复杂性理论在河川径流时间序列分析中的应用研究
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摘要
河川径流过程的描述和预测历来是水文水资源系统十分重要的课题之一,它是水
资源规划、配置与调控的基本依据。本文结合国家自然科学基金和国家重大基础规
划项目,以黄河干流径流序列为例,采用复杂性理论及方法,对河川径流变化的复
杂性、长程相关性、可预测能力和预测方法进行了研究,主要取得了以下具有特色
和创新性研究成果:
(1) 基于径流是多因素耦合作用的一种涌现的思想,提出了径流时间序列的“解
耦、提纯、耦合”分析及预测建模方法,初步构建了径流序列分析的复杂性理论框
架,丰富了水文水资源系统理论,为研究径流演变规律提供了一种新的技术。
(2) 针对关联维数、李亚普诺夫指数、K熵等算法对时间序列长度的依赖性等问题,
引入了具有计算方便、适应于有限数据的复杂性测度分析方法,对河川径流的复杂性
进行了分析;并采用空心比率准则对复杂性测度算法进行了改进,较好地避免了“过
分粗粒化”的问题。分析结果表明,径流量多与少的变化过程反映的是径流的有序与
无序的演变过程;近似熵测度高低值后的低高值异常变化特征反映了径流峰谷值前径
流变化的动力学特征,为深入认识径流时间序列的动力学特征提供了一种新的分析方
法,同时为径流峰谷预测提供了一种新的定性手段。
(3) 针对径流时间序列的趋势和非平稳特征,引入了非趋势波动分析方法对黄河
干流径流时间序列长程相关性进行了实证分析:首次应用递归图方法诊断黄河干流天
西安理工大学博士学位论文
然和实测径流”打司序列的可预测能力。结果表明,黄河干流大然和实测径流时间序列
中均存在肴一定程度的长程相关性(持久性),井可以进行短期预测,为径流时间序
列的长程相关性和预测能力诊断切f究提供了新的方法。
(封乍!对径流的多囚素祸合特征,提出了参与径流演变的最小囚素(变量)集的
概念,引入相空间重构技术和独立分量分析方法,实现了径流时间序列的“解祸和
提纯”,井一拓展了相空间重构技术的应用范围。结果表明,影响黄河干流上中卜游径
流变化的因素至少有3个:各站大然径流的影响因素中,有一个因素的变化具有明
显的规律性,另两个囚素的变化较为复杂,而实测径流的影响因素的变化均较为址
杂,为径流时间序列影响因素分析研究提供了新的思路。
(5)考虑到径流序列的长度和峰值突变性的特点,本文采用小样本机器学习理论
中的最小止乘支持向量机进行预测建模。并针对支持向量机算法存在的参数优化、训
约、和测试速度等问题,建立了一种基r混沌优化的峰值识别最小_一乘支持向童机径流
顶测模型;提出J’运用相空间重构技术和独立分量分析对样本进行分离的混沌优化峰
值识别最小_一乘支持向量机算法,为提高模型的学习能力和顶测能力提供了技术保
障。仿真结果表明,该模型不仅学习能力较强、预测精度较高,而_1」.训练和测试速度
陕,为径流时间序夕lJ的预测提供了一种新的l一具。
关键词:复杂性理论:复杂性测度;人类活动;非趋势波动分析:独立分晕_分析:
支持向量机:混沌优化;径流预测
本论文得到了国家自然科学基金项目(批准号50479024)和国家重
大基础规划项目(G199904360801)的资助。
One of the most important tasks of water resources and hydrology is description and forecasting of river runoff course that is basis of water resources planning, disposition, regulation and control. Supported by the National Natural Science Foundation of China and the Major State Basic Research Development Program of China, make runoff series of the Yellow River main stream as an example, applied complexity theory and its methods to study complexity, long relativity, forecasting ability and forecasting methods of river runoff variety. Main characteristic and innovation results as follows:1. Based on the thought that runoff is a swarm many factors coupling, analysis and forecasting modeling method of runoff time series-'decoupling, purification, coupling' are put forward, complexity theory frame of runoff series analysis is built up, which enrich water resources and hydrology system theory and provide a new technology for runoff evolvement law.2. Aimed at problems of relationship dimension, Lyapunov index, K entropy arithmetic and so on relying on time series length, complexity measure analysis method
adapting limited data is introduced to analyze river runoff complexity. Adopted empty ratio rule to improve complexity measure arithmetic, preferably excessive coarseness is avoided. Results indicate much or little runoff variety reflect runoff order or out-of-order evolvement course, low value abnormity variety of approximate entropy measure after high value reflects runoff evolvement dynamics character before runoff peak and paddy value, which provide a new analysis method to recognize runoff series dynamics character and provide a new qualitative measure to forecast runoff peak and paddy value.3. Aimed at tendency and instability characters of runoff time series, detrended fluctuation analysis method is introduced to analyze runoff time series long relativity of the Yellow River main stream. Firstly recursion figure method is adopted to diagnose forecasting ability of measured and natural runoff time series of the Yellow River. Results indicate certain long relativity exist in measured and natural runoff time series of the Yellow River main stream, and they can be forecasted in short time, which provide a new method to study long relativity and forecasting ability of runoff time series.4. Aimed at runoff many factors coupling characters, least factor gather participating runoff evolvement is provided; phase space reconstruction technology and independent component analysis method are introduced to realize decoupling and purification of runoff time series and to develop phase space reconstruction technology range. Results indicate there is three factors affecting runoff change at least of the Yellow River upstream, midstream and downstream. Among natural runoff affecting factors, one factor variety has being obvious law and the other two variety being complex. It provides a new thought to study affecting factors of runoff time series.5. Considered runoff series length and runoff peak break characters, adopted least squares support vector machine arithmetic in small-sample machine learning theory to forecast and model. Aimed at problems of parameter optimization, training and testing
speed of support vector machine arithmetic, a least squares support vector machine runoff forecasting model based on chaos optimization peak identification is built up; a least squares support vector machine arithmetic based on chaos optimization peak identification is put forward to separate sample adopting phase space reconstruction technology and independent component analysis, which provide technology guarantee for arithmetic learning and forecasting ability. Simulation results indicate this arithmetic not only has strong learning and forecasting ability but also has high training and testing speed, which provide a new tool for runoff time series forecasting.
资源规划、配置与调控的基本依据。本文结合国家自然科学基金和国家重大基础规
划项目,以黄河干流径流序列为例,采用复杂性理论及方法,对河川径流变化的复
杂性、长程相关性、可预测能力和预测方法进行了研究,主要取得了以下具有特色
和创新性研究成果:
(1) 基于径流是多因素耦合作用的一种涌现的思想,提出了径流时间序列的“解
耦、提纯、耦合”分析及预测建模方法,初步构建了径流序列分析的复杂性理论框
架,丰富了水文水资源系统理论,为研究径流演变规律提供了一种新的技术。
(2) 针对关联维数、李亚普诺夫指数、K熵等算法对时间序列长度的依赖性等问题,
引入了具有计算方便、适应于有限数据的复杂性测度分析方法,对河川径流的复杂性
进行了分析;并采用空心比率准则对复杂性测度算法进行了改进,较好地避免了“过
分粗粒化”的问题。分析结果表明,径流量多与少的变化过程反映的是径流的有序与
无序的演变过程;近似熵测度高低值后的低高值异常变化特征反映了径流峰谷值前径
流变化的动力学特征,为深入认识径流时间序列的动力学特征提供了一种新的分析方
法,同时为径流峰谷预测提供了一种新的定性手段。
(3) 针对径流时间序列的趋势和非平稳特征,引入了非趋势波动分析方法对黄河
干流径流时间序列长程相关性进行了实证分析:首次应用递归图方法诊断黄河干流天
西安理工大学博士学位论文
然和实测径流”打司序列的可预测能力。结果表明,黄河干流大然和实测径流时间序列
中均存在肴一定程度的长程相关性(持久性),井可以进行短期预测,为径流时间序
列的长程相关性和预测能力诊断切f究提供了新的方法。
(封乍!对径流的多囚素祸合特征,提出了参与径流演变的最小囚素(变量)集的
概念,引入相空间重构技术和独立分量分析方法,实现了径流时间序列的“解祸和
提纯”,井一拓展了相空间重构技术的应用范围。结果表明,影响黄河干流上中卜游径
流变化的因素至少有3个:各站大然径流的影响因素中,有一个因素的变化具有明
显的规律性,另两个囚素的变化较为复杂,而实测径流的影响因素的变化均较为址
杂,为径流时间序列影响因素分析研究提供了新的思路。
(5)考虑到径流序列的长度和峰值突变性的特点,本文采用小样本机器学习理论
中的最小止乘支持向量机进行预测建模。并针对支持向量机算法存在的参数优化、训
约、和测试速度等问题,建立了一种基r混沌优化的峰值识别最小_一乘支持向童机径流
顶测模型;提出J’运用相空间重构技术和独立分量分析对样本进行分离的混沌优化峰
值识别最小_一乘支持向量机算法,为提高模型的学习能力和顶测能力提供了技术保
障。仿真结果表明,该模型不仅学习能力较强、预测精度较高,而_1」.训练和测试速度
陕,为径流时间序夕lJ的预测提供了一种新的l一具。
关键词:复杂性理论:复杂性测度;人类活动;非趋势波动分析:独立分晕_分析:
支持向量机:混沌优化;径流预测
本论文得到了国家自然科学基金项目(批准号50479024)和国家重
大基础规划项目(G199904360801)的资助。
One of the most important tasks of water resources and hydrology is description and forecasting of river runoff course that is basis of water resources planning, disposition, regulation and control. Supported by the National Natural Science Foundation of China and the Major State Basic Research Development Program of China, make runoff series of the Yellow River main stream as an example, applied complexity theory and its methods to study complexity, long relativity, forecasting ability and forecasting methods of river runoff variety. Main characteristic and innovation results as follows:1. Based on the thought that runoff is a swarm many factors coupling, analysis and forecasting modeling method of runoff time series-'decoupling, purification, coupling' are put forward, complexity theory frame of runoff series analysis is built up, which enrich water resources and hydrology system theory and provide a new technology for runoff evolvement law.2. Aimed at problems of relationship dimension, Lyapunov index, K entropy arithmetic and so on relying on time series length, complexity measure analysis method
adapting limited data is introduced to analyze river runoff complexity. Adopted empty ratio rule to improve complexity measure arithmetic, preferably excessive coarseness is avoided. Results indicate much or little runoff variety reflect runoff order or out-of-order evolvement course, low value abnormity variety of approximate entropy measure after high value reflects runoff evolvement dynamics character before runoff peak and paddy value, which provide a new analysis method to recognize runoff series dynamics character and provide a new qualitative measure to forecast runoff peak and paddy value.3. Aimed at tendency and instability characters of runoff time series, detrended fluctuation analysis method is introduced to analyze runoff time series long relativity of the Yellow River main stream. Firstly recursion figure method is adopted to diagnose forecasting ability of measured and natural runoff time series of the Yellow River. Results indicate certain long relativity exist in measured and natural runoff time series of the Yellow River main stream, and they can be forecasted in short time, which provide a new method to study long relativity and forecasting ability of runoff time series.4. Aimed at runoff many factors coupling characters, least factor gather participating runoff evolvement is provided; phase space reconstruction technology and independent component analysis method are introduced to realize decoupling and purification of runoff time series and to develop phase space reconstruction technology range. Results indicate there is three factors affecting runoff change at least of the Yellow River upstream, midstream and downstream. Among natural runoff affecting factors, one factor variety has being obvious law and the other two variety being complex. It provides a new thought to study affecting factors of runoff time series.5. Considered runoff series length and runoff peak break characters, adopted least squares support vector machine arithmetic in small-sample machine learning theory to forecast and model. Aimed at problems of parameter optimization, training and testing
speed of support vector machine arithmetic, a least squares support vector machine runoff forecasting model based on chaos optimization peak identification is built up; a least squares support vector machine arithmetic based on chaos optimization peak identification is put forward to separate sample adopting phase space reconstruction technology and independent component analysis, which provide technology guarantee for arithmetic learning and forecasting ability. Simulation results indicate this arithmetic not only has strong learning and forecasting ability but also has high training and testing speed, which provide a new tool for runoff time series forecasting.
引文
[1] 张升堂,拜存有,万三强等.人类活动的水文效应研究综述[J].水土保持研究,2004,11(3) :316～319
[2] 冯国章.水事活动对区域水文生态系统的影响[M].北京:高等教育出版社,2002:2～4
[3] 左其亭,王中根.现代水文学[M].郑州:黄河水利出版社,2002:2～3
[4] 徐建华.人类活动对自然环境演变的影响及其定量评估模型[J].兰州大学学报(社会科学版),1995,23(3) :144～150
[5] 长江水利委员会.水文预报方法[M].北京:水利电力出版社,1993
[6] 刘洪,李必强.混沌理论的未来观及其对技术经济预测的影响[J].科技导报,1995,(12) :7～10
[7] 冯文权.经济预测与经济决策技术[M].武汉:武汉大学出版社,1994
[8] 陈玉祥,张汉亚.预测技术与应用[M].北京:机械工业出版社,1985
[9] Makridakis,S.Forecasting in the 21st century[J].International Journal of Forecasting,1991,7(2) :123-126
[10] De Masi P R.The Difficult Art of Economic Forecasting[J].Finance & Development,1996,33(4) :29-31
[11] Winklhofer H,Diamantopoulos A,Witt S F.Forecasting Practice:A Review of the Empirical Literature and Agenda for Future Research[J].International Journal of Forecasting,1996,12(2) :193-221
[12] 李学伟,关忠良.现代经济预测的发展特征[J].数量经济技术经济研究,1998(1) :39～42
[13] 杨东升.经济分析中的预测方法评述[J].预测.1998,17(1) :45～47,50
[14] 刘豹,胡代平.神经网络在预测中的一些应用研究[J].系统工程学报,1999,14(4) :338～344
[15] Sohl J.An Intelligent Model Selection and Forecasting System[J].Journal of Forecasting,1999,18:167-180
[1
[16] 蔡文.可拓论及其应用[J].科学通报.1999,44(3) :673~682
[17] Wen Cai.Extension Management Engineering and Application[J].Chinese Science Bulletin,1999,44(17) :1538-1548
[18] 蔡文,杨春燕,何斌.可拓学基础理论研究的新进展[J].中国工程科学,2003,5(2) :80～87
[19] Yoping Huang,Hungjin Chen,Chipeng Ouyang.The Integration of Extension Theory to Design a New Fuzzy Inference Model[J].International Journal on Intelligence Tools,2000,9(4) :473-492
[20] He Xulian,Liu Wei,Ye Jian.Extension Information and Its Application to Criminal Investigation.Proceedings of 98 International Conference on Management Science & Engineering,1998
[21] 涂序彦.可拓学--研究“矛盾转化,开拓创新”的新学科[J].中国科学工程,2000,2(12) :97
[22] 苗东升.浑沌与世界可知性[J].中国人民大学学报,1993(3) :83-84
[23] 刘洪,刘志迎等.论经济系统的特征[J].系统辩证学学报,1998,7(4) :29-32
[24] Zhao Yanan,Liu Yanyu,Zhang Guowu.Research on Methodology of Open Complex Giant System.Systems Engineering,Systems Science and Complexity Research.Research Information Ltd,2000:158-164
[25] Zhang Cao,Chen Wu.A Study on General Property and Operating &Scheduling Simulation Models of Big Complex River Diversion Project.Systems Engineering,Systems Science and Complexity Research.Research Information Ltd,2000:620-627
[26] Michaels M.An Interview with Ilya Prigogine[J].The Chaos Network,1992,4(17) :61801
[27] Albert A.Chaos and Society[M].IOS Press,1995:1-13
[28] 刘华杰.论浑沌对决定论的影响[J].自然辩证法研究,1994,10(12) :1～12,57
[29] 窦学诚.社会地理关系本体模态--描述人类社会复杂性的一种全新尝试[会议交流论文].西安:全国复杂性与系统科学理论、方法及其应用学术研讨会,2004. 10
[30] 李景平,刘军海.复杂科学的研究对象:非线性复杂系统[会议交流论文].西安:全国复杂性与系统科学碑论、方法及其应用学术研讨会.2004. 10
[31] Cowan G A,Pines D,Meltzer D,etal.Complexity:Metaphors,Models,And Reality[C].Proc Vol XIX,Addison-wesley,1994
[32] 贝塔朗菲.一般系统论:基础、发展、应用[M].北京:社会科学文献出版社,1987
[33] 维纳.控制论--或关于在动物和机器中控制和通讯的科学[M].郝季仁译.北京:科学出版社,1984
[34] 尼科里斯,普利高津.探索复杂性[M].四川教育出版社,1986
[35] 格莱克,张淑誉译.混沌:开创新科学[M].上海:上海译文出版社,1990:13～17
[36] Knox L.Mastering Imperfect Markets:the Gospel according to Edgar Peters [J].Institutional Investor,1994,28(1) :21
[37] Rasband S N.Chaotic Dynamics of Nonlinear Systems[M].John & Sons,Inc,1989
[38] 姚勇.熵、分维、李雅普诺夫指数与混沌[J].自然杂志,1988,10(5) :359-365
[39] 冯国章,宋松柏,李佩成.水文系统复杂性的统计测度[J].水利学报,1998(11) :76～81
[40] Kolmogorov A N.Three approaches to the quantitative definition of information[J].Problems of information Transimissin,1965(1) :1-7
[41] Lempel A,Ziv J.On the Complexity of Finite Sequences[J].IEEE Transactions on Information Theory,1976,22(1) :75-81
[42] Jinghua Xu,Zengrong Liu.Information Transmission in Human Cerebral Cortex[J].Physical,1997,106(3-4) :363-374
[43] Tong Q,Kong J,Xu J.A Note,on Analyzing Schizophrenic EEG with Complexity Measure[J].Chaos,Solitions & Fractals,1996,7(3) :371-375
[44] Pincus S M.Approximate entropy as a measure of system complexity[J].Proc Natl Acad Sci,1991,88:2297-2301
[4
[45] Pincus S M.Approximate entropy(ApEn) as a complexity measure[J].Chaos,1995,5(1) ,110-117
[46] Pincus S M,Goldberger A L.Physiological time series analysis:What does regularity quantify?[J].Am J Physiol,1994,266(4) :1643-1656
[47] 杨福生,廖旺才.近似熵:一种适用于短数据的复杂性度量[J].中国医疗器械杂志,1997,21(5) :283-286
[48] 李素兰.脑电时间序列分析的非线性动力学方法.浙江大学硕士论文,1998
[49] Rodriguez-Iturbe I,De Power B F,Sharifi M B,etal.Chaos in Rainfall[J].Water Resour Res,1989,25(7) :1667-1675
[50] Wilcox B P,Seyfried M S,Blackburn W H,etal.Chaotic characteristics of snowmelt runoff:a preliminary study[J].American Society of Civil Engineers Watershed Management Symposium,Watershed Planning and Analysis in Action,1990:125-134
[51] Wilcox B P,Seyfried M S,Matison T H.Searching for Chaotic Dynamics in Snowmelt Runoff[J].Water Resour Res,1991,27:1005-5010
[52] Rodriguez-Iturbe I,Enteknabi D,Lee J S,etal.Nonlinear Dynamics of Soil Moistureat at Climate Scales,2. Chaotic Analysis[J].Water Resour Res,1991,27:1907-1915
[53] Jayawardena A W,Feizhou L.Analysis and Prediction of Chaos in Rainfall and Stream Flow Time Series[J].J Hydrol,1994,153:23-52
[54] 王文均,叶敏,陈显维.长江径流时间序列混沌特性的定量分析[J].水科学进展,1994,5(2) :87-94
[55] 丁晶.探索水文现象的复杂性--混沌分析.夏军等编:现代水科学不确定性研究与进展[M].成都:成都科技大学出版社,1994
[56] 傅军,丁晶,邓育仁.洪水混沌特性初步研究[J].水科学进展,1996,7(3) :226-230
[57] Mandelbrot B B,Wallis J R.Some Long Run Properties of Geophysical Records [J].Water Resour Res,1969,5(3) :321-340
[58] Mandelbrot B B,Van Ness J W.Fractional Brownian Motion,Fractional Noise and Application[J].Slam Rev,1968,(10) :422
[59] Feder T.Fractals[M].New York:Plenum Press.1988. 1-214
[60] 黄登仕,李后强.分形几何学、R/S分析与分式布朗运动[J].自然杂志,1990,13(8) :477～482
[61] 周寅康.淮河流域洪涝特征初步分析[J].地理研究,1996,15(1) :22-28
[62] 李祚泳,邓新民.四川旱涝震的分形时间特征及其与统计时间特征比较[J].自然灾害学报,1997,6(2) :65-69
[63] 王良健.分形方法在洪涝灾害预测中的应用[J].地理科学,1998,18(3) :242-247
[64] 杜兴信.自然灾害的白相似性质[J].灾害学,1995,10(2) :1～5
[65] 朱晓华.中国1840-1996年洪水灾害若干特征分析[J].灾害学,1999,14(2) :6～11
[66] 朱晓华,杨秀春.水旱灾害时间序列的分形研究方法[J].安徽农业科学,2000,28(1) :35～36,38
[67] 冯利华.基于R/S分析的水资源预测[J].系统工程理论与实践,2002(4) :115～118
[68] 维纳.郝季仁译.控制论[M].北京:科学出版社,1962
[69] Paul Cilliers.Complexity and Postmodernism:Understanding Complex Systems [M].New York:Routledge,1998
[70] Murray Gel1-Mann.Let's all it plexctics[J].Complexity,1995/96,1(5)
[71] 约翰·霍根.科学的终结[M].呼和浩特:远方出版社,1997
[72] Horgan J.From Complexity to Perplexity[J].Scientific Awerica,1995,272:74-79
[73] 弗里德里希·克拉默.混沌与秩序[M].上海:上海科学技术教育出版社,2000:284～294
[74] Warren Weaner.Science and Complexity[J].Scientist,1948,36(4) :536~544
[75] 郝柏林.复杂性的刻画和“复杂性科学”[J].自然杂志,1999(3) :5
[76] 盖尔曼.夸克与美洲豹[M].长沙:湖南科学技术出版社,1997
[77] 吴彤.复杂性范式的兴起[J].科学技术与辩证法,2001(6) :20-24
[78] 黄欣荣.复杂性究竟是什么--复杂性的语义分析[J].自然辩证法研究,2004,20(5) :31～35
[79] 方锦清.令人关注的复杂性科学和复杂性研究[J].自然杂志,24(1) :8～10
[80] 张焘.复杂性研究--当代科学重大变革的重要标志.复杂性科学探索.http://ai.ia.ac.cn/Chinese/publication/complexity/scjence.htm
[81] 秦书生.复杂性的哲学评析[J].哲学动态,2004(5) :38-41
[82] 苗东升.论复杂性[J].自然辩证法通讯,2000,22(6) :87-92
[83] 吴彤.复杂性、科学与后现代思潮[J].内蒙古大学学报,2003 C4) :8～12
[84] 吴彤.复杂性范式的兴起[J].科学技术与辩证法,2001(6) :20～24
[85] Nerenberg M A,Essex C.Correlation dimension and systematic geometric effects[J].PHYSICAL REVIEW A,1990,42(12) :7065-7074
[86] 同[41]
[87] Grassberger P.Toward a Quantitative Theory of Self-Generated Complexity[J].International Journal of Theoretical Physics,1986,25(9) ,907-938
[88] Wackerbauer R,Witt A,Altmanspracher H,etal.A Comparative Classification of Complexity Measures Based on Distiguishing Partitions in Phase Space as Well as StructurlV,Dynamic Elements[J].Chaos.Solitons & Fractals,1994,4(1) :133-173
[89] Kasper F,Schuster H G.Easily Calculable Measure for the Complexity of Spatiotemporal Patterns[J].PHYSICAL REVIEW A,1987,36(2) :842-848
[90] 吕悦军,陆远忠.用算法复杂性分析时间序列[J].中国地震,1993,9(3) :229-234
[91] Xu J H.The Measure of Sequence Complexity of EEG[J].Chaos,Soliton & Fractals,1994,4:2111-2119
[92] 徐京华,吴祥宝.以复杂度测度刻划人脑皮层上的信息传输[J].中国科学(B 辑),1994,24(1) :58~62
[9
[93] 李素兰.脑电时间序列分析的非线性动力学方法[M].杭州:浙江大学出版社,1998
[94-97] 同[44-47]
[98] 孟欣,沈恩华,陈芳等.脑电图复杂度分析中的粗粒化问题Ⅰ.过分粗粒化和三种复杂度的比较[J].生物物理学报:2000,16(4) :701～706
[99] 陈芳,顾凡及,徐京华等.一种新的人脑信息传输复杂性的研究[J].生物物理学报,1998,14:508-512
[100] 张筑生.微分动力系统原理[M].北京:科学出版社,1987
[101] 胡晓棠,胡茑庆,陈敏.一种改进的选择相空间重构参数的方法[J].震动工程学报,2002(2) :242
[102] Albano A M.SVD and Grassberger Procaccia algorithm[J],Phy Rev:A,1988,38(20) -.3017-3026.
[103] Fraser A M.Information and entropy in strange attractors[J].IEEE Trans on IT Mar,1989,35(2) :245-262.
[104] Albano A M.Using high-order correlations to define an embedding window [J].Physical,1991,54(1) :85-97
[105] Buzug P T.Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors[J].Phy Rev:A,1992,45(10) :7073-7084.
[106] Buzug P T.Comparison of algorithms calculating optimal embedding parameters for delay time coordinates[J].Physica:D,1992,58(2) :127-137
[107] Rossenstein M T,Colins J J,De Luca C J.Reconstruction expansion as a geometry-based framework for choosing proper delay times[J].Physica:D,1994,73(1) :82-98
[108] Kember G,Fowler A C.A correlation function for choosing time delays in phase portrait reconstructions[J].Phy Lett:A,1993,179(2) :72-80
[109] 林嘉宇,王跃科,黄芝平等.语音信号相空间重构中时间延迟的选择--复自相 关法[J].信号处理,1999,15(3) :220-225
[1
[110] Kugiumtzis D.State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length[J].Physica:D,1996,95(1) :13-28
[111] Kim H S,Eykholt R.Salas J D.Nonlinear Dynamics,Delay Times,and Embedding Windows[J].Physica D Nonlinear Phenomena,Physica,1999,127(1) :48-60
[112] Otani M,Jones A.Automated embedding and creep phenomenon in chaotic time series[EB/OL].http://www.cs.cf.ac.Uk/ec/aecp.html,2000-10-14/2003-05-15
[113] 向小东,郭耀煌.对基于递归的时间序列可预测性的进一步研究[J].管理工程学报,2003,17(2) :103~105
[114] 贝达特J S,皮尔索A G.随机数据分析方法[M].国防工业出版社,1976
[115] Smith L A.Intrinsic limits on dimension calculations[J].Phys Lett A,1988,133(6) :283-288
[116] Havstad J W,Ehlers C L.Attractor dimension of nonstationary dynamical systems from small datd sets[J].Phys Rev A,1989,39(2) :845-853
[117] Nerenberg M A H,Essex C.Correlation dimension and systematic geometric effects[J].Phys Rev A,1990,42(12) :7065-7074
[118] 洪时中,洪时明.用Grassberger-Procaccia方法计算吸引子维数的基本限制[J].物理学报,1994,43(8) :1228~1233
[119] Sivakumar B,Phoon K K,Liong S Y.A systematic approach to noise reduction in observed chaotic time series[J].Journal of hydrology,1999,219:103-135
[120] Sivakumar B,Liong S Y,Liaw C Y.Singapore raifall behavior:chaotic?[J].Journal of Hydro Eng,ASCE,1999,4(1) :38-48
[121] Sivakumar B,Liong S Y,Liaw C Y.Evidence of chaotic behavior in Singapore raifall[J].J AM Water Resour Assoc,1998,34(2) :301~310
[122] Sivakumar B.Chaos theory in hydrology:important issues and interpreta_ tions[J].Journal of hydrology,2000,227:1-20
[123] 黑晓军,程文青,郑凛等.一种增加混沌信号有效数据长度的新方法[J].华中理工大学学报,1999,27(4) :84-86
[124] Zhenshan Lin.Jian Liu.Fangbin Shi.A study to establish the retrieved model of local climate[J].Meteorology and Atmospheric Physics,1993,52:177-182
[125] 黄建平,衣育红.利用观测资料重建非线性模式[J].中国科学(B),1991,18:331～336
[126] 屈世显,张建华.复杂系统的分形理论与应用[M].西安:陕西人民出版社,1996:337～345
[127] Peng C K,Buldrev S V,Goudberger A L,etal.Finite size effects on long range correlations:implications for analyzing DNA sequences[J].Physical Review E,1993,47(5) :3730-3733
[128] Peng C K,Buldyrev S V.Havlin S,etal.Mosaic organization of DNA nucleo_ tides[J].Physical Review E,1994,49(2) :1685-1689
[129] Lux T,Marchesi M.Scaling and criticality in a stochastic multi-agent model of financial market[J].Nature,1999,397(11) :498-500
[130] Mantegna R N,Stanley H E.Scaling behavior in the dynamics of an economic index[J].Nature,1995,376(6) :46-49
[131] Cuniberti G,Raberto M,Scalas E.Correlations in the bound future market [J].Physica A,1999,269(1) :90-97
[132] Scalas E.Scaling in the market of futures[J].Physica A,1998,253(1-4) :394-402
[133] Janosi I M,Janecsko B,Kondor I.Statistical analysis of 5s index data of the Budapest Stock Exchange[J].Physica A,1999,269(1) :111-124
[134] 黄登仕.金融市场的标度理论[J].管理科学学报,2000,3(2) :27~33
[135] 宋学峰,顾世清.深沪证券市场股价波动的浑沌度及其调控方法[J].管理科学学报,2000,3(1) :53-57
[136] 周奕,陈收,汪寿阳.资本结构作用下市场投资组合轨迹的研究[J].管理科学学报,2000,3(3) :75~81
[137] Stanley H E,Amaral L A N,Canning D,etal.Econophysics:Can physicists contribute to the science of economics?[J].Physica A,1999,269(1) :156-169
[138] Stanley H E,Afanasyevr V,Amaral L A N,etal.Anomalous fluctuations in the dynamics of complex systems:from DNA and physiology to econophysics[J]. Physica A,1996,224(2) :302-321
[139] 黄小原,庄新田,张泉.股市波动的标度无关性算法及应用研究[J].管理科学学报,2001,4(6) :55~59
[140] Detrended Fluctuation Analysis.http://www.cbi.dongnocchi.it/glossary/ Detrended Fluctuation Analysis.html
[141] 魏宇.基于多标度分形理论的金融风险管理方法研究.西安交通大学博士研究生学位论文,2004:23～30
[142] 金林,赵俊和.混沌理论及其在经济周期理论中的应用[J].上海交通大学学报,1996,30(2) :77~82
[143] 刘舒,孟建.样本序列的可预测性研究[J].预测,1997,(2) :47~49
[144] Babloyantz A.Some remarks on nonlinear data analysis of physiological time series[M].Measures of Complexity and Chaos.Edited by N B A raham etal. plenum Press,1993
[145] Pawel K,Remigiusz T.Recurrence plots of neuronal spike trains[J].Bio_ logical Cybernetics.1993,68:527~534
[146] Eckmann J P,Kamphorst O R S.Recurrence plots of dynamical systems[J]. Euro_phys Lett.1987,4:973-977
[147] 向小东,郭耀煌.对基于递归图的时间序列可预测性的进一步研究[J].管理工程 学报,2003,17(2) :103-105
[1
[148] Farmer J D,Didorowich J J.predicting chaotic time series[J].phys Rev,Lett,1987,59:845-848
[149] Oja E.Principal Components,Minor Components,and linearneural networks [J],Neural Networks,1992:5(6) :927-935
[150] Oja E.The nonlinear PCA learning rule in independent component analysis [J].Neurocomputing,1997,17(1) :25-45
[151] 焦李成.神经网络的应用与实现[M].西安:西安电子科技大学出版社,1996
[152] 孙即祥.数字图像处理[M].石家庄:河北教育出版社,1993
[153] Karhunen,J.,Hyvarinen,A.,Vigario,R.,Hurri,J.& Oja,E.Applications of Neural Blind Separation to Signal and Image Processing.Proc.of 1997 International Conference on Acoustics,Speech,and Signal Processing (ICASSP-97) ,Munich,Germany,April 21-24,1997:131-134
[154] 郭晓静,吴小培,张道信等.基于独立分量分析的脑电消噪与特征提取[J].系统仿真学报,2003,15(2) :287~289
[155] Cardoso J F,Laheld B H.Equivariant adaptive source separation[J].IEEE Trans On Signal Processing,1996,44(12) :3017~3030
[156] Oja E,Yang Howard Hua,Amari S I.Adaptive on line learning algorithms for blind separation:Maximum entropy and minimum mutual information[J]. Neural Computation,1997,9(7) :1457-1482
[157] McKeown M J,Jung T P,Makeig S,etal.Spatially independent activity pa_ tterns in functional MRI data during the stroop color-naming task[J].In: Proceedings of the National Academy of Sciences,1998,95(6) :803-810
[158] Stone J V,Porrill J,Porter N R,etal.Spatiotemporal ICA of fMRI Data[J].In: Computational Neuroscience Report 202,IEEE International workshop on Biologically Motiviated Vision,2000
[159] Vigario R,Jousmaki V,Oja E,etal.Independent component analysis for identification of artifacts in magnetoencephalographic recordings[M],In Neural Information Processing Systems 10,(proc NIPS' 97) ,Tordan,Kearns and Solla,Eds,Cambridge,MA:MIT Press,1998:229-235
[1
[160] Vigario R.Extraction of ocular artifacts from EEG using independent component analysis[J].Electroenceph Clin Neurophysiol,1997,103(3) :395-404
[161] Vigario R,Sarela J,Oja E.Independent component analysis in wave decom_ position of auditor yevoked fields.In:Proc Int Conf on Artificial Neural Networks (ICANN'98) ,Skovde,Sweden,1998,287-292
[162] 01shausen B A,Field D J.Emergence of simple-cell receptive field pro_ perties by learning a sparse code for natural images[J].Nature,1996, 381 (6583) :607-609
[163] Torkkola K.Blind separation for audio signals-are we there yet?In:Proc. Int.Workshop on Independent Component Analysis and Signal Separation(ICA' 99) ,Aussois,France:1999,239-244
[164] Bell A J,Sejnowski T J.The' independent components' of natural scenes are edge filters.Vision Research,1997,37(23) :3327-3338
[165] Yuen P C,Lai J H.Face representation using independent component analysis [J].Pattern Recognition,2001,34(3) :545-553
[166] 毕贤,李通化,吴亮等.独立组分分析在红外光谱分析中的应用[J].高等学校化学学报,2004,25(6) :1023-1027
[167] 刘喜武,刘洪,李幼铭等.独立分量分析及其在地震信息处理中的应用初探[J].地球物理学进展,2003,18(1) :090-096
[168] 王泽,朱贻盛,李音等,独立分量分析在混沌信号分析中的应用[J].电子学报,2002,30(10) :1505-1507
[169] Jutten C,Herault J.Independent component analysis versus PCA.In:Pro_ ceeding of European Signal Processing Conf,1988:287-314
[170] Comon P.Independent component analysis--Anewconcept?[J].Signal Processing,1994,36(3) :287-314
[171] Jutten C,Herault J.Blind separation of sources,partⅠ:An adaptive Algo_ rithm based on neurom imetic architecture[J].Signal Processing,1991,24 (1) -1-10
[172] 同[150]
[173] Hyvarinen A.Survey on independent component analysis[J].Neural Computing Surveys,1999,2(4) :94-128
[174] Hyvarinen A.Fast and robust fixed-point algorithms for independent component analysis[J].IEEE Trans,on Neural Networks,1999,10(3) :626~634
[175] Hyvarinen A.independent Component Analysis:A Tutorial[EB/OL].http://cis.hut.fi/projects/ica/
[176] Giannakopoulos X,Karhunen J,Oja E.Experimental comparison of neural ICA algorithms.In:Proc Int Conf,On Artificial Neural Networks(ICANN'98) , Skovde,Sweden,1998:651-656
[177] 张贤达.盲信号分离[J].电子学报,2001(12A):1765-1771
[178] 叶守泽,夏军.水文系统识别原理与方法[M].北京:水利电力出版社,1989
[179] 夏军.现代水科学不确定性研究与进展(全国首届水文水资源与水环境中的不确定性研究新理论新方法学术讨论会论文集)[C].成都:成都科技大学出版社.1994
[180] 李致家,孔祥光.非线性水文系统的实时预报方法比较研究[J].水文,1997(1) :24～28
[181] Vapnik V N.Estimation of dependencies based on empirical data[M].Berlin: Springer Verlag,1982
[182] Vapnik V N.Thenature of statistical learning theory[M].New York:Spring Verlag,1995
[183] Cherkassky V,Mulier F.Learning from data:concepts,theory and methods[M]. New York John Viley & Sons,1997
[184] Cherkassky V,Muulier F.Learning from Data:Concepts,Theory and Methods [M].NY:Tohn Viley & Sons,1997
[185] Vapnik V N,Levin E,Le Cun Y.Measuring the VC dimension of a learning machine[J].Neural Computation,MIT Press,1994(6) :851-876
[186] 加肇祺.模式识别[M].北京:清华大学出版社.1988
[187] Vapnik V N,张学工译.统计学习理论的本质[M].北京:清华大学山版社,2000
[188] Zhang Ling.The Relationship Between Kernel Functions Based SVM and Three-layer Feedforward Neural Networks[J].Chinese J Computer,2002,25(7) :1-5
[189] Zhang Ling,Zhang Bo.Relationship Between Support Vector Set and Kernel Functions in SVM[J].J Comput Sci & Technol,2002,17(5) :549
[190] Ou T J,Lakshman T V,Wong L H.SRED:stabilized RED[A].Proc IEEE Infocom[C].New York USA:IEEE,1999:1346-1355
[191] Vapink V.The Nature of Statistical Learning Theory[M],New York:Springer Verlag,1999
[192] 陈永义,俞小鼎,高学浩等.处理非线性分类和回归问题的一种新方法(Ⅰ)--支持向量机方法简介[J].应用气象学报,2004,15(3) :345-354
[193] 李兵,蒋慰孙.混沌忧化方法及其应用[J].控制理论与应用,1997,14(4) :613～615
[194] 张彤,王宏伟,王子才.变尺度混沌忧化方法及其应用[J].控制与决策,1999,14(3) :285～288
[195] 冯国章,李佩成.论水文系统混沌特征的研究方向[J].西北农业大学学报.1997,25(4) :97～101
[196～198] 同[54-56]
[199] 刘德平.分形理论在水文过程形态特征分析中的应用[J].水利学报,1998,(2) :20～25
[200] 魏一鸣.洪水灾害研究的复杂性理论[J].自然杂志,21(3) :139～142
[201] Rundle J.Workshop Held on Natural Disasters.EOS,1994,13:103
[202] Barbera L P,Rosso R.On the Fractal Dimension of Stream Network[J].Water Resources Research,1989,25(4) :735-741
[203] Tanzhou Luo.Fractal Structure and Properties of Stream Network[J].Water Resources Research,1992,28(11) :2981-2988
[204] Mandelbrot B B.How long is the coast of Britain?.Statistical selfsimi-larity and fractional dimension.Science,1967,156(3775) :636-638
[205] 陈树群,钱沧海,冯智伟.台湾地区河川型态之碎形维度[J].中国台北:中国土木水利工程学刊,1995,7(1) :63~71
[206] Mandelbrot B B,Wallis J R.Som long run properties of geophysical records [J].Water Resources Research,1969,5(3) :321-340
[207] Mandelbrot B B,Van Ness J W.Fractional Brownian motion,fractional noise and application[J].Slam Rev,1968(10) :422-437
[208] Feder J.Fractals[M].New Yock:Plenum Press,1988:1-214
[209] 同[39]
[2] 冯国章.水事活动对区域水文生态系统的影响[M].北京:高等教育出版社,2002:2～4
[3] 左其亭,王中根.现代水文学[M].郑州:黄河水利出版社,2002:2～3
[4] 徐建华.人类活动对自然环境演变的影响及其定量评估模型[J].兰州大学学报(社会科学版),1995,23(3) :144～150
[5] 长江水利委员会.水文预报方法[M].北京:水利电力出版社,1993
[6] 刘洪,李必强.混沌理论的未来观及其对技术经济预测的影响[J].科技导报,1995,(12) :7～10
[7] 冯文权.经济预测与经济决策技术[M].武汉:武汉大学出版社,1994
[8] 陈玉祥,张汉亚.预测技术与应用[M].北京:机械工业出版社,1985
[9] Makridakis,S.Forecasting in the 21st century[J].International Journal of Forecasting,1991,7(2) :123-126
[10] De Masi P R.The Difficult Art of Economic Forecasting[J].Finance & Development,1996,33(4) :29-31
[11] Winklhofer H,Diamantopoulos A,Witt S F.Forecasting Practice:A Review of the Empirical Literature and Agenda for Future Research[J].International Journal of Forecasting,1996,12(2) :193-221
[12] 李学伟,关忠良.现代经济预测的发展特征[J].数量经济技术经济研究,1998(1) :39～42
[13] 杨东升.经济分析中的预测方法评述[J].预测.1998,17(1) :45～47,50
[14] 刘豹,胡代平.神经网络在预测中的一些应用研究[J].系统工程学报,1999,14(4) :338～344
[15] Sohl J.An Intelligent Model Selection and Forecasting System[J].Journal of Forecasting,1999,18:167-180
[1
[16] 蔡文.可拓论及其应用[J].科学通报.1999,44(3) :673~682
[17] Wen Cai.Extension Management Engineering and Application[J].Chinese Science Bulletin,1999,44(17) :1538-1548
[18] 蔡文,杨春燕,何斌.可拓学基础理论研究的新进展[J].中国工程科学,2003,5(2) :80～87
[19] Yoping Huang,Hungjin Chen,Chipeng Ouyang.The Integration of Extension Theory to Design a New Fuzzy Inference Model[J].International Journal on Intelligence Tools,2000,9(4) :473-492
[20] He Xulian,Liu Wei,Ye Jian.Extension Information and Its Application to Criminal Investigation.Proceedings of 98 International Conference on Management Science & Engineering,1998
[21] 涂序彦.可拓学--研究“矛盾转化,开拓创新”的新学科[J].中国科学工程,2000,2(12) :97
[22] 苗东升.浑沌与世界可知性[J].中国人民大学学报,1993(3) :83-84
[23] 刘洪,刘志迎等.论经济系统的特征[J].系统辩证学学报,1998,7(4) :29-32
[24] Zhao Yanan,Liu Yanyu,Zhang Guowu.Research on Methodology of Open Complex Giant System.Systems Engineering,Systems Science and Complexity Research.Research Information Ltd,2000:158-164
[25] Zhang Cao,Chen Wu.A Study on General Property and Operating &Scheduling Simulation Models of Big Complex River Diversion Project.Systems Engineering,Systems Science and Complexity Research.Research Information Ltd,2000:620-627
[26] Michaels M.An Interview with Ilya Prigogine[J].The Chaos Network,1992,4(17) :61801
[27] Albert A.Chaos and Society[M].IOS Press,1995:1-13
[28] 刘华杰.论浑沌对决定论的影响[J].自然辩证法研究,1994,10(12) :1～12,57
[29] 窦学诚.社会地理关系本体模态--描述人类社会复杂性的一种全新尝试[会议交流论文].西安:全国复杂性与系统科学理论、方法及其应用学术研讨会,2004. 10
[30] 李景平,刘军海.复杂科学的研究对象:非线性复杂系统[会议交流论文].西安:全国复杂性与系统科学碑论、方法及其应用学术研讨会.2004. 10
[31] Cowan G A,Pines D,Meltzer D,etal.Complexity:Metaphors,Models,And Reality[C].Proc Vol XIX,Addison-wesley,1994
[32] 贝塔朗菲.一般系统论:基础、发展、应用[M].北京:社会科学文献出版社,1987
[33] 维纳.控制论--或关于在动物和机器中控制和通讯的科学[M].郝季仁译.北京:科学出版社,1984
[34] 尼科里斯,普利高津.探索复杂性[M].四川教育出版社,1986
[35] 格莱克,张淑誉译.混沌:开创新科学[M].上海:上海译文出版社,1990:13～17
[36] Knox L.Mastering Imperfect Markets:the Gospel according to Edgar Peters [J].Institutional Investor,1994,28(1) :21
[37] Rasband S N.Chaotic Dynamics of Nonlinear Systems[M].John & Sons,Inc,1989
[38] 姚勇.熵、分维、李雅普诺夫指数与混沌[J].自然杂志,1988,10(5) :359-365
[39] 冯国章,宋松柏,李佩成.水文系统复杂性的统计测度[J].水利学报,1998(11) :76～81
[40] Kolmogorov A N.Three approaches to the quantitative definition of information[J].Problems of information Transimissin,1965(1) :1-7
[41] Lempel A,Ziv J.On the Complexity of Finite Sequences[J].IEEE Transactions on Information Theory,1976,22(1) :75-81
[42] Jinghua Xu,Zengrong Liu.Information Transmission in Human Cerebral Cortex[J].Physical,1997,106(3-4) :363-374
[43] Tong Q,Kong J,Xu J.A Note,on Analyzing Schizophrenic EEG with Complexity Measure[J].Chaos,Solitions & Fractals,1996,7(3) :371-375
[44] Pincus S M.Approximate entropy as a measure of system complexity[J].Proc Natl Acad Sci,1991,88:2297-2301
[4
[45] Pincus S M.Approximate entropy(ApEn) as a complexity measure[J].Chaos,1995,5(1) ,110-117
[46] Pincus S M,Goldberger A L.Physiological time series analysis:What does regularity quantify?[J].Am J Physiol,1994,266(4) :1643-1656
[47] 杨福生,廖旺才.近似熵:一种适用于短数据的复杂性度量[J].中国医疗器械杂志,1997,21(5) :283-286
[48] 李素兰.脑电时间序列分析的非线性动力学方法.浙江大学硕士论文,1998
[49] Rodriguez-Iturbe I,De Power B F,Sharifi M B,etal.Chaos in Rainfall[J].Water Resour Res,1989,25(7) :1667-1675
[50] Wilcox B P,Seyfried M S,Blackburn W H,etal.Chaotic characteristics of snowmelt runoff:a preliminary study[J].American Society of Civil Engineers Watershed Management Symposium,Watershed Planning and Analysis in Action,1990:125-134
[51] Wilcox B P,Seyfried M S,Matison T H.Searching for Chaotic Dynamics in Snowmelt Runoff[J].Water Resour Res,1991,27:1005-5010
[52] Rodriguez-Iturbe I,Enteknabi D,Lee J S,etal.Nonlinear Dynamics of Soil Moistureat at Climate Scales,2. Chaotic Analysis[J].Water Resour Res,1991,27:1907-1915
[53] Jayawardena A W,Feizhou L.Analysis and Prediction of Chaos in Rainfall and Stream Flow Time Series[J].J Hydrol,1994,153:23-52
[54] 王文均,叶敏,陈显维.长江径流时间序列混沌特性的定量分析[J].水科学进展,1994,5(2) :87-94
[55] 丁晶.探索水文现象的复杂性--混沌分析.夏军等编:现代水科学不确定性研究与进展[M].成都:成都科技大学出版社,1994
[56] 傅军,丁晶,邓育仁.洪水混沌特性初步研究[J].水科学进展,1996,7(3) :226-230
[57] Mandelbrot B B,Wallis J R.Some Long Run Properties of Geophysical Records [J].Water Resour Res,1969,5(3) :321-340
[58] Mandelbrot B B,Van Ness J W.Fractional Brownian Motion,Fractional Noise and Application[J].Slam Rev,1968,(10) :422
[59] Feder T.Fractals[M].New York:Plenum Press.1988. 1-214
[60] 黄登仕,李后强.分形几何学、R/S分析与分式布朗运动[J].自然杂志,1990,13(8) :477～482
[61] 周寅康.淮河流域洪涝特征初步分析[J].地理研究,1996,15(1) :22-28
[62] 李祚泳,邓新民.四川旱涝震的分形时间特征及其与统计时间特征比较[J].自然灾害学报,1997,6(2) :65-69
[63] 王良健.分形方法在洪涝灾害预测中的应用[J].地理科学,1998,18(3) :242-247
[64] 杜兴信.自然灾害的白相似性质[J].灾害学,1995,10(2) :1～5
[65] 朱晓华.中国1840-1996年洪水灾害若干特征分析[J].灾害学,1999,14(2) :6～11
[66] 朱晓华,杨秀春.水旱灾害时间序列的分形研究方法[J].安徽农业科学,2000,28(1) :35～36,38
[67] 冯利华.基于R/S分析的水资源预测[J].系统工程理论与实践,2002(4) :115～118
[68] 维纳.郝季仁译.控制论[M].北京:科学出版社,1962
[69] Paul Cilliers.Complexity and Postmodernism:Understanding Complex Systems [M].New York:Routledge,1998
[70] Murray Gel1-Mann.Let's all it plexctics[J].Complexity,1995/96,1(5)
[71] 约翰·霍根.科学的终结[M].呼和浩特:远方出版社,1997
[72] Horgan J.From Complexity to Perplexity[J].Scientific Awerica,1995,272:74-79
[73] 弗里德里希·克拉默.混沌与秩序[M].上海:上海科学技术教育出版社,2000:284～294
[74] Warren Weaner.Science and Complexity[J].Scientist,1948,36(4) :536~544
[75] 郝柏林.复杂性的刻画和“复杂性科学”[J].自然杂志,1999(3) :5
[76] 盖尔曼.夸克与美洲豹[M].长沙:湖南科学技术出版社,1997
[77] 吴彤.复杂性范式的兴起[J].科学技术与辩证法,2001(6) :20-24
[78] 黄欣荣.复杂性究竟是什么--复杂性的语义分析[J].自然辩证法研究,2004,20(5) :31～35
[79] 方锦清.令人关注的复杂性科学和复杂性研究[J].自然杂志,24(1) :8～10
[80] 张焘.复杂性研究--当代科学重大变革的重要标志.复杂性科学探索.http://ai.ia.ac.cn/Chinese/publication/complexity/scjence.htm
[81] 秦书生.复杂性的哲学评析[J].哲学动态,2004(5) :38-41
[82] 苗东升.论复杂性[J].自然辩证法通讯,2000,22(6) :87-92
[83] 吴彤.复杂性、科学与后现代思潮[J].内蒙古大学学报,2003 C4) :8～12
[84] 吴彤.复杂性范式的兴起[J].科学技术与辩证法,2001(6) :20～24
[85] Nerenberg M A,Essex C.Correlation dimension and systematic geometric effects[J].PHYSICAL REVIEW A,1990,42(12) :7065-7074
[86] 同[41]
[87] Grassberger P.Toward a Quantitative Theory of Self-Generated Complexity[J].International Journal of Theoretical Physics,1986,25(9) ,907-938
[88] Wackerbauer R,Witt A,Altmanspracher H,etal.A Comparative Classification of Complexity Measures Based on Distiguishing Partitions in Phase Space as Well as StructurlV,Dynamic Elements[J].Chaos.Solitons & Fractals,1994,4(1) :133-173
[89] Kasper F,Schuster H G.Easily Calculable Measure for the Complexity of Spatiotemporal Patterns[J].PHYSICAL REVIEW A,1987,36(2) :842-848
[90] 吕悦军,陆远忠.用算法复杂性分析时间序列[J].中国地震,1993,9(3) :229-234
[91] Xu J H.The Measure of Sequence Complexity of EEG[J].Chaos,Soliton & Fractals,1994,4:2111-2119
[92] 徐京华,吴祥宝.以复杂度测度刻划人脑皮层上的信息传输[J].中国科学(B 辑),1994,24(1) :58~62
[9
[93] 李素兰.脑电时间序列分析的非线性动力学方法[M].杭州:浙江大学出版社,1998
[94-97] 同[44-47]
[98] 孟欣,沈恩华,陈芳等.脑电图复杂度分析中的粗粒化问题Ⅰ.过分粗粒化和三种复杂度的比较[J].生物物理学报:2000,16(4) :701～706
[99] 陈芳,顾凡及,徐京华等.一种新的人脑信息传输复杂性的研究[J].生物物理学报,1998,14:508-512
[100] 张筑生.微分动力系统原理[M].北京:科学出版社,1987
[101] 胡晓棠,胡茑庆,陈敏.一种改进的选择相空间重构参数的方法[J].震动工程学报,2002(2) :242
[102] Albano A M.SVD and Grassberger Procaccia algorithm[J],Phy Rev:A,1988,38(20) -.3017-3026.
[103] Fraser A M.Information and entropy in strange attractors[J].IEEE Trans on IT Mar,1989,35(2) :245-262.
[104] Albano A M.Using high-order correlations to define an embedding window [J].Physical,1991,54(1) :85-97
[105] Buzug P T.Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors[J].Phy Rev:A,1992,45(10) :7073-7084.
[106] Buzug P T.Comparison of algorithms calculating optimal embedding parameters for delay time coordinates[J].Physica:D,1992,58(2) :127-137
[107] Rossenstein M T,Colins J J,De Luca C J.Reconstruction expansion as a geometry-based framework for choosing proper delay times[J].Physica:D,1994,73(1) :82-98
[108] Kember G,Fowler A C.A correlation function for choosing time delays in phase portrait reconstructions[J].Phy Lett:A,1993,179(2) :72-80
[109] 林嘉宇,王跃科,黄芝平等.语音信号相空间重构中时间延迟的选择--复自相 关法[J].信号处理,1999,15(3) :220-225
[1
[110] Kugiumtzis D.State space reconstruction parameters in the analysis of chaotic time series-the role of the time window length[J].Physica:D,1996,95(1) :13-28
[111] Kim H S,Eykholt R.Salas J D.Nonlinear Dynamics,Delay Times,and Embedding Windows[J].Physica D Nonlinear Phenomena,Physica,1999,127(1) :48-60
[112] Otani M,Jones A.Automated embedding and creep phenomenon in chaotic time series[EB/OL].http://www.cs.cf.ac.Uk/ec/aecp.html,2000-10-14/2003-05-15
[113] 向小东,郭耀煌.对基于递归的时间序列可预测性的进一步研究[J].管理工程学报,2003,17(2) :103~105
[114] 贝达特J S,皮尔索A G.随机数据分析方法[M].国防工业出版社,1976
[115] Smith L A.Intrinsic limits on dimension calculations[J].Phys Lett A,1988,133(6) :283-288
[116] Havstad J W,Ehlers C L.Attractor dimension of nonstationary dynamical systems from small datd sets[J].Phys Rev A,1989,39(2) :845-853
[117] Nerenberg M A H,Essex C.Correlation dimension and systematic geometric effects[J].Phys Rev A,1990,42(12) :7065-7074
[118] 洪时中,洪时明.用Grassberger-Procaccia方法计算吸引子维数的基本限制[J].物理学报,1994,43(8) :1228~1233
[119] Sivakumar B,Phoon K K,Liong S Y.A systematic approach to noise reduction in observed chaotic time series[J].Journal of hydrology,1999,219:103-135
[120] Sivakumar B,Liong S Y,Liaw C Y.Singapore raifall behavior:chaotic?[J].Journal of Hydro Eng,ASCE,1999,4(1) :38-48
[121] Sivakumar B,Liong S Y,Liaw C Y.Evidence of chaotic behavior in Singapore raifall[J].J AM Water Resour Assoc,1998,34(2) :301~310
[122] Sivakumar B.Chaos theory in hydrology:important issues and interpreta_ tions[J].Journal of hydrology,2000,227:1-20
[123] 黑晓军,程文青,郑凛等.一种增加混沌信号有效数据长度的新方法[J].华中理工大学学报,1999,27(4) :84-86
[124] Zhenshan Lin.Jian Liu.Fangbin Shi.A study to establish the retrieved model of local climate[J].Meteorology and Atmospheric Physics,1993,52:177-182
[125] 黄建平,衣育红.利用观测资料重建非线性模式[J].中国科学(B),1991,18:331～336
[126] 屈世显,张建华.复杂系统的分形理论与应用[M].西安:陕西人民出版社,1996:337～345
[127] Peng C K,Buldrev S V,Goudberger A L,etal.Finite size effects on long range correlations:implications for analyzing DNA sequences[J].Physical Review E,1993,47(5) :3730-3733
[128] Peng C K,Buldyrev S V.Havlin S,etal.Mosaic organization of DNA nucleo_ tides[J].Physical Review E,1994,49(2) :1685-1689
[129] Lux T,Marchesi M.Scaling and criticality in a stochastic multi-agent model of financial market[J].Nature,1999,397(11) :498-500
[130] Mantegna R N,Stanley H E.Scaling behavior in the dynamics of an economic index[J].Nature,1995,376(6) :46-49
[131] Cuniberti G,Raberto M,Scalas E.Correlations in the bound future market [J].Physica A,1999,269(1) :90-97
[132] Scalas E.Scaling in the market of futures[J].Physica A,1998,253(1-4) :394-402
[133] Janosi I M,Janecsko B,Kondor I.Statistical analysis of 5s index data of the Budapest Stock Exchange[J].Physica A,1999,269(1) :111-124
[134] 黄登仕.金融市场的标度理论[J].管理科学学报,2000,3(2) :27~33
[135] 宋学峰,顾世清.深沪证券市场股价波动的浑沌度及其调控方法[J].管理科学学报,2000,3(1) :53-57
[136] 周奕,陈收,汪寿阳.资本结构作用下市场投资组合轨迹的研究[J].管理科学学报,2000,3(3) :75~81
[137] Stanley H E,Amaral L A N,Canning D,etal.Econophysics:Can physicists contribute to the science of economics?[J].Physica A,1999,269(1) :156-169
[138] Stanley H E,Afanasyevr V,Amaral L A N,etal.Anomalous fluctuations in the dynamics of complex systems:from DNA and physiology to econophysics[J]. Physica A,1996,224(2) :302-321
[139] 黄小原,庄新田,张泉.股市波动的标度无关性算法及应用研究[J].管理科学学报,2001,4(6) :55~59
[140] Detrended Fluctuation Analysis.http://www.cbi.dongnocchi.it/glossary/ Detrended Fluctuation Analysis.html
[141] 魏宇.基于多标度分形理论的金融风险管理方法研究.西安交通大学博士研究生学位论文,2004:23～30
[142] 金林,赵俊和.混沌理论及其在经济周期理论中的应用[J].上海交通大学学报,1996,30(2) :77~82
[143] 刘舒,孟建.样本序列的可预测性研究[J].预测,1997,(2) :47~49
[144] Babloyantz A.Some remarks on nonlinear data analysis of physiological time series[M].Measures of Complexity and Chaos.Edited by N B A raham etal. plenum Press,1993
[145] Pawel K,Remigiusz T.Recurrence plots of neuronal spike trains[J].Bio_ logical Cybernetics.1993,68:527~534
[146] Eckmann J P,Kamphorst O R S.Recurrence plots of dynamical systems[J]. Euro_phys Lett.1987,4:973-977
[147] 向小东,郭耀煌.对基于递归图的时间序列可预测性的进一步研究[J].管理工程 学报,2003,17(2) :103-105
[1
[148] Farmer J D,Didorowich J J.predicting chaotic time series[J].phys Rev,Lett,1987,59:845-848
[149] Oja E.Principal Components,Minor Components,and linearneural networks [J],Neural Networks,1992:5(6) :927-935
[150] Oja E.The nonlinear PCA learning rule in independent component analysis [J].Neurocomputing,1997,17(1) :25-45
[151] 焦李成.神经网络的应用与实现[M].西安:西安电子科技大学出版社,1996
[152] 孙即祥.数字图像处理[M].石家庄:河北教育出版社,1993
[153] Karhunen,J.,Hyvarinen,A.,Vigario,R.,Hurri,J.& Oja,E.Applications of Neural Blind Separation to Signal and Image Processing.Proc.of 1997 International Conference on Acoustics,Speech,and Signal Processing (ICASSP-97) ,Munich,Germany,April 21-24,1997:131-134
[154] 郭晓静,吴小培,张道信等.基于独立分量分析的脑电消噪与特征提取[J].系统仿真学报,2003,15(2) :287~289
[155] Cardoso J F,Laheld B H.Equivariant adaptive source separation[J].IEEE Trans On Signal Processing,1996,44(12) :3017~3030
[156] Oja E,Yang Howard Hua,Amari S I.Adaptive on line learning algorithms for blind separation:Maximum entropy and minimum mutual information[J]. Neural Computation,1997,9(7) :1457-1482
[157] McKeown M J,Jung T P,Makeig S,etal.Spatially independent activity pa_ tterns in functional MRI data during the stroop color-naming task[J].In: Proceedings of the National Academy of Sciences,1998,95(6) :803-810
[158] Stone J V,Porrill J,Porter N R,etal.Spatiotemporal ICA of fMRI Data[J].In: Computational Neuroscience Report 202,IEEE International workshop on Biologically Motiviated Vision,2000
[159] Vigario R,Jousmaki V,Oja E,etal.Independent component analysis for identification of artifacts in magnetoencephalographic recordings[M],In Neural Information Processing Systems 10,(proc NIPS' 97) ,Tordan,Kearns and Solla,Eds,Cambridge,MA:MIT Press,1998:229-235
[1
[160] Vigario R.Extraction of ocular artifacts from EEG using independent component analysis[J].Electroenceph Clin Neurophysiol,1997,103(3) :395-404
[161] Vigario R,Sarela J,Oja E.Independent component analysis in wave decom_ position of auditor yevoked fields.In:Proc Int Conf on Artificial Neural Networks (ICANN'98) ,Skovde,Sweden,1998,287-292
[162] 01shausen B A,Field D J.Emergence of simple-cell receptive field pro_ perties by learning a sparse code for natural images[J].Nature,1996, 381 (6583) :607-609
[163] Torkkola K.Blind separation for audio signals-are we there yet?In:Proc. Int.Workshop on Independent Component Analysis and Signal Separation(ICA' 99) ,Aussois,France:1999,239-244
[164] Bell A J,Sejnowski T J.The' independent components' of natural scenes are edge filters.Vision Research,1997,37(23) :3327-3338
[165] Yuen P C,Lai J H.Face representation using independent component analysis [J].Pattern Recognition,2001,34(3) :545-553
[166] 毕贤,李通化,吴亮等.独立组分分析在红外光谱分析中的应用[J].高等学校化学学报,2004,25(6) :1023-1027
[167] 刘喜武,刘洪,李幼铭等.独立分量分析及其在地震信息处理中的应用初探[J].地球物理学进展,2003,18(1) :090-096
[168] 王泽,朱贻盛,李音等,独立分量分析在混沌信号分析中的应用[J].电子学报,2002,30(10) :1505-1507
[169] Jutten C,Herault J.Independent component analysis versus PCA.In:Pro_ ceeding of European Signal Processing Conf,1988:287-314
[170] Comon P.Independent component analysis--Anewconcept?[J].Signal Processing,1994,36(3) :287-314
[171] Jutten C,Herault J.Blind separation of sources,partⅠ:An adaptive Algo_ rithm based on neurom imetic architecture[J].Signal Processing,1991,24 (1) -1-10
[172] 同[150]
[173] Hyvarinen A.Survey on independent component analysis[J].Neural Computing Surveys,1999,2(4) :94-128
[174] Hyvarinen A.Fast and robust fixed-point algorithms for independent component analysis[J].IEEE Trans,on Neural Networks,1999,10(3) :626~634
[175] Hyvarinen A.independent Component Analysis:A Tutorial[EB/OL].http://cis.hut.fi/projects/ica/
[176] Giannakopoulos X,Karhunen J,Oja E.Experimental comparison of neural ICA algorithms.In:Proc Int Conf,On Artificial Neural Networks(ICANN'98) , Skovde,Sweden,1998:651-656
[177] 张贤达.盲信号分离[J].电子学报,2001(12A):1765-1771
[178] 叶守泽,夏军.水文系统识别原理与方法[M].北京:水利电力出版社,1989
[179] 夏军.现代水科学不确定性研究与进展(全国首届水文水资源与水环境中的不确定性研究新理论新方法学术讨论会论文集)[C].成都:成都科技大学出版社.1994
[180] 李致家,孔祥光.非线性水文系统的实时预报方法比较研究[J].水文,1997(1) :24～28
[181] Vapnik V N.Estimation of dependencies based on empirical data[M].Berlin: Springer Verlag,1982
[182] Vapnik V N.Thenature of statistical learning theory[M].New York:Spring Verlag,1995
[183] Cherkassky V,Mulier F.Learning from data:concepts,theory and methods[M]. New York John Viley & Sons,1997
[184] Cherkassky V,Muulier F.Learning from Data:Concepts,Theory and Methods [M].NY:Tohn Viley & Sons,1997
[185] Vapnik V N,Levin E,Le Cun Y.Measuring the VC dimension of a learning machine[J].Neural Computation,MIT Press,1994(6) :851-876
[186] 加肇祺.模式识别[M].北京:清华大学出版社.1988
[187] Vapnik V N,张学工译.统计学习理论的本质[M].北京:清华大学山版社,2000
[188] Zhang Ling.The Relationship Between Kernel Functions Based SVM and Three-layer Feedforward Neural Networks[J].Chinese J Computer,2002,25(7) :1-5
[189] Zhang Ling,Zhang Bo.Relationship Between Support Vector Set and Kernel Functions in SVM[J].J Comput Sci & Technol,2002,17(5) :549
[190] Ou T J,Lakshman T V,Wong L H.SRED:stabilized RED[A].Proc IEEE Infocom[C].New York USA:IEEE,1999:1346-1355
[191] Vapink V.The Nature of Statistical Learning Theory[M],New York:Springer Verlag,1999
[192] 陈永义,俞小鼎,高学浩等.处理非线性分类和回归问题的一种新方法(Ⅰ)--支持向量机方法简介[J].应用气象学报,2004,15(3) :345-354
[193] 李兵,蒋慰孙.混沌忧化方法及其应用[J].控制理论与应用,1997,14(4) :613～615
[194] 张彤,王宏伟,王子才.变尺度混沌忧化方法及其应用[J].控制与决策,1999,14(3) :285～288
[195] 冯国章,李佩成.论水文系统混沌特征的研究方向[J].西北农业大学学报.1997,25(4) :97～101
[196～198] 同[54-56]
[199] 刘德平.分形理论在水文过程形态特征分析中的应用[J].水利学报,1998,(2) :20～25
[200] 魏一鸣.洪水灾害研究的复杂性理论[J].自然杂志,21(3) :139～142
[201] Rundle J.Workshop Held on Natural Disasters.EOS,1994,13:103
[202] Barbera L P,Rosso R.On the Fractal Dimension of Stream Network[J].Water Resources Research,1989,25(4) :735-741
[203] Tanzhou Luo.Fractal Structure and Properties of Stream Network[J].Water Resources Research,1992,28(11) :2981-2988
[204] Mandelbrot B B.How long is the coast of Britain?.Statistical selfsimi-larity and fractional dimension.Science,1967,156(3775) :636-638
[205] 陈树群,钱沧海,冯智伟.台湾地区河川型态之碎形维度[J].中国台北:中国土木水利工程学刊,1995,7(1) :63~71
[206] Mandelbrot B B,Wallis J R.Som long run properties of geophysical records [J].Water Resources Research,1969,5(3) :321-340
[207] Mandelbrot B B,Van Ness J W.Fractional Brownian motion,fractional noise and application[J].Slam Rev,1968(10) :422-437
[208] Feder J.Fractals[M].New Yock:Plenum Press,1988:1-214
[209] 同[39]