电力短期负荷时间序列混沌特性分析及预测研究
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摘要
短期负荷预测是电力系统调度运营部门一项重要的基础工作,预测精度的高低直接影响到电网运行的安全性、经济性以及电能质量。由于电力负荷表现出复杂性、不确定性、非线性的特点,使得传统的电力负荷时间序列预处理技术得不到令人满意的效果。混沌是确定性的非线性系统中出现的类似随机的现象。随着非线性混沌动力学的发展,人们对时间序列的复杂性有了更深刻的认识,尤其是混沌时间序列的分析已经成为一个非常重要的研究方向,这给短期负荷时间序列分析与预测提供了科学的方法。
本文基于混沌理论,对短期负荷的变化规律进行分析和预测。主要研究内容如下:
1.从重构相空间理论出发,探讨了相空间参数对重构空间质量的影响,以及确定相空间嵌入维数和延迟时间各种不同的方法。在短期负荷重构参数的选取上,一方面,使用Cao方法弥补了伪最近邻域法进行短期负荷相空间重构不准确的缺陷;另一方面,引入改进的C-C方法求取嵌入参数。两种方法互相结合,以验证本文求得的延迟时间和嵌入维数的准确性。
2.对电力小时负荷时间序列进行混沌性质识别。一方面,采用Cao方法从定性的角度分析短期负荷的混沌特性;另一方面,通过提取短期负荷时间序列的混沌特征量:饱和关联维数、Lyapunov指数和Kolmogorov熵,从定量的角度分析电力负荷时间序列的混沌特性。另外,由于G-P关联维数的计算结果易受多种因素的影响,通过引入非主观关联维以弥补G-P关联维数判断时间序列混沌特性的局限性。
3.针对加权一阶局域法预测模型计算量较大,而且会产生累积误差这一问题,采用加权一阶局域法多步预测模型进行预测。对华北某电网1998年全年负荷时间序列进行相空间重构,并使用加权一阶局域法多步预测模型和基于最大Lyapunov指数的预测模型做对比实验,分别对一天和一周的负荷进行预测仿真实验,研究表明,两种相空间预测模型对电力负荷短期预测是有效的。
4.在研究了混沌时间序列的可预测尺度问题的基础上,提出了一种运用RBF神经网络平均可预测尺度内对短期负荷进行直接多步预测的方法,通过对本文所用的短期负荷时间序列进行相应的预测研究,实例应用表明直接多步预测方法的预报精度较高,预报效果令人满意。
Short-term load forecasting(STLF)is an important and basal component in the operation of any electric utility whose accuracy directly influence power system's security, profit and quality. Because of the highly nonlinear, complexity and indeterminacy of the power load, means that the traditional load time series pretreatment technology can not be achieved satisfactory results. Chaos is a quasi-stochastic phenomenon appearing in deterministic nonlinear dynamic system. With the development of nonlinear chaotic dynamic, there are more profound recognitions to the complexity of time series. Especially the analysis of time series is becoming an important research aspect that provides a scientific basis for analysis and prediction of short load time series.
Based on the chaos theory, characteristic of short-term load time series is analyzed and its forecasting methods are studied in this paper. The main contents discussed in this thesis are described as follows:
1. The influence of phase space parameters on phase space quality and the methods for determining delay time & embedding dimension are discussed on the reconstruction theory. About selection of reconstruction parameters, on the one hand, False Nearest Neighbors method is improved by Cao method, and accurate phase reconstruction parameters of short-term load; on the other hand, improved C-C method is introduced into selection of reconstruction parameters. The results of the two methods were mutually supplemented and verified.
2. For electric hourly load, on the one hand, short-term load is analyzed qualitatively be Cao methed; on the other hand, quantitative calculation about saturation correlation dimension, the largest Lyapunov exponent and Kolmogorov entropy of power load is used to identity their chaotic characteristics. In addition, it is found that the calculation of correlation dimension is seriously influenced by many factors. Through introducing non subjective approach, to avoid the limitations of judging whether time series has chaotic character or not by the invariants are pointed out.
3. Large computational quantity and cumulative error are main shortcomings of add- weighted one-rank local-region method for prediction of chaotic time series. Local-region multi-steps forecasting model based on phase reconstruction is adopted for short-term load time series prediction. When using the method for the STLF of a certain power network in the north china, 1998. The chaotic characteristics of the load time series in this case are analyzed, and the phase space reconstruction parameters are deduced. Local-region multi-steps forecasting model and the largest Lyapunov method are used in the forecasting experiment for the load in one day and one week. The prediction results indicated that the chaotic model is effective for short term load forecasting.
4. Studied on the predictable size of chaotic time series, a method of direct multi-step prediction of Short-term load is proposed, which is based on the average predictable size and radial basis functions neural networks. And short-term load that have been used in this paper is predicted by the method. Simulation results for direct multi-step prediction method could get high precision.
本文基于混沌理论,对短期负荷的变化规律进行分析和预测。主要研究内容如下:
1.从重构相空间理论出发,探讨了相空间参数对重构空间质量的影响,以及确定相空间嵌入维数和延迟时间各种不同的方法。在短期负荷重构参数的选取上,一方面,使用Cao方法弥补了伪最近邻域法进行短期负荷相空间重构不准确的缺陷;另一方面,引入改进的C-C方法求取嵌入参数。两种方法互相结合,以验证本文求得的延迟时间和嵌入维数的准确性。
2.对电力小时负荷时间序列进行混沌性质识别。一方面,采用Cao方法从定性的角度分析短期负荷的混沌特性;另一方面,通过提取短期负荷时间序列的混沌特征量:饱和关联维数、Lyapunov指数和Kolmogorov熵,从定量的角度分析电力负荷时间序列的混沌特性。另外,由于G-P关联维数的计算结果易受多种因素的影响,通过引入非主观关联维以弥补G-P关联维数判断时间序列混沌特性的局限性。
3.针对加权一阶局域法预测模型计算量较大,而且会产生累积误差这一问题,采用加权一阶局域法多步预测模型进行预测。对华北某电网1998年全年负荷时间序列进行相空间重构,并使用加权一阶局域法多步预测模型和基于最大Lyapunov指数的预测模型做对比实验,分别对一天和一周的负荷进行预测仿真实验,研究表明,两种相空间预测模型对电力负荷短期预测是有效的。
4.在研究了混沌时间序列的可预测尺度问题的基础上,提出了一种运用RBF神经网络平均可预测尺度内对短期负荷进行直接多步预测的方法,通过对本文所用的短期负荷时间序列进行相应的预测研究,实例应用表明直接多步预测方法的预报精度较高,预报效果令人满意。
Short-term load forecasting(STLF)is an important and basal component in the operation of any electric utility whose accuracy directly influence power system's security, profit and quality. Because of the highly nonlinear, complexity and indeterminacy of the power load, means that the traditional load time series pretreatment technology can not be achieved satisfactory results. Chaos is a quasi-stochastic phenomenon appearing in deterministic nonlinear dynamic system. With the development of nonlinear chaotic dynamic, there are more profound recognitions to the complexity of time series. Especially the analysis of time series is becoming an important research aspect that provides a scientific basis for analysis and prediction of short load time series.
Based on the chaos theory, characteristic of short-term load time series is analyzed and its forecasting methods are studied in this paper. The main contents discussed in this thesis are described as follows:
1. The influence of phase space parameters on phase space quality and the methods for determining delay time & embedding dimension are discussed on the reconstruction theory. About selection of reconstruction parameters, on the one hand, False Nearest Neighbors method is improved by Cao method, and accurate phase reconstruction parameters of short-term load; on the other hand, improved C-C method is introduced into selection of reconstruction parameters. The results of the two methods were mutually supplemented and verified.
2. For electric hourly load, on the one hand, short-term load is analyzed qualitatively be Cao methed; on the other hand, quantitative calculation about saturation correlation dimension, the largest Lyapunov exponent and Kolmogorov entropy of power load is used to identity their chaotic characteristics. In addition, it is found that the calculation of correlation dimension is seriously influenced by many factors. Through introducing non subjective approach, to avoid the limitations of judging whether time series has chaotic character or not by the invariants are pointed out.
3. Large computational quantity and cumulative error are main shortcomings of add- weighted one-rank local-region method for prediction of chaotic time series. Local-region multi-steps forecasting model based on phase reconstruction is adopted for short-term load time series prediction. When using the method for the STLF of a certain power network in the north china, 1998. The chaotic characteristics of the load time series in this case are analyzed, and the phase space reconstruction parameters are deduced. Local-region multi-steps forecasting model and the largest Lyapunov method are used in the forecasting experiment for the load in one day and one week. The prediction results indicated that the chaotic model is effective for short term load forecasting.
4. Studied on the predictable size of chaotic time series, a method of direct multi-step prediction of Short-term load is proposed, which is based on the average predictable size and radial basis functions neural networks. And short-term load that have been used in this paper is predicted by the method. Simulation results for direct multi-step prediction method could get high precision.
引文
[1] Papalexopoulos A D, Hesterberg T C. A regression-based approach to short-term system load forecasting. IEEE Transactions on Power Systems, 1990, 5(4): 1535 - 1547P
[2]赵宏伟,任震,黄雯莹.基于周期自回归模型的短期负荷预测.中国电机工程学报.1997,17(5):347-351页
[3]康重庆,夏清,刘梅等.应用于负荷预测中的回归分析的特殊问题.电力系统自动化.1998,22(10):38-41页
[4] Park D C, E1-Sharkawi M A, Marks II R J. Electric load forecasting using an artificial neural network. IEEE Transactions on Power Systems, 1991, 6(2):442-449P
[5] Chen S T, David C.Y. Weather sensitive short-term load forecasting using nonfully connected artificial neural network. IEEE Transactions on Power Systems, 1992, 7(3):1098-1105P
[6] Hippert H S, Pedreira C E, Souza R C. Neural networks for short-term load forecasting: A review and evaluation. IEEE Transactions on Power Systems, 2001, 16(1):44-45P
[7] Xiao Zhi, Ye Shijie, Zhong Bo, Sun Caixin. BP neural network with rough set for short term load forecasting.Expert Systems with Applications, 2009, 36(1):273-279P
[8] LI Ling-chun,TIAN Li. A combined model of genetic algorithm and BP Neural Network for short-term load forecasting. Journal of AnhuiUniversity of Technology and Science(Natural Science) ,2009, 03-015P
[9] Che-Chiang Hsu, Chia-Yon Chen. Regional load forecasting in Taiwan—applications of artificial neural networks.PARGAMON.2003,1942-1949P
[10] Liu Wei. Exploring of related issues of BP algorithm in load forecasting. IEEE ICICTA 2th, 2009, 1:71-74P
[11]甘文泉,王朝晖,胡保生.结合神经元网络和模糊专家系统进行电力短期负荷预测.西安交通大学学报.1998,32(3):28-32页
[12]招海丹,余德伟.模糊专家系统用于短期负荷预测修正的初步探讨.华东电力.2000,5:24-26页
[13]张涛,赵登福,周琳等.基于RBF神经网络和专家系统的短期负荷预测方法.西安交通大学学报.2001,35(4):331-334页
[14]邰能灵,侯志俭,李涛等.基于小波分析的电力系统短期负荷预测方法.中国电机工程学报.2003,23(1):45-50页
[15]宋超,黄民翔,叶剑斌.小波分析方法在电力系统短期负荷预测中的应用.电力系统及其自动化学报.2002,14(3):8-12页
[16]徐军华,刘天琪.基于小波分解和人工神经网络的短期负荷预测.电网技术.2004,28(8):30-33页
[17]尹成群,康丽峰,李丽等.基于小波变换和混合神经网络的短期负荷预测.电力自动化设备.2007,27(5):40-44页
[18] Amjady N, Keynia F. Short-term load forecasting of power systems by combination of wavelet transform and neuro-evolutionary algorithm. Energy, 2009,34(1):46-57P
[19]严华,吴捷,马志强等.模糊集理论在电力系统短期负荷预测中的应用.电力系统自动化.2000,6:67-71页
[20] Ling S H, Leung F H F, Lam H K, Tam P K S. Short-term electric forecasting based on a neural fuzzy network. IEEE Transactions on Industrial Elecronics, 2003, 50(6):1305-1316P
[21] Yang Kuihe, Zhu Jinjun, Wang Baoshu, Zhao Lingling. Design of short-term load forecasting model based on fuzzy neural networks. WCICA 2004-Fifth World Congress on Intelligent Control and Automation, 2004, 3:2038-2041P
[22] Mori Hiroyuki, Jiang Wenjun. Integration of graphical modeling with fuzzy clustering for casual relationship of electric load forecasting. Proceedings of the Ninth International Conference on Intelligent Systems Design and Applications, 2009,1377-1382P
[23] Rusturm M, Omar B, Emad A. A fuzzy inference model for short-term load forecasting.Energy Policy, 2009, 37(4):1239-1248P
[24]李鹰,赵振江,吴松涛.灰色模型在普通日短期电力负荷预测中的应用.长沙电力学院学报(自然科学版) .2003,18(l):15-17页
[25]张俊芳,吴伊昂,吴军基.基于灰色理论负荷预测的应用研究.电力自动化设备.2004,24(5):24-27页
[26]邢棉,于兰香,刘晓霞.基于神经网络校正的电力负荷灰色预测.华北电力大学学报.2006,33(4):93-95页
[27]蒋传文,权先障,李承军等.混沌理论在电力负荷预测中的应用.武汉交通科技大学学报.1999,23 (6):608-611页
[28]温权,张勇传,程时杰.负荷预报的混沌时间序列分析方法.电网技术.2001,25(10):13-16页
[29]姜勇.电力系统短期负荷的特征指数相空间重构预测法.继电器.2003,31(3):11-14页
[30]吉国力,程军,米红.应用混沌相空间模线性回归模型研究短期负荷预报.系统工程理论与实践.2001,6:138-140,144页
[31]吕金虎,张锁春.加权一阶局域法在电力系统短期负荷预测中的应用.控制理论与应用.2002,19(5):767-770页
[32] Cai Minglun, Cai Feng, Shi Aiguo, et al. Chaotic time series prediction based on local-region multi-steps forecasting model. Advances in Neural Networks-ISNN2004: International Symposium on Neural Networks, PartII, Dalian, China, 2004, 8: 418 - 423P
[33]郑永康,陈维荣,蒋刚等.基于混沌理论的短期负荷局域多步预测法.电力系统及其自动化学报.2007,19(4):76-79页
[34]杨正瓴,林孔元,余贻鑫.短期负荷预报的“双周期加混沌”法中的子模型优选理论探讨.电网技术.2003,27(5):33-36页
[35]杨正瓴,田勇,林孔元.短期负荷预测“双周期加混沌”法中多步法与气象因子的使用.电网技术.2004,28(12):20-24页
[36] Jiang Chuanwen, Li Tao. Forecasting method study on chaotic load series with high embedded dimension. Energy Conversion and Management, 2005, 46(5): 667-676P
[37]杜杰,陆金桂,曹一家.短期负荷预测最大Lyapunov指数预报模式预测值的判定.电网技术.2006,30(20):20-24页
[38]杨正瓴,田勇,张广涛等.短期负荷预测最大李亚普诺夫指数法的改进.电网技术.2005,29(7):31-35页
[39]方仍存,周建中,彭兵等.电力负荷混沌动力特性及其短期预测.电网技术.2008,32(4):61-66页
[40]李兰友,杜杰,邵定宏等.最大Lyapunov指数短期电力负荷预测模型仿真.计算机工程与设计.2007,28(24):5935-5937页
[41] Chen Bojuen, Chang Mingmei. Load forecasting using support vector machines: a study on EUNITE competition 2001. IEEE Transactions on Power Systems, 2004, 19(4):1821-1830P
[42] Niu Dongxiao, Wang Yongli. Power load forecasting using support vector machine and ant colony optimization. Expert Systems with Applications, 2010, 37(3): 2531-2539P
[43]姜惠兰,刘晓津,关颖等.基于硬C均值聚类算法和支持向量机的电力系统短期负荷预测.电网技术.2006,30(8):81-85页
[44] Jordaan J A, Ukil A. Load forecasting with support vector machines and semi-parametric method. The 8th Inteligent Date Engineering and Automated Learning, Birmingham,UK,2007,4881:258-267P
[45]李元诚,方廷健,于尔铿.短期负荷预测的支持向量机方法研究.中国电机工程学报.2003,23(6):55-59页
[46]谢宏,魏江平,刘鹤立.短期负荷预测中支持向量机模型的参数选取和优化方法.中国电机工程学报.2006,26(22):17-22页
[47] Wang Jingmin, Zhou Yamin, Chen Xiaoyu. Electricity load forecasting based on support vector machines and simulated annealing particle swarm optimization algorithm. Proceedings of the IEEE International Conferenceon Automation and Logistics,Jinan,China, 2007:2836-2841P
[48]安德洪,韩文秀,岳毅宏.组合预测法的改进及其在负荷预测中的应用.系统工程与电子技术.2004,26(6):842-844页
[49]孙海斌,周淑雄,谢敬东等.模糊综合评价在负荷最优组合预测中的应用.电力系统及其自动化学报.2001,13(4):8-11页
[50]谢开贵,李春燕,俞集辉.基于遗传算法的短期负荷组合预测模型.电网技术.2001,25(8):20-23页
[51]赵海青,牛东晓.负荷预测的交叉式自适应优选组合预测模型.华北电力大学学报.2000,27(4):13-17页
[52] Niu Dongxiao, Wang Yongli, Duan Chunming. A New Short-term Power Load Forecasting Model Based on Chaotic Time Series and SVM. Journal of Universal Computer Science, 2009, 15(13):2726-2745P
[53] Wu Qi. A hybrid-forecasting model based on Gaussian support vector machine and chaotic particle swarm optimization. Expert Systems with Applications, 2010, 37(3):2388-2394P
[54] Hong Weichiang. Hybrid evolutionary algorithms in a SVR-based electric load forecasting model. International Journal of Electrical Power & Energy Systems, 2009, 31(7-8):409-417P
[55] Packard N H, Crutchfield J P, Farmer J D, Shaw R S. Geometry from a Time Series. Physical Review Letters, 1980,45(9):712-716P
[56] Takens F. Determing strange attractors in turbulence. Lecture notes in Math, 1981,898: 361-381P
[57] Mori H,Drano S. Chaotic Time Series Analysis for Short-term PowerSystem Load Forecasting. Proc of the 3rd Int '1 Conf on Fuzzy Logic Neural Nets and Soft Computing(IIZUKA' 94).lizuka;(Japan).1994. 441-442P
[58]蒋传文,侯志俭,李承军.求取混沌时间序列嵌入维数的一种神经元网络方法.水电能源科学.2000,18(4):12-14,43页
[59]杨正瓴,林孔元.短期负荷预测相空间重构法参数优选的数值测试与分析.电力系统自动化.2003,27(16):40-44页
[60]谷子,唐巍.电力短期负荷时间序列混沌相空间重构参数优选法.中国电机工程学报. 2006,26(14):18-23页
[61]杨正瓴,曹东波,张广涛等.用奇异性的短期负荷预测混沌方法优化参数.天津大学学报.2006,39(3):334-337页
[62] Mori H, Urano S. Short-term load forecasting with chaos time series analysis. Proceedings of International Conference on Intelligent Systems Applications to Power Systems, France, 1996: 133-137P
[63]丁军威,孙雅明.基于混沌学习算法的神经网络短期负荷预测.电力系统自动化.2000,24(2):32-35页
[64]李天云,刘自发.电力系统负荷的混沌特性及预测.中国电机工程学报.2000,20(11):36-40页
[65] Chen Luonan. Application of Chaotic Simulation and Self-organizing Neural Net to Power System Voltage Stability Monitoring. IEEE, 1993: 367-372P
[66] Liu Shuliang, Hu Zhiqiang,Chi Xiukai. Power load forecasting based on neural network and time series. Proceedings of the 5th International Conference on Wireless communications, networking and mobilecomputing, Beijing, China, 2009: 5047 - 5051P
[67]尤勇,盛万兴,王孙安.基于人工免疫网络的短期负荷预测模型.中国电机工程学报.2003,23(3):26-29,98页
[68] Park Jae-gyun, Park Jong-keun,Kim Kwang-ho, et al. A Daily Peak Load Forecasting System Using a Chaotic Time Series. IEEE,1996:283-287P
[69] Camastra F, Colla M. Neural Short-term Prediction Based on Dynamics Reconstruction. Neural Processing Lerrers, 1999, 9(1):45-52P
[70]蒋传文,侯志俭,李承军.基于混沌理论的电力负荷短期预报的神经网络方法.水电能源科学.2001,19(3):59-61页
[71] Michano S P, Tsakoumis A C,Fessas P, et al. Short-term Load Forecasting Using a Chaotic Time Series. IEEE International Symposium on Signals, Circuits and Systems. Proceedings,2003,2:437-440P
[72]张智晟,孙雅明,王兆峰等.优化相空间近邻点与递归神经网络融合的短期负荷预测.中国电机工程学报.2003 , 23 (8):44-49页
[73] Iokibe T, Mochizuki N. Short-term Prediction Based on Fuzzy logic and Chaos. Proc of FAN Symp. Tsuku-ba:(Japan) 1994.77-82P
[74] Iokibe T, Kanke M,Fujimoto Y,et al. Short-term Prediction on Chaotic Time Series by Local Fuzzy Reconstruction Method. Proc of the 3rd lntemat Conf on Fuzzy Logic, Neural Nets and Soft Computing. Lizuka (Japan):1994.491-492P
[75] Iokibe T, Fujimoto Y,Kanke M. Short-term prediction of chaotic time series by local fuzzy reconstruction meth. J Intell Fuzzy Systems, 1997, 5: 3-21P
[76] Wu Haishan,Chang Xiaoling. Power Load Forecasting with Least Squares Support Vector Machines and Chaos Theory. Proceedings of the 6th World Congress on Control, and Automation, 2006, 1:4369-4373P
[77] Wang J, Ren G. Load forecasting based on chaotic support vector machine with incorporated intelligence algorithm. Proceeding of the first International Conference on Innovative Computing, Information and Control IEEE, 2006:378-381P
[78] Sauer T, Yorke J A, and Casdagli M. Embedology. Journal of Statistical Physics, 1991, 64:579-616P
[79] Takens F. Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence. Berlin:Springer-Verlag,New York,1981,898:366-381P
[80] Williams G P. Chaos theory tamed. Washington, DC: Joseph Henry, 1997,516 P
[81] Rosenstein M T, Collins J J, Deluca C J. Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physical D: Nonlinear Phenomena,1994,73(1-2):82-98P
[82] Fraser A M, Swinney H L. Independent coordinates for strange attractors from mutual information. Physical Review A,1986,33(2):1134-1140P
[83] Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physical D:Nonlinear Phenomena,1983,9(1-2):189-208P
[84] Kennel M B, Brown R, Abarbanel H D. Determining embedding dimension for phase space reconstruction using a geometrical construction. Physical Review A,1992,45(6):3403-3411P
[85] Cao Liangyue. Practical method for determining the minimum embedding dimension of a scalar time series. Physical D:Nonlinear Phenomena, 1997, 110(1-2):43-50P
[86]马红光,李夕海,王国华等.相空间重构中嵌入维和时间延迟的选择.西安交通大学学报.2004,38(4): 335-338页
[87] Kuqiumtzis D. State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length. Physical D, 1996, 95(1):13-28P
[88] Kim H S, Eykholt R, Salas J D. Nonlinear dynamics, delay times, and embedding windows. Physical D,1999,127(1):48-60P
[89]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择.系统仿真学报.2007,19(11): 2527-2530,2538页
[90]杨绍清,章新华,赵长安等.基于混沌理论的水声信号辨识方法.火力与指挥控制.2000,25( 3):17-20页
[91] Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series . Physical D:Nonlinear Phenomena,1985,16(3):285-317P
[92] Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets. Physical D: Nonlinear Phenomena, 1993, 65(1-2):117-134P
[93] Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Physics Letters A, 1994, 185(1):77 -87P
[94] Kolmogorov A. N. A new metric invariant of transient dynamical systems and automorphisms of Lebesgue spaces, Dokl .Akad. Sci .SSSR. 1958,119:861-864 P
[95] Grassberger P, Procaccia J. Dimension and entropies of strange at t ractors from a fluctuating dynamics approach. Physica D, 1984, 1 (13) : 189- 208 P
[96] Farmer J D, Sidorowich J J. Predicting chaotic time series. Physical Review Letters,1987,59(8):845-848P
[97]韩敏.混沌时间序列预测理论与方法.北京:中国水利水电出版社.2007:50,162页
[98]吕金虎,张锁春.加权一阶局域法在电力系统短期负荷预测中的应用.控制理论与应用,2002,19(5):767-770页
[99] Giona M, Cimagalli V, Morgavi G, et al. Local prediction of chaotic time series. Proceedings of IEEE workshop on nonlinear signal and image proceeding, 1991, 894-897P
[100] Cai Minglun, Cai Feng, Shi Aiguo, et al. Chaotic time series prediction based on local-region multi-steps forecasting model. Advances in Neural Networks-ISNN, 2004: International Symposium on Neural Networks, Part II, Dalian, China, 2004,8:418-423P
[101] Lapedes A, Robert F. How neural nets work. In Advances in Neural Information Processing Systems,1988,442-456P
[102] Haykin S, Principe J. Making sense of a complex world. IEEE Signal Processing Magazine,1998,15(3):66-68P
[103] Martin C. Nonlinear prediction of chaotic time series. Physica D:Nonlinear Phenomena,1989,35(3):335-356P
[104] Wan E A. Finite Impulse response neural networks with applications intime series prediction. PhD thesis,Stanford University,1993, 56-58P
[105] Vesanto J. Using the SOM and local models in time-series prediction. In Proceedings of WSOM’97,Workshop on Self-Organizing Maps, Espoo, Finland,June 4~6,1997,209-214P
[106] Cowper M R, Mulgrew B, Unsworth C P. Nonlinear prediction of chaotic signals using a normalized radial basis function network. Signal Procedding, 2002, 82(5) : 775-789P
[107] Han M, Xi J,Xu S,Yin F. Prediction of chaotic time series based on the recurrent predictor neural network. IEEE Transactions on Signal Processing, 2004, 52(12): 3409-3416P
[108] Principe J C, Rathie A, Kuo J M. Prediction of chaotic time series with neural networks and the issue of dynamic modeling. Int.J.Bifurcation and Chaos, 1992, 2(4): 989-996P
[109] Mohamed O M M, Jaidane-Saidane M, Ezzine J, Souissi J, Hizaoui N. Variability of Predictability of the Daily Peak Load Using Lyapunov Exponent Approach : Case of Tunisian Power System Power Tech.2007 IEEE Lausanne , 2007, 1078 - 1083 P
[110] Martinerie J M, Albano A M, Mess A I, Rapp P E. Mutual information, strange attractors, and the optimalestimation of dimension.Physical Review A,1992, 45: 7058- 7064 P
[111] Henry D I, Abarbanel. The analysis of observed chaotic data in physical system. Reviews of Modem Physics, 1993,65(4) P
[112] Camastra F, Colla A M. Short Term Load Forecasting based on CorrelationDimension Estimation and Neural Nets, Lecture Notes in Computer Science, 1997, 1035-1040 P
[113]于青.关联维数计算的分析研究.天津理工学院学报.2004, 20(4):60-62页
[114]党建武,黄建国.基于G.P算法的关联维计算中参数取值的研究.计算机应用研究.2004(1):48-51页
[115] Logan D, Mathew J. Using the correlation dimension for vibration fault diagnosis of rolling element Bearings-1. Basic concepts. Mechanical Systems and Signal Processing, 1996, 10(3):241-250P
[116] Harikrishnan K P, Misra R, Ambika G, et al. Anon-subjective approach to the GPalgorithm for analyzing noisy time series. Physical D:Nonlinear Phenomena. 2006, 215(2):137-145P
[117] Sprott J C, Rowlands G. Improved Correlation Dimension Calculation. Int. J. Bif. Chaos, 2001, 11: 1865P
[118]黄润生,黄浩.混沌及其应用.第二版,武汉:武汉大学出版社.2005:373-374页
[119] Martin M T, Pennini F, Plastino A . Fisher’s information and the analysis of complex signals, Phys.Lett.A, 1999, 256:173~180P
[120] Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy form a chaotic signal. Physical review A, 1983, 28(4):2591-2593P
[121] Grassberger P. An optimized box-assisted algorithm for fractal dimension Characterization of strange attractors, Physics Letters A, 1990, 148(1-2): 63-68P
[122]吕金虎,占勇,陆君安.电力系统短期负荷预测的非线性混沌改进模型.中国电机工程学报, 2000, 20(12):80-83页
[123]陆君安,吕金虎,陈士华. Chen’s混沌吸引子及其特征量.控制理论与应用,2002,19(2):308-310页
[124]刘明言,胡宗定.气液两相单孔鼓泡流体动力学行为混沌预测.化工学报,2000,51(4):475-479页
[125] Tim Sauer. Time series prediction by using delay coordinate embedding. In: Coping with chaos: analysis of chaotic data and the exploitation of chaotic systems, A Wiley-Interscience Publication, 1994: 241-260P
[126] Chen S, Cowan C F N, Grant P M. Orthogonal least squares learning algorithm for radial basis function networks. IEEE Transactions on Neural Networks,1991,2(2): 302-309P
[127] Hagan M T, Demuth H B, Beale M H.戴葵等译.神经网络设计.北京:机械工业出版社,2002,82-83页
[128]张玉瑞,陈剑波.基于RBF神经网络的时间序列预测.计算机工程与应用.2005,11:74-76页
[129]许东,吴铮.基于MATLAB 6.X系统分析与设计—神经网络.西安电子科技大学出版社,2002,13-15页
[130]胡迎松,陈明,范志明.一种电力系统短期负荷预测的RBF优化算法.华中科技大学学报.2003,20(3):8-10页
[131]曹安照,田丽.基于RBF神经网络的短期电力负荷预测.电子科技大学学报.2006,35(4):507-509页
[132]王黎明,王艳松.基于RBF神经网络的短期负荷预测.电气技术.2007,4:53-55页
[133]陶维青,石万清.基于径向基函数和模糊逻辑的短期电力负荷预测.合肥工业大学学报.2005,28(6):631-634页
[134]吴宏晓,侯志俭,刘涌等.基于免疫聚类径向基函数网络模型的短期负荷预测.中国电机工程学报.2005,25(16):53-56页
[135]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉大学出版社.2002,106页
[2]赵宏伟,任震,黄雯莹.基于周期自回归模型的短期负荷预测.中国电机工程学报.1997,17(5):347-351页
[3]康重庆,夏清,刘梅等.应用于负荷预测中的回归分析的特殊问题.电力系统自动化.1998,22(10):38-41页
[4] Park D C, E1-Sharkawi M A, Marks II R J. Electric load forecasting using an artificial neural network. IEEE Transactions on Power Systems, 1991, 6(2):442-449P
[5] Chen S T, David C.Y. Weather sensitive short-term load forecasting using nonfully connected artificial neural network. IEEE Transactions on Power Systems, 1992, 7(3):1098-1105P
[6] Hippert H S, Pedreira C E, Souza R C. Neural networks for short-term load forecasting: A review and evaluation. IEEE Transactions on Power Systems, 2001, 16(1):44-45P
[7] Xiao Zhi, Ye Shijie, Zhong Bo, Sun Caixin. BP neural network with rough set for short term load forecasting.Expert Systems with Applications, 2009, 36(1):273-279P
[8] LI Ling-chun,TIAN Li. A combined model of genetic algorithm and BP Neural Network for short-term load forecasting. Journal of AnhuiUniversity of Technology and Science(Natural Science) ,2009, 03-015P
[9] Che-Chiang Hsu, Chia-Yon Chen. Regional load forecasting in Taiwan—applications of artificial neural networks.PARGAMON.2003,1942-1949P
[10] Liu Wei. Exploring of related issues of BP algorithm in load forecasting. IEEE ICICTA 2th, 2009, 1:71-74P
[11]甘文泉,王朝晖,胡保生.结合神经元网络和模糊专家系统进行电力短期负荷预测.西安交通大学学报.1998,32(3):28-32页
[12]招海丹,余德伟.模糊专家系统用于短期负荷预测修正的初步探讨.华东电力.2000,5:24-26页
[13]张涛,赵登福,周琳等.基于RBF神经网络和专家系统的短期负荷预测方法.西安交通大学学报.2001,35(4):331-334页
[14]邰能灵,侯志俭,李涛等.基于小波分析的电力系统短期负荷预测方法.中国电机工程学报.2003,23(1):45-50页
[15]宋超,黄民翔,叶剑斌.小波分析方法在电力系统短期负荷预测中的应用.电力系统及其自动化学报.2002,14(3):8-12页
[16]徐军华,刘天琪.基于小波分解和人工神经网络的短期负荷预测.电网技术.2004,28(8):30-33页
[17]尹成群,康丽峰,李丽等.基于小波变换和混合神经网络的短期负荷预测.电力自动化设备.2007,27(5):40-44页
[18] Amjady N, Keynia F. Short-term load forecasting of power systems by combination of wavelet transform and neuro-evolutionary algorithm. Energy, 2009,34(1):46-57P
[19]严华,吴捷,马志强等.模糊集理论在电力系统短期负荷预测中的应用.电力系统自动化.2000,6:67-71页
[20] Ling S H, Leung F H F, Lam H K, Tam P K S. Short-term electric forecasting based on a neural fuzzy network. IEEE Transactions on Industrial Elecronics, 2003, 50(6):1305-1316P
[21] Yang Kuihe, Zhu Jinjun, Wang Baoshu, Zhao Lingling. Design of short-term load forecasting model based on fuzzy neural networks. WCICA 2004-Fifth World Congress on Intelligent Control and Automation, 2004, 3:2038-2041P
[22] Mori Hiroyuki, Jiang Wenjun. Integration of graphical modeling with fuzzy clustering for casual relationship of electric load forecasting. Proceedings of the Ninth International Conference on Intelligent Systems Design and Applications, 2009,1377-1382P
[23] Rusturm M, Omar B, Emad A. A fuzzy inference model for short-term load forecasting.Energy Policy, 2009, 37(4):1239-1248P
[24]李鹰,赵振江,吴松涛.灰色模型在普通日短期电力负荷预测中的应用.长沙电力学院学报(自然科学版) .2003,18(l):15-17页
[25]张俊芳,吴伊昂,吴军基.基于灰色理论负荷预测的应用研究.电力自动化设备.2004,24(5):24-27页
[26]邢棉,于兰香,刘晓霞.基于神经网络校正的电力负荷灰色预测.华北电力大学学报.2006,33(4):93-95页
[27]蒋传文,权先障,李承军等.混沌理论在电力负荷预测中的应用.武汉交通科技大学学报.1999,23 (6):608-611页
[28]温权,张勇传,程时杰.负荷预报的混沌时间序列分析方法.电网技术.2001,25(10):13-16页
[29]姜勇.电力系统短期负荷的特征指数相空间重构预测法.继电器.2003,31(3):11-14页
[30]吉国力,程军,米红.应用混沌相空间模线性回归模型研究短期负荷预报.系统工程理论与实践.2001,6:138-140,144页
[31]吕金虎,张锁春.加权一阶局域法在电力系统短期负荷预测中的应用.控制理论与应用.2002,19(5):767-770页
[32] Cai Minglun, Cai Feng, Shi Aiguo, et al. Chaotic time series prediction based on local-region multi-steps forecasting model. Advances in Neural Networks-ISNN2004: International Symposium on Neural Networks, PartII, Dalian, China, 2004, 8: 418 - 423P
[33]郑永康,陈维荣,蒋刚等.基于混沌理论的短期负荷局域多步预测法.电力系统及其自动化学报.2007,19(4):76-79页
[34]杨正瓴,林孔元,余贻鑫.短期负荷预报的“双周期加混沌”法中的子模型优选理论探讨.电网技术.2003,27(5):33-36页
[35]杨正瓴,田勇,林孔元.短期负荷预测“双周期加混沌”法中多步法与气象因子的使用.电网技术.2004,28(12):20-24页
[36] Jiang Chuanwen, Li Tao. Forecasting method study on chaotic load series with high embedded dimension. Energy Conversion and Management, 2005, 46(5): 667-676P
[37]杜杰,陆金桂,曹一家.短期负荷预测最大Lyapunov指数预报模式预测值的判定.电网技术.2006,30(20):20-24页
[38]杨正瓴,田勇,张广涛等.短期负荷预测最大李亚普诺夫指数法的改进.电网技术.2005,29(7):31-35页
[39]方仍存,周建中,彭兵等.电力负荷混沌动力特性及其短期预测.电网技术.2008,32(4):61-66页
[40]李兰友,杜杰,邵定宏等.最大Lyapunov指数短期电力负荷预测模型仿真.计算机工程与设计.2007,28(24):5935-5937页
[41] Chen Bojuen, Chang Mingmei. Load forecasting using support vector machines: a study on EUNITE competition 2001. IEEE Transactions on Power Systems, 2004, 19(4):1821-1830P
[42] Niu Dongxiao, Wang Yongli. Power load forecasting using support vector machine and ant colony optimization. Expert Systems with Applications, 2010, 37(3): 2531-2539P
[43]姜惠兰,刘晓津,关颖等.基于硬C均值聚类算法和支持向量机的电力系统短期负荷预测.电网技术.2006,30(8):81-85页
[44] Jordaan J A, Ukil A. Load forecasting with support vector machines and semi-parametric method. The 8th Inteligent Date Engineering and Automated Learning, Birmingham,UK,2007,4881:258-267P
[45]李元诚,方廷健,于尔铿.短期负荷预测的支持向量机方法研究.中国电机工程学报.2003,23(6):55-59页
[46]谢宏,魏江平,刘鹤立.短期负荷预测中支持向量机模型的参数选取和优化方法.中国电机工程学报.2006,26(22):17-22页
[47] Wang Jingmin, Zhou Yamin, Chen Xiaoyu. Electricity load forecasting based on support vector machines and simulated annealing particle swarm optimization algorithm. Proceedings of the IEEE International Conferenceon Automation and Logistics,Jinan,China, 2007:2836-2841P
[48]安德洪,韩文秀,岳毅宏.组合预测法的改进及其在负荷预测中的应用.系统工程与电子技术.2004,26(6):842-844页
[49]孙海斌,周淑雄,谢敬东等.模糊综合评价在负荷最优组合预测中的应用.电力系统及其自动化学报.2001,13(4):8-11页
[50]谢开贵,李春燕,俞集辉.基于遗传算法的短期负荷组合预测模型.电网技术.2001,25(8):20-23页
[51]赵海青,牛东晓.负荷预测的交叉式自适应优选组合预测模型.华北电力大学学报.2000,27(4):13-17页
[52] Niu Dongxiao, Wang Yongli, Duan Chunming. A New Short-term Power Load Forecasting Model Based on Chaotic Time Series and SVM. Journal of Universal Computer Science, 2009, 15(13):2726-2745P
[53] Wu Qi. A hybrid-forecasting model based on Gaussian support vector machine and chaotic particle swarm optimization. Expert Systems with Applications, 2010, 37(3):2388-2394P
[54] Hong Weichiang. Hybrid evolutionary algorithms in a SVR-based electric load forecasting model. International Journal of Electrical Power & Energy Systems, 2009, 31(7-8):409-417P
[55] Packard N H, Crutchfield J P, Farmer J D, Shaw R S. Geometry from a Time Series. Physical Review Letters, 1980,45(9):712-716P
[56] Takens F. Determing strange attractors in turbulence. Lecture notes in Math, 1981,898: 361-381P
[57] Mori H,Drano S. Chaotic Time Series Analysis for Short-term PowerSystem Load Forecasting. Proc of the 3rd Int '1 Conf on Fuzzy Logic Neural Nets and Soft Computing(IIZUKA' 94).lizuka;(Japan).1994. 441-442P
[58]蒋传文,侯志俭,李承军.求取混沌时间序列嵌入维数的一种神经元网络方法.水电能源科学.2000,18(4):12-14,43页
[59]杨正瓴,林孔元.短期负荷预测相空间重构法参数优选的数值测试与分析.电力系统自动化.2003,27(16):40-44页
[60]谷子,唐巍.电力短期负荷时间序列混沌相空间重构参数优选法.中国电机工程学报. 2006,26(14):18-23页
[61]杨正瓴,曹东波,张广涛等.用奇异性的短期负荷预测混沌方法优化参数.天津大学学报.2006,39(3):334-337页
[62] Mori H, Urano S. Short-term load forecasting with chaos time series analysis. Proceedings of International Conference on Intelligent Systems Applications to Power Systems, France, 1996: 133-137P
[63]丁军威,孙雅明.基于混沌学习算法的神经网络短期负荷预测.电力系统自动化.2000,24(2):32-35页
[64]李天云,刘自发.电力系统负荷的混沌特性及预测.中国电机工程学报.2000,20(11):36-40页
[65] Chen Luonan. Application of Chaotic Simulation and Self-organizing Neural Net to Power System Voltage Stability Monitoring. IEEE, 1993: 367-372P
[66] Liu Shuliang, Hu Zhiqiang,Chi Xiukai. Power load forecasting based on neural network and time series. Proceedings of the 5th International Conference on Wireless communications, networking and mobilecomputing, Beijing, China, 2009: 5047 - 5051P
[67]尤勇,盛万兴,王孙安.基于人工免疫网络的短期负荷预测模型.中国电机工程学报.2003,23(3):26-29,98页
[68] Park Jae-gyun, Park Jong-keun,Kim Kwang-ho, et al. A Daily Peak Load Forecasting System Using a Chaotic Time Series. IEEE,1996:283-287P
[69] Camastra F, Colla M. Neural Short-term Prediction Based on Dynamics Reconstruction. Neural Processing Lerrers, 1999, 9(1):45-52P
[70]蒋传文,侯志俭,李承军.基于混沌理论的电力负荷短期预报的神经网络方法.水电能源科学.2001,19(3):59-61页
[71] Michano S P, Tsakoumis A C,Fessas P, et al. Short-term Load Forecasting Using a Chaotic Time Series. IEEE International Symposium on Signals, Circuits and Systems. Proceedings,2003,2:437-440P
[72]张智晟,孙雅明,王兆峰等.优化相空间近邻点与递归神经网络融合的短期负荷预测.中国电机工程学报.2003 , 23 (8):44-49页
[73] Iokibe T, Mochizuki N. Short-term Prediction Based on Fuzzy logic and Chaos. Proc of FAN Symp. Tsuku-ba:(Japan) 1994.77-82P
[74] Iokibe T, Kanke M,Fujimoto Y,et al. Short-term Prediction on Chaotic Time Series by Local Fuzzy Reconstruction Method. Proc of the 3rd lntemat Conf on Fuzzy Logic, Neural Nets and Soft Computing. Lizuka (Japan):1994.491-492P
[75] Iokibe T, Fujimoto Y,Kanke M. Short-term prediction of chaotic time series by local fuzzy reconstruction meth. J Intell Fuzzy Systems, 1997, 5: 3-21P
[76] Wu Haishan,Chang Xiaoling. Power Load Forecasting with Least Squares Support Vector Machines and Chaos Theory. Proceedings of the 6th World Congress on Control, and Automation, 2006, 1:4369-4373P
[77] Wang J, Ren G. Load forecasting based on chaotic support vector machine with incorporated intelligence algorithm. Proceeding of the first International Conference on Innovative Computing, Information and Control IEEE, 2006:378-381P
[78] Sauer T, Yorke J A, and Casdagli M. Embedology. Journal of Statistical Physics, 1991, 64:579-616P
[79] Takens F. Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence. Berlin:Springer-Verlag,New York,1981,898:366-381P
[80] Williams G P. Chaos theory tamed. Washington, DC: Joseph Henry, 1997,516 P
[81] Rosenstein M T, Collins J J, Deluca C J. Reconstruction expansion as a geometry-based framework for choosing proper delay times. Physical D: Nonlinear Phenomena,1994,73(1-2):82-98P
[82] Fraser A M, Swinney H L. Independent coordinates for strange attractors from mutual information. Physical Review A,1986,33(2):1134-1140P
[83] Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physical D:Nonlinear Phenomena,1983,9(1-2):189-208P
[84] Kennel M B, Brown R, Abarbanel H D. Determining embedding dimension for phase space reconstruction using a geometrical construction. Physical Review A,1992,45(6):3403-3411P
[85] Cao Liangyue. Practical method for determining the minimum embedding dimension of a scalar time series. Physical D:Nonlinear Phenomena, 1997, 110(1-2):43-50P
[86]马红光,李夕海,王国华等.相空间重构中嵌入维和时间延迟的选择.西安交通大学学报.2004,38(4): 335-338页
[87] Kuqiumtzis D. State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length. Physical D, 1996, 95(1):13-28P
[88] Kim H S, Eykholt R, Salas J D. Nonlinear dynamics, delay times, and embedding windows. Physical D,1999,127(1):48-60P
[89]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择.系统仿真学报.2007,19(11): 2527-2530,2538页
[90]杨绍清,章新华,赵长安等.基于混沌理论的水声信号辨识方法.火力与指挥控制.2000,25( 3):17-20页
[91] Wolf A, Swift J B, Swinney H L, et al. Determining Lyapunov exponents from a time series . Physical D:Nonlinear Phenomena,1985,16(3):285-317P
[92] Rosenstein M T, Collins J J, De Luca C J. A practical method for calculating largest Lyapunov exponents from small data sets. Physical D: Nonlinear Phenomena, 1993, 65(1-2):117-134P
[93] Kantz H. A robust method to estimate the maximal Lyapunov exponent of a time series. Physics Letters A, 1994, 185(1):77 -87P
[94] Kolmogorov A. N. A new metric invariant of transient dynamical systems and automorphisms of Lebesgue spaces, Dokl .Akad. Sci .SSSR. 1958,119:861-864 P
[95] Grassberger P, Procaccia J. Dimension and entropies of strange at t ractors from a fluctuating dynamics approach. Physica D, 1984, 1 (13) : 189- 208 P
[96] Farmer J D, Sidorowich J J. Predicting chaotic time series. Physical Review Letters,1987,59(8):845-848P
[97]韩敏.混沌时间序列预测理论与方法.北京:中国水利水电出版社.2007:50,162页
[98]吕金虎,张锁春.加权一阶局域法在电力系统短期负荷预测中的应用.控制理论与应用,2002,19(5):767-770页
[99] Giona M, Cimagalli V, Morgavi G, et al. Local prediction of chaotic time series. Proceedings of IEEE workshop on nonlinear signal and image proceeding, 1991, 894-897P
[100] Cai Minglun, Cai Feng, Shi Aiguo, et al. Chaotic time series prediction based on local-region multi-steps forecasting model. Advances in Neural Networks-ISNN, 2004: International Symposium on Neural Networks, Part II, Dalian, China, 2004,8:418-423P
[101] Lapedes A, Robert F. How neural nets work. In Advances in Neural Information Processing Systems,1988,442-456P
[102] Haykin S, Principe J. Making sense of a complex world. IEEE Signal Processing Magazine,1998,15(3):66-68P
[103] Martin C. Nonlinear prediction of chaotic time series. Physica D:Nonlinear Phenomena,1989,35(3):335-356P
[104] Wan E A. Finite Impulse response neural networks with applications intime series prediction. PhD thesis,Stanford University,1993, 56-58P
[105] Vesanto J. Using the SOM and local models in time-series prediction. In Proceedings of WSOM’97,Workshop on Self-Organizing Maps, Espoo, Finland,June 4~6,1997,209-214P
[106] Cowper M R, Mulgrew B, Unsworth C P. Nonlinear prediction of chaotic signals using a normalized radial basis function network. Signal Procedding, 2002, 82(5) : 775-789P
[107] Han M, Xi J,Xu S,Yin F. Prediction of chaotic time series based on the recurrent predictor neural network. IEEE Transactions on Signal Processing, 2004, 52(12): 3409-3416P
[108] Principe J C, Rathie A, Kuo J M. Prediction of chaotic time series with neural networks and the issue of dynamic modeling. Int.J.Bifurcation and Chaos, 1992, 2(4): 989-996P
[109] Mohamed O M M, Jaidane-Saidane M, Ezzine J, Souissi J, Hizaoui N. Variability of Predictability of the Daily Peak Load Using Lyapunov Exponent Approach : Case of Tunisian Power System Power Tech.2007 IEEE Lausanne , 2007, 1078 - 1083 P
[110] Martinerie J M, Albano A M, Mess A I, Rapp P E. Mutual information, strange attractors, and the optimalestimation of dimension.Physical Review A,1992, 45: 7058- 7064 P
[111] Henry D I, Abarbanel. The analysis of observed chaotic data in physical system. Reviews of Modem Physics, 1993,65(4) P
[112] Camastra F, Colla A M. Short Term Load Forecasting based on CorrelationDimension Estimation and Neural Nets, Lecture Notes in Computer Science, 1997, 1035-1040 P
[113]于青.关联维数计算的分析研究.天津理工学院学报.2004, 20(4):60-62页
[114]党建武,黄建国.基于G.P算法的关联维计算中参数取值的研究.计算机应用研究.2004(1):48-51页
[115] Logan D, Mathew J. Using the correlation dimension for vibration fault diagnosis of rolling element Bearings-1. Basic concepts. Mechanical Systems and Signal Processing, 1996, 10(3):241-250P
[116] Harikrishnan K P, Misra R, Ambika G, et al. Anon-subjective approach to the GPalgorithm for analyzing noisy time series. Physical D:Nonlinear Phenomena. 2006, 215(2):137-145P
[117] Sprott J C, Rowlands G. Improved Correlation Dimension Calculation. Int. J. Bif. Chaos, 2001, 11: 1865P
[118]黄润生,黄浩.混沌及其应用.第二版,武汉:武汉大学出版社.2005:373-374页
[119] Martin M T, Pennini F, Plastino A . Fisher’s information and the analysis of complex signals, Phys.Lett.A, 1999, 256:173~180P
[120] Grassberger P, Procaccia I. Estimation of the Kolmogorov entropy form a chaotic signal. Physical review A, 1983, 28(4):2591-2593P
[121] Grassberger P. An optimized box-assisted algorithm for fractal dimension Characterization of strange attractors, Physics Letters A, 1990, 148(1-2): 63-68P
[122]吕金虎,占勇,陆君安.电力系统短期负荷预测的非线性混沌改进模型.中国电机工程学报, 2000, 20(12):80-83页
[123]陆君安,吕金虎,陈士华. Chen’s混沌吸引子及其特征量.控制理论与应用,2002,19(2):308-310页
[124]刘明言,胡宗定.气液两相单孔鼓泡流体动力学行为混沌预测.化工学报,2000,51(4):475-479页
[125] Tim Sauer. Time series prediction by using delay coordinate embedding. In: Coping with chaos: analysis of chaotic data and the exploitation of chaotic systems, A Wiley-Interscience Publication, 1994: 241-260P
[126] Chen S, Cowan C F N, Grant P M. Orthogonal least squares learning algorithm for radial basis function networks. IEEE Transactions on Neural Networks,1991,2(2): 302-309P
[127] Hagan M T, Demuth H B, Beale M H.戴葵等译.神经网络设计.北京:机械工业出版社,2002,82-83页
[128]张玉瑞,陈剑波.基于RBF神经网络的时间序列预测.计算机工程与应用.2005,11:74-76页
[129]许东,吴铮.基于MATLAB 6.X系统分析与设计—神经网络.西安电子科技大学出版社,2002,13-15页
[130]胡迎松,陈明,范志明.一种电力系统短期负荷预测的RBF优化算法.华中科技大学学报.2003,20(3):8-10页
[131]曹安照,田丽.基于RBF神经网络的短期电力负荷预测.电子科技大学学报.2006,35(4):507-509页
[132]王黎明,王艳松.基于RBF神经网络的短期负荷预测.电气技术.2007,4:53-55页
[133]陶维青,石万清.基于径向基函数和模糊逻辑的短期电力负荷预测.合肥工业大学学报.2005,28(6):631-634页
[134]吴宏晓,侯志俭,刘涌等.基于免疫聚类径向基函数网络模型的短期负荷预测.中国电机工程学报.2005,25(16):53-56页
[135]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉大学出版社.2002,106页