基于智能计算技术的时间序列分割及预测研究
|
摘要
径流、降水、温度等水文气象时间序列是用于研究与地球相关现象的基本数据之一自然因素与人类活动引起环境的渐进性与颠覆性改变会导致水文气象时间序列的渐进变化或跳跃变化。水文气象时间序列的分割与预测研究有助于理解自然因素或人类活动引起的人类生存环境的改变。由于在研究与实践中的重要性,对径流、降水、温度等水文气象记录的分割与预测问题已经受到广泛关注。水文气象时间序列的分割与预测问题已成为水文气象科学研究的重要课题。新兴的智能计算技术在计算效率上具有十分显著的优越性,并已广泛应用于水文气象时间序列的分割与预测研究。本文采用智能计算技术对水文气象时间序列进行分割与预测,主要研究内容包括三个部分：
(1)提出用于自动模糊分割一元与多元水文气象时间序列的改进的Gath-Geva聚类算法。该算法把时间序列分割问题看成是Gath-Geva聚类,采用最小信息长度准则作为分割阶数的选择标准。改进的Gath-Geva聚类算法具有以下优点：首先,具有非监督特性,可以自动确定最优的分割阶数；其次,在经典Gath-Geva聚类中采用分量形式的期望最大化算法以避免经典的期望最大化算法中对初值敏感及需要避免收敛到参数空间的边界等缺点；另外.通过把分割阶数选择与模型参数估计过程紧密结合,可以提高算法的稳定性。
(2)提出一种用于自动模糊分割多元时间序列的竞争模糊聚类算法。该算法基于新的竞争机制,能够自动确定聚类数目并有效的选择“分裂”或“合并”操作。而且该算法对聚类数目与模型参数不敏感。人工数据实验表明该算法能够检测出多元时间序列的概率特性的改变(均值改变、方差改变与变量相关结构的改变)。
(3)注意到用于水文气象时间序列预测的神经网络结构通常是静态的,而静态神经网络无法有效反映系统动态的变化。本文利用序贯学习的径向基函数神经网络对水文气象时间序列进行精确实时预测。该预测模型采用滑动数据窗口作为动态观测器来调整网络结构和参数以适应水文气象时间序列的动态变化。
采用这三个算法对人工和水文气象时间序列进行分割与预测仿真实验,结果验证了这三个算法对于时间序列分割与预测的有效性。
Hydrometeorological time series such as streamflow, precipitation and temperature are among the basic data used to study earth-related phenomena. Evolutionary and disruptive changes in the environment caused by natural factors and human activities result in trends or jumps in hydrometeorological time series. Segmentation and prediction for hydrometeorological time series help men understand natural factors or human-induced changes in human living environment. Due to the importance in research and practice, segmentation and prediction of hydrometeorological records such as streamflow, precipitation and temperature have been received extensive attention. Segmentation and prediction for hydrometeorological time series have always been important topics in hydrometeorological sciences. The emerging intelligent computing techniques have shown their power in computational efficiency, and have been widely applied in segmentation and prediction of hydrometeorological time series. In this paper, intelligent computing techniques are conducted to segmentation and prediction of hydrometeorological time series. The main research contents of this paper include three parts:
Firstly, an improved Gath-Geva clustering algorithm is proposed for automatic fuzzy segmentation of univariate and multivariate hydrometeorological time series. The algorithm considers time series segmentation problem as Gath-Geva clustering with the minimum message length criterion as segmentation order selection criterion. One characteristic of the improved Gath-Geva clustering algorithm is its unsupervised nature which can automatically determine the optimal segmentation order. Another characteristic is the application of the modified component-wise expectation maximization algorithm in Gath-Geva clustering which can avoid the drawbacks of the classical expectation maximization algorithm:the sensitivity to initialization and the need to avoid the boundary of the parameter space. The other characteristic is the improvement of numerical stability by integrating segmentation order selection into model parameter estimation procedure.
Secondly, a competitive fuzzy clustering algorithm is presented for automatic fuzzy segmentation of multivariate time series. The proposed algorithm is capable of automatically choosing the clustering number and selecting the "split" or "merge" operations efficiently based on the new competitive mechanism. It is insensitive to the initial configuration of the cluster component number and model parameters. Experiments on synthetic data show that the proposed algorithm is able to handle time-varying characteristics of multivariate time series:changes in the mean:changes in the variance; and changes in the correlation structure among the variables.
Thirdly, noticed that the structures of the commonly implemented neural networks for the prediction of hydrometeorological time series are static, while the static neural network cannot represent the changes of system dynamics efficiently. In this paper, the application of a sequential learning radial basis function is presented for accurate real-time prediction of hydrometeorological time series. The prediction model employs a sliding data window as dynamical observer, and tunes the structure and parameters of radial basis function neural network to adapt to the dynamical changes of hydrometeorological time series.
The three algorithms have been experimentally tested on artificial and hydrometeorological time series. The obtained results show the effectiveness of the algorithm for time series segmentation and prediction.
(1)提出用于自动模糊分割一元与多元水文气象时间序列的改进的Gath-Geva聚类算法。该算法把时间序列分割问题看成是Gath-Geva聚类,采用最小信息长度准则作为分割阶数的选择标准。改进的Gath-Geva聚类算法具有以下优点：首先,具有非监督特性,可以自动确定最优的分割阶数；其次,在经典Gath-Geva聚类中采用分量形式的期望最大化算法以避免经典的期望最大化算法中对初值敏感及需要避免收敛到参数空间的边界等缺点；另外.通过把分割阶数选择与模型参数估计过程紧密结合,可以提高算法的稳定性。
(2)提出一种用于自动模糊分割多元时间序列的竞争模糊聚类算法。该算法基于新的竞争机制,能够自动确定聚类数目并有效的选择“分裂”或“合并”操作。而且该算法对聚类数目与模型参数不敏感。人工数据实验表明该算法能够检测出多元时间序列的概率特性的改变(均值改变、方差改变与变量相关结构的改变)。
(3)注意到用于水文气象时间序列预测的神经网络结构通常是静态的,而静态神经网络无法有效反映系统动态的变化。本文利用序贯学习的径向基函数神经网络对水文气象时间序列进行精确实时预测。该预测模型采用滑动数据窗口作为动态观测器来调整网络结构和参数以适应水文气象时间序列的动态变化。
采用这三个算法对人工和水文气象时间序列进行分割与预测仿真实验,结果验证了这三个算法对于时间序列分割与预测的有效性。
Hydrometeorological time series such as streamflow, precipitation and temperature are among the basic data used to study earth-related phenomena. Evolutionary and disruptive changes in the environment caused by natural factors and human activities result in trends or jumps in hydrometeorological time series. Segmentation and prediction for hydrometeorological time series help men understand natural factors or human-induced changes in human living environment. Due to the importance in research and practice, segmentation and prediction of hydrometeorological records such as streamflow, precipitation and temperature have been received extensive attention. Segmentation and prediction for hydrometeorological time series have always been important topics in hydrometeorological sciences. The emerging intelligent computing techniques have shown their power in computational efficiency, and have been widely applied in segmentation and prediction of hydrometeorological time series. In this paper, intelligent computing techniques are conducted to segmentation and prediction of hydrometeorological time series. The main research contents of this paper include three parts:
Firstly, an improved Gath-Geva clustering algorithm is proposed for automatic fuzzy segmentation of univariate and multivariate hydrometeorological time series. The algorithm considers time series segmentation problem as Gath-Geva clustering with the minimum message length criterion as segmentation order selection criterion. One characteristic of the improved Gath-Geva clustering algorithm is its unsupervised nature which can automatically determine the optimal segmentation order. Another characteristic is the application of the modified component-wise expectation maximization algorithm in Gath-Geva clustering which can avoid the drawbacks of the classical expectation maximization algorithm:the sensitivity to initialization and the need to avoid the boundary of the parameter space. The other characteristic is the improvement of numerical stability by integrating segmentation order selection into model parameter estimation procedure.
Secondly, a competitive fuzzy clustering algorithm is presented for automatic fuzzy segmentation of multivariate time series. The proposed algorithm is capable of automatically choosing the clustering number and selecting the "split" or "merge" operations efficiently based on the new competitive mechanism. It is insensitive to the initial configuration of the cluster component number and model parameters. Experiments on synthetic data show that the proposed algorithm is able to handle time-varying characteristics of multivariate time series:changes in the mean:changes in the variance; and changes in the correlation structure among the variables.
Thirdly, noticed that the structures of the commonly implemented neural networks for the prediction of hydrometeorological time series are static, while the static neural network cannot represent the changes of system dynamics efficiently. In this paper, the application of a sequential learning radial basis function is presented for accurate real-time prediction of hydrometeorological time series. The prediction model employs a sliding data window as dynamical observer, and tunes the structure and parameters of radial basis function neural network to adapt to the dynamical changes of hydrometeorological time series.
The three algorithms have been experimentally tested on artificial and hydrometeorological time series. The obtained results show the effectiveness of the algorithm for time series segmentation and prediction.
引文
[1]国务院.中国的减灾行动[D].白皮书,2009.
[2]Zhao X, Chu P S. Bayesian changepoint analysis for extreme events (typhoons, heavy rainfall, and heat waves):An RJMCMC approach[J]. Journal of Climate,2010,23(5): 1034-1046.
[3]Gedikli A, Aksoy H, Unal N E, et al. Modified dynamic programming approach for offline segmentation of long hydrometeorological time series [J]. Stochastic Environmental Research and Risk Assessment,2010,24(5):547-557.
[4]Chu P S, Zhao X. Bayesian Analysis for Extreme Climatic Events:A Review[J]. Atmospheric Research,2011,102:243-262.
[5]Climate change 1995:The science of climate change:contribution of working group I to the second assessment report of the Intergovernmental Panel on Climate Change[M]. Cambridge University Press,1996.
[6]Gedikli A, Aksoy H, Unal N E. Segmentation algorithm for long time series analysis[J]. Stochastic Environmental Research and Risk Assessment,2008,22(3):291-302.
[7]Haan C T. Statistical methods in hydrology[J].1977.
[8]Mantua N J, Hare S R, Zhang Y, et al. A Pacific interdecadal climate oscillation with impacts on salmon production[J]. Bulletin of the American Meteorological Society,1997,78(6):1069-1079.
[9]Goldenberg S B, Landsea C W, Mestas-Nunez A M, et al. The recent increase in Atlantic hurricane activity:Causes and implications[J]. Science,2001,293(5529):474-479.
[10]Scheffer M, Carpenter S, Foley J A, et al. Catastrophic shifts in ecosystems[J]. Nature,2001,413(6856):591-596.
[11]Hejazi M I, Moglen G E. Regression-based approach to low flow prediction in the Maryland Piedmont region under joint climate and land use change [J]. Hydrological processes,2007,21(14):1793-1801.
[12]Hejazi M I, Moglen G E. The effect of climate and land use change on flow duration in the Maryland Piedmont regionQ]. Hydrological Processes,2008,22(24): 4710-4722.
[13]Rouge C, Ge Y, Cai X. Detecting gradual and abrupt changes in hydrological records[J]. Advances in Water Resources,2012.
[14]Milly P C D, Julio B, Malin F, et al. Stationarity is dead[J]. Ground Water News & Views,2007,4(1):6-8.
[15]Kiely G. Climate change in Ireland from precipitation and streamflow observations[J]. Advances in Water Resources,1999,23(2):141-151.
[16]Aksoy H, Unal, NE, Gedikli A. Letter to the editor[J]. Stochastic Environmental Research and Risk Assessment,2007,21(4):447-449.
[17]Vasko K T, Toivonen H T T. Estimating the number of segments in time series data using permutation tests [C]//ICDM'02 Proceedings of the 2002 IEEE International Conference on Data Mining,2002:466-473.
[18]Tsakalias G, Koutsoyiannis D. A comprehensive system for the exploration and analysis of hydrological data[J]. Water resources management,1999,13(4): 269-302.
[19]Last M, Klein Y, Kandel A. Knowledge discovery in time series databases[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,2001, 31(1):160-169.
[20]Glantz M, editor. Creeping environmental problems and sustainable development in the Aral Sea basin[M]. Cambridge University Press,1999.
[21]Cai X, McKinney D C, Lasdon L S. A framework for sustainability analysis in water resources management and application to the Syr Darya Basin[J]. Water Resources Research,2002,38(6):1085.
[22]Cai X, McKinney D C, Lasdon L S. Integrated hydrologic-agronomic-economic model for river basin management [J]. Journal of water resources planning and management, 2002,129(1):4-17.
[23]Cai X, Rosegrant M W. Optional water development strategies for the Yellow River Basin:Balancing agricultural and ecological water demands[J]. Water Resources Research,2004,40(8):W08S04.
[24]Fu G, Chen S, Liu C, et al. Hydro-climatic trends of the Yellow River basin for the last 50 years[J]. Climatic Change,2004,65(1):149-178.
[25]Cong Z, Yang D, Gao B, et al. Hydrological trend analysis in the Yellow River basin using a distributed hydrological model [J]. Water Resources Research,2009, 45(7):WOOA13.
[26]Zheng H, Zhang L, Liu C, et al. Changes in stream flow regime in headwater catchments of the Yellow River basin since the 1950s [J]. Hydrological processes, 2007,21(7):886-893.
[27]Perreault L, Bernier J, Bobee B. Bayesian change-point analysis in hydrometeorological time series. Part 2. Comparison of change-point models and forecasting[J]. Journal of Hydrology,2000,235:242-263.
[28]Abonyi J, Nemeth S, Arva P, et al. Modified Gath-Geva clustering for fuzzy segmentation of multivariate time-series[J]. Fuzzy Sets and Systems,2005,149: 39-56.
[29]Aksoy H, Dahamsheh A. Artificial neural network models for forecasting monthly precipitation in Jordan[J]. Stochastic Environmental Research and Risk Assessment,2009,23(7):917-931.
[30]Guha-Sapir D, Hargitt D, Hoyois P. Thirty years of natural disasters 1974-2003: The numbers[M]. Presses univ. de Louvain,2004.
[31]Wei S, Song J, Khan N I. Simulating and predicting river discharge time series using a wavelet-neural network hybrid modelling approach[J]. Hydrological Processes,2012,26(2):281-296.
[32]Fortin V, Perreault L, Salas J D, Restropective analysis and forecasting of streamflows using a shifting level models[J]. Journal of Hydrology,2004,296: 135-163.
[33]Kerh T, Lee C S. Neural networks forecasting of flood discharge at an unmeasured station using river upstream information[J]. Advances in Engineering Software, 2006,37(8):533-543.
[34]Chu P S, Zhao X. Bayesian Change-Point Analysis of Tropical Cyclone Activity: The Central North Pacific Case[J]. Journal of Climate,2004,17(24):4893-4901.
[35]Zhao X, Chu P S. Bayesian multiple changepoint analysis of hurricane activity in the eastern North Pacific:A Markov chain Monte Carlo approach[J]. Journal of climate,2006,19(4):564-578.
[36]Hejazi M I, Moglen G E. Regression-based approach to low flow prediction in the Maryland Piedmont region under joint climate and land use change [J]. Hydrological processes,2007,21(14):1793-1801.
[37]Damle C, Yalcin A. Flood prediction using time series data mining[J]. Journal of Hydrology,2007,333(2):305-316.
[38]Lohani A K, Goel N K, Bhatia K K S. Comparative study of neural network, fuzzy logic and linear transfer function techniques in daily rainfall-runoff modelling under different input domains [J]. Hydrological Processes,2010,25(2): 175-193.
[39]Claessens L, Hopkinson C, Rastetter E, et al. Effect of historical changes in land use and climate on the water budget of an urbanizing watershed[J]. Water Resources Research,2006,42(3).
[40]Haykin S S. Neural networks:a comprehensive foundation[M]. Englewood Cliffs, NJ:Prentice Hall,2007.
[41]Basheer I A, Hajmeer M. Artificial neural networks:fundamentals, computing, design, and application[J]. Journal of microbiological methods,2000,43(1): 3-31.
[42]Wasserman P D. Advanced methods in neural computing[M]. John Wiley & Sons, Inc. 1993.
[43]Platt J. A resource-allocating network for function interpolation[J]. Neural computation,1991,3(2):213-225.
[44]Liang N Y, Huang G B, Saratchandran P, et al. A fast and accurate online sequential learning algorithm for feedforward networks[J]. Neural Networks, IEEE Transactions on,2006,17(6):1411-1423.
[45]Chang L C, Chang F J, Wang Y P. Auto-configuring radial basis function networks for chaotic time series and flood forecast ing [J]. Hydrological Processes,2009, 23(17):2450-2459.
[46]尹建川,胡江强,何庆华.变结构径向基函数网络及其在混沌序列在线预测中的应用[J].模式识别与人工智能,2010,6：023.
[47]Basseville M, Nikiforov I V. Detection of abrupt changes:theory and application[J]. Englewood Cliffs:Prentice Hall,1993.
[48]Pettitt A N. A non-parametric approach to the change-point problem[J]. Applied Statistics,1979,28(2):126-135.
[49]Buishand T A. Some methods for testing the homogeneity of rainfall records[J]. Journal of Hydrology,1982,58:11-27.
[50]Hubert P. The segmentation procedure as a tool for discrete modeling of hydrometeorological regimes[J]. Stochastic Environmental Research and Risk Assessment,2000,14:297-304.
[51]Kehagias A. A hidden markov model segmentation procedure for hydrological and environmental time series[J], Stochastic Environmental Research and Risk Assessment,2004,18:117-130.
[52]Fortin V, Perreault L, Salas J D. Retrospective analysis and forecasting of streamflows using a shifting level model [J]. Journal of hydrology,2004,296(1): 135-163.
[53]Kehagias A, Nidelkou E, Petridis V. A dynamic programming segmentation procedure for hydrological and environmental time series[J]. Stochastic Environmental Research and Risk Assessment,2005,20:77-94.
[54]Schwarz, G. Estimating the dimension of a model [J]. Annals of Statistics,1978, 6(2):461-464.
[55]Seghouane A K, Amari S I. The AIC criterion and symmetrizing the Kullback-Leibler divergence[J]. Neural Networks, IEEE Transactions on,2007,18(1):97-106.
[56]Kehagias A, Fortin V. Time series segmentation with shifting means hidden Markov models[J]. Nonlinear Processes in Geophysics,2006,13:339-352.
[57]Chernoff H, Zacks S. Estimating the current mean of a normal distribution which is subject to changes in time[J]. The Annals of Mathematical Statistics,1964, 35(3):999-1018.
[58]Salas J D, Boes D C. Shifting level modelling of hydrologic time series[J]. Advances in Water Resources,1980,3:59-63.
[59]Aksoy H, Gedikli A, Unal N E, et al. Fast segmentation algorithms for long hydrometeorological time series[J]. Hydrological Processes,2008,22(23): 4600-4608.
[60]Scheffe H. The analysis of variance[M]. Wiley, com,1999.
[61]Perreault L, Bernier J, Bobee B, et al. Bayesian change-point analysis in hydrometeorological time series. Part 1. The normal model revisited[J]. Journal of Hydrology,2000,235(3):221-241.
[62]Hanlon B, Forbes C. Model selection criteria for segmented time series from a bayesian approach to information compression[R]. Monash University, Department of Econometrics and Business Statistics,2002.
[63]刘攀,郭生练,王才君,等.三峡水库汛期分期的变点分析方法研究[J].水文,2005,25(1)：18-23.
[64]张一驰,周成虎,李宝林.基于Brown-Forsythe检验的水文序列变异点识别[J].地理研究,2005,24(5)：741-748.
[65]胡安焱,刘秀花,姜凌.汉江流域水文序列变点分析[J].灌溉排水学报,2009,28(006)：128-129.
[66]周园园,师长兴,范小黎,等.国内水文序列变异点分析方法及在各流域应用研究进展[J].地理科学进展,2011,30(11)：1361-1369.
[67]金菊良,魏一鸣,丁晶.基于遗传算法的水文时间序列变点分析方法[J].地理科学,2005,25(6)：720-723.
[68]汪丽娜,陈晓宏,李粤安,等.水文时间序列突变点分析的启发式分割方法[J].人民长江,2009(9)：15-17.
[69]Himberg J, Korpiaho K, Mannila H, et al. Time series segmentation for context recognition in mobile devices[C]//Data Mining,2001. ICDM 2001, Proceedings IEEE International Conference on. IEEE,2001:203-210.
[70]Abonyi J, Feil B, Nemeth S, et al. Fuzzy clustering based segmentation of time-series[J]. Advances in Intelligent Data Analysis V,2003:275-285.
[71]Abonyi J, Feil B, Nemeth S, et al. Principal component analysis based time series segmentation:A new sensor fusion algorithm[J]. preprint,2004.
[72]Feil B, Abonyi J, Nemeth S, et al. Monitoring process transitions by Kalman filtering and time-series segmentation[J]. Computers & chemical engineering, 2005,29(6):1423-1431.
[73]Dahamsheh A, Aksoy H. Artificial neural network models for forecasting intermittent monthly precipitation in arid regions[J]. Meteorological Applications,2009,16(3):325-337.
[74]Chang L C, Chang F J, Wang Y P. Auto-configuring radial basis function networks for chaotic time series and flood forecasting[J]. Hydrological Processes,2009, 23(17):2450-2459.
[75]Aizerman M A, Braverman E M, Rozonoer L I. Theoretical foundations of the potential function method in pattern recognition learning[J]. Automation and Remote Control,1964,25,821-837.
[76]Looney C G. Radial basis functional link nets and fuzzy reasoning[J]. Neurocomputing,2002,48:489-509.
[77]Moody J, Darken C J. Fast learning in networks of locally-tuned processing units[J]. Neural computation,1989,1(2):281-294.
[78]Hartman E J, Keeler J D, Kowalski J M. Layered neural networks with Gaussian hidden units as universal approximations[J]. Neural Computation,1990,2:210-215.
[79]Poggio T, Girosi F. Networks for approximation and learning[J]. Proceedings of the IEEE,1990,78(9):1481-1497.
[80]Ham F M, Kostanic I. Principles of neurocomputing for science and engineering[M], McGraw-Hill Higher Education,2000.
[81]Chang F J, Liang J M, Chen Y C. Flood forecasting using radial basis function neural networks[J]. Systems, Man, and Cybernetics, Part C:Applications and Reviews, IEEE Transactions on,2001,31(4):530-535.
[82]黄国如,胡和平,田富强.用径向基函数神经网络模型预报感潮河段洪水位[J].水科学进展,2003,14(2)：158-162.
[83]Chang F J, Chen Y C. Estuary water-stage forecasting by using radial basis function neural network[J]. Journal of Hydrology,2003,270(1):158-166.
[84]Jayawardena A W, Xu P C, Tsang F L, et al. Determining the structure of a radial basis function network for prediction of nonlinear hydrological time series [J]. Hydrological sciences journal,2006,51(1):21-44.
[85]胡坚,严敏,刘俊萍,等.径向基函数人工神经网络预测污水处理厂出水水质[J].浙江工业大学学报,2006,34(6)：633-636.
[86]刘俊萍,畅明琦.径向基函数神经网络需水预测研究[J].水文,2007,27(5)：12-16.
[87]Staiano A, Tagliaferri R, Pedrycz W. Improving RBF networks performance in regression tasks by means of a supervised fuzzy clustering[J]. Neurocomputing, 2006,69(13):1570-1581.
[88]Xu L. RBF nets, mixture experts, and Bayesian Ying-Yang learning[J]. Neurocomputing,1998,19(1-3):223-257.
[89]Senthil Kumar A R, Sudheer K P, Jain S K, et al. Rainfall-runoff modelling using artificial neural networks:Comparison of network types[J]. Hydrological processes,2005,19(6):1277-1291.
[90]Bugmann G. Normalized Gaussian radial basis function networks[J]. Neurocomputing, 1998,20(1):97-110.
[91]Yin J, Zou Z, Xu F. Sequential learning radial basis function network for real-time tidal level predictions[J]. Ocean Engineering,2013,57:49-55.
[92]薛小杰,黄强,惠泱河,等.基于径向基函数神经网络与改进遗传算法的黄河流域需水预测[J].水土保持学报,2002,16(3)：83285.
[93]张建龙,解建仓,韩宇平,等.基于混沌径向基神经网络模型的洪水预测研究[J].西北农林科技大学学报：自然科学版,2009(8)：221-227.
[94]王军栋,张巧玲,齐维贵.基于相空间重构的RBF江水浊度预报研究[J].系统仿真学报,2009(024)：7906-7909.
[95]闭祖良,张展羽,朱新国,等.基于RBF神经网络马尔可夫模型的降水量预测[J].节水灌溉,2010,11：1-3.
[96]黄国如,芮孝芳.河道洪水演算的径向基函数神经网络模型[J].河海大学学报：自然科学版,2003,31(6)：621-625.
[97]Lin G F, Chen L H. Time series forecasting by combining the radial basis function network and the self-organizing map[J]. Hydrological Processes,2005,19(10): 1925-1937.
[98]Figueiredo M A T, Jain A K. Unsupervised learning of finite mixture models[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2002,24(3): 381-396.
[99]Wallace C S, Freeman P R. Estimation and inference by compact coding[J]. Journal of the Royal Statistical Society. Series B (Methodological),1987:240-265.
[100]Wallace C S, Dowe D L. Minimum message length and Kolmogorov complexity [J]. The Computer Journal,1999,42(4):270-283.
[101]Chen J, Gupta A K, Pan J. Information criterion and change point problem for regular models[J]. Sankhya:The Indian Journal of Statistics,2006:252-282.
[102]Kearns M, Mansour Y, Ng A Y, et al. An experimental and theoretical comparison of model selection methods[J]. Machine Learning,1997,27(1):7-50.
[103]Rabiner L R. A tutorial on hidden Markov models and selected applications in speech recognition[J]. Proceedings of the IEEE,1989,77(2):257-286.
[104]Yao Y C. Estimating the number of change-points via Schwarz'criterion[J]. Statistics & Probability Letters,1988,6(3):181-189.
[105]Gath I, Geva A B. Unsupervised optimal fuzzy clustering[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1989,11(7):773-780.
[106]Bezdek J C, Dunn J C. Optimal fuzzy partitions:A heuristic for estimating the parameters in a mixture of normal distributions[J]. Computers, IEEE Transactions on,1975,100(8):835-838.
[107]Tipping M E, Bishop C M. Mixtures of probabilistic principal component analyzers[J]. Neural computation,1999,11(2):443-482.
[108]Klawonn F, Kruse R, Runkler T. Fuzzy cluster analysis:methods for classification, data analysis and image recognition[M]. J. Wiley,1999.
[109]Kaymak U, Babuska R. Compatible cluster merging for fuzzy modelling[C]//Fuzzy Systems,1995. International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium., Proceedings of 1995 IEEE International Conference on. IEEE,1995, 2:897-904.
[110]Kelly P M. An algorithm for merging hyperellipsoidal clusters[J]. Los Alamos National Laboratory, Tech. Rep,1994.
[111]Bouguila N, Ziou D. Unsupervised selection of a finite Dirichlet mixture model: an MML-based approach[J]. Knowledge and Data Engineering, IEEE Transactions on, 2006,18(8):993-1009.
[112]Akaike H. A new look at the statistical model identification[J]. Automatic Control, IEEE Transactions on,1974,19(6):716-723.
[113]Wallace C S, Boulton D M. An information measure for classification[J]. The Computer Journal,1968,11(2):185-194.
[114]Rissanen J. Modeling by shortest data description[J]. Automatica,1978,14(5): 465-471.
[115]Bezdek J C. Pattern recognition with fuzzy objective function algorithms[M]. Kluwer Academic Publishers,1981.
[116]McLachlan G, Peel D. Finite mixture models[M]. Wiley, com,2004.
[117]Roeder K, Wasserman L. Practical Bayesian density estimation using mixtures of normals[J]. Journal of the American Statistical Association,1997,92(439): 894-902.
[118]Cheeseman P, Stuz J. Bayesian Classification (AUTOCLASS):Theory and Results[J]. Advances in Knowledge Discovery and Data Mining,1996,180:153-180.
[119]Baxter R A, Oliver J J. Finding overlapping components with MML[J]. Statistics and Computing,2000,10(1):5-16.
[120]Rissanen J. Stochastic complexity in statistical inquiry theory[M]. World Scientific Publishing Co., Inc.,1989.
[121]Shannon C E. A mathematical theory of communication[J]. ACM SIGMOBILE Mobile Computing and Communications Review,2001,5(1):3-55.
[122]Fu Z, Robles-Kelly A, Zhou J. Mixing linear SVMs for nonlinear classification[J]. Neural Networks, IEEE Transactions on,2010,21(12):1963-1975.
[123]Celeux G, Chretien S, Forbes F, et al. A component-wise EM algorithm for mixtures [J]. Journal of Computational and Graphical Statistics,2001,10(4).
[l24]Ueda N, Nakano R, Ghahramani Z, et al. SMEM algorithm for mixture models[J]. Neural computation,2000,12(9):2109-2128.
[125]Keogh E, Chu S, Hart D, et al. An online algorithm for segmenting time series[C]//Data Mining,2001. ICDM 2001, Proceedings IEEE International Conference on. IEEE,2001:289-296.
[126]Stephanopoulos G, Han C. Intelligent systems in process engineering:Areview[J]. Computers & chemical engineering,1996,20(6):743-791.
[127]Beeferman D, Berger A, Lafferty J. Statistical models for text segmentation[J]. Machine learning,1999,34(1-3):177-210.
[128]Zhang B, Zhang C, Yi X. Competitive EM algorithm for finite mixture models[J]. Pattern recognition,2004,37(1):131-144.
[129]Yin J, Wang L, Wang N. A variable-structure gradient RBF network with its application to predictive ship motion control [J]. Asian J. Control,2012,14(3): 716-725.
[130]Gunaydin K. The estimation of monthly mean significant wave heights by using artificial neural network and regression methods[J]. Ocean Engineering,2008, 35(14):1406-1415.
[131]Huang W, Murray C, Kraus N, et al. Development of a regional neural network for coastal water level predictions[J]. Ocean Engineering,2003,30(17):2275-2295.
[132]Deo M C, Sridhar Naidu C. Real time wave forecasting using neural networks[J]. Ocean Engineering,1998,26(3):191-203.
[133]Suresh S, Dong K, Kim H J. A sequential learning algorithm for self-adaptive resource allocation network classifier[J]. Neurocomputing,2010,73.(16): 3012-3019.
[134]Chen S, Grant P M, Cowan C F N. Orthogonal least-squares algorithm for training multioutput radial basis function networks[C]//Radar and Signal Processing, IEE Proceedings F. IET,1992,139(6):378-384.
[135]李亚娇.基于现代分析技术的水文时间序列预测方法研究[D].西安理工大学,2007.
[136]Lowe D, Broomhead D. Multivariable functional interpolation and adaptive networks[J]. Complex systems,1988,2:321-355.
[2]Zhao X, Chu P S. Bayesian changepoint analysis for extreme events (typhoons, heavy rainfall, and heat waves):An RJMCMC approach[J]. Journal of Climate,2010,23(5): 1034-1046.
[3]Gedikli A, Aksoy H, Unal N E, et al. Modified dynamic programming approach for offline segmentation of long hydrometeorological time series [J]. Stochastic Environmental Research and Risk Assessment,2010,24(5):547-557.
[4]Chu P S, Zhao X. Bayesian Analysis for Extreme Climatic Events:A Review[J]. Atmospheric Research,2011,102:243-262.
[5]Climate change 1995:The science of climate change:contribution of working group I to the second assessment report of the Intergovernmental Panel on Climate Change[M]. Cambridge University Press,1996.
[6]Gedikli A, Aksoy H, Unal N E. Segmentation algorithm for long time series analysis[J]. Stochastic Environmental Research and Risk Assessment,2008,22(3):291-302.
[7]Haan C T. Statistical methods in hydrology[J].1977.
[8]Mantua N J, Hare S R, Zhang Y, et al. A Pacific interdecadal climate oscillation with impacts on salmon production[J]. Bulletin of the American Meteorological Society,1997,78(6):1069-1079.
[9]Goldenberg S B, Landsea C W, Mestas-Nunez A M, et al. The recent increase in Atlantic hurricane activity:Causes and implications[J]. Science,2001,293(5529):474-479.
[10]Scheffer M, Carpenter S, Foley J A, et al. Catastrophic shifts in ecosystems[J]. Nature,2001,413(6856):591-596.
[11]Hejazi M I, Moglen G E. Regression-based approach to low flow prediction in the Maryland Piedmont region under joint climate and land use change [J]. Hydrological processes,2007,21(14):1793-1801.
[12]Hejazi M I, Moglen G E. The effect of climate and land use change on flow duration in the Maryland Piedmont regionQ]. Hydrological Processes,2008,22(24): 4710-4722.
[13]Rouge C, Ge Y, Cai X. Detecting gradual and abrupt changes in hydrological records[J]. Advances in Water Resources,2012.
[14]Milly P C D, Julio B, Malin F, et al. Stationarity is dead[J]. Ground Water News & Views,2007,4(1):6-8.
[15]Kiely G. Climate change in Ireland from precipitation and streamflow observations[J]. Advances in Water Resources,1999,23(2):141-151.
[16]Aksoy H, Unal, NE, Gedikli A. Letter to the editor[J]. Stochastic Environmental Research and Risk Assessment,2007,21(4):447-449.
[17]Vasko K T, Toivonen H T T. Estimating the number of segments in time series data using permutation tests [C]//ICDM'02 Proceedings of the 2002 IEEE International Conference on Data Mining,2002:466-473.
[18]Tsakalias G, Koutsoyiannis D. A comprehensive system for the exploration and analysis of hydrological data[J]. Water resources management,1999,13(4): 269-302.
[19]Last M, Klein Y, Kandel A. Knowledge discovery in time series databases[J]. Systems, Man, and Cybernetics, Part B:Cybernetics, IEEE Transactions on,2001, 31(1):160-169.
[20]Glantz M, editor. Creeping environmental problems and sustainable development in the Aral Sea basin[M]. Cambridge University Press,1999.
[21]Cai X, McKinney D C, Lasdon L S. A framework for sustainability analysis in water resources management and application to the Syr Darya Basin[J]. Water Resources Research,2002,38(6):1085.
[22]Cai X, McKinney D C, Lasdon L S. Integrated hydrologic-agronomic-economic model for river basin management [J]. Journal of water resources planning and management, 2002,129(1):4-17.
[23]Cai X, Rosegrant M W. Optional water development strategies for the Yellow River Basin:Balancing agricultural and ecological water demands[J]. Water Resources Research,2004,40(8):W08S04.
[24]Fu G, Chen S, Liu C, et al. Hydro-climatic trends of the Yellow River basin for the last 50 years[J]. Climatic Change,2004,65(1):149-178.
[25]Cong Z, Yang D, Gao B, et al. Hydrological trend analysis in the Yellow River basin using a distributed hydrological model [J]. Water Resources Research,2009, 45(7):WOOA13.
[26]Zheng H, Zhang L, Liu C, et al. Changes in stream flow regime in headwater catchments of the Yellow River basin since the 1950s [J]. Hydrological processes, 2007,21(7):886-893.
[27]Perreault L, Bernier J, Bobee B. Bayesian change-point analysis in hydrometeorological time series. Part 2. Comparison of change-point models and forecasting[J]. Journal of Hydrology,2000,235:242-263.
[28]Abonyi J, Nemeth S, Arva P, et al. Modified Gath-Geva clustering for fuzzy segmentation of multivariate time-series[J]. Fuzzy Sets and Systems,2005,149: 39-56.
[29]Aksoy H, Dahamsheh A. Artificial neural network models for forecasting monthly precipitation in Jordan[J]. Stochastic Environmental Research and Risk Assessment,2009,23(7):917-931.
[30]Guha-Sapir D, Hargitt D, Hoyois P. Thirty years of natural disasters 1974-2003: The numbers[M]. Presses univ. de Louvain,2004.
[31]Wei S, Song J, Khan N I. Simulating and predicting river discharge time series using a wavelet-neural network hybrid modelling approach[J]. Hydrological Processes,2012,26(2):281-296.
[32]Fortin V, Perreault L, Salas J D, Restropective analysis and forecasting of streamflows using a shifting level models[J]. Journal of Hydrology,2004,296: 135-163.
[33]Kerh T, Lee C S. Neural networks forecasting of flood discharge at an unmeasured station using river upstream information[J]. Advances in Engineering Software, 2006,37(8):533-543.
[34]Chu P S, Zhao X. Bayesian Change-Point Analysis of Tropical Cyclone Activity: The Central North Pacific Case[J]. Journal of Climate,2004,17(24):4893-4901.
[35]Zhao X, Chu P S. Bayesian multiple changepoint analysis of hurricane activity in the eastern North Pacific:A Markov chain Monte Carlo approach[J]. Journal of climate,2006,19(4):564-578.
[36]Hejazi M I, Moglen G E. Regression-based approach to low flow prediction in the Maryland Piedmont region under joint climate and land use change [J]. Hydrological processes,2007,21(14):1793-1801.
[37]Damle C, Yalcin A. Flood prediction using time series data mining[J]. Journal of Hydrology,2007,333(2):305-316.
[38]Lohani A K, Goel N K, Bhatia K K S. Comparative study of neural network, fuzzy logic and linear transfer function techniques in daily rainfall-runoff modelling under different input domains [J]. Hydrological Processes,2010,25(2): 175-193.
[39]Claessens L, Hopkinson C, Rastetter E, et al. Effect of historical changes in land use and climate on the water budget of an urbanizing watershed[J]. Water Resources Research,2006,42(3).
[40]Haykin S S. Neural networks:a comprehensive foundation[M]. Englewood Cliffs, NJ:Prentice Hall,2007.
[41]Basheer I A, Hajmeer M. Artificial neural networks:fundamentals, computing, design, and application[J]. Journal of microbiological methods,2000,43(1): 3-31.
[42]Wasserman P D. Advanced methods in neural computing[M]. John Wiley & Sons, Inc. 1993.
[43]Platt J. A resource-allocating network for function interpolation[J]. Neural computation,1991,3(2):213-225.
[44]Liang N Y, Huang G B, Saratchandran P, et al. A fast and accurate online sequential learning algorithm for feedforward networks[J]. Neural Networks, IEEE Transactions on,2006,17(6):1411-1423.
[45]Chang L C, Chang F J, Wang Y P. Auto-configuring radial basis function networks for chaotic time series and flood forecast ing [J]. Hydrological Processes,2009, 23(17):2450-2459.
[46]尹建川,胡江强,何庆华.变结构径向基函数网络及其在混沌序列在线预测中的应用[J].模式识别与人工智能,2010,6：023.
[47]Basseville M, Nikiforov I V. Detection of abrupt changes:theory and application[J]. Englewood Cliffs:Prentice Hall,1993.
[48]Pettitt A N. A non-parametric approach to the change-point problem[J]. Applied Statistics,1979,28(2):126-135.
[49]Buishand T A. Some methods for testing the homogeneity of rainfall records[J]. Journal of Hydrology,1982,58:11-27.
[50]Hubert P. The segmentation procedure as a tool for discrete modeling of hydrometeorological regimes[J]. Stochastic Environmental Research and Risk Assessment,2000,14:297-304.
[51]Kehagias A. A hidden markov model segmentation procedure for hydrological and environmental time series[J], Stochastic Environmental Research and Risk Assessment,2004,18:117-130.
[52]Fortin V, Perreault L, Salas J D. Retrospective analysis and forecasting of streamflows using a shifting level model [J]. Journal of hydrology,2004,296(1): 135-163.
[53]Kehagias A, Nidelkou E, Petridis V. A dynamic programming segmentation procedure for hydrological and environmental time series[J]. Stochastic Environmental Research and Risk Assessment,2005,20:77-94.
[54]Schwarz, G. Estimating the dimension of a model [J]. Annals of Statistics,1978, 6(2):461-464.
[55]Seghouane A K, Amari S I. The AIC criterion and symmetrizing the Kullback-Leibler divergence[J]. Neural Networks, IEEE Transactions on,2007,18(1):97-106.
[56]Kehagias A, Fortin V. Time series segmentation with shifting means hidden Markov models[J]. Nonlinear Processes in Geophysics,2006,13:339-352.
[57]Chernoff H, Zacks S. Estimating the current mean of a normal distribution which is subject to changes in time[J]. The Annals of Mathematical Statistics,1964, 35(3):999-1018.
[58]Salas J D, Boes D C. Shifting level modelling of hydrologic time series[J]. Advances in Water Resources,1980,3:59-63.
[59]Aksoy H, Gedikli A, Unal N E, et al. Fast segmentation algorithms for long hydrometeorological time series[J]. Hydrological Processes,2008,22(23): 4600-4608.
[60]Scheffe H. The analysis of variance[M]. Wiley, com,1999.
[61]Perreault L, Bernier J, Bobee B, et al. Bayesian change-point analysis in hydrometeorological time series. Part 1. The normal model revisited[J]. Journal of Hydrology,2000,235(3):221-241.
[62]Hanlon B, Forbes C. Model selection criteria for segmented time series from a bayesian approach to information compression[R]. Monash University, Department of Econometrics and Business Statistics,2002.
[63]刘攀,郭生练,王才君,等.三峡水库汛期分期的变点分析方法研究[J].水文,2005,25(1)：18-23.
[64]张一驰,周成虎,李宝林.基于Brown-Forsythe检验的水文序列变异点识别[J].地理研究,2005,24(5)：741-748.
[65]胡安焱,刘秀花,姜凌.汉江流域水文序列变点分析[J].灌溉排水学报,2009,28(006)：128-129.
[66]周园园,师长兴,范小黎,等.国内水文序列变异点分析方法及在各流域应用研究进展[J].地理科学进展,2011,30(11)：1361-1369.
[67]金菊良,魏一鸣,丁晶.基于遗传算法的水文时间序列变点分析方法[J].地理科学,2005,25(6)：720-723.
[68]汪丽娜,陈晓宏,李粤安,等.水文时间序列突变点分析的启发式分割方法[J].人民长江,2009(9)：15-17.
[69]Himberg J, Korpiaho K, Mannila H, et al. Time series segmentation for context recognition in mobile devices[C]//Data Mining,2001. ICDM 2001, Proceedings IEEE International Conference on. IEEE,2001:203-210.
[70]Abonyi J, Feil B, Nemeth S, et al. Fuzzy clustering based segmentation of time-series[J]. Advances in Intelligent Data Analysis V,2003:275-285.
[71]Abonyi J, Feil B, Nemeth S, et al. Principal component analysis based time series segmentation:A new sensor fusion algorithm[J]. preprint,2004.
[72]Feil B, Abonyi J, Nemeth S, et al. Monitoring process transitions by Kalman filtering and time-series segmentation[J]. Computers & chemical engineering, 2005,29(6):1423-1431.
[73]Dahamsheh A, Aksoy H. Artificial neural network models for forecasting intermittent monthly precipitation in arid regions[J]. Meteorological Applications,2009,16(3):325-337.
[74]Chang L C, Chang F J, Wang Y P. Auto-configuring radial basis function networks for chaotic time series and flood forecasting[J]. Hydrological Processes,2009, 23(17):2450-2459.
[75]Aizerman M A, Braverman E M, Rozonoer L I. Theoretical foundations of the potential function method in pattern recognition learning[J]. Automation and Remote Control,1964,25,821-837.
[76]Looney C G. Radial basis functional link nets and fuzzy reasoning[J]. Neurocomputing,2002,48:489-509.
[77]Moody J, Darken C J. Fast learning in networks of locally-tuned processing units[J]. Neural computation,1989,1(2):281-294.
[78]Hartman E J, Keeler J D, Kowalski J M. Layered neural networks with Gaussian hidden units as universal approximations[J]. Neural Computation,1990,2:210-215.
[79]Poggio T, Girosi F. Networks for approximation and learning[J]. Proceedings of the IEEE,1990,78(9):1481-1497.
[80]Ham F M, Kostanic I. Principles of neurocomputing for science and engineering[M], McGraw-Hill Higher Education,2000.
[81]Chang F J, Liang J M, Chen Y C. Flood forecasting using radial basis function neural networks[J]. Systems, Man, and Cybernetics, Part C:Applications and Reviews, IEEE Transactions on,2001,31(4):530-535.
[82]黄国如,胡和平,田富强.用径向基函数神经网络模型预报感潮河段洪水位[J].水科学进展,2003,14(2)：158-162.
[83]Chang F J, Chen Y C. Estuary water-stage forecasting by using radial basis function neural network[J]. Journal of Hydrology,2003,270(1):158-166.
[84]Jayawardena A W, Xu P C, Tsang F L, et al. Determining the structure of a radial basis function network for prediction of nonlinear hydrological time series [J]. Hydrological sciences journal,2006,51(1):21-44.
[85]胡坚,严敏,刘俊萍,等.径向基函数人工神经网络预测污水处理厂出水水质[J].浙江工业大学学报,2006,34(6)：633-636.
[86]刘俊萍,畅明琦.径向基函数神经网络需水预测研究[J].水文,2007,27(5)：12-16.
[87]Staiano A, Tagliaferri R, Pedrycz W. Improving RBF networks performance in regression tasks by means of a supervised fuzzy clustering[J]. Neurocomputing, 2006,69(13):1570-1581.
[88]Xu L. RBF nets, mixture experts, and Bayesian Ying-Yang learning[J]. Neurocomputing,1998,19(1-3):223-257.
[89]Senthil Kumar A R, Sudheer K P, Jain S K, et al. Rainfall-runoff modelling using artificial neural networks:Comparison of network types[J]. Hydrological processes,2005,19(6):1277-1291.
[90]Bugmann G. Normalized Gaussian radial basis function networks[J]. Neurocomputing, 1998,20(1):97-110.
[91]Yin J, Zou Z, Xu F. Sequential learning radial basis function network for real-time tidal level predictions[J]. Ocean Engineering,2013,57:49-55.
[92]薛小杰,黄强,惠泱河,等.基于径向基函数神经网络与改进遗传算法的黄河流域需水预测[J].水土保持学报,2002,16(3)：83285.
[93]张建龙,解建仓,韩宇平,等.基于混沌径向基神经网络模型的洪水预测研究[J].西北农林科技大学学报：自然科学版,2009(8)：221-227.
[94]王军栋,张巧玲,齐维贵.基于相空间重构的RBF江水浊度预报研究[J].系统仿真学报,2009(024)：7906-7909.
[95]闭祖良,张展羽,朱新国,等.基于RBF神经网络马尔可夫模型的降水量预测[J].节水灌溉,2010,11：1-3.
[96]黄国如,芮孝芳.河道洪水演算的径向基函数神经网络模型[J].河海大学学报：自然科学版,2003,31(6)：621-625.
[97]Lin G F, Chen L H. Time series forecasting by combining the radial basis function network and the self-organizing map[J]. Hydrological Processes,2005,19(10): 1925-1937.
[98]Figueiredo M A T, Jain A K. Unsupervised learning of finite mixture models[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,2002,24(3): 381-396.
[99]Wallace C S, Freeman P R. Estimation and inference by compact coding[J]. Journal of the Royal Statistical Society. Series B (Methodological),1987:240-265.
[100]Wallace C S, Dowe D L. Minimum message length and Kolmogorov complexity [J]. The Computer Journal,1999,42(4):270-283.
[101]Chen J, Gupta A K, Pan J. Information criterion and change point problem for regular models[J]. Sankhya:The Indian Journal of Statistics,2006:252-282.
[102]Kearns M, Mansour Y, Ng A Y, et al. An experimental and theoretical comparison of model selection methods[J]. Machine Learning,1997,27(1):7-50.
[103]Rabiner L R. A tutorial on hidden Markov models and selected applications in speech recognition[J]. Proceedings of the IEEE,1989,77(2):257-286.
[104]Yao Y C. Estimating the number of change-points via Schwarz'criterion[J]. Statistics & Probability Letters,1988,6(3):181-189.
[105]Gath I, Geva A B. Unsupervised optimal fuzzy clustering[J]. Pattern Analysis and Machine Intelligence, IEEE Transactions on,1989,11(7):773-780.
[106]Bezdek J C, Dunn J C. Optimal fuzzy partitions:A heuristic for estimating the parameters in a mixture of normal distributions[J]. Computers, IEEE Transactions on,1975,100(8):835-838.
[107]Tipping M E, Bishop C M. Mixtures of probabilistic principal component analyzers[J]. Neural computation,1999,11(2):443-482.
[108]Klawonn F, Kruse R, Runkler T. Fuzzy cluster analysis:methods for classification, data analysis and image recognition[M]. J. Wiley,1999.
[109]Kaymak U, Babuska R. Compatible cluster merging for fuzzy modelling[C]//Fuzzy Systems,1995. International Joint Conference of the Fourth IEEE International Conference on Fuzzy Systems and The Second International Fuzzy Engineering Symposium., Proceedings of 1995 IEEE International Conference on. IEEE,1995, 2:897-904.
[110]Kelly P M. An algorithm for merging hyperellipsoidal clusters[J]. Los Alamos National Laboratory, Tech. Rep,1994.
[111]Bouguila N, Ziou D. Unsupervised selection of a finite Dirichlet mixture model: an MML-based approach[J]. Knowledge and Data Engineering, IEEE Transactions on, 2006,18(8):993-1009.
[112]Akaike H. A new look at the statistical model identification[J]. Automatic Control, IEEE Transactions on,1974,19(6):716-723.
[113]Wallace C S, Boulton D M. An information measure for classification[J]. The Computer Journal,1968,11(2):185-194.
[114]Rissanen J. Modeling by shortest data description[J]. Automatica,1978,14(5): 465-471.
[115]Bezdek J C. Pattern recognition with fuzzy objective function algorithms[M]. Kluwer Academic Publishers,1981.
[116]McLachlan G, Peel D. Finite mixture models[M]. Wiley, com,2004.
[117]Roeder K, Wasserman L. Practical Bayesian density estimation using mixtures of normals[J]. Journal of the American Statistical Association,1997,92(439): 894-902.
[118]Cheeseman P, Stuz J. Bayesian Classification (AUTOCLASS):Theory and Results[J]. Advances in Knowledge Discovery and Data Mining,1996,180:153-180.
[119]Baxter R A, Oliver J J. Finding overlapping components with MML[J]. Statistics and Computing,2000,10(1):5-16.
[120]Rissanen J. Stochastic complexity in statistical inquiry theory[M]. World Scientific Publishing Co., Inc.,1989.
[121]Shannon C E. A mathematical theory of communication[J]. ACM SIGMOBILE Mobile Computing and Communications Review,2001,5(1):3-55.
[122]Fu Z, Robles-Kelly A, Zhou J. Mixing linear SVMs for nonlinear classification[J]. Neural Networks, IEEE Transactions on,2010,21(12):1963-1975.
[123]Celeux G, Chretien S, Forbes F, et al. A component-wise EM algorithm for mixtures [J]. Journal of Computational and Graphical Statistics,2001,10(4).
[l24]Ueda N, Nakano R, Ghahramani Z, et al. SMEM algorithm for mixture models[J]. Neural computation,2000,12(9):2109-2128.
[125]Keogh E, Chu S, Hart D, et al. An online algorithm for segmenting time series[C]//Data Mining,2001. ICDM 2001, Proceedings IEEE International Conference on. IEEE,2001:289-296.
[126]Stephanopoulos G, Han C. Intelligent systems in process engineering:Areview[J]. Computers & chemical engineering,1996,20(6):743-791.
[127]Beeferman D, Berger A, Lafferty J. Statistical models for text segmentation[J]. Machine learning,1999,34(1-3):177-210.
[128]Zhang B, Zhang C, Yi X. Competitive EM algorithm for finite mixture models[J]. Pattern recognition,2004,37(1):131-144.
[129]Yin J, Wang L, Wang N. A variable-structure gradient RBF network with its application to predictive ship motion control [J]. Asian J. Control,2012,14(3): 716-725.
[130]Gunaydin K. The estimation of monthly mean significant wave heights by using artificial neural network and regression methods[J]. Ocean Engineering,2008, 35(14):1406-1415.
[131]Huang W, Murray C, Kraus N, et al. Development of a regional neural network for coastal water level predictions[J]. Ocean Engineering,2003,30(17):2275-2295.
[132]Deo M C, Sridhar Naidu C. Real time wave forecasting using neural networks[J]. Ocean Engineering,1998,26(3):191-203.
[133]Suresh S, Dong K, Kim H J. A sequential learning algorithm for self-adaptive resource allocation network classifier[J]. Neurocomputing,2010,73.(16): 3012-3019.
[134]Chen S, Grant P M, Cowan C F N. Orthogonal least-squares algorithm for training multioutput radial basis function networks[C]//Radar and Signal Processing, IEE Proceedings F. IET,1992,139(6):378-384.
[135]李亚娇.基于现代分析技术的水文时间序列预测方法研究[D].西安理工大学,2007.
[136]Lowe D, Broomhead D. Multivariable functional interpolation and adaptive networks[J]. Complex systems,1988,2:321-355.