基于混沌时间序列分析的测井曲线识别研究
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摘要
测井是用现代电子仪器,通过电缆将仪器送入井下,测量地层的电、声和放射性参数;测井相是使油层与其它层相区别的一套测井响应。测井相识别是正确认识油层沉积构造的根本途径。随着油田的加密开采,单靠人工来完成油层的测井相识别早已不能满足油田开发进度上的需要。采用计算机进行自动测井解释越来越受到人们的关注。
测井曲线是油层沉积相判别的主要依据。测井曲线识别属于经验性和领域知识要求很高的模式识别问题。本文围绕着测井时间序列的解释与识别这一核心任务,以实际工程背景为依托,应用混沌理论及混沌时间序列分析的理论与方法,开展了以下新的研究课题:
(1)测井时间序列的混沌检测
首先分析了测井时间序列产生混沌的机理,首次提出测井时间序列是一种混沌时间序列,并应用替代数据法证明了测井时间序列的确存在混沌。这一结论为混沌时间序列分析方法应用于测井曲线识别领域提供了前提条件。
(2)测井曲线的混沌特征提取
在第一部分研究结论的基础上,本文先后提取了测井曲线的两种混沌特征——关联维数和最大Lyapunov指数。在关联维数的计算中,发现不同油层组的测井曲线具有较明显的分维特征,并可以初步用于主力油层组的预测。在本课题研究中,提出一种改进的测井时间序列最大Lyapunov指数求取方法,该算法简单易行,且具有较好的计算精度。同时,油层组测井曲线的最大Lyapunov指数均大于零,也进一步证实了前一部分结论的正确性。
(3)油层测井曲线的平滑及特征提取
本文利用不对称高斯型函数的非线性最小二乘拟合对单峰曲线进行了平滑处理,并给出了一种针对测井曲线特点的简化平滑算法。同时利用曲线的模型参数直接作为特征值,对油层测井曲线的形状进行分类,结果令人满意。最后,文中还对不对称高斯型函数进行了改进,使之更加逼真地描述测井曲线的峰形态。
(4)基于高斯混合模型的油层测井相分类算法
Logging is measuring the parameters of earth layers in electronics, acoustics and radioactivity by sending the cables into the wells underground using modern electrical apparatus. Logfacies of an oil-layer is a set of logging response which can distinguish from other kinds of oil-layers. Logfacies recognition is a primary way to understand the sedimentary structures of oil layers correctly. As the development of oil field becomes larger and larger in scale, the manual recognizing operation cannot satisfy the need of the oil field of the development. The automatic interpretation of oil layers by computer becomes more and more interested.Well-logs are the main bases of discrimination of sedimentary facies of oil layers. Doing this task needs rich experiences, so well-log facies recognition is a special domain of pattern recognition that needs large amount of geological knowledge. The purpose of this thesis is to develop some novel methods and algorithms for solving the practical issues. Based on the chaotic time series analysis theories and methods, this paper carried out following main tasks:(1) Chaos identification of well-log time series. By analyzing the reasons of chaos formation in well-logs, it was presented for the first time that chaos exists in well-logs. And surrogate data method was used for proving that well-logs contain chaos indeed. The obtained conclusion provides a premise for the application of chaotic time series analysis in well-log facies recognition.(2) Chaotic feature extraction of well-logs. Based on the obtained conclusion of part 1, two different chaotic features of well-logs, correlation dimension and maximal Lyapunov exponents, were extracted. Calculation of the correlation dimensions shows that different oil layer groups have clearly different fractal dimension. These results can be used in predicting the main oil layer group in the early period. An improved method to estimate maximal Lyapunov exponents for well-logs was presented. This algorithm has many advantages such
as easy calculation and good precision. At the same time, experiment results show that all the oil layer groups' maximal Lyapunov exponents are larger than zero. It is testified again that the conclusion of part 1 is correct.(3) Smoothing and feature extraction of oil layer well-logs. In this paper, a type of asymmetric Gaussian function fitted by nonlinear least square method is used to data smoothing of oil layer well-logs. After studying the shapes of oil layer well-logs, a special algorithm suitable for these time series was presented. At the same time, asymmetric Gaussian model parameters can be used directly as feature values for the classification of well-log shapes. The recognition results are satisfactory. At last, an improved asymmetric Gaussian function was presented for better fitting for the shapes of well-logs of oil layer.(4) Well-log fades classification algorithm using Gaussian mixture models. Other than traditional well-log fades recognition, a new well-log classification approach was given. This method is based on reconstructing the chaotic attractors of the nonlinear dynamics in the phase spaces. The modeling of the different attractors was done using Gaussian mixture models. The algorithm only needs the numbers of mixtures, the well-logs samples of oil layers and their class labels as input during learning process. The experiment results for 4 kinds of main sandstones are satisfactory. This shows that the chaotic modeling is very promising for complex pattern recognition.It can be seen that this thesis enriches the application domains of chaotic time series analysis and provides new ways for well-log representation and recognition. The paper has strong engineering background, novel thinking and nice future.
测井曲线是油层沉积相判别的主要依据。测井曲线识别属于经验性和领域知识要求很高的模式识别问题。本文围绕着测井时间序列的解释与识别这一核心任务,以实际工程背景为依托,应用混沌理论及混沌时间序列分析的理论与方法,开展了以下新的研究课题:
(1)测井时间序列的混沌检测
首先分析了测井时间序列产生混沌的机理,首次提出测井时间序列是一种混沌时间序列,并应用替代数据法证明了测井时间序列的确存在混沌。这一结论为混沌时间序列分析方法应用于测井曲线识别领域提供了前提条件。
(2)测井曲线的混沌特征提取
在第一部分研究结论的基础上,本文先后提取了测井曲线的两种混沌特征——关联维数和最大Lyapunov指数。在关联维数的计算中,发现不同油层组的测井曲线具有较明显的分维特征,并可以初步用于主力油层组的预测。在本课题研究中,提出一种改进的测井时间序列最大Lyapunov指数求取方法,该算法简单易行,且具有较好的计算精度。同时,油层组测井曲线的最大Lyapunov指数均大于零,也进一步证实了前一部分结论的正确性。
(3)油层测井曲线的平滑及特征提取
本文利用不对称高斯型函数的非线性最小二乘拟合对单峰曲线进行了平滑处理,并给出了一种针对测井曲线特点的简化平滑算法。同时利用曲线的模型参数直接作为特征值,对油层测井曲线的形状进行分类,结果令人满意。最后,文中还对不对称高斯型函数进行了改进,使之更加逼真地描述测井曲线的峰形态。
(4)基于高斯混合模型的油层测井相分类算法
Logging is measuring the parameters of earth layers in electronics, acoustics and radioactivity by sending the cables into the wells underground using modern electrical apparatus. Logfacies of an oil-layer is a set of logging response which can distinguish from other kinds of oil-layers. Logfacies recognition is a primary way to understand the sedimentary structures of oil layers correctly. As the development of oil field becomes larger and larger in scale, the manual recognizing operation cannot satisfy the need of the oil field of the development. The automatic interpretation of oil layers by computer becomes more and more interested.Well-logs are the main bases of discrimination of sedimentary facies of oil layers. Doing this task needs rich experiences, so well-log facies recognition is a special domain of pattern recognition that needs large amount of geological knowledge. The purpose of this thesis is to develop some novel methods and algorithms for solving the practical issues. Based on the chaotic time series analysis theories and methods, this paper carried out following main tasks:(1) Chaos identification of well-log time series. By analyzing the reasons of chaos formation in well-logs, it was presented for the first time that chaos exists in well-logs. And surrogate data method was used for proving that well-logs contain chaos indeed. The obtained conclusion provides a premise for the application of chaotic time series analysis in well-log facies recognition.(2) Chaotic feature extraction of well-logs. Based on the obtained conclusion of part 1, two different chaotic features of well-logs, correlation dimension and maximal Lyapunov exponents, were extracted. Calculation of the correlation dimensions shows that different oil layer groups have clearly different fractal dimension. These results can be used in predicting the main oil layer group in the early period. An improved method to estimate maximal Lyapunov exponents for well-logs was presented. This algorithm has many advantages such
as easy calculation and good precision. At the same time, experiment results show that all the oil layer groups' maximal Lyapunov exponents are larger than zero. It is testified again that the conclusion of part 1 is correct.(3) Smoothing and feature extraction of oil layer well-logs. In this paper, a type of asymmetric Gaussian function fitted by nonlinear least square method is used to data smoothing of oil layer well-logs. After studying the shapes of oil layer well-logs, a special algorithm suitable for these time series was presented. At the same time, asymmetric Gaussian model parameters can be used directly as feature values for the classification of well-log shapes. The recognition results are satisfactory. At last, an improved asymmetric Gaussian function was presented for better fitting for the shapes of well-logs of oil layer.(4) Well-log fades classification algorithm using Gaussian mixture models. Other than traditional well-log fades recognition, a new well-log classification approach was given. This method is based on reconstructing the chaotic attractors of the nonlinear dynamics in the phase spaces. The modeling of the different attractors was done using Gaussian mixture models. The algorithm only needs the numbers of mixtures, the well-logs samples of oil layers and their class labels as input during learning process. The experiment results for 4 kinds of main sandstones are satisfactory. This shows that the chaotic modeling is very promising for complex pattern recognition.It can be seen that this thesis enriches the application domains of chaotic time series analysis and provides new ways for well-log representation and recognition. The paper has strong engineering background, novel thinking and nice future.
引文
[1] [美]迈克尔·埃克诺米迪斯,罗纳德·奥利格尼 著,刘振武,刁顺,张镇 译.石油的色彩-世界最大产业的历史、金钱和政治.北京:石油工业出版社.2003
[2] Herrmann F J, Lyons W J. Stratigraphy and lithology classification by singularity analysis.http://www.aseg.org.au/wa/meetings/June2000.htm
[3] Global Environmental Outlook 2003. United Nations Environment Program. Sep 2003. http://www.unep.org/unep/eia/geo2003/
[4] 曾文冲.测井地层分析与油气评价.北京:石油工业部勘探培训中心,1982
[5] 杨永国,韩宝平.地质时间序列的频谱分析方法及应用.煤田地质与勘探,1998,26(4):35-37页
[6] Casti J. Searching for certainty. New York: Morrow Press, 1990
[7] Lorenz E N. The essence of chaos. Washington: the University of Washington Press, 1993
[8] Li Tianyan, Yorke J. Period three implies chaos. American Mathematics Monthly. 1975, 82: 985-992P
[9] [美]C.格里博格J.A.约克 编,杨立 等译.混沌对科学和社会的冲击.长沙:湖南科学技术出版社,2001
[10] Mandelbrot B B. The fractal geometry of nature. San Francisco: Freeman Press, 1982
[11] [法]弗朗索瓦.吕尔萨 著,马金章 译.混沌.北京:科学出版社,2005
[12] 梁美灵,王则柯.童心与发现——混沌与均衡纵横谈.北京:生活·读书.新知 三联书店,1996
[13] 杨叔子,吴雅.时间序列分析的工程应用(上、下册).武汉:华中理工大学出版社,1992
[14] Duda R and Nart P. Pattern classification and scene analysis. New York: John Wiley and Sons Press, 1983
[15] Jain A, Duin R, Mao Jianchang. Statistical pattern recognition: a review. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2000, 22(1): 4-37P
[16] Pandit S M, Wu X M. Time series and system analysis with applications. New York: John Wiley and Sons Press, 1983
[17] Brockwell P J, Davis R A. Time series: Theory and methods(Second Edition).北京:高等教育出版社,施普格林出版社,2001
[18] 阮大成.国外时间序列应用研究最新动态.上海统计,2001,(12):27-29页
[19] 周汉明,吴雅,杨叔子.非线性时间序列分析的发展.动态分析与测试技术,1994,(1):13-24页
[20] 洪时中.非线性时间序列分析的最新进展及其在地球科学中的应用前景.地球科学进展.1999,14(6):559-565页
[21] Kumar A, Mulich S K. Attractor dimension, entropy and modeling of speech time series. Electron Letters. 1990, 26(21): 1790-1792P
[22] Haykin S, Li X B. Detection of signals in chaos. Proc IEEE. 1983(1):95-122P
[23] Leung H, Haykin S. Is there a radar cluster attractor. Application Physics Letters. 1990, 56(6): 593-596P
[24] Leung H, Lo T, Litva J. Angle-of-arrival estimation in multipath environment using chaos theory. Signal Processing. 1993, 31(1):57-68P
[25] Golden M P, Ydsfie B E. Small amplitude chaos and ergodicity in adaptive control. Automatica. 1992, 28(1):11-25P
[26] Gonzalez G A, Troparevsky M I, Dattellis C E. A remark on chaotic behavior in adaptive control systems. IEEE Trans. on Automatic Control. 1994, 39(10): 2145-2148P
[27] Vakakis A F, Burdick J W. Chaotic motions of a hopping robot. Proc of the IEEE Conf on Robot and Automat. Los Alamitos, California, 1990: 1464-1469P
[28] Closkey R T, Burdick J W. An analytical study of simple hopping robots with vertical and forward motion. Proc of the IEEE Conf on Robot and Automat. Los Alamitos, California, 1991: 1392-1397P
[29] Rudas I J. Robustness analysis of a paradigm for non-linear robot controllers based on soft computing techniques. Proceedings of Industdcal Electronics Conference, IEEE. Los Alamitos, California, 1994: 1663-1638P
[30] Thuilot B, Goswami A Espiau B, et al. Bifurcation and chaos in a simple passive bipedal gait. Proc of the IEEE Conf on Robot and Automat. Washington DC, 1997: 792-798P
[31] Kantz H, Schreiber T. Nonlinear Time Series Analysis. Cambridge: Cambridge University press, 1997
[32] 吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002
[33] 梁志珊,王丽敏.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报.1998,18(5):368-371页
[34] Hesieh D. Testing for nonlinear dependence in daily foreign exchange rates. Journal of Business. 1989, 62(3): 339-359P
[35] Kodres L E, Papell D H. Nonlinear dynamics in foreign exchange futures market. Working Paper, University of Michigan, 1991
[36] Philipatos G C, Pilamu E, Mailiads A G. Chaotic behavior in stock price of European stock markets: a comparative analysis of major economic regions. Working paper, University of Tenessee, 1993
[37] Driebe D J. Fully chaotic maps and broken time symmetry. Netherland: Kluwer Academic Publishers, 1999
[38] Zheng J, Yu Z G. Correlation dimension and Kolmogorov entropy of DNA sequences.湘潭大学自然科学学报.2000,22(1):115-119页
[39] 文政,雍世和,王文中.应用测井资料定量识别沉积微相.沉积学报. 1996,14(1):40-46页
[40] 徐开志,唐勇,王海东,赵铮亚.用计算机实现判别沉积微相方法.新疆石油地质.2000,20(2):35-39页
[41] Yong S H, Chen G H. Automatic Logging Facies Analyzing. ACTA Petrolei Sinica. 1990,11(4): 43-49P
[42] 王仁铎.利用测井曲线形态特征定量判别沉积相.中国地质大学学报.1991,16(3):303-309页
[43] 谢丛娇,侯俊胜.吉林油区大老爷府低阻油层成因及测井解释.吉林地质.2002,21(1-2):50-55页
[44] [法]O·塞拉 著,谭廷栋 等译.测井解释基础与数据采集.北京:石油工业出版社,1992
[45] 雍世和.测井资料数字处理与综合解释.北京:石油工业出版社,1982
[46] 丁次乾.矿场地球物理.北京:石油大学出版社,1992
[47] 隋军,吕晓光,赵翰卿,许运新.大庆油田河流.三角洲相储层研究.北京:石油大学出版社,2000
[48] 刘咏梅.油层沉积相模式识别与绘图系统.哈尔滨:哈尔滨工程大学硕士学位论文,1999
[49] 刘咏梅,钱真,宋克欧.一种基于多级神经网络分类器的沉积相识别方法.应用科技.2003,30(3):39-41页
[50] 钱真,刘咏梅.基于小波变换的测井曲线识别系统.应用科技.2001,28(9):42-44页
[51] 杨成,李雪耀,申丽然,刘咏梅.沃尔什变换在油田测井相识别中的应用研究.哈尔滨工程大学学报.2001,22(6):322-326页
[52] 阎辉,张学工,李衍达.应用SVM方法进行沉积微相识别.物探化探计算技术.2000,22(2):158-164页
[53] Vibe K, Vesin J M. On chaos detection methods. International Journal of Bifurcation and chaos. 1996, 6(3): 529-543P
[54] 关新平,范正平,陈彩莲,华长春.混沌控制及其在保密通信中的应用.北京:国防工业出版社,2002
[55] Small M, Judd K. Detecting nonlinearity in experimental data. International Journal of Bifurcation and chaos. 1998, 8(6): 1231-1244P
[56] Wolf A, Swift J B, Swinney H L, Vastano J A. Determining Lyapunov exponents from a time series. Physica D. 1985, 16(9): 285-317P
[57] Grassberger P, Proeaecia I. Measuring the strangeness of strange attractors. Physica D. 1983, 9: 189-208P
[58] Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer J D. Testing for nonliearity in time series: the method of surrogate data. Physica D, 1992, 58: 77-94P
[59] Sivakumar B. Chaos theory in hydrology: important issues and interpretation. Journal of Hydrology. 2000, 227: 1-20P
[60] Elshorbagy A, Simonovie S, Panu U. Estimation of missing streamflow data using principles of chaos theory. Journal of Hydropology. 2002, 255: 123-133P
[61] 马军海,陈予恕等.动力系统实测数据的非线性混沌模型重构.应用数学和力学.1999,20(11):481-488页
[62] 朱学峰,顾世清.深沪证券市场股价波动的混沌度及其调控方法.管理科学学报.2000,3(1):53-56页
[63] Fell J, Mann K, Roschke J, Gopinathan M S. Nonlinear analysis of continuous ECG during sleep Ⅰ-reconstruction. Biological Cybernetics. 2000, 82: 447-483P
[64] Fell J, Mann K, Roschke J, Gopinathan M S. Nonlinear analysis of continuous ECG during sleep Ⅱ-dynamical measures. Biological Cybernetics. 2000, 82: 485-491P
[65] Schreiber T. Interdisciplinary application of nonlinear time series methods. Physics Reports, 1999, 308: 1-64P
[66] 雷敏,王志中.非线性时间序列分析的替代数据检验方法研究.电子信息学报.2001,23(3):248～254P
[67] Schreiber T, Schmitz A. Improved surrogate data for nonlinearity tests. Physics Review Letters, 1996, 77(4): 635-638P
[68] Prichard D, Theiler J. Generating surrogate data for time series with several simultaneously measured variable. Physical Review Letters, 1994, 73(7): 951-954P
[69] Rombouts S, Keunen R. Investigation of nonlinear structure in multichannel EEG. Physical Letters, A. 1995, 202: 352-358P
[70] 章新华.基于智能信息处理理论的水下目标识别研究.浙江大学博士学位论文,1996
[71] 毕思文.地球系统科学导论.北京:科学出版社,2003
[72] 刘式达,刘式适.地球物理中的混沌.长春:东北师范大学出版社,2000
[73] Takens F. Determining strange attractors in turbulence. Lecture notes in Math, 1981, 898: 361-381P
[74] Packard N H, Crutehfield J P, Farmer J D and Shaw R S. Geometry from a time series. Physical Review Letters. 1980, 45:712-716P
[75] 谢红梅 等.非线性时间序列分析的关键技术及其应用研究.计算机工程与应用.2002,14:79-81页
[76] Cao Liangyue. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D, 1997, 110: 43-50P
[77] 修春波,刘向东 等.相空间重构延迟时间与嵌入维数的选择.北京理工大学学报.2003,23(2):219-224页
[78] Cartwright J H E. Nonlinear stiffness, Lyapunov exponents, and attractor dimension. Physics Letters A. 1999, 264: 298-302P
[79] 蔡聪波.混沌系统最大Lyapunov指数的计算及其在脑电数据分析中的应用.厦门:厦门大学硕士学位论文,2001
[80] Tang Tong-kui, et al. Process Data Compression: A Review. Comput and Applied Chem. 2000, 17(3): 193-197P
[81] Mah R S H, et al. Process Trending with Piecewise Linear Smoothing. Comput Chem Engng. 1995, 19(2):129-137P
[82] Jonsson P and Eklundh L. Seasonality extraction by function fitting to time-series of satellite sensor data. IEEE Trans. on Geoscience and Remote Sensing, 2002, 40(8): 1824-1832P
[83] 梅红,张厚福,孙红军,钟兴水.神经网络技术在测井相分析及水淹层判别中的应用.石油大学学报(自然科学版).1997,21(3):24-28页
[84] Dennis J E, Gay D M, and Welsch R E. A adaptive nonlinear least-squares algorithm. ACM Trans. Math. Soft. 1981, 7: 348-368P
[85] Dennis J E, Gay D M, and Welsch R E. Algorithm 573, NL2SOL: an adaptive nonlinear least-squares algorithm. ACM Trans. Math. Soft. 1981, 17: 369-383P
[86] Ansari N and Delp E J. Partial Shape Recognition: a Landmark-based Approach. IEEE Trans. on Pattern Analysis and Machine Intelligence. 1990, 12(5): 470-483P
[87] Morimoto T, Takeuchi T, Miyata H, Hashimoto Y. Pattern recognition of fruit shape based on the concept of chaos and neural networks. Computers and electronics in agriculture. 2000, 26: 171-186P
[88] Ataei M, B.Lohmarm, Khaki S A, Lucas C. Model based method for estimating an attractor dimension from uni/multivariate chaotic time series with application to Bremen-climatic dynamics. Chaos, Solitons. and Fractals. 2004, 19: 1131-1139P
[89] Dempster A P, Laird N M, Rubin D B.Maximum-likelihood from incomplete data via the EM algorithm. Journal of Royal Statistical Society B. 1977, 39: 1-38P
[90] Ueda N, Nakano R. Deterministic annealing EM algorithm. Neural Networks. 1998, 11 (2): 271-282P
[91] Celeux G, Chretien S, Forbes F, Mkhadfi A. A component-wise EM algorithm for mixtures. Technical report 3746, INRIA Rhone-Alpes, Frances, 1999
[92] Ueda N, Nakano R, Ghahramani Z, and Hinton G E. SMEM algorithm for mixture models. Neural Computation. 2000, 12:2109-2128P
[93] Figueiredo M A T, Jain A K. Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2002, 24(3): 381-396P
[94] Zhang Zhihua, Chen Chibiao, Sun Jian and Chan K L. EM algorithms for Learning Gaussian Mixture Models with Split-and-Merge Operation. Pattern Recognition. 2003, 36(9): 1973-1983P
[95] Verbeek J J, Vlassis N, KrAose B. Efficient Greedy Learning of Gaussian Mixture Models. Neural Computation, 2003, 5(2): 469-485P
[96] Young-Sup Hwang, Sung-Yang Bang. Recognition of unconstrained handwritten numerals by a radical basis function neural network classifier. Pattern Recognition Letters. 1997, 18: 657-664P
[97] Fuh C C, Tsai H H. Control of discrete-time chaotic systems via feedback linearization. Chaos, Solutions and Fractals. 2002, 13(2): 285-294P
[98] Yang D K, Chen C L, Yau H T. Control of chaos in Lorenz system. Chaos, Solutions and Fractals. 2002, 13(4): 767-780P
[99] Shahverdiev E M, Sivaprakasam S, Shore K A. Lag synchronization in time-delayed systems. Physica Letters A. 2002, 292(6): 320-327P
[100] Shu-Kay Ng, McLachlan G. On some variants of the EM Algorithm for the fitting of finite mixture models. Austrian Journal of Statistics. 2003, 32(1): 143-161P
[101] Lindgren A, Johnson M, Povinell R. Speech recognition using reconstructed phase space features. Proc. IEEE ICASSP'03. 2003: I 60-63P
[102] Povinell R, Johnson M, Lindgren A, Ye J. Time series classification using Gaussian mixture models of reconstructed phase spaces. IEEE Trans on Knowledge and Data Engineering. 2004, 16(6): 779-783P
[103] Pitsikalis V and Maragos P. Speech analysis and feature extraction using chaotic models. Proc. IEEE ICASSP'02. 2002: 533-536P
[104] Gray R. Statistical Signal Processing. www.-isl.stanford.edu/～gray/
[105] Dagum E, Luati A. A Linear Transformation and its Properties with Special Applications in Time Series Filtering. Linear Algebra and its applications. 2004, 388: 107-117P
[106] Ran Q Q, Li S L, Gu X Y. Identification of sedimentary microfacies with neural network. ACTA Sedimentologica Siniea. 1996, 14, supp: 186-191P
[107] 许少华,陈可为,梁久祯,郑生民.基于遗传-BP神经网络的沉积微相自动识别.大庆石油学院学报.2001,25(1):39-43页
[108] 王洪元,史国栋.人工神经网络技术及其应用.北京:中国石化出版社,2002
[109] Yang Y W, Liu G H, Zhang Z P. Stock Market Trend Prediction Based on Neural Networks. Multiresolution analysis and dynamical reconstruction. IEEE/IAFE Conference on Computational Intelligence for Financial Engineering. 2000, March 26-28:155-157P
[110] Jiao L C, Pan J, Fang Y W. Multiwavelet neural networks and its approximation propertise. IEEE Trans on Neural Network. 2001, 12(5): 1060-1066P
[111] 刘志刚,王晓茹等.小波变换、神经网络和小波网络的函数逼近能力分析与比较.电力系统自动化.2002,26(20):39-43页
[112] 吴佑寿,丁晓青.树分类器性能析.电子学报.1991,19(4):1-7页
[2] Herrmann F J, Lyons W J. Stratigraphy and lithology classification by singularity analysis.http://www.aseg.org.au/wa/meetings/June2000.htm
[3] Global Environmental Outlook 2003. United Nations Environment Program. Sep 2003. http://www.unep.org/unep/eia/geo2003/
[4] 曾文冲.测井地层分析与油气评价.北京:石油工业部勘探培训中心,1982
[5] 杨永国,韩宝平.地质时间序列的频谱分析方法及应用.煤田地质与勘探,1998,26(4):35-37页
[6] Casti J. Searching for certainty. New York: Morrow Press, 1990
[7] Lorenz E N. The essence of chaos. Washington: the University of Washington Press, 1993
[8] Li Tianyan, Yorke J. Period three implies chaos. American Mathematics Monthly. 1975, 82: 985-992P
[9] [美]C.格里博格J.A.约克 编,杨立 等译.混沌对科学和社会的冲击.长沙:湖南科学技术出版社,2001
[10] Mandelbrot B B. The fractal geometry of nature. San Francisco: Freeman Press, 1982
[11] [法]弗朗索瓦.吕尔萨 著,马金章 译.混沌.北京:科学出版社,2005
[12] 梁美灵,王则柯.童心与发现——混沌与均衡纵横谈.北京:生活·读书.新知 三联书店,1996
[13] 杨叔子,吴雅.时间序列分析的工程应用(上、下册).武汉:华中理工大学出版社,1992
[14] Duda R and Nart P. Pattern classification and scene analysis. New York: John Wiley and Sons Press, 1983
[15] Jain A, Duin R, Mao Jianchang. Statistical pattern recognition: a review. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2000, 22(1): 4-37P
[16] Pandit S M, Wu X M. Time series and system analysis with applications. New York: John Wiley and Sons Press, 1983
[17] Brockwell P J, Davis R A. Time series: Theory and methods(Second Edition).北京:高等教育出版社,施普格林出版社,2001
[18] 阮大成.国外时间序列应用研究最新动态.上海统计,2001,(12):27-29页
[19] 周汉明,吴雅,杨叔子.非线性时间序列分析的发展.动态分析与测试技术,1994,(1):13-24页
[20] 洪时中.非线性时间序列分析的最新进展及其在地球科学中的应用前景.地球科学进展.1999,14(6):559-565页
[21] Kumar A, Mulich S K. Attractor dimension, entropy and modeling of speech time series. Electron Letters. 1990, 26(21): 1790-1792P
[22] Haykin S, Li X B. Detection of signals in chaos. Proc IEEE. 1983(1):95-122P
[23] Leung H, Haykin S. Is there a radar cluster attractor. Application Physics Letters. 1990, 56(6): 593-596P
[24] Leung H, Lo T, Litva J. Angle-of-arrival estimation in multipath environment using chaos theory. Signal Processing. 1993, 31(1):57-68P
[25] Golden M P, Ydsfie B E. Small amplitude chaos and ergodicity in adaptive control. Automatica. 1992, 28(1):11-25P
[26] Gonzalez G A, Troparevsky M I, Dattellis C E. A remark on chaotic behavior in adaptive control systems. IEEE Trans. on Automatic Control. 1994, 39(10): 2145-2148P
[27] Vakakis A F, Burdick J W. Chaotic motions of a hopping robot. Proc of the IEEE Conf on Robot and Automat. Los Alamitos, California, 1990: 1464-1469P
[28] Closkey R T, Burdick J W. An analytical study of simple hopping robots with vertical and forward motion. Proc of the IEEE Conf on Robot and Automat. Los Alamitos, California, 1991: 1392-1397P
[29] Rudas I J. Robustness analysis of a paradigm for non-linear robot controllers based on soft computing techniques. Proceedings of Industdcal Electronics Conference, IEEE. Los Alamitos, California, 1994: 1663-1638P
[30] Thuilot B, Goswami A Espiau B, et al. Bifurcation and chaos in a simple passive bipedal gait. Proc of the IEEE Conf on Robot and Automat. Washington DC, 1997: 792-798P
[31] Kantz H, Schreiber T. Nonlinear Time Series Analysis. Cambridge: Cambridge University press, 1997
[32] 吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002
[33] 梁志珊,王丽敏.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报.1998,18(5):368-371页
[34] Hesieh D. Testing for nonlinear dependence in daily foreign exchange rates. Journal of Business. 1989, 62(3): 339-359P
[35] Kodres L E, Papell D H. Nonlinear dynamics in foreign exchange futures market. Working Paper, University of Michigan, 1991
[36] Philipatos G C, Pilamu E, Mailiads A G. Chaotic behavior in stock price of European stock markets: a comparative analysis of major economic regions. Working paper, University of Tenessee, 1993
[37] Driebe D J. Fully chaotic maps and broken time symmetry. Netherland: Kluwer Academic Publishers, 1999
[38] Zheng J, Yu Z G. Correlation dimension and Kolmogorov entropy of DNA sequences.湘潭大学自然科学学报.2000,22(1):115-119页
[39] 文政,雍世和,王文中.应用测井资料定量识别沉积微相.沉积学报. 1996,14(1):40-46页
[40] 徐开志,唐勇,王海东,赵铮亚.用计算机实现判别沉积微相方法.新疆石油地质.2000,20(2):35-39页
[41] Yong S H, Chen G H. Automatic Logging Facies Analyzing. ACTA Petrolei Sinica. 1990,11(4): 43-49P
[42] 王仁铎.利用测井曲线形态特征定量判别沉积相.中国地质大学学报.1991,16(3):303-309页
[43] 谢丛娇,侯俊胜.吉林油区大老爷府低阻油层成因及测井解释.吉林地质.2002,21(1-2):50-55页
[44] [法]O·塞拉 著,谭廷栋 等译.测井解释基础与数据采集.北京:石油工业出版社,1992
[45] 雍世和.测井资料数字处理与综合解释.北京:石油工业出版社,1982
[46] 丁次乾.矿场地球物理.北京:石油大学出版社,1992
[47] 隋军,吕晓光,赵翰卿,许运新.大庆油田河流.三角洲相储层研究.北京:石油大学出版社,2000
[48] 刘咏梅.油层沉积相模式识别与绘图系统.哈尔滨:哈尔滨工程大学硕士学位论文,1999
[49] 刘咏梅,钱真,宋克欧.一种基于多级神经网络分类器的沉积相识别方法.应用科技.2003,30(3):39-41页
[50] 钱真,刘咏梅.基于小波变换的测井曲线识别系统.应用科技.2001,28(9):42-44页
[51] 杨成,李雪耀,申丽然,刘咏梅.沃尔什变换在油田测井相识别中的应用研究.哈尔滨工程大学学报.2001,22(6):322-326页
[52] 阎辉,张学工,李衍达.应用SVM方法进行沉积微相识别.物探化探计算技术.2000,22(2):158-164页
[53] Vibe K, Vesin J M. On chaos detection methods. International Journal of Bifurcation and chaos. 1996, 6(3): 529-543P
[54] 关新平,范正平,陈彩莲,华长春.混沌控制及其在保密通信中的应用.北京:国防工业出版社,2002
[55] Small M, Judd K. Detecting nonlinearity in experimental data. International Journal of Bifurcation and chaos. 1998, 8(6): 1231-1244P
[56] Wolf A, Swift J B, Swinney H L, Vastano J A. Determining Lyapunov exponents from a time series. Physica D. 1985, 16(9): 285-317P
[57] Grassberger P, Proeaecia I. Measuring the strangeness of strange attractors. Physica D. 1983, 9: 189-208P
[58] Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer J D. Testing for nonliearity in time series: the method of surrogate data. Physica D, 1992, 58: 77-94P
[59] Sivakumar B. Chaos theory in hydrology: important issues and interpretation. Journal of Hydrology. 2000, 227: 1-20P
[60] Elshorbagy A, Simonovie S, Panu U. Estimation of missing streamflow data using principles of chaos theory. Journal of Hydropology. 2002, 255: 123-133P
[61] 马军海,陈予恕等.动力系统实测数据的非线性混沌模型重构.应用数学和力学.1999,20(11):481-488页
[62] 朱学峰,顾世清.深沪证券市场股价波动的混沌度及其调控方法.管理科学学报.2000,3(1):53-56页
[63] Fell J, Mann K, Roschke J, Gopinathan M S. Nonlinear analysis of continuous ECG during sleep Ⅰ-reconstruction. Biological Cybernetics. 2000, 82: 447-483P
[64] Fell J, Mann K, Roschke J, Gopinathan M S. Nonlinear analysis of continuous ECG during sleep Ⅱ-dynamical measures. Biological Cybernetics. 2000, 82: 485-491P
[65] Schreiber T. Interdisciplinary application of nonlinear time series methods. Physics Reports, 1999, 308: 1-64P
[66] 雷敏,王志中.非线性时间序列分析的替代数据检验方法研究.电子信息学报.2001,23(3):248～254P
[67] Schreiber T, Schmitz A. Improved surrogate data for nonlinearity tests. Physics Review Letters, 1996, 77(4): 635-638P
[68] Prichard D, Theiler J. Generating surrogate data for time series with several simultaneously measured variable. Physical Review Letters, 1994, 73(7): 951-954P
[69] Rombouts S, Keunen R. Investigation of nonlinear structure in multichannel EEG. Physical Letters, A. 1995, 202: 352-358P
[70] 章新华.基于智能信息处理理论的水下目标识别研究.浙江大学博士学位论文,1996
[71] 毕思文.地球系统科学导论.北京:科学出版社,2003
[72] 刘式达,刘式适.地球物理中的混沌.长春:东北师范大学出版社,2000
[73] Takens F. Determining strange attractors in turbulence. Lecture notes in Math, 1981, 898: 361-381P
[74] Packard N H, Crutehfield J P, Farmer J D and Shaw R S. Geometry from a time series. Physical Review Letters. 1980, 45:712-716P
[75] 谢红梅 等.非线性时间序列分析的关键技术及其应用研究.计算机工程与应用.2002,14:79-81页
[76] Cao Liangyue. Practical method for determining the minimum embedding dimension of a scalar time series. Physica D, 1997, 110: 43-50P
[77] 修春波,刘向东 等.相空间重构延迟时间与嵌入维数的选择.北京理工大学学报.2003,23(2):219-224页
[78] Cartwright J H E. Nonlinear stiffness, Lyapunov exponents, and attractor dimension. Physics Letters A. 1999, 264: 298-302P
[79] 蔡聪波.混沌系统最大Lyapunov指数的计算及其在脑电数据分析中的应用.厦门:厦门大学硕士学位论文,2001
[80] Tang Tong-kui, et al. Process Data Compression: A Review. Comput and Applied Chem. 2000, 17(3): 193-197P
[81] Mah R S H, et al. Process Trending with Piecewise Linear Smoothing. Comput Chem Engng. 1995, 19(2):129-137P
[82] Jonsson P and Eklundh L. Seasonality extraction by function fitting to time-series of satellite sensor data. IEEE Trans. on Geoscience and Remote Sensing, 2002, 40(8): 1824-1832P
[83] 梅红,张厚福,孙红军,钟兴水.神经网络技术在测井相分析及水淹层判别中的应用.石油大学学报(自然科学版).1997,21(3):24-28页
[84] Dennis J E, Gay D M, and Welsch R E. A adaptive nonlinear least-squares algorithm. ACM Trans. Math. Soft. 1981, 7: 348-368P
[85] Dennis J E, Gay D M, and Welsch R E. Algorithm 573, NL2SOL: an adaptive nonlinear least-squares algorithm. ACM Trans. Math. Soft. 1981, 17: 369-383P
[86] Ansari N and Delp E J. Partial Shape Recognition: a Landmark-based Approach. IEEE Trans. on Pattern Analysis and Machine Intelligence. 1990, 12(5): 470-483P
[87] Morimoto T, Takeuchi T, Miyata H, Hashimoto Y. Pattern recognition of fruit shape based on the concept of chaos and neural networks. Computers and electronics in agriculture. 2000, 26: 171-186P
[88] Ataei M, B.Lohmarm, Khaki S A, Lucas C. Model based method for estimating an attractor dimension from uni/multivariate chaotic time series with application to Bremen-climatic dynamics. Chaos, Solitons. and Fractals. 2004, 19: 1131-1139P
[89] Dempster A P, Laird N M, Rubin D B.Maximum-likelihood from incomplete data via the EM algorithm. Journal of Royal Statistical Society B. 1977, 39: 1-38P
[90] Ueda N, Nakano R. Deterministic annealing EM algorithm. Neural Networks. 1998, 11 (2): 271-282P
[91] Celeux G, Chretien S, Forbes F, Mkhadfi A. A component-wise EM algorithm for mixtures. Technical report 3746, INRIA Rhone-Alpes, Frances, 1999
[92] Ueda N, Nakano R, Ghahramani Z, and Hinton G E. SMEM algorithm for mixture models. Neural Computation. 2000, 12:2109-2128P
[93] Figueiredo M A T, Jain A K. Unsupervised learning of finite mixture models. IEEE Transactions on Pattern Analysis and Machine Intelligence. 2002, 24(3): 381-396P
[94] Zhang Zhihua, Chen Chibiao, Sun Jian and Chan K L. EM algorithms for Learning Gaussian Mixture Models with Split-and-Merge Operation. Pattern Recognition. 2003, 36(9): 1973-1983P
[95] Verbeek J J, Vlassis N, KrAose B. Efficient Greedy Learning of Gaussian Mixture Models. Neural Computation, 2003, 5(2): 469-485P
[96] Young-Sup Hwang, Sung-Yang Bang. Recognition of unconstrained handwritten numerals by a radical basis function neural network classifier. Pattern Recognition Letters. 1997, 18: 657-664P
[97] Fuh C C, Tsai H H. Control of discrete-time chaotic systems via feedback linearization. Chaos, Solutions and Fractals. 2002, 13(2): 285-294P
[98] Yang D K, Chen C L, Yau H T. Control of chaos in Lorenz system. Chaos, Solutions and Fractals. 2002, 13(4): 767-780P
[99] Shahverdiev E M, Sivaprakasam S, Shore K A. Lag synchronization in time-delayed systems. Physica Letters A. 2002, 292(6): 320-327P
[100] Shu-Kay Ng, McLachlan G. On some variants of the EM Algorithm for the fitting of finite mixture models. Austrian Journal of Statistics. 2003, 32(1): 143-161P
[101] Lindgren A, Johnson M, Povinell R. Speech recognition using reconstructed phase space features. Proc. IEEE ICASSP'03. 2003: I 60-63P
[102] Povinell R, Johnson M, Lindgren A, Ye J. Time series classification using Gaussian mixture models of reconstructed phase spaces. IEEE Trans on Knowledge and Data Engineering. 2004, 16(6): 779-783P
[103] Pitsikalis V and Maragos P. Speech analysis and feature extraction using chaotic models. Proc. IEEE ICASSP'02. 2002: 533-536P
[104] Gray R. Statistical Signal Processing. www.-isl.stanford.edu/～gray/
[105] Dagum E, Luati A. A Linear Transformation and its Properties with Special Applications in Time Series Filtering. Linear Algebra and its applications. 2004, 388: 107-117P
[106] Ran Q Q, Li S L, Gu X Y. Identification of sedimentary microfacies with neural network. ACTA Sedimentologica Siniea. 1996, 14, supp: 186-191P
[107] 许少华,陈可为,梁久祯,郑生民.基于遗传-BP神经网络的沉积微相自动识别.大庆石油学院学报.2001,25(1):39-43页
[108] 王洪元,史国栋.人工神经网络技术及其应用.北京:中国石化出版社,2002
[109] Yang Y W, Liu G H, Zhang Z P. Stock Market Trend Prediction Based on Neural Networks. Multiresolution analysis and dynamical reconstruction. IEEE/IAFE Conference on Computational Intelligence for Financial Engineering. 2000, March 26-28:155-157P
[110] Jiao L C, Pan J, Fang Y W. Multiwavelet neural networks and its approximation propertise. IEEE Trans on Neural Network. 2001, 12(5): 1060-1066P
[111] 刘志刚,王晓茹等.小波变换、神经网络和小波网络的函数逼近能力分析与比较.电力系统自动化.2002,26(20):39-43页
[112] 吴佑寿,丁晓青.树分类器性能析.电子学报.1991,19(4):1-7页