify 8 kinds of over-voltages. And in this system, 3 types of power frequency over-voltage: fundmental ferroresonance, single phase-to-ground and wire breakage, which are highly similar in the voltage signal’s features, are combined into one type to be dealed with. Based on the main features analysis of each kind of over-voltage, 6 different characteristic quantities are proposed.
Based on the feature extraction of large mount of field over-voltage signals, the value distribution of each kind of characteristic quantity are obtained by statistical analysis. A complete initial identification system is built by employing the fuzzy expert system and support vector machine, which can meet the requirement of practical applications.
Aiming at the identification problem of three kinds of power frequency over-voltages, fundmental ferroresonance, single phase-to-ground and wire breakage, an identicication system is built by compareing their major features in voltage and current signals, which is obtained through deducing their voltage and current analytical expressions. Meanwhiling, a new identification criterion based on zero sequence current is presented in this paper for the difficulty of classification of single phase-to-ground and fundamental ferroresonance, which is also called‘false grounding’.
Through large amount of field over-voltage signals, this paper researches the decomposition algorithm and identification method of mixed over-voltage. In order to recougnize each kind of over-voltage in the mixed signals, based on the analysis of posbale type of mixed over-voltage, a decomposition algorithm based on actomix decomposition and damped sinusoidal atom dictionary is proposed.
In order to reduce the computational complexity of the atomic decomposition and improve the accuracy of the decomposition, the FFT, GA and PSO are employed in the application.
Aiming at the possible incorrect decomposition coursed by simply using of atomic decomposition, an improved time support searching method based on STFT and Hilbert transform and a double-atoms decomposition algorithm are proposed. Based on these methods, a well designed mixed over-voltage identification system is proposed based on fractal, and the acutrace of this system is vrified by field mixed over-voltage signals.
Based on the iffective identification and classification of each kind of over-voltage through severl algorithms, a single type over-voltage identification system, power frequency over-voltage identification system and a mixed over-voltage decomposition and identification system are composed into a complete practicality identification system.
本文构建了一个完整的过电压识别系统,该系统能够对金属性接地、分频铁磁谐振、工频铁磁谐振、高频铁磁谐振、合闸空载线路、合闸电容器组、雷电、弧光接地、单相接地等几种过电压类型进行有效识别区分。同时针对工频过电压识别难点与混合过电压问题,在单一类型识别系统的基础上,本文分别通过工频过电压识别子系统与混合过电压分解识别子系统对其进行了进一步的分类识别。
单一类型过电压识别系统采用S变换作为信号处理及分析算法,对8种过电压类型进行了分析,在该部分识别系统中,本文将三种在电压特征上具有高度相似性的基频铁磁谐振、单相接地以及3种断线引起的工频电压升高,合并为一类工频过电压。通过对几种过电压主要特征的分析,本文设计提出了6种基于时频特征的特征量。
通过对大量实测过电压信号进行特征计算,并对各种特征量的量值分布范围进行统计分析,采用模糊专家系统,结合支持向量机技术,构建了一套面向现场实际应用的、完整的过电压初步识别系统。
针对工频铁磁谐振、单相接地故障以及3种断线故障引起的在波形上高度相似的工频过电压,本文从典型故障电路计算入手,详细推导了几种工频过电压的电压电流解析表达式,通过综合对比其三相电压电流特征,有效的对断线故障进行了识别。同时,提出了一种基于系统零序相位的识别判据,成功的解决了称为“虚幻接地”的工频铁磁谐振过电压与单相接地过电压之间的识别难点。
通过大量实测过电压信号数据分析与对比,本文首次对混合过电压信号分解以及分类识别方法问题进行了研究。初步对混合过电压类型进行了探讨,在此基础上,以过电压类型识别为研究目标,研究了基于阻尼正弦原子库与匹配追踪算法的混合过电压原子分解方法。针对该算法原子库过于庞大以及分解计算量过大的问题,引入快速傅里叶变换、遗传算法与粒子群算法,对该算法的计算速度进行了优化。通过实测数据的检测,发现了两种在实际应用中有可能出现的分解错误,针对这两种分解错误,分别提出了一种基于短时傅里叶变换与希尔伯特变换的时域分段搜索算法和双原子分解算法,提高了分解精度与准确性。在原子分解的基础上,采用分形理论,构建了一个完整的混合过电压在线识别子系统,经实测数据检验,该系统能够有效的对混合过电压进行类型分解与识别应用。
在从不同研究层面结合多种算法,对不同类型过电压进行有效识别的方法与技术的研究基础上,本文将单一过电压识别系统、工频过电压识别系统以及混合过电压分解识别系统三部分,有机的结合起来构成一套完整的,具有现场实用价值的过电压综合识别体系。
In recent years, the smart grid technologies is developmented rapidly, a lot of countries and regions in the world have taken the construction of smart grid into their planning. China also has been upgrading the constricution of smart grid as the national strategy. State grid corporation of china proposes to build the“Strong and smart grid”based on the UHV power grid, which has the features of information, automation, and interactive. One of the main features of smart grid is the self-healing, which can continuously carry out on-line self-evaluation to predict the problems the grid may meet, discover existing faults, and immediately take control to ensure the reliability, safety and efficiency of the grid. The over-voltage caused by switching, lightning or system faults affects the security and stability of the power system. And it will become more dangerous to the system equipment with the increasing of voltage level. In order to improve the saftiy and staibility of power system, the research of over-voltage online monitoring and identification is ver important and has great practical significance for the protection of the safe operation of power grid. At present, a lot of over-voltage online monitoring equipment and waveform recorder have been put into field operation. However, accurate and effective over-voltage identification methold is still a problem need to be solved.
In this paper, a whole complete over-voltage identification system is built, which has ability to identify and classify the metallic grounding, sub-frequency ferroresonance, power frequency over-voltage, high frequency ferroresonance, switching line, switching capators, lightning, arc grounding over-voltage. Meanwhile, aiming at the problem of power frequency over-voltage and mixed over-voltage identification, two recognition subsystems are built out.
The main single-type identification system adopts the S-transform as the signals time-frequency analysis and feature extration algorithm, identify 8 kinds of over-voltages. And in this system, 3 types of power frequency over-voltage: fundmental ferroresonance, single phase-to-ground and wire breakage, which are highly similar in the voltage signal’s features, are combined into one type to be dealed with. Based on the main features analysis of each kind of over-voltage, 6 different characteristic quantities are proposed.
Based on the feature extraction of large mount of field over-voltage signals, the value distribution of each kind of characteristic quantity are obtained by statistical analysis. A complete initial identification system is built by employing the fuzzy expert system and support vector machine, which can meet the requirement of practical applications.
Aiming at the identification problem of three kinds of power frequency over-voltages, fundmental ferroresonance, single phase-to-ground and wire breakage, an identicication system is built by compareing their major features in voltage and current signals, which is obtained through deducing their voltage and current analytical expressions. Meanwhiling, a new identification criterion based on zero sequence current is presented in this paper for the difficulty of classification of single phase-to-ground and fundamental ferroresonance, which is also called‘false grounding’.
Through large amount of field over-voltage signals, this paper researches the decomposition algorithm and identification method of mixed over-voltage. In order to recougnize each kind of over-voltage in the mixed signals, based on the analysis of posbale type of mixed over-voltage, a decomposition algorithm based on actomix decomposition and damped sinusoidal atom dictionary is proposed.
In order to reduce the computational complexity of the atomic decomposition and improve the accuracy of the decomposition, the FFT, GA and PSO are employed in the application.
Aiming at the possible incorrect decomposition coursed by simply using of atomic decomposition, an improved time support searching method based on STFT and Hilbert transform and a double-atoms decomposition algorithm are proposed. Based on these methods, a well designed mixed over-voltage identification system is proposed based on fractal, and the acutrace of this system is vrified by field mixed over-voltage signals.
Based on the iffective identification and classification of each kind of over-voltage through severl algorithms, a single type over-voltage identification system, power frequency over-voltage identification system and a mixed over-voltage decomposition and identification system are composed into a complete practicality identification system.
引文
[1] Office of Electricity Delivery and Energy Reliability. The smart grid: an introduction[EB/OL]. http://www.oe.energy.gov/SmartGridIntroduction.htm, 2011-02-28.
[2] SmartGrids Technology Platform. Vision and strategy for Europe’s electricity networks of the future[EB/OL]. http://www.smartgrids.eu/, 2011-02-28.
[3] Fangxing Li, Wei Qiao, Hongbin Sun, et al.Smart Transmission Grid: Vision and Framework[J]. IEEE Trans. Smart Grid, 2010, 1(2): 168-177.
[4]刘振亚.智能电网技术[M].北京:中国电力出版社, 2010.
[5]李振杰,袁越.智能微网—未来智能配电网新的组织形式[J].电力系统自动化, 2009, 33(17): 42-48.
[6] Juan L., Chenching L., and Schneider K.P. .Controlled Partitioning of a Power Network Considering Real and Reactive Power Balance[J]. IEEE Trans. Smart grid, 2010, 1(3): 261-269.
[7] Pei Z., Fangxing L., Bhatt N..Next-Generation Monitoring, Analysis, and Control for the Future Smart Control Center[J].IEEE Trans. Smart grid, 2010, 1(2): 186-192.
[8]张纬钹,何金良,高玉明.过电压防护及绝缘配合[M].清华大学出版社, 2002.
[9]司马文霞,兰海涛,杜林,孙才新,姚陈果,杨庆.套管末屏电压传感器响应特性研究[J].中国电机学报. 2006, 26(21): 172-176.
[10]王士彬,孙才新,姚陈果,熊兰,米彦,杜林,席世友. 10kV配网内外过电压在线监测系统及波形分析[J].高电压技术, 2004, 30(6): 64-66.
[11]杨保初,刘晓波,戴玉松.高电压技术[M].重庆:重庆大学出版社, 2002.
[12]杨晓辉,蔡旭,分形理论在中压电网故障辨识中的应用[J].电力系统自动化, 2006, 30(4): 59-64.
[13]孙雅明,王俊丰.基于分形理论的输电线路故障分类识别新方法[J].电力系统自动化, 2005, 29(12): 23-28.
[14]赵军,吕艳萍,王汉广.基于多尺度形态分解的特高压线路雷击干扰识别新方法[J].高电压技术, 2009, 35(5): 994-998.
[15]肖先勇,李逢,邓武军.雷击与短路故障的S变换特征量识别方法[J].高电压技术, 2009, 35(4): 817-822.
[16]何正友,陈小勤.基于多尺度能量统计和小波熵测度的电力暂态信号识别方法[J].中国电机工程学报, 2006, 26(10): 33-39.
[17]陈小勤,何正友,符玲.基于小波能谱的电力暂态信号分类识别方法[J].电网技术, 2006, 30(17): 59-63.
[18]王丽霞,何正友,赵静.基于数学形态学的电能质量扰动检测和定位[J].电网技术, 2008, 32(10): 63-68.
[19]操丰梅,苏沛浦.小波变换在配电自动化接地故障检测中的应用研究[J].高电压技术, 1999, 23(13): 33-36.
[20]周海.电力系统操作过电压类型识别的研究[D].重庆大学,硕士学位论文, 2008.
[21]郭良峰.基于遗传算法的电力系统过电压分层模糊聚类识别[D].重庆大学,硕士学位论文, 2009.
[22] Mokryani G., Siano P., Piccolo A.. Identification of ferroresonance based on S-transform and support vector machine[J]. Simul. Model. Pract. Theory, 2010, 18 (9): 1412-1424.
[23] T. X. Zhu. Detection and Characterization of Oscillatory Transients Using Matching Pursuits With a Damped Sinusoidal Dictionary[J]. IEEE Trans. Power Del., 2007, 22(2): 1093-1099.
[24] Zwe-Lee Gaing. Wavelet-Based Neural Network for Power Disturbance Recognition and Classification[J]. IEEE Trans. Power Del., 2004, 19(4): 1560-1568.
[25] Voislav J. Estimation of the maximal voltage induced in an overhead line due to the nearby lightning[J]. IEEE Trans. Power Del., 1997, 12(1): 315-324.
[26]李海锋,王钢,赵建仓.输电线路感应雷击暂态特性分析及其识别方法[J].中国电机工程学报, 2004, 24(3): 114-119.
[27]王钢,李海锋,赵建仓,吴敏.基于小波多尺度分析的输电线路直击雷暂态识别[J].中国电机工程学报, 2004, 24(4): 139-144.
[28]束洪春,王永治,程春和,孙士云.±800kV直流输电线路雷击电磁暂态分析与故障识别[J].中国电机工程学报, 2008, 28(19): 93-100.
[29]束洪春,张广斌,孙士云,王永治,朱子钊,朱盛强.±800kV直流输电线路雷电绕击与反击的识别方法[J].中国电机工程学报, 2009, 29(7): 13-19.
[30]彭勇,王志新,陈军,刘凯,胡建勋,吴田,刘庭,肖宾.输电线路雷击故障定位与识别[J].高电压技术. 2010, 36(2):406-410.
[31]司马文霞,谢博,杨庆,王荆.特高压输电线路雷电过电压的分类识别方法[J].高电压技术, 2010, 36(2): 306-312..
[32]司大军,束洪春,陈学允,于继来.输电线路雷击的电磁暂态特征分析及其识别方法研究[J].中国电机学报, 2005, 25(7): 64-69.
[33]李庚银,王洪磊,周明.基于改进小波能熵和支持向量机的短时电能质量扰动识别[J].电工技术学报, 2009. 24(4): 161-167.
[34]司马文霞,冉锐,袁涛.采用数学形态学的弧光接地过电压识别方法研究[J].高电压技术. 2010. 36(4): 835-841.
[35]杜林,郭良峰,司马文霞,陈明瑛.基于遗传算法的电力系统过电压分层模糊聚类识别[J].中国电机工程学报, 2010. 30(10): 119-124.
[36]何友全,肖建,熊启军.基于分形理论的电力系统高频暂态波形特征识别[J].电力系统自动化, 2005, 29(2): 29-33.
[37]杨秋霞,宗伟,田璧元.基于小波分析的铁磁谐振检测[J].电网技术, 2001, 25(11): 55-61.
[38] Mokryani G., Haghifam M.R., Esmaeilpoor J.. Identification of ferroresonance based on wavelet transform and artificial neural network[J]. Euro. Trans. Electr. Power, 2009, 19(3): 474-486.
[39] Mokryani, G.,Haghifam, M.-R.,Latafat, H.,Aliparast, P.,Abdolahi, A.. Wavelet Based Kernel Fisher Classifier For Ferroresonance Identification[C]. 15th International Conference on Intelligent System Applications to Power Systems, 2009: 1-6.
[40] G. Mokryani, M.R. Haghifam. Application of wavelet transform and MLP neural network for Ferroresonance identification[C], IEEE Gen. Meet., 2008: 1–6.
[41] G. Mokryani, M.R. Haghifam, J. Esmaeilpoor. Identification of ferroresonance based on wavelet transform and artificial neural network[C]. Aust. Univ.Power Eng. Conf., 2007: 1–6.
[42]刘凡,司马文霞,等.多重分形在铁磁谐振过电压信号分析中的应用[J].中国电机工程学报, 2006, 26 (18): 138-142.
[43] Ali-Reza Sedighi, Mahmood-Reza Haghifam, O. P. Malik, Mohammad-Hassan Ghassemian. High Impedance Fault Detection Based on Wavelet Transform and Statistical Pattern Recognition[J]. IEEE Trans. Power Del., 2005, 20(4): 2414-2421.
[44]齐郑,董迪,杨以涵.中性点不接地系统铁磁谐振与单相接地辨识技术[J].电力系统自动化, 2010, 34 (1):55-58.
[45]全惠敏,王炼红,戴瑜兴.采用广义S变换的电能质量扰动免疫分类算法[J].高电压技术, 2009, 35(9): 2280-2285.
[46] I. W. C. Lee, P. K. Dash. S-Transform-Based Intelligent System for Classification of Power Quality Disturbance Signals[J]. IEEE Trans. Ind. Electron., 2003, 50(4): 800-805.
[47] Fengzhan Zhao,Rengang Yang. Power-Quality Disturbance Recognition Using S-Transform[J]. IEEE Trans. Power Del., 2007, 22(2): 944-950.
[48] H.S. Behera, P.K. Dash, B. Biswal. Power quality time series data mining using S-transform and fuzzy expert system[J]. Applied Soft Computing, 2010, 10(3): 943-955.
[49] Gu Y.H., Bollen, M.H.J. Time-frequency and time-scale domain analysis of voltage disturbances[J]. IEEE Trans. Power Del. 2000, 15, 1279-1284.
[50] Gaing, Z. L.. Wavelet-based neural network for power disturbance recognition and classification[J]. IEEE Trans. Power Del., 2004, 19: 1560-1568.
[51] Kezunovic M., Yuan L.. A novel software implementation concept for power quality study[J]. IEEE Trans. Power Del., 2002, 17: 544-549.
[52] Stockwell R. G., Mansinha L., Lowe R. P.. Localization of the complex spectrum: the S Transform[J]. IEEE Tran. Signal Process, 1996, 44: 998-1001.
[53] Fengzhan Z.; Rengang Y. Power-quality disturbance recognition using s-transform[J]. IEEE Trans. Power Del., 2007, 22: 944-950.
[54] Dash P. K., Panigrahi B. K., Panda G.. Power quality analysis using s-transform[J]. IEEE Trans. Power Del., 2003, 18: 406-411.
[55] Mishra S., Bhende C. N., Panigrahi B. K.. Detection and classification of power quality disturbances using s-transform and probabilistic neural network[J]. IEEE Trans. Power Del., 2008, 23: 280-287.
[56] Zadeh L. A.. Fuzzy sets[J]. Inform. Control, 1965, 8: 338–353.
[57]刘有才,刘增良.模糊专家系统原理与设计[M].北京:北京航空航天大学出版社, 1995.
[58]àkànbíL. A., OdéjobíO.à.. Automatic recognition of oral vowels in tone language: Experiments with fuzzy logic and neural network models[J]. Appl. Soft Comput, 2011, 11: 1467-1480.
[59] Liao Y., Lee J. B.. A fuzzy-expert system for classifying power quality disturbances[J]. Int. J. Elec. Power, 2004, 26: 199-205.
[60] Monsef H., Ranjbar A. M., Jadid S.. Fuzzy rule-based expert system for power system fault diagnosis[J]. IEE Proc. Gener. Transsm. Distrib, 1997, 144: 186-192.
[61] Yen, V. C.. Rule selections in fuzzy expert systems[J]. Expert Syst. Appl., 1999, 16: 79-84
[62]杨纶标,高英仪.模糊数学原理及应用[M].广州:华南理工大学出版社, 2005.
[63] Cortes C., Vapnik V.. Support-vector networks[J]. Mach. Learn., 1995, 20: 273-297.
[64] Emin Z., Al Zahawi B.A.T., Auckland D.W., Tong Y.K.. Ferroresonance in electromagnetic voltage transformers: a study based on nonlinear dynamics[J]. IEE Proc. Gener. Transsm. Distrib., 1997, 144, (4): 383-387.
[65] Kang Y. C., Lee B. E., Zheng T. Y., Kim Y. H., Crossley P. A.. Analytical analysis of PT ferroresonance in the transient-state[C]. 10th IET Int. Conf. Dev. Power Syst. Prot., Manchester, UK, March, 2010: 1-5.
[66] Yunge L., Wei S., Furong L.. Novel Analytical Solution to Fundamental Ferroresonance—Part I: Power Frequency Excitation Characteristic[J]. IEEE Trans. Power Del., 2006, 21 (2): 788-793.
[67]陈禾,陈维贤,钱珞江.配电网络断线谐振及抑制方法[J].高电压技术, 1995, 21(1): 32-36.
[68] Iravani M. R., Chaudhary A. K. S., Giesbrecht W. J., Hassan I. E., Keri A. J. F., Lee K. C., Martinez J. A., Morched A. S., Mork B. A., Parniani M., Sharshar A., Shirmohammadi D., Walling R. A., Woodford D. A.. Modeling and analysis guidelines for slow transients—Part III: The study of ferroresonance[J]. IEEE Trans. Power Del., 2000, 15(1): 255–265.
[69] Shott H. S., Peterson H. S.. Criteria for neutral stability of wye-grounded-primary broken-delta-secondary transformer circuits[J]. Trans. Am. Inst. Elect. Eng., 1941, 60(11): 997-1002.
[70] Kadomskaya K. P., Ivanov A. V., Laptev O. I.. Ferroresonance processes in electrical networks caused by saturation of voltage-transformer cores[C]. IEEE Russ. Power Tech., St. Petersburg, Russia, June, 2005: 1-4.
[71] G. T. Heydt, P. S. Fjeld, C. C. Liu, D. Pierce, L. Tu, G. Hensley. Applications of the windowed FFT to electric power quality assessment[J]. IEEE Trans. Power Del., 1999, 14(4): 1411–1416.
[72] P. S. Wright. Short-time Fourier transforms and Wigner-Ville distributions applied to the calibration of power frequency harmonic analyzers[J]. IEEE Trans. Instrum. Meas., 1999, 48(2): 475–478.
[73] S. Santoso, E. J. Powers, W. M. Grady, P. Hofmann. Power quality assessment via wavelet transform analysis[J]. IEEE Trans. Power Del., 1996, 11(2): 924–930.
[74] P. Pillay, A. Bhattachariee. Application of wavelets to model short-term power system disturbances[J]. IEEE Trans. Power Syst., 1996, 11(4): 2031–2037.
[75] D. C. Robertson, O. I. Camps, J. S. Mayer, and W. B. Gish. Wavelets and electromagnetic power system transients[J]. IEEE Trans. Power Del., 1996, 11(2): 1050–1057.
[76] S. Mallat, Z. Zhang. Matching Pursuit with time frequency dictionaries[J]. IEEE Trans. Signal Process, 1993, 41(12): 3397–3415.
[77]王建英,尹忠科,张春梅.信号与图像的稀疏分解及初步应用[M].成都:西南交通大学出版社, 2006.
[78] R. Gribonval, E. Bacry. Harmonic Decomposition of Audio Signals With Matching Pursuit[J]. IEEE Trans. Signal Process, 2003, 51(1): 101–111.
[79] L. Sturm, J. D. Gibson. Matching Pursuit Decompositions of Non-Noisy Speech Signals Using Several Dictionaries[C]. 1997 IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 1997: 456-459.
[80] R. Neff, A. Zakhor. Very low bit-rate video coding based on matching pursuit[J]. IEEE Trans. Circuits Syst. Video Technol., 1997, 7(1): 158–171.
[81] R. Neff, A. Zakhor. Modulus quantization for matching-pursuit video coding[J]. IEEE Trans. Circuits Syst. Video Technol., 2000, 10(6): 895-912.
[82] Shoa, S. Shirani. Optimized Atom Position and Coefficient Coding for Matching Pursuit-Based Image Compression[J]. IEEE Trans. Image Process, 2009, 18(12): 2686–2694.
[83] M. Goodwin. Matching pursuit with damped sinusoids[C]. 1997 IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 1997, 3: 2037-2040.
[84] John H. Holland.自然与人工系统中的适应[M].北京:高等教育出版社, 2008.
[85] Hong Y. Y., Chen Y. Y.. Placement of power quality monitors using enhanced genetic algorithm and wavelet transform[J]. IET Proc. Gener. Transsm. Distrib, 2011, 5(4): 461-466.
[86] Bull D. R., Redmill D. W.. Optimization of image coding algorithms and architectures using genetic algorithms[J]. IEEE Trans. Ind. Electron., 1996, 43(5): 549-558.
[87] Kennedy J., Eberhart R.. Particle swarm optimization[C]. 1995 IEEE Int. Conf. Neural Networks Proceedings, 1995, 4: 1942-1948.
[88] Shigenori Naka, Takamu Genji, Toshiki Yura, Yoshikazu Fukuyama. A Hybrid Particle Swarm Optimization for Distribution State Estimation[J]. IEEE Trans. Power Syst., 2003, 18(1): 60-68.
[89] M. R. AlRashidi, M. E. El-Hawary. Hybrid Particle Swarm Optimization Approach for Solving the Discrete OPF Problem Considering the Valve Loading Effects[J]. IEEE Trans. Power Syst., 2007, 22(4): 2030-2038.
[90] Biswal B., Dash P. K., Panigrahi B. K.. Power Quality Disturbance Classification Using Fuzzy C-Means Algorithm and Adaptive Particle Swarm Optimization[J]. IEEE Trans. Ind. Electron. 2009, 56(1): 212.
[91] L. Lovisolo, E. A. B. da Silva, M. A. M. Rodrigues, P. S. R. Diniz. Coherent Decompositons of Power Systems Signals using Damped Sinusoids with Application to Denoising[C]. 2002 IEEE Int. Symposium on Circuits and Systems, 2002, 5: 685-688.
[92] L. Lovisolo, E. A. B. da Silva, M. A. M. Rodrigues, P. S. R. Diniz. Efficient Coherent Adaptive Representations of Monitored Electric Signals in Power Systems Using Damped Sinusoids[J]. IEEE Trans. Signal Process, 2005, 53(10): 3831–3846.
[93] L. Lovisolo, M. P. Tcheou, E. A. B. da Silva, M. A. M. Rodrigues, P. S. R. Diniz. Modeling of Electric Disturbance Signals Using Damped Sinusoids via Atomic Decompositions and Its Applications[J]. EURASIP Journal on Advances in Signal Processing, 2007: 1-15.
[94] Benoit Mandelbrot. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension[J]. Science. 1967, 156(3775): 636-638.
[95]罗世华,曾九孙.基于多分辨分析的高炉铁水含硅量波动多重分形辨识[J].物理学报, 2009, 25(1): 150-156.
[96] Xia Sun, Zhuxi Fu, Ziqin Wu. Multifractal analysis and scaling range of ZnO AFM images[J]. Physica A., 2002, 311(3): 327-338.
[97]陈颙,陈凌.分形几何学[M].北京:地震出版社, 2005.
[98]孙霞,吴自勤.分形原理及其应用[M].合肥:中国科技大学出版社, 2006.
[99] Yang Wang, Yi-Sheng Zhu, Nitish V. Thakor, Yu-Hong Xu. A Short-Time Multifractal Approach for Arrhythmia Detection Based on Fuzzy Neural Network[J]. IEEE Trans Biomed. Eng., 2001, 48(9): 989-995.
[100] Donoho D. L.. De-Noising by Soft-Thresholding[J]. IEEE Trans. Inform. Theory, 1995, 41: 613-627.
[101] Hao Z., Blackburn T. R., Phung B. T., Sen D.. A novel wavelet transform technique for on-line partial discharge measurements. Part 1: WT de-noising algorithm[J]. IEEE Trans. Dielect. El. In.. 2007, 14: 3-14.
[102]刘明才.小波分析及其应用[M].北京:清华大学出版社, 2005.
[2] SmartGrids Technology Platform. Vision and strategy for Europe’s electricity networks of the future[EB/OL]. http://www.smartgrids.eu/, 2011-02-28.
[3] Fangxing Li, Wei Qiao, Hongbin Sun, et al.Smart Transmission Grid: Vision and Framework[J]. IEEE Trans. Smart Grid, 2010, 1(2): 168-177.
[4]刘振亚.智能电网技术[M].北京:中国电力出版社, 2010.
[5]李振杰,袁越.智能微网—未来智能配电网新的组织形式[J].电力系统自动化, 2009, 33(17): 42-48.
[6] Juan L., Chenching L., and Schneider K.P. .Controlled Partitioning of a Power Network Considering Real and Reactive Power Balance[J]. IEEE Trans. Smart grid, 2010, 1(3): 261-269.
[7] Pei Z., Fangxing L., Bhatt N..Next-Generation Monitoring, Analysis, and Control for the Future Smart Control Center[J].IEEE Trans. Smart grid, 2010, 1(2): 186-192.
[8]张纬钹,何金良,高玉明.过电压防护及绝缘配合[M].清华大学出版社, 2002.
[9]司马文霞,兰海涛,杜林,孙才新,姚陈果,杨庆.套管末屏电压传感器响应特性研究[J].中国电机学报. 2006, 26(21): 172-176.
[10]王士彬,孙才新,姚陈果,熊兰,米彦,杜林,席世友. 10kV配网内外过电压在线监测系统及波形分析[J].高电压技术, 2004, 30(6): 64-66.
[11]杨保初,刘晓波,戴玉松.高电压技术[M].重庆:重庆大学出版社, 2002.
[12]杨晓辉,蔡旭,分形理论在中压电网故障辨识中的应用[J].电力系统自动化, 2006, 30(4): 59-64.
[13]孙雅明,王俊丰.基于分形理论的输电线路故障分类识别新方法[J].电力系统自动化, 2005, 29(12): 23-28.
[14]赵军,吕艳萍,王汉广.基于多尺度形态分解的特高压线路雷击干扰识别新方法[J].高电压技术, 2009, 35(5): 994-998.
[15]肖先勇,李逢,邓武军.雷击与短路故障的S变换特征量识别方法[J].高电压技术, 2009, 35(4): 817-822.
[16]何正友,陈小勤.基于多尺度能量统计和小波熵测度的电力暂态信号识别方法[J].中国电机工程学报, 2006, 26(10): 33-39.
[17]陈小勤,何正友,符玲.基于小波能谱的电力暂态信号分类识别方法[J].电网技术, 2006, 30(17): 59-63.
[18]王丽霞,何正友,赵静.基于数学形态学的电能质量扰动检测和定位[J].电网技术, 2008, 32(10): 63-68.
[19]操丰梅,苏沛浦.小波变换在配电自动化接地故障检测中的应用研究[J].高电压技术, 1999, 23(13): 33-36.
[20]周海.电力系统操作过电压类型识别的研究[D].重庆大学,硕士学位论文, 2008.
[21]郭良峰.基于遗传算法的电力系统过电压分层模糊聚类识别[D].重庆大学,硕士学位论文, 2009.
[22] Mokryani G., Siano P., Piccolo A.. Identification of ferroresonance based on S-transform and support vector machine[J]. Simul. Model. Pract. Theory, 2010, 18 (9): 1412-1424.
[23] T. X. Zhu. Detection and Characterization of Oscillatory Transients Using Matching Pursuits With a Damped Sinusoidal Dictionary[J]. IEEE Trans. Power Del., 2007, 22(2): 1093-1099.
[24] Zwe-Lee Gaing. Wavelet-Based Neural Network for Power Disturbance Recognition and Classification[J]. IEEE Trans. Power Del., 2004, 19(4): 1560-1568.
[25] Voislav J. Estimation of the maximal voltage induced in an overhead line due to the nearby lightning[J]. IEEE Trans. Power Del., 1997, 12(1): 315-324.
[26]李海锋,王钢,赵建仓.输电线路感应雷击暂态特性分析及其识别方法[J].中国电机工程学报, 2004, 24(3): 114-119.
[27]王钢,李海锋,赵建仓,吴敏.基于小波多尺度分析的输电线路直击雷暂态识别[J].中国电机工程学报, 2004, 24(4): 139-144.
[28]束洪春,王永治,程春和,孙士云.±800kV直流输电线路雷击电磁暂态分析与故障识别[J].中国电机工程学报, 2008, 28(19): 93-100.
[29]束洪春,张广斌,孙士云,王永治,朱子钊,朱盛强.±800kV直流输电线路雷电绕击与反击的识别方法[J].中国电机工程学报, 2009, 29(7): 13-19.
[30]彭勇,王志新,陈军,刘凯,胡建勋,吴田,刘庭,肖宾.输电线路雷击故障定位与识别[J].高电压技术. 2010, 36(2):406-410.
[31]司马文霞,谢博,杨庆,王荆.特高压输电线路雷电过电压的分类识别方法[J].高电压技术, 2010, 36(2): 306-312..
[32]司大军,束洪春,陈学允,于继来.输电线路雷击的电磁暂态特征分析及其识别方法研究[J].中国电机学报, 2005, 25(7): 64-69.
[33]李庚银,王洪磊,周明.基于改进小波能熵和支持向量机的短时电能质量扰动识别[J].电工技术学报, 2009. 24(4): 161-167.
[34]司马文霞,冉锐,袁涛.采用数学形态学的弧光接地过电压识别方法研究[J].高电压技术. 2010. 36(4): 835-841.
[35]杜林,郭良峰,司马文霞,陈明瑛.基于遗传算法的电力系统过电压分层模糊聚类识别[J].中国电机工程学报, 2010. 30(10): 119-124.
[36]何友全,肖建,熊启军.基于分形理论的电力系统高频暂态波形特征识别[J].电力系统自动化, 2005, 29(2): 29-33.
[37]杨秋霞,宗伟,田璧元.基于小波分析的铁磁谐振检测[J].电网技术, 2001, 25(11): 55-61.
[38] Mokryani G., Haghifam M.R., Esmaeilpoor J.. Identification of ferroresonance based on wavelet transform and artificial neural network[J]. Euro. Trans. Electr. Power, 2009, 19(3): 474-486.
[39] Mokryani, G.,Haghifam, M.-R.,Latafat, H.,Aliparast, P.,Abdolahi, A.. Wavelet Based Kernel Fisher Classifier For Ferroresonance Identification[C]. 15th International Conference on Intelligent System Applications to Power Systems, 2009: 1-6.
[40] G. Mokryani, M.R. Haghifam. Application of wavelet transform and MLP neural network for Ferroresonance identification[C], IEEE Gen. Meet., 2008: 1–6.
[41] G. Mokryani, M.R. Haghifam, J. Esmaeilpoor. Identification of ferroresonance based on wavelet transform and artificial neural network[C]. Aust. Univ.Power Eng. Conf., 2007: 1–6.
[42]刘凡,司马文霞,等.多重分形在铁磁谐振过电压信号分析中的应用[J].中国电机工程学报, 2006, 26 (18): 138-142.
[43] Ali-Reza Sedighi, Mahmood-Reza Haghifam, O. P. Malik, Mohammad-Hassan Ghassemian. High Impedance Fault Detection Based on Wavelet Transform and Statistical Pattern Recognition[J]. IEEE Trans. Power Del., 2005, 20(4): 2414-2421.
[44]齐郑,董迪,杨以涵.中性点不接地系统铁磁谐振与单相接地辨识技术[J].电力系统自动化, 2010, 34 (1):55-58.
[45]全惠敏,王炼红,戴瑜兴.采用广义S变换的电能质量扰动免疫分类算法[J].高电压技术, 2009, 35(9): 2280-2285.
[46] I. W. C. Lee, P. K. Dash. S-Transform-Based Intelligent System for Classification of Power Quality Disturbance Signals[J]. IEEE Trans. Ind. Electron., 2003, 50(4): 800-805.
[47] Fengzhan Zhao,Rengang Yang. Power-Quality Disturbance Recognition Using S-Transform[J]. IEEE Trans. Power Del., 2007, 22(2): 944-950.
[48] H.S. Behera, P.K. Dash, B. Biswal. Power quality time series data mining using S-transform and fuzzy expert system[J]. Applied Soft Computing, 2010, 10(3): 943-955.
[49] Gu Y.H., Bollen, M.H.J. Time-frequency and time-scale domain analysis of voltage disturbances[J]. IEEE Trans. Power Del. 2000, 15, 1279-1284.
[50] Gaing, Z. L.. Wavelet-based neural network for power disturbance recognition and classification[J]. IEEE Trans. Power Del., 2004, 19: 1560-1568.
[51] Kezunovic M., Yuan L.. A novel software implementation concept for power quality study[J]. IEEE Trans. Power Del., 2002, 17: 544-549.
[52] Stockwell R. G., Mansinha L., Lowe R. P.. Localization of the complex spectrum: the S Transform[J]. IEEE Tran. Signal Process, 1996, 44: 998-1001.
[53] Fengzhan Z.; Rengang Y. Power-quality disturbance recognition using s-transform[J]. IEEE Trans. Power Del., 2007, 22: 944-950.
[54] Dash P. K., Panigrahi B. K., Panda G.. Power quality analysis using s-transform[J]. IEEE Trans. Power Del., 2003, 18: 406-411.
[55] Mishra S., Bhende C. N., Panigrahi B. K.. Detection and classification of power quality disturbances using s-transform and probabilistic neural network[J]. IEEE Trans. Power Del., 2008, 23: 280-287.
[56] Zadeh L. A.. Fuzzy sets[J]. Inform. Control, 1965, 8: 338–353.
[57]刘有才,刘增良.模糊专家系统原理与设计[M].北京:北京航空航天大学出版社, 1995.
[58]àkànbíL. A., OdéjobíO.à.. Automatic recognition of oral vowels in tone language: Experiments with fuzzy logic and neural network models[J]. Appl. Soft Comput, 2011, 11: 1467-1480.
[59] Liao Y., Lee J. B.. A fuzzy-expert system for classifying power quality disturbances[J]. Int. J. Elec. Power, 2004, 26: 199-205.
[60] Monsef H., Ranjbar A. M., Jadid S.. Fuzzy rule-based expert system for power system fault diagnosis[J]. IEE Proc. Gener. Transsm. Distrib, 1997, 144: 186-192.
[61] Yen, V. C.. Rule selections in fuzzy expert systems[J]. Expert Syst. Appl., 1999, 16: 79-84
[62]杨纶标,高英仪.模糊数学原理及应用[M].广州:华南理工大学出版社, 2005.
[63] Cortes C., Vapnik V.. Support-vector networks[J]. Mach. Learn., 1995, 20: 273-297.
[64] Emin Z., Al Zahawi B.A.T., Auckland D.W., Tong Y.K.. Ferroresonance in electromagnetic voltage transformers: a study based on nonlinear dynamics[J]. IEE Proc. Gener. Transsm. Distrib., 1997, 144, (4): 383-387.
[65] Kang Y. C., Lee B. E., Zheng T. Y., Kim Y. H., Crossley P. A.. Analytical analysis of PT ferroresonance in the transient-state[C]. 10th IET Int. Conf. Dev. Power Syst. Prot., Manchester, UK, March, 2010: 1-5.
[66] Yunge L., Wei S., Furong L.. Novel Analytical Solution to Fundamental Ferroresonance—Part I: Power Frequency Excitation Characteristic[J]. IEEE Trans. Power Del., 2006, 21 (2): 788-793.
[67]陈禾,陈维贤,钱珞江.配电网络断线谐振及抑制方法[J].高电压技术, 1995, 21(1): 32-36.
[68] Iravani M. R., Chaudhary A. K. S., Giesbrecht W. J., Hassan I. E., Keri A. J. F., Lee K. C., Martinez J. A., Morched A. S., Mork B. A., Parniani M., Sharshar A., Shirmohammadi D., Walling R. A., Woodford D. A.. Modeling and analysis guidelines for slow transients—Part III: The study of ferroresonance[J]. IEEE Trans. Power Del., 2000, 15(1): 255–265.
[69] Shott H. S., Peterson H. S.. Criteria for neutral stability of wye-grounded-primary broken-delta-secondary transformer circuits[J]. Trans. Am. Inst. Elect. Eng., 1941, 60(11): 997-1002.
[70] Kadomskaya K. P., Ivanov A. V., Laptev O. I.. Ferroresonance processes in electrical networks caused by saturation of voltage-transformer cores[C]. IEEE Russ. Power Tech., St. Petersburg, Russia, June, 2005: 1-4.
[71] G. T. Heydt, P. S. Fjeld, C. C. Liu, D. Pierce, L. Tu, G. Hensley. Applications of the windowed FFT to electric power quality assessment[J]. IEEE Trans. Power Del., 1999, 14(4): 1411–1416.
[72] P. S. Wright. Short-time Fourier transforms and Wigner-Ville distributions applied to the calibration of power frequency harmonic analyzers[J]. IEEE Trans. Instrum. Meas., 1999, 48(2): 475–478.
[73] S. Santoso, E. J. Powers, W. M. Grady, P. Hofmann. Power quality assessment via wavelet transform analysis[J]. IEEE Trans. Power Del., 1996, 11(2): 924–930.
[74] P. Pillay, A. Bhattachariee. Application of wavelets to model short-term power system disturbances[J]. IEEE Trans. Power Syst., 1996, 11(4): 2031–2037.
[75] D. C. Robertson, O. I. Camps, J. S. Mayer, and W. B. Gish. Wavelets and electromagnetic power system transients[J]. IEEE Trans. Power Del., 1996, 11(2): 1050–1057.
[76] S. Mallat, Z. Zhang. Matching Pursuit with time frequency dictionaries[J]. IEEE Trans. Signal Process, 1993, 41(12): 3397–3415.
[77]王建英,尹忠科,张春梅.信号与图像的稀疏分解及初步应用[M].成都:西南交通大学出版社, 2006.
[78] R. Gribonval, E. Bacry. Harmonic Decomposition of Audio Signals With Matching Pursuit[J]. IEEE Trans. Signal Process, 2003, 51(1): 101–111.
[79] L. Sturm, J. D. Gibson. Matching Pursuit Decompositions of Non-Noisy Speech Signals Using Several Dictionaries[C]. 1997 IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 1997: 456-459.
[80] R. Neff, A. Zakhor. Very low bit-rate video coding based on matching pursuit[J]. IEEE Trans. Circuits Syst. Video Technol., 1997, 7(1): 158–171.
[81] R. Neff, A. Zakhor. Modulus quantization for matching-pursuit video coding[J]. IEEE Trans. Circuits Syst. Video Technol., 2000, 10(6): 895-912.
[82] Shoa, S. Shirani. Optimized Atom Position and Coefficient Coding for Matching Pursuit-Based Image Compression[J]. IEEE Trans. Image Process, 2009, 18(12): 2686–2694.
[83] M. Goodwin. Matching pursuit with damped sinusoids[C]. 1997 IEEE Int. Conf. Acoustics, Speech, and Signal Processing, 1997, 3: 2037-2040.
[84] John H. Holland.自然与人工系统中的适应[M].北京:高等教育出版社, 2008.
[85] Hong Y. Y., Chen Y. Y.. Placement of power quality monitors using enhanced genetic algorithm and wavelet transform[J]. IET Proc. Gener. Transsm. Distrib, 2011, 5(4): 461-466.
[86] Bull D. R., Redmill D. W.. Optimization of image coding algorithms and architectures using genetic algorithms[J]. IEEE Trans. Ind. Electron., 1996, 43(5): 549-558.
[87] Kennedy J., Eberhart R.. Particle swarm optimization[C]. 1995 IEEE Int. Conf. Neural Networks Proceedings, 1995, 4: 1942-1948.
[88] Shigenori Naka, Takamu Genji, Toshiki Yura, Yoshikazu Fukuyama. A Hybrid Particle Swarm Optimization for Distribution State Estimation[J]. IEEE Trans. Power Syst., 2003, 18(1): 60-68.
[89] M. R. AlRashidi, M. E. El-Hawary. Hybrid Particle Swarm Optimization Approach for Solving the Discrete OPF Problem Considering the Valve Loading Effects[J]. IEEE Trans. Power Syst., 2007, 22(4): 2030-2038.
[90] Biswal B., Dash P. K., Panigrahi B. K.. Power Quality Disturbance Classification Using Fuzzy C-Means Algorithm and Adaptive Particle Swarm Optimization[J]. IEEE Trans. Ind. Electron. 2009, 56(1): 212.
[91] L. Lovisolo, E. A. B. da Silva, M. A. M. Rodrigues, P. S. R. Diniz. Coherent Decompositons of Power Systems Signals using Damped Sinusoids with Application to Denoising[C]. 2002 IEEE Int. Symposium on Circuits and Systems, 2002, 5: 685-688.
[92] L. Lovisolo, E. A. B. da Silva, M. A. M. Rodrigues, P. S. R. Diniz. Efficient Coherent Adaptive Representations of Monitored Electric Signals in Power Systems Using Damped Sinusoids[J]. IEEE Trans. Signal Process, 2005, 53(10): 3831–3846.
[93] L. Lovisolo, M. P. Tcheou, E. A. B. da Silva, M. A. M. Rodrigues, P. S. R. Diniz. Modeling of Electric Disturbance Signals Using Damped Sinusoids via Atomic Decompositions and Its Applications[J]. EURASIP Journal on Advances in Signal Processing, 2007: 1-15.
[94] Benoit Mandelbrot. How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension[J]. Science. 1967, 156(3775): 636-638.
[95]罗世华,曾九孙.基于多分辨分析的高炉铁水含硅量波动多重分形辨识[J].物理学报, 2009, 25(1): 150-156.
[96] Xia Sun, Zhuxi Fu, Ziqin Wu. Multifractal analysis and scaling range of ZnO AFM images[J]. Physica A., 2002, 311(3): 327-338.
[97]陈颙,陈凌.分形几何学[M].北京:地震出版社, 2005.
[98]孙霞,吴自勤.分形原理及其应用[M].合肥:中国科技大学出版社, 2006.
[99] Yang Wang, Yi-Sheng Zhu, Nitish V. Thakor, Yu-Hong Xu. A Short-Time Multifractal Approach for Arrhythmia Detection Based on Fuzzy Neural Network[J]. IEEE Trans Biomed. Eng., 2001, 48(9): 989-995.
[100] Donoho D. L.. De-Noising by Soft-Thresholding[J]. IEEE Trans. Inform. Theory, 1995, 41: 613-627.
[101] Hao Z., Blackburn T. R., Phung B. T., Sen D.. A novel wavelet transform technique for on-line partial discharge measurements. Part 1: WT de-noising algorithm[J]. IEEE Trans. Dielect. El. In.. 2007, 14: 3-14.
[102]刘明才.小波分析及其应用[M].北京:清华大学出版社, 2005.