风速时间序列混沌判定方法比较研究
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摘要
混沌识别是对非线性时间序列进行混沌预测的前提。针对时间序列风速确定性与随机性相结合的复杂非线性特征,研究了不同的混沌识别方法,并对风速时间序列进行混沌特征识别。应用随机噪声、周期运动及经典混沌系统的时间序列对所选方法进行可靠性验证。对美国国家风能研究中心M2测风塔实测时间序列风速数据进行非线性混沌特征识别。结果表明:风速时间序列具有明显的混沌特征;各风速时间序列表现出不同程度的混沌特征;各混沌识别方法对风速时间序列混沌特征的表达形式不同,互为补充,相互验证。
Chaotic identification is a prerequisite for chaos prediction of nonlinear time series. Aiming at the complex nonlinear characteristics of time series wind speed which is deterministic and stochastic,different chaos identification methods are studied,and chaotic characteristics of wind speed time series are identified. First,the reliabilities of the proposed methods are verified by using the time series of random noise,periodic motion and classical chaotic system. Secondly,the nonlinear chaotic characteristics of the wind speed data from NWTC M2 tower are studied. The results show that the wind speed time series have clear chaotic characteristics. Different wind speed time series show different degrees of chaotic characteristics. Different chaos recognition methods are different from each other and complement each other to verify the chaotic characteristics of wind speed time series.
Chaotic identification is a prerequisite for chaos prediction of nonlinear time series. Aiming at the complex nonlinear characteristics of time series wind speed which is deterministic and stochastic,different chaos identification methods are studied,and chaotic characteristics of wind speed time series are identified. First,the reliabilities of the proposed methods are verified by using the time series of random noise,periodic motion and classical chaotic system. Secondly,the nonlinear chaotic characteristics of the wind speed data from NWTC M2 tower are studied. The results show that the wind speed time series have clear chaotic characteristics. Different wind speed time series show different degrees of chaotic characteristics. Different chaos recognition methods are different from each other and complement each other to verify the chaotic characteristics of wind speed time series.
引文
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[11]李玲玲,李俊豪,王成山,等.基于混沌支持向量机的短期风速预测[J].电器与能效管理技术,2012,36(16):48-52.LI Ling-ling,LI Jun-hao,WANG Cheng-shan,et al.Wind speed forecasting based on chaotic theory and support vector machine[J].Electrical&Energy Management Technology,2012,36(16):48-52.
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[13]袁东锋,杜恒.基于小波分析和相空重构相融合的风速预测[J].计算机仿真,2013,30(3):331-334.YUAN Dong-feng,DU Heng.Wind speed forecasting model based on wavelet analysis and support vector machine[J].Computer Simulation,2013,30(3):331-334.
[14]张博.混沌支持向量机风速短期预测及其在Pc Duino平台实现[D].太原:中北大学,2014.ZHANG Bo.Study on short-term wind forecasting with chaoticsupport vector machine in Pc Duino platform[D].Taiyuan:North University of China,2014.
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[16]YAJUN H,JING L.The online forecasting research of short-term wind speed and power generation at wind farm based on phase space reconstruction[J].International Conference on Measuring Technology&Mechatronics Automation.IEEE,2015,6(12):1234-1237.
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[18]吕金虎.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002.LV Jin-hu.Chaotic time series analysis and its application[M].Wuhan:Wuhan University Press,2002.
[19]BERROU C,GLAVIEUX A,THITIMAISHIMA P.Near Shannon limit error-correcting coding and decoding:turbo-codes(1)[C].Communications,1993:1064-1070.
[20]付彧.股票市场混沌特征量的提取及其分析[J].中外企业家,2015,46(4):99-101.FU Yu.Extraction and analysis of the chaotic characteristics of the stock market[J].Chinese&Foreign Entrepreneurs,2015,46(4):99-101.
[21]GRASSBERGER P,PROCACCIA I.Estimation of the Kolmogorov entropy from a chaotic signal[J].Physical Review A,1983,28(4):2591-2593.
[22]董春娇,邵春福,张辉,等.基于G-P算法的快速路交通流参数相空间重构[J].吉林大学学报:工学版,2012,42(3):594-599.DONG Chun-jiao,SHAO Chun-fu,ZHANG Hui,et al.Phase space reconstruction of traffic flow parameters on expressway based on G-P algorithm[J].Journal of Jilin University(Engineering and Technology Edition),2012,42(3):594-599.
[23]王秀杰,练继建,费守明,等.基于小波消噪的混沌多元回归日径流预测模型[J].系统仿真学报,2007,19(15):3605-3608.WANG Xiu-jie,LIAN Ji-jian,FEI Shou-ming,et al.Chaotic multicariate autoregressive model of daily runoff prediction based on wavelet de-noising[J].Journal of System Simulation,2007,19(15):3605-3608.
[24]郭伯和.油水两相流流型的混沌时间序列分析[D].天津:天津大学,2005.GUO Bo-he.Chaotic time series analysis of oil/water two phase flow patterns[D].Tianjin:Tianjin University,2005.
[25]李新杰.河川径流时间序列的非线性特征识别与分析[D].武汉:武汉大学,2013.LI Xin-jie.Nonlinear characteristics identification and analysis for river runoff time series[D].Wuhan:Wuhan University,2013.
[26]Bla6 KRESE,Edvard GOVEKAR.Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos[J].Nonlinear Dynamics,2012,67(3):2101-2109.
[27]GOTTWALD G A,MELBOURNE I.On the implementation of the0~1 test for chaos[J].Siam Journal on Applied Dynamical Systems,2009,8(1):129-145.
[28]PYNDIAH,R.M.Near-optimum decoding of product codes:block turbo codes[J].Communications IEEE Transactions on,1998,46(8):1003-1010.
[29]KIM H S,EYKHOLT R,SALAS J D.Nonlinear dynamics,delay times,and embedding windows[J].Physica D Nonlinear Phenomena,1999,127(1-2):48-60.
[30]王海燕.非线性时间序列分析及其应用[M].北京:科学出版社,2006.WANG Hai-yan.Nonlinear time series analysis and its application[M].Beijing:Science Press,2006.
[31]陶慧,李莹,马小平.含噪声多变量混沌时间序列的最大Lyapunov指数计算[J].河南理工大学学报(自然科学版),2014,33(6):770-775.TAO Hui,LI Ying,MA Xiao-ping.Calculation for the largest Lyaponuv exponent of multivariate chaotic time-series with noise[J].Journal of Henan Polytechnic University(Natural Science),2014,33(6):770-775.
[32]WOLF A,SWIFT J B,SWINNEY H L,et al.Determining Lyapunov exponents from a time series[J].Physica D Nonlinear Phenomena,1985,16(3):285-317.
[33]陈志刚,梁涤青,邓小鸿,等.Logistic混沌映射性能分析与改进[J].电子与信息学报,2016,38(6):1547-1551.CHEN Zhi-gang,LIANG Di-qing,DENG Xiao-hong,et al.Performance analysis and improvement of Logistic chaotic mapping[J].Journal of Electronics&Information Technology,2016,38(6):1547-1551.
[34]左飞.数字图像处理—技术详解与Visual C++实践[M].北京:电子工业出版社,2014.ZUO Fei.Digital image processing—Technical explanation and Visual C++practice[M].Beijing:Publishing House of Electronics Industry,2014.
[35]National wind technology center M2 tower[EB/OL].[2015-09-20].http://www.nrel.gov/midc/nwtc_m2/
[2]LI G,SHI J,ZHOU J.Bayesian adaptive combination of short-term wind speed forecasts from neural network models[J].Renewable Energy,2011,36(1):352-359.
[3]李艳晴.风速时间序列预测算法研究[D].北京:北京科技大学,2016.LI Yan-qing.Study on the prediction of the wind speed series[D].Beijing:University of Science and Technology Beijing,2016.
[4]MILLIGAN M,SCHWARTZ M N,WAN Y.Statistical wind power forecasting for U.S.wind farms:preprint[C].Conference on Probability&Statistics in the Atmospheric Sciences/American Meteorological Society Meeting,2003:1-8.
[5]徐蓓蓓.风电场风速和发电功率预测研究[D].长沙:长沙理工大学,2012.XU Bei-bei.The research on wind speed and wind power forecasting of wind farm[D].Changsha:Changsha University of Science and Technology,2012.
[6]姜言,黄国庆,彭新艳,等.基于GARCH的短时风速预测方法[J].西南交通大学学报,2016,51(4):663-669.JIANG Yan,HUANG Guo-qing,PENG Xin-yan,et al.Method of short-term wind speed forecasting based on generalized autoregressive conditional heteroscedasticity model[J].Journal of Southwest Jiaotong University,2016,51(4):663-669.
[7]罗海洋,刘天琪,李兴源.风电场短期风速的混沌预测方法[J].电网技术,2009,33(9):67-71.LUO Hai-yang,LIU Tian-qi,LI Xing-yuan.Chaotic forecasting method of short-term wind speed in wind farm[J].Power System Technology,2009,33(9):67-71.
[8]华琦,王雷,陆金桂,等.基于混沌理论与神经网络的短期风速滚动预测[J].电测与仪表,2013,50(7):16-20.HUA Qi,WANG Lei,LU Jin-gui,et al.Short-term wind speed rolling forecast based on chaos theory and neural network[J].Electrical Measurement&Instrumentation,2013,50(7):16-20.
[9]Luo H Y,Liu T Q,Li X Y.Chaotic forecasting method of shortterm wind speed in wind farm[J].Power System Technology,2009,33(9):67-71.
[10]丁涛,肖宏飞.基于最优邻域的动态加权混沌风速预测模型[J].太阳能学报,2011,32(4):560-564.DING Tao,XIAO Hong-fei.Wind speed chaotic prediction model based on optimal neighborhood[J].Acta Energiae Solaris Sinica,2011,32(4):560-564.
[11]李玲玲,李俊豪,王成山,等.基于混沌支持向量机的短期风速预测[J].电器与能效管理技术,2012,36(16):48-52.LI Ling-ling,LI Jun-hao,WANG Cheng-shan,et al.Wind speed forecasting based on chaotic theory and support vector machine[J].Electrical&Energy Management Technology,2012,36(16):48-52.
[12]Zhu C H,Li L L,Li J H,et al.Short-term wind speed forecasting by using chaotic theory and SVM[J].Applied Mechanics&Materials,2013,300(12):842-847
[13]袁东锋,杜恒.基于小波分析和相空重构相融合的风速预测[J].计算机仿真,2013,30(3):331-334.YUAN Dong-feng,DU Heng.Wind speed forecasting model based on wavelet analysis and support vector machine[J].Computer Simulation,2013,30(3):331-334.
[14]张博.混沌支持向量机风速短期预测及其在Pc Duino平台实现[D].太原:中北大学,2014.ZHANG Bo.Study on short-term wind forecasting with chaoticsupport vector machine in Pc Duino platform[D].Taiyuan:North University of China,2014.
[15]GUO Z,CHI D,WU J,et al.A new wind speed forecasting strategy based on the chaotic time series modelling technique and the Apriori algorithm[J].Energy Conversion&Management,2014,84(6):140–151.
[16]YAJUN H,JING L.The online forecasting research of short-term wind speed and power generation at wind farm based on phase space reconstruction[J].International Conference on Measuring Technology&Mechatronics Automation.IEEE,2015,6(12):1234-1237.
[17]TAKENS F.Detecting strange attractors in turbulence[C].Dynamical systems and turbulence,Lecture Notes in Mathematics.New York:spriger-verlay,1981:366-381.
[18]吕金虎.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2002.LV Jin-hu.Chaotic time series analysis and its application[M].Wuhan:Wuhan University Press,2002.
[19]BERROU C,GLAVIEUX A,THITIMAISHIMA P.Near Shannon limit error-correcting coding and decoding:turbo-codes(1)[C].Communications,1993:1064-1070.
[20]付彧.股票市场混沌特征量的提取及其分析[J].中外企业家,2015,46(4):99-101.FU Yu.Extraction and analysis of the chaotic characteristics of the stock market[J].Chinese&Foreign Entrepreneurs,2015,46(4):99-101.
[21]GRASSBERGER P,PROCACCIA I.Estimation of the Kolmogorov entropy from a chaotic signal[J].Physical Review A,1983,28(4):2591-2593.
[22]董春娇,邵春福,张辉,等.基于G-P算法的快速路交通流参数相空间重构[J].吉林大学学报:工学版,2012,42(3):594-599.DONG Chun-jiao,SHAO Chun-fu,ZHANG Hui,et al.Phase space reconstruction of traffic flow parameters on expressway based on G-P algorithm[J].Journal of Jilin University(Engineering and Technology Edition),2012,42(3):594-599.
[23]王秀杰,练继建,费守明,等.基于小波消噪的混沌多元回归日径流预测模型[J].系统仿真学报,2007,19(15):3605-3608.WANG Xiu-jie,LIAN Ji-jian,FEI Shou-ming,et al.Chaotic multicariate autoregressive model of daily runoff prediction based on wavelet de-noising[J].Journal of System Simulation,2007,19(15):3605-3608.
[24]郭伯和.油水两相流流型的混沌时间序列分析[D].天津:天津大学,2005.GUO Bo-he.Chaotic time series analysis of oil/water two phase flow patterns[D].Tianjin:Tianjin University,2005.
[25]李新杰.河川径流时间序列的非线性特征识别与分析[D].武汉:武汉大学,2013.LI Xin-jie.Nonlinear characteristics identification and analysis for river runoff time series[D].Wuhan:Wuhan University,2013.
[26]Bla6 KRESE,Edvard GOVEKAR.Nonlinear analysis of laser droplet generation by means of 0–1 test for chaos[J].Nonlinear Dynamics,2012,67(3):2101-2109.
[27]GOTTWALD G A,MELBOURNE I.On the implementation of the0~1 test for chaos[J].Siam Journal on Applied Dynamical Systems,2009,8(1):129-145.
[28]PYNDIAH,R.M.Near-optimum decoding of product codes:block turbo codes[J].Communications IEEE Transactions on,1998,46(8):1003-1010.
[29]KIM H S,EYKHOLT R,SALAS J D.Nonlinear dynamics,delay times,and embedding windows[J].Physica D Nonlinear Phenomena,1999,127(1-2):48-60.
[30]王海燕.非线性时间序列分析及其应用[M].北京:科学出版社,2006.WANG Hai-yan.Nonlinear time series analysis and its application[M].Beijing:Science Press,2006.
[31]陶慧,李莹,马小平.含噪声多变量混沌时间序列的最大Lyapunov指数计算[J].河南理工大学学报(自然科学版),2014,33(6):770-775.TAO Hui,LI Ying,MA Xiao-ping.Calculation for the largest Lyaponuv exponent of multivariate chaotic time-series with noise[J].Journal of Henan Polytechnic University(Natural Science),2014,33(6):770-775.
[32]WOLF A,SWIFT J B,SWINNEY H L,et al.Determining Lyapunov exponents from a time series[J].Physica D Nonlinear Phenomena,1985,16(3):285-317.
[33]陈志刚,梁涤青,邓小鸿,等.Logistic混沌映射性能分析与改进[J].电子与信息学报,2016,38(6):1547-1551.CHEN Zhi-gang,LIANG Di-qing,DENG Xiao-hong,et al.Performance analysis and improvement of Logistic chaotic mapping[J].Journal of Electronics&Information Technology,2016,38(6):1547-1551.
[34]左飞.数字图像处理—技术详解与Visual C++实践[M].北京:电子工业出版社,2014.ZUO Fei.Digital image processing—Technical explanation and Visual C++practice[M].Beijing:Publishing House of Electronics Industry,2014.
[35]National wind technology center M2 tower[EB/OL].[2015-09-20].http://www.nrel.gov/midc/nwtc_m2/