基于遗传算法的BP神经网络气象预报建模
|
摘要
20世纪90年代以来，国内外在大气学科中开展了很多有关神经网络预报建模和气候分析等应用研究。然而随着神经网络方法在大气科学领域研究的不断深入，研究人员发现神经网络方法在实际业务天气预报应用中存在一个重要的问题，即在利用神经网络方法进行气象预报建模时，神经网络的初始权值、网络结构以及网络的学习参数，动量因子难以确定，往往是通过反复训练来确定网络的结构和各种参数，这样会导致在应用中出现过拟合问题，严重影响网络的泛化能力，极大限制神经网络在实际天气业务中的应用([1-8])。该问题的研究不仅关系到在大气学科中能否进一步深入开展有关人工神经网络方法的业务预报应用，并且也是目前人工神经网络应用理论研究中尚未得到很好解决的关键技术问题。
近年来，国内外众多学者将遗传算法和神经网络结合，利用遗传算法的全局搜索能力来优化神经网络。杨晓红和刘乐善（[9]，1997）利用遗传算法优化异或问题的神经网络结构及其连接权。孙晓光和傅云义等人（[10]，1998）利用遗传算法对热轧带钢精轧机组负荷分配BP网络参数进行优化。李敏强和徐博艺等人([11]，1999)利用遗传算法优化三层BP网络的连接权并建立短期地震预报模型，取得很好的效果。李祚泳和彭荔红([12]，2003)用遗传算法进行了暴雨强度公式参数优化的研究。饶文碧和徐锐等人（[13]，2003）利用遗传算法优化BP神经网络权系数的方法，解决了结构损伤模型的识别问题。李发斌和崔鹏等人（[14]，2003）利用遗传算法优化BP神经网络的权系数建立分析泥石流活动性的模型。但是目前在预测研究领域，很少见到有关同时优化网络结构和权系数的预报建模研究，并且在大气学科中也尚未有人研究利用遗传算法优化BP神经网络的权系数及其结构，建立短期气候预测模型。
本文主要是针对BP神经网络在实际应用中的弱点，如BP网络算法收敛速度较慢，对于较大的搜索空间，多峰值和不可微函数，再加之实际问题往往是极其复杂的多维曲面，存在多个局部极值点，使得网络极易陷入局部极值点；另外神经网络的初始权值，阀值以及网络结构的选择缺乏依据，具有很大的随机性，很难选取出具有全局性的初始点，因而求得全局最优的可能性较小，这些都影响了BP神经网络的泛化能力，限制了它在实际天气预报中的应用。本文利用遗传算法优化三层BP神经网络的连接权和网络结构，并在遗传进化过程中提出了采取保留最佳个体的方法，建立基于遗传算法的BP神经网络预报模型一。由于GA在进化过程中能以较大概率搜索到全局最优解存在的区域，在遗传算法搜索到最优解附近时，却无法精确地确定最优解的位置，为此本文进一步采用从进化后的结果中，再次利用
训练样本挑选最佳网络权系数和网络结构，建立基于遗传算法的BP神经网络预报模型二。
1． 本文提出的这种方法克服了由于神经网络初始权值的随机性和网络结构确定过程中所带来的网络振荡，以及网络极易陷入局部解问题并且有效提高神经网络的泛化能力。作为应用实例，以广西全区4月份平均降水作为预报量及前期500pha月平均高度场，海温场高相关区作为预报因子，建立基于遗传算法的BP神经网络短期气候预测模型。将这种方法与传统的逐步回归方法作对比分析，在回归模型、回归系数非常显著时，以相同的因子建立逐步回归模型。在建模因子为8个时，对5个独立样本的预测结果表明，逐步回归模型的平均相对误差为：41.39%；基于遗传算法的BP神经网络模型一的平均相对误差为：16.49％，模型二的平均相对误差为：13.48％，即预报精度明显提高。当改变建模因子为4个时，基于遗传算法的BP神经网络模型的预报效果依然优于逐步回归模型，显示了较好的预报稳定性。
2．该方法在进行独立样本的逐年预报时，基于遗传算法的BP网络模型一和二的预报能力，都随着训练样本的增加，预报的精度会有所提高。体现出随着学习样本增加，它的“学习”能力增强的特点。
3．本文在建立基于遗传算法的BP网络模型二中，特别提出了从进化过的权系数和网络结构中，再次利用训练样本挑选的方法，充分发挥了遗传算法和神经网络的长处，综合了神经网络泛化映射能力和遗传算法全局收敛能力，并且克服遗传算法的局部调节能力比较弱的问题，相对基于遗传算法的BP神经网络网络模型一，该方法进一步提高预报能力，在以往的文献中尚未见到有相类似的研究研究工作报导。
4．本文在利用遗传算法优化BP神经网络隐节点（网络结构）的过程中，也检验分析了神经网络方法在实际应用中，隐节点个数最有可能在输入节点个数附近变化（即比输入节点数略多或者略少）的经验性结论。
本文在利用遗传算法优化BP神经网络和网络权系数的过程，同时也对遗传算法的收敛性进行一些讨论。GA全局性收敛问题的研究至关重要，因为不仅具有理论指导意义，而且也有重要的实践价值。Goldberg和Segrest（[15]，1987）是首次使用马尔可夫链分析了遗传算法；Eiben等人（[16]，1991）用马尔可夫链分析证明了保留最佳个体的GA以概率1收敛到全局最优解； Rudolph（[17]，1994）用齐次有限马尔可夫链分析证明了带有复制、交叉、变异操作的标准遗传算法收敛不到全局最优解；Qi和Palmie
Since the 90’s of 20 centuries, Some the Neural Network forecast mold were applied in domestic and international atmosphere course. With the research be made a thorough and careful, the researcher discovered an important problem in the actual weather forecast application, which the Neural Network beginning connection weights, the network construction, learning factor and momentum factor were hard certain. Because the researcher need train many times so that all kinds of parameters can be definite, the Neural Network become over-fitting and the serious influence the Neural Network generation ability. This problem will limit the Neural Network in the actual forecast application ([1-8]). The research of that problem not only relate to whether to can go deep into the Neural Network business forecast research in atmosphere course but also is the key technique in the theories research.
In recent years, the numerous scholar in the domestic and international combinate the Genetic Algorithms with the Neural Network, make use of the GAs optimized the NN. Sun Xiaoguang and Fu Yunyi（[10]，1998）optimized the BP network connection weights using genetic algorithm and the scheduling problem on hot strip mill has been solved. Li Mingqiang and Xu Boyi ([11]，1999) combine the GAs and the NN for solving short term earth quake forecasting problem, design a novel method of using GAs to train connection weights of NN. LI Zuoyong and Peng Lihong（[14]，2003）make use GAs optimized parameter model and set up storm rainfall intensity formulae of different repeat periods in Beijing suburban. Rao Wenbi and Xu Rui（[13]，2003） studied the problem of structure damage identification based on combination of GAs and NN, the study the possibility of solving the problem of structure damage with this model. Li Fanbin and Cui Peng （[14]，2003）set up GNN Debris flow model, which s the combination of NN and AGs. The model is suitable for analyzing the activity of debris flows. But current in the atmosphere course no one study the Neural Network constructers and connection weights and establish the short-term weather forecast model.
The paper aims at some weakness the BP(Back-Propagation) Neural Network in the actual application, such as the astringency slow, easily falling into local solutions concerning bigger search space and complex function, another the Neural Network beginning construction and connection weights having no way in definition. These affect biggest the Neural Network generalization ability and limit in the actual weather forecast application. Optimized the neural network and connection weights by means of genetic algorithm, reserved the best individual in evolution process, this method be established up the research of climate prediction the first forecast model. Because GAs can search the superior solution region in evolution process and don’t make certain situation the superior solution exists. The paper set up the second BP Neural Network forecast model based GAs, using training sample to choose the best network connection
weights and network structure form the result of evolution.
1. The method can overcome the defects of unsteady and falling into local solution and validly increase generalization ability. The applied example is setted up a climate forecast model, with monthly mean rainfall the whole area of Guangxi in April and the predicted factors of previous 500hpa height and sea surface temperatures. Predictive capability between the new model and linear regression model for the predictors is discussed based on the independent samples. Evidence suggests that the prognostic ability of the model with high accuracy and stability is superior to that of a traditional method.
2. The method forecast ability and accuracy increase as sample be increased, embody strongly learning ability.
3.The paper specially put forward to make use of the training sample from the result of evolution and choose the best network connection weights and network structure, this method brings their advantage into full play and combine t
近年来，国内外众多学者将遗传算法和神经网络结合，利用遗传算法的全局搜索能力来优化神经网络。杨晓红和刘乐善（[9]，1997）利用遗传算法优化异或问题的神经网络结构及其连接权。孙晓光和傅云义等人（[10]，1998）利用遗传算法对热轧带钢精轧机组负荷分配BP网络参数进行优化。李敏强和徐博艺等人([11]，1999)利用遗传算法优化三层BP网络的连接权并建立短期地震预报模型，取得很好的效果。李祚泳和彭荔红([12]，2003)用遗传算法进行了暴雨强度公式参数优化的研究。饶文碧和徐锐等人（[13]，2003）利用遗传算法优化BP神经网络权系数的方法，解决了结构损伤模型的识别问题。李发斌和崔鹏等人（[14]，2003）利用遗传算法优化BP神经网络的权系数建立分析泥石流活动性的模型。但是目前在预测研究领域，很少见到有关同时优化网络结构和权系数的预报建模研究，并且在大气学科中也尚未有人研究利用遗传算法优化BP神经网络的权系数及其结构，建立短期气候预测模型。
本文主要是针对BP神经网络在实际应用中的弱点，如BP网络算法收敛速度较慢，对于较大的搜索空间，多峰值和不可微函数，再加之实际问题往往是极其复杂的多维曲面，存在多个局部极值点，使得网络极易陷入局部极值点；另外神经网络的初始权值，阀值以及网络结构的选择缺乏依据，具有很大的随机性，很难选取出具有全局性的初始点，因而求得全局最优的可能性较小，这些都影响了BP神经网络的泛化能力，限制了它在实际天气预报中的应用。本文利用遗传算法优化三层BP神经网络的连接权和网络结构，并在遗传进化过程中提出了采取保留最佳个体的方法，建立基于遗传算法的BP神经网络预报模型一。由于GA在进化过程中能以较大概率搜索到全局最优解存在的区域，在遗传算法搜索到最优解附近时，却无法精确地确定最优解的位置，为此本文进一步采用从进化后的结果中，再次利用
训练样本挑选最佳网络权系数和网络结构，建立基于遗传算法的BP神经网络预报模型二。
1． 本文提出的这种方法克服了由于神经网络初始权值的随机性和网络结构确定过程中所带来的网络振荡，以及网络极易陷入局部解问题并且有效提高神经网络的泛化能力。作为应用实例，以广西全区4月份平均降水作为预报量及前期500pha月平均高度场，海温场高相关区作为预报因子，建立基于遗传算法的BP神经网络短期气候预测模型。将这种方法与传统的逐步回归方法作对比分析，在回归模型、回归系数非常显著时，以相同的因子建立逐步回归模型。在建模因子为8个时，对5个独立样本的预测结果表明，逐步回归模型的平均相对误差为：41.39%；基于遗传算法的BP神经网络模型一的平均相对误差为：16.49％，模型二的平均相对误差为：13.48％，即预报精度明显提高。当改变建模因子为4个时，基于遗传算法的BP神经网络模型的预报效果依然优于逐步回归模型，显示了较好的预报稳定性。
2．该方法在进行独立样本的逐年预报时，基于遗传算法的BP网络模型一和二的预报能力，都随着训练样本的增加，预报的精度会有所提高。体现出随着学习样本增加，它的“学习”能力增强的特点。
3．本文在建立基于遗传算法的BP网络模型二中，特别提出了从进化过的权系数和网络结构中，再次利用训练样本挑选的方法，充分发挥了遗传算法和神经网络的长处，综合了神经网络泛化映射能力和遗传算法全局收敛能力，并且克服遗传算法的局部调节能力比较弱的问题，相对基于遗传算法的BP神经网络网络模型一，该方法进一步提高预报能力，在以往的文献中尚未见到有相类似的研究研究工作报导。
4．本文在利用遗传算法优化BP神经网络隐节点（网络结构）的过程中，也检验分析了神经网络方法在实际应用中，隐节点个数最有可能在输入节点个数附近变化（即比输入节点数略多或者略少）的经验性结论。
本文在利用遗传算法优化BP神经网络和网络权系数的过程，同时也对遗传算法的收敛性进行一些讨论。GA全局性收敛问题的研究至关重要，因为不仅具有理论指导意义，而且也有重要的实践价值。Goldberg和Segrest（[15]，1987）是首次使用马尔可夫链分析了遗传算法；Eiben等人（[16]，1991）用马尔可夫链分析证明了保留最佳个体的GA以概率1收敛到全局最优解； Rudolph（[17]，1994）用齐次有限马尔可夫链分析证明了带有复制、交叉、变异操作的标准遗传算法收敛不到全局最优解；Qi和Palmie
Since the 90’s of 20 centuries, Some the Neural Network forecast mold were applied in domestic and international atmosphere course. With the research be made a thorough and careful, the researcher discovered an important problem in the actual weather forecast application, which the Neural Network beginning connection weights, the network construction, learning factor and momentum factor were hard certain. Because the researcher need train many times so that all kinds of parameters can be definite, the Neural Network become over-fitting and the serious influence the Neural Network generation ability. This problem will limit the Neural Network in the actual forecast application ([1-8]). The research of that problem not only relate to whether to can go deep into the Neural Network business forecast research in atmosphere course but also is the key technique in the theories research.
In recent years, the numerous scholar in the domestic and international combinate the Genetic Algorithms with the Neural Network, make use of the GAs optimized the NN. Sun Xiaoguang and Fu Yunyi（[10]，1998）optimized the BP network connection weights using genetic algorithm and the scheduling problem on hot strip mill has been solved. Li Mingqiang and Xu Boyi ([11]，1999) combine the GAs and the NN for solving short term earth quake forecasting problem, design a novel method of using GAs to train connection weights of NN. LI Zuoyong and Peng Lihong（[14]，2003）make use GAs optimized parameter model and set up storm rainfall intensity formulae of different repeat periods in Beijing suburban. Rao Wenbi and Xu Rui（[13]，2003） studied the problem of structure damage identification based on combination of GAs and NN, the study the possibility of solving the problem of structure damage with this model. Li Fanbin and Cui Peng （[14]，2003）set up GNN Debris flow model, which s the combination of NN and AGs. The model is suitable for analyzing the activity of debris flows. But current in the atmosphere course no one study the Neural Network constructers and connection weights and establish the short-term weather forecast model.
The paper aims at some weakness the BP(Back-Propagation) Neural Network in the actual application, such as the astringency slow, easily falling into local solutions concerning bigger search space and complex function, another the Neural Network beginning construction and connection weights having no way in definition. These affect biggest the Neural Network generalization ability and limit in the actual weather forecast application. Optimized the neural network and connection weights by means of genetic algorithm, reserved the best individual in evolution process, this method be established up the research of climate prediction the first forecast model. Because GAs can search the superior solution region in evolution process and don’t make certain situation the superior solution exists. The paper set up the second BP Neural Network forecast model based GAs, using training sample to choose the best network connection
weights and network structure form the result of evolution.
1. The method can overcome the defects of unsteady and falling into local solution and validly increase generalization ability. The applied example is setted up a climate forecast model, with monthly mean rainfall the whole area of Guangxi in April and the predicted factors of previous 500hpa height and sea surface temperatures. Predictive capability between the new model and linear regression model for the predictors is discussed based on the independent samples. Evidence suggests that the prognostic ability of the model with high accuracy and stability is superior to that of a traditional method.
2. The method forecast ability and accuracy increase as sample be increased, embody strongly learning ability.
3.The paper specially put forward to make use of the training sample from the result of evolution and choose the best network connection weights and network structure, this method brings their advantage into full play and combine t
引文
[1] Dean, Andrew R, Brian H Fiedler. Forecasting warm-season burn-off low clouds at the San Francisco international airport using linear regression and a neural network[J]. Appl Meteor, 2002, 41(6):629-639.
[2] Hsieh William W. Nonlinear canonical correlation analysis of the tropical Pacific climate variability using neural network approach [J]. 2001, 14(12): 2528-2539.
[3] Jin Long, Ju Weimin, Miao Qilong. Study on Ann-based multi-step prediction model of short-term climatic variation[J]. Advances Atmosphere Sciences, 2000, 17(1):157-164.
[4] 胡江林, 张礼平, 宇如聪. 神经网络模型预报湖北汛期降水量的应用研究[J]. 气象学报, 2001, 59 (6): 776-783.
[5] 金龙, 苗春生.定性和定量的长期预报模型的综合分析[J]. 气象学报, 2000, 58 (4) :479-484.
[6] Wu Yan, Zhang Liming. A new regularization learning method for improving generalization capability of neural network[C]. Proceedings of 4th world congress on intelligent control and automation, Shanghai, 2002,3: 2011-2015.
[7] 江学军, 唐焕文. 前馈神经网络泛化性能的系统分析[J]. 系统工程理论与实践, 2000, 28(8): 36-40.
[8] 彭汉川, 甘强,韦钰. 提高前馈神经网络推广能力的若干实际方法[J]. 电子学报,1998, 26(4):
116-119.
[9] 杨晓红,刘乐善. 用遗传算法优化神经网络结构[J]. 计算机应用与软件, 1997, 14(3): 59-65.
[10] 李敏强. 遗传算法和神经网络的结合[J]. 系统工程理论与实践,1999, (2): 65-69.
[11] 孙晓光. 遗传算法对热轧带钢精轧机组负荷分配BP网络参数的优化[J]. 钢铁, 1998, 33(7): 33-36.
[12] 李祚泳, 彭荔红. 基于遗传算法的暴雨强度公式参数的优化[J]. 高原气象, 2003, 22(6): 637-639.
[13] 饶文碧, 徐锐, 尚钢. 基于遗传算法的结构损伤识别[J]. 武汉理工大学学报, 2003, 25(7):75-77.
[14] 李发斌, 崔鹏等. 用遗传神经网络分析泥石流活动性[J]. 中国地质灾害与防治学报, 2003,14(3):16-18.
[15] Goldberg, D. E., Segrest, P. Finite Markov Chain Analysis of Genetic Algorithms[C]. Proc. Of Second International Conference on Genetic Algorithms. 1987,1-8.
[16] Eiben, A. E., Aarts, E. H., and Van Hee, K. M., Global Convergence of Genetic Algorithms; An Infinite Markov Chain Analysis. Parallel Problem Solving from Nature[M]. Berlin: Spring-Verlag, 1991: 4-12.
[17] Rudolph, G., Convergence Properties of Canonical Genetic Algorithms[J]. IEEE Trans. On Neural Networks. 1994,5 (1): 96-101.
[18] Qi, X., Palmieri, F.. Theoretical Analysis of Evolutionary Algorithms with an Infinite Population Size in Continuous Space, Part I: Basic Properties of selection and Mutation. IEEE Trans. On Neural Network, 1994, 102-119.
[19] 恽为民, 席裕庚. 遗传算法的全局收敛性和计算效率分析[J]. 控制理论与应用, 1996,13(4):455-460.
[20] 徐总本, 聂赞坎, 张文修. 遗传算法的几乎必然强收敛-鞅方法[J]. 计算机学报, 2002, 25(8):785-793.
[21] 王霞, 周国标. 遗传算法收敛的下鞅分析[J]. 应用数学, 2003, 16(4):130-135.
[22] 宋正山, 杨辉. 夏季东亚季风区500hPa月环流异常及其与我国降水关系的向量EOF分析[J]. 大气
科学, 2001,25(3): 401-404.
[23] 白人海. 大西洋海表温度异常与中国东北地区夏季降水的关系[J]. 海洋通报, 2001, 20(1):23-29.
[24] 辛若桂, 屠其璞. 我国气温长期变化的区域特征[J]. 南京气象学院学报, 1997, 20(1):54-63.
[25] Jinglong, et al. Comparison of Long-term forecasting June-August rainfall over Changjiang Huaihe vallay . Advance in Atmospheric Science (大气科学进展英文版). 1997,14(1):87-92.
[26] 袁曾任. 人工神经网络及其应用[M]. 清华大学出版社, 1998.
[27] Youmin Tang and William W. Hsieh,. Coupling Neural Network to Incomplete Dynamical System via Variational Data Assimilation[J]. Monthly Weather Review, 2000,129(4):818-834.
[28] Mccann D W., A neural network short-term forecast of significant thunderstorms[J]. Weather and Forecasting, 1992,7:525-534.
[29] Lei shi. Retrieval of Atmospheric Temperature Profiles form AMSU-A Measurement Using a Neural Network Approach[J]. Journal of Atmospheric and Oceanic Technology, 2000,18(3):340-347.
[30] Hongping Liu, V. Chandrasekar and Gang Xu. An adaptive Neural Network Scheme for Radar Rainfall Estimation form WSR-88D Observations[J]. Journal of Applied Meteorology,2001,40(11):2038-2050.
[31] G. Mihalakakou, M, Sanmtanmouris, D. N. Asimakopoulos., The total solar radiation time series simulation in Athens[J]. Using Neural Networks, Theoretical and Applied Climatology, 2000,66(3):185-197.
[32]郭光,严绍谨等. 人工神经网络用于我国东部汛期降水预测研究[J]. 南京气象学院学报,1996,19(3):354-357.
[33]王成刚, 吴保俊等. BP网络在鲁西地区西南涡流降水量级中应用实验[J]. 气象科学,1999,19(2):158-165.
[34]盛永宽. 短期气象(月、季、年)逐月降水系统研究[J]. 气象,1996,22(1)：3-8.
[35]金龙, 罗莹等. 农田土壤湿度的人工神经网络预报模型研究[J]. 土壤学报,1998,35(1):25-32.
[36] 秦伟良, 金龙. 小波神经网络方法用于时间序列分析中非线性模型的研究[J]. 南京气象学院学报, 1997, 20 (3): 370-374
[37] 金龙, 秦伟良等. 多步预测的小波神经网络预报模型[J]. 大气科学, 2000, 24 (1) :79-86
[38] 马革新,张大力等. 非线性系统定阶的神经网络方法[J]. 清华大学学报,1997,37(26):55-58
[39] 金龙, 林振山等. 基于人工神经网络的集成预报方法的研究和比较[J]. 气象学报, 1999, 57 (2): 198-207
[40] 金龙等. 各种最优定阶准则的自回归模型集成预报方法研究[J]. 预测, 1996, 15(6): 57-59
[41] 陈云浩, 史培军等. 不同热力背景对城市降雨(暴雨)的影响(III):一种基于人工神经网络的集成预报模型[J]. 自然灾害学报,2001,10(3):26-31
[42] 陈国良,王熙法. 遗传算法及其应用[M].北京:人民邮电出版社,1996.
[43] Holland John H. Adaptation in Natural and Artificial Systems. The University of Michigan Press 1975; The MIT Press, 1992
[44] 王小平, 曹立明. 遗传算法－理论应用与软件实现[M]. 陕西: 西安交通大学出版社, 2002 15－17.
[45] 周明, 孙树栋. 遗传算法原理及其应用[M]. 北京: 国防工业出版社, 1999： 35－47
[46] 金菊良, 杨晓华, 丁晶. 基于实数编码的快速遗传算法[J]. 四川大学学报, 2000(7):20-24
[47] Goldberg D. F, Real Coded Genetic Algorithm, Virtual Alphabcts and Blocking. Complex Systems, 1991(5): 139-167
[48] Bagley J.D, The behavior of adaptation system which employ genetic and correlation algorithm, Dissertation abstracts international: 1967，28(12)
[49] Goldberg D E. Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA, Addision Wisely, 1989
[50] Davis, L.D. Handbook of genetic algorithms, Van Nostrand Reinhold 1991
[51] Koza,J.R. Genetic programming 1. Cambridge, MA: the MIT Press, 1992
[52] Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs. Springer－Verlag, Second, Extended Edition, 1994
[53] Hofbauer J, Sigmud K. The Theory of Evolution and Dynamical Systems. Cambrige University Press, 1989
[54] Melanie Mitchell. An introduction to genetic algorithms. Cambridge, MA: The MIT Press,1996
[55] Kadaba,N.,Nygard,K.E.,and Juell,P.J.,Integration of adaptive machine learning and knowledgecased systems for routing and scheduling applications. Expert Systems with Application,Vol 2,No.1,1991:15-27
[56] Lin, S. H., Goodman, E. D., and Paunch, W. F., Investigating Parallel Genetic Algorithms on Job Shop Scheduling Problem. In the Sixth International Conference on Evolutionary Programming, Angeline, P., Reynolds, R. J. M., and Eberhart, R. (ed.), Berlin: Springer-Verlag, April 1997: 383-393
[57] Maclay, D., and Dorey, R. Applying genetic search techniques to drivetrain modeling. IEEE Control Systems, Special Issue on Intelligent Control, Vol. 13, No. 3, 1993: 50-55
[58] Freeman, L. M., et al. Turning fuzzy logic controller using genetic algorithms aerospace applications. In Proceedings of the AAAIC’90 Conference, Dayton, Oct., 1990:351-358
[59] McCallum, R. A.,and Spackman, K. A. Using genetic algorithm to learn disjunctive rules form examples. In Proceeding of the International Conference on Machine Learning, San Mateo, CA: Morgan Kaufmann, 1990: 149-152
[60] Bennett, K., A genetic algorithm for database query optimization. IEEE conference on Evolutionary Computation, 1994: 400-407
[61] Xin Yao. A review of evolutionary artifical neural network. International Journal of Intelligent Systems, 1993,8(3): 539-565
[62] Montana, D.J.,and Davis, L., Training feed-forward neutral networks using genetic algorithms. In Proceeding of the International Joint Conference on Artificial Intelligence, Los Altos, CA: Morgan Kaufmann Publishers, 1989:762-767
[63] Bala, J., De Jong, K.A., Haung, J., Vafaie, H., and Wechsler, H.Hybrid learning using genetic algorithm and decision trees for pattern classification. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, August 19-25, 1995, Montreal, Canada
[64] Nikolopoulos, C., and Fellrath, P., et al. Hybrid expert system for investment advising. Expert System, 1994, 11(4): 245-248
[65] 李敏强, 寇纪凇等. 遗传算法的基本理论与应用[M]. 北京: 科学出版社, 2002.
[66] 张 波. 应用随机过程[M]. 北京: 中国人民大学出版社, 2001. 84－85
[67] 林正炎, 陆传荣. 概率极限理论基础[M]. 北京: 高等教育出版社, 2001. 27－28
[68] De Jong K A. Genetic algorithms: a 25 years perspective. Computational intelligence imitating life. New Yourk: IEEE press 1994:125-136
[69] Martin T. Hagan, Howard B. Demuth, Mark H.Beale著. 神经网络设计[M]. 戴葵等译. 北京: 机械工业出版社. 2002.
[70] Simon Haykin著. 神经网络原理[M]. 叶世伟, 史忠植译. 北京: 机械工业出版社. 2004.
[71] 蒋宗礼著. 人工神经网络导论[M]. 北京: 高等教育出版社. 2001.
[72] 徐丽娜编著. 神经网络控制[M]. 黑龙江: 哈尔滨工业大学出版社. 2003.
[73] 王旭, 王宏等编著. 人工神经网络原理与应用[M]. 辽宁: 东北大学出版社. 2000.
[74] 闻新, 周露等. Matlab神经网络仿真与应用[M]. 北京: 科学技术出版社. 2003,5.
[75] 高隽编著. 人工神经网络原理及仿真实例[M]. 北京: 机械工业出版社. 2003,8.
[76] 从爽编著. 面向Matlab工具箱的神经网络理论与应用[M]. 安徽: 中国科学技术大学出版社. 1998,8.
[77] 董聪. 多层前向网络的全局最优问题[J]. 大自然探索, 1996,15 (58): 27-31.
[78] 董聪. 多层前向网络的逼近与泛化机制[J]. 控制与决策, 1998, 13 (4): 414-417.
[79] Funahshi K I. On the Approxirnate Realization of Continuous Mappings by Neutral Networks[J]. Neural Network, 1989,2: 183-192.
[80] Hornik K, Strinchcomber M, Whiter H. Mutilayer Feedforward Networks Are Universal Approximators[J]. Neural Networks. 1989,2:359-366.
[81] Honik K. Approximation Capabilities of Multilayer Feedforward Networks Neural[J]. Neural Network, 1991,4: 551-557.
[82] 陈天平. 神经网络及其在系统识别应用中的逼近问题[J]. 中国科学(A辑), 1994,24 (1): 1-7.
[83] 董聪. 前向网络全局最优化问题研究[J].中国科学基金, 1997,1:23-29.
[84] 懂聪. 人工神经网络: 当前的进展与问题[J]. 科技导报,1999,7:26-30.
[85] 懂聪, 郭晓华. 计算智能中若干热点问题的研究与进展[J]. 控制理论与应用, 2000, 17(5):691-697.
[86] Tom M. Mitchell著. 机器学习[M]. 曾华军, 张银奎等译. 北京: 机械工业出版社. 2003, 1.
[87] 金龙著. 神经网络预报建模理论方法与应用[M]. 北京: 气象出版社. 将于2004年出版.
[88] 王成名, 余鑫辉等编著. 应用概率统计[M]. 广西: 广西师范大学出版社. 1994, 3.
[89] 杨善朝, 张军舰编著. SPSS统计软件应用基础[M]. 广西: 广西师范大学出版社. 2001, 9.
[90] 苏金明, 张莲花, 刘波等编著. Matlab工具箱应用[M]. 北京: 电子工业出版社. 2004, 1.
[91] 张志涌等编著. 精通Matlab6.5版. 北京: 北京航空航天大学出版社. 2003, 5.
[2] Hsieh William W. Nonlinear canonical correlation analysis of the tropical Pacific climate variability using neural network approach [J]. 2001, 14(12): 2528-2539.
[3] Jin Long, Ju Weimin, Miao Qilong. Study on Ann-based multi-step prediction model of short-term climatic variation[J]. Advances Atmosphere Sciences, 2000, 17(1):157-164.
[4] 胡江林, 张礼平, 宇如聪. 神经网络模型预报湖北汛期降水量的应用研究[J]. 气象学报, 2001, 59 (6): 776-783.
[5] 金龙, 苗春生.定性和定量的长期预报模型的综合分析[J]. 气象学报, 2000, 58 (4) :479-484.
[6] Wu Yan, Zhang Liming. A new regularization learning method for improving generalization capability of neural network[C]. Proceedings of 4th world congress on intelligent control and automation, Shanghai, 2002,3: 2011-2015.
[7] 江学军, 唐焕文. 前馈神经网络泛化性能的系统分析[J]. 系统工程理论与实践, 2000, 28(8): 36-40.
[8] 彭汉川, 甘强,韦钰. 提高前馈神经网络推广能力的若干实际方法[J]. 电子学报,1998, 26(4):
116-119.
[9] 杨晓红,刘乐善. 用遗传算法优化神经网络结构[J]. 计算机应用与软件, 1997, 14(3): 59-65.
[10] 李敏强. 遗传算法和神经网络的结合[J]. 系统工程理论与实践,1999, (2): 65-69.
[11] 孙晓光. 遗传算法对热轧带钢精轧机组负荷分配BP网络参数的优化[J]. 钢铁, 1998, 33(7): 33-36.
[12] 李祚泳, 彭荔红. 基于遗传算法的暴雨强度公式参数的优化[J]. 高原气象, 2003, 22(6): 637-639.
[13] 饶文碧, 徐锐, 尚钢. 基于遗传算法的结构损伤识别[J]. 武汉理工大学学报, 2003, 25(7):75-77.
[14] 李发斌, 崔鹏等. 用遗传神经网络分析泥石流活动性[J]. 中国地质灾害与防治学报, 2003,14(3):16-18.
[15] Goldberg, D. E., Segrest, P. Finite Markov Chain Analysis of Genetic Algorithms[C]. Proc. Of Second International Conference on Genetic Algorithms. 1987,1-8.
[16] Eiben, A. E., Aarts, E. H., and Van Hee, K. M., Global Convergence of Genetic Algorithms; An Infinite Markov Chain Analysis. Parallel Problem Solving from Nature[M]. Berlin: Spring-Verlag, 1991: 4-12.
[17] Rudolph, G., Convergence Properties of Canonical Genetic Algorithms[J]. IEEE Trans. On Neural Networks. 1994,5 (1): 96-101.
[18] Qi, X., Palmieri, F.. Theoretical Analysis of Evolutionary Algorithms with an Infinite Population Size in Continuous Space, Part I: Basic Properties of selection and Mutation. IEEE Trans. On Neural Network, 1994, 102-119.
[19] 恽为民, 席裕庚. 遗传算法的全局收敛性和计算效率分析[J]. 控制理论与应用, 1996,13(4):455-460.
[20] 徐总本, 聂赞坎, 张文修. 遗传算法的几乎必然强收敛-鞅方法[J]. 计算机学报, 2002, 25(8):785-793.
[21] 王霞, 周国标. 遗传算法收敛的下鞅分析[J]. 应用数学, 2003, 16(4):130-135.
[22] 宋正山, 杨辉. 夏季东亚季风区500hPa月环流异常及其与我国降水关系的向量EOF分析[J]. 大气
科学, 2001,25(3): 401-404.
[23] 白人海. 大西洋海表温度异常与中国东北地区夏季降水的关系[J]. 海洋通报, 2001, 20(1):23-29.
[24] 辛若桂, 屠其璞. 我国气温长期变化的区域特征[J]. 南京气象学院学报, 1997, 20(1):54-63.
[25] Jinglong, et al. Comparison of Long-term forecasting June-August rainfall over Changjiang Huaihe vallay . Advance in Atmospheric Science (大气科学进展英文版). 1997,14(1):87-92.
[26] 袁曾任. 人工神经网络及其应用[M]. 清华大学出版社, 1998.
[27] Youmin Tang and William W. Hsieh,. Coupling Neural Network to Incomplete Dynamical System via Variational Data Assimilation[J]. Monthly Weather Review, 2000,129(4):818-834.
[28] Mccann D W., A neural network short-term forecast of significant thunderstorms[J]. Weather and Forecasting, 1992,7:525-534.
[29] Lei shi. Retrieval of Atmospheric Temperature Profiles form AMSU-A Measurement Using a Neural Network Approach[J]. Journal of Atmospheric and Oceanic Technology, 2000,18(3):340-347.
[30] Hongping Liu, V. Chandrasekar and Gang Xu. An adaptive Neural Network Scheme for Radar Rainfall Estimation form WSR-88D Observations[J]. Journal of Applied Meteorology,2001,40(11):2038-2050.
[31] G. Mihalakakou, M, Sanmtanmouris, D. N. Asimakopoulos., The total solar radiation time series simulation in Athens[J]. Using Neural Networks, Theoretical and Applied Climatology, 2000,66(3):185-197.
[32]郭光,严绍谨等. 人工神经网络用于我国东部汛期降水预测研究[J]. 南京气象学院学报,1996,19(3):354-357.
[33]王成刚, 吴保俊等. BP网络在鲁西地区西南涡流降水量级中应用实验[J]. 气象科学,1999,19(2):158-165.
[34]盛永宽. 短期气象(月、季、年)逐月降水系统研究[J]. 气象,1996,22(1)：3-8.
[35]金龙, 罗莹等. 农田土壤湿度的人工神经网络预报模型研究[J]. 土壤学报,1998,35(1):25-32.
[36] 秦伟良, 金龙. 小波神经网络方法用于时间序列分析中非线性模型的研究[J]. 南京气象学院学报, 1997, 20 (3): 370-374
[37] 金龙, 秦伟良等. 多步预测的小波神经网络预报模型[J]. 大气科学, 2000, 24 (1) :79-86
[38] 马革新,张大力等. 非线性系统定阶的神经网络方法[J]. 清华大学学报,1997,37(26):55-58
[39] 金龙, 林振山等. 基于人工神经网络的集成预报方法的研究和比较[J]. 气象学报, 1999, 57 (2): 198-207
[40] 金龙等. 各种最优定阶准则的自回归模型集成预报方法研究[J]. 预测, 1996, 15(6): 57-59
[41] 陈云浩, 史培军等. 不同热力背景对城市降雨(暴雨)的影响(III):一种基于人工神经网络的集成预报模型[J]. 自然灾害学报,2001,10(3):26-31
[42] 陈国良,王熙法. 遗传算法及其应用[M].北京:人民邮电出版社,1996.
[43] Holland John H. Adaptation in Natural and Artificial Systems. The University of Michigan Press 1975; The MIT Press, 1992
[44] 王小平, 曹立明. 遗传算法－理论应用与软件实现[M]. 陕西: 西安交通大学出版社, 2002 15－17.
[45] 周明, 孙树栋. 遗传算法原理及其应用[M]. 北京: 国防工业出版社, 1999： 35－47
[46] 金菊良, 杨晓华, 丁晶. 基于实数编码的快速遗传算法[J]. 四川大学学报, 2000(7):20-24
[47] Goldberg D. F, Real Coded Genetic Algorithm, Virtual Alphabcts and Blocking. Complex Systems, 1991(5): 139-167
[48] Bagley J.D, The behavior of adaptation system which employ genetic and correlation algorithm, Dissertation abstracts international: 1967，28(12)
[49] Goldberg D E. Genetic Algorithms in Search, Optimization, and Machine Learning. Reading, MA, Addision Wisely, 1989
[50] Davis, L.D. Handbook of genetic algorithms, Van Nostrand Reinhold 1991
[51] Koza,J.R. Genetic programming 1. Cambridge, MA: the MIT Press, 1992
[52] Michalewicz Z. Genetic Algorithms + Data Structures = Evolution Programs. Springer－Verlag, Second, Extended Edition, 1994
[53] Hofbauer J, Sigmud K. The Theory of Evolution and Dynamical Systems. Cambrige University Press, 1989
[54] Melanie Mitchell. An introduction to genetic algorithms. Cambridge, MA: The MIT Press,1996
[55] Kadaba,N.,Nygard,K.E.,and Juell,P.J.,Integration of adaptive machine learning and knowledgecased systems for routing and scheduling applications. Expert Systems with Application,Vol 2,No.1,1991:15-27
[56] Lin, S. H., Goodman, E. D., and Paunch, W. F., Investigating Parallel Genetic Algorithms on Job Shop Scheduling Problem. In the Sixth International Conference on Evolutionary Programming, Angeline, P., Reynolds, R. J. M., and Eberhart, R. (ed.), Berlin: Springer-Verlag, April 1997: 383-393
[57] Maclay, D., and Dorey, R. Applying genetic search techniques to drivetrain modeling. IEEE Control Systems, Special Issue on Intelligent Control, Vol. 13, No. 3, 1993: 50-55
[58] Freeman, L. M., et al. Turning fuzzy logic controller using genetic algorithms aerospace applications. In Proceedings of the AAAIC’90 Conference, Dayton, Oct., 1990:351-358
[59] McCallum, R. A.,and Spackman, K. A. Using genetic algorithm to learn disjunctive rules form examples. In Proceeding of the International Conference on Machine Learning, San Mateo, CA: Morgan Kaufmann, 1990: 149-152
[60] Bennett, K., A genetic algorithm for database query optimization. IEEE conference on Evolutionary Computation, 1994: 400-407
[61] Xin Yao. A review of evolutionary artifical neural network. International Journal of Intelligent Systems, 1993,8(3): 539-565
[62] Montana, D.J.,and Davis, L., Training feed-forward neutral networks using genetic algorithms. In Proceeding of the International Joint Conference on Artificial Intelligence, Los Altos, CA: Morgan Kaufmann Publishers, 1989:762-767
[63] Bala, J., De Jong, K.A., Haung, J., Vafaie, H., and Wechsler, H.Hybrid learning using genetic algorithm and decision trees for pattern classification. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, August 19-25, 1995, Montreal, Canada
[64] Nikolopoulos, C., and Fellrath, P., et al. Hybrid expert system for investment advising. Expert System, 1994, 11(4): 245-248
[65] 李敏强, 寇纪凇等. 遗传算法的基本理论与应用[M]. 北京: 科学出版社, 2002.
[66] 张 波. 应用随机过程[M]. 北京: 中国人民大学出版社, 2001. 84－85
[67] 林正炎, 陆传荣. 概率极限理论基础[M]. 北京: 高等教育出版社, 2001. 27－28
[68] De Jong K A. Genetic algorithms: a 25 years perspective. Computational intelligence imitating life. New Yourk: IEEE press 1994:125-136
[69] Martin T. Hagan, Howard B. Demuth, Mark H.Beale著. 神经网络设计[M]. 戴葵等译. 北京: 机械工业出版社. 2002.
[70] Simon Haykin著. 神经网络原理[M]. 叶世伟, 史忠植译. 北京: 机械工业出版社. 2004.
[71] 蒋宗礼著. 人工神经网络导论[M]. 北京: 高等教育出版社. 2001.
[72] 徐丽娜编著. 神经网络控制[M]. 黑龙江: 哈尔滨工业大学出版社. 2003.
[73] 王旭, 王宏等编著. 人工神经网络原理与应用[M]. 辽宁: 东北大学出版社. 2000.
[74] 闻新, 周露等. Matlab神经网络仿真与应用[M]. 北京: 科学技术出版社. 2003,5.
[75] 高隽编著. 人工神经网络原理及仿真实例[M]. 北京: 机械工业出版社. 2003,8.
[76] 从爽编著. 面向Matlab工具箱的神经网络理论与应用[M]. 安徽: 中国科学技术大学出版社. 1998,8.
[77] 董聪. 多层前向网络的全局最优问题[J]. 大自然探索, 1996,15 (58): 27-31.
[78] 董聪. 多层前向网络的逼近与泛化机制[J]. 控制与决策, 1998, 13 (4): 414-417.
[79] Funahshi K I. On the Approxirnate Realization of Continuous Mappings by Neutral Networks[J]. Neural Network, 1989,2: 183-192.
[80] Hornik K, Strinchcomber M, Whiter H. Mutilayer Feedforward Networks Are Universal Approximators[J]. Neural Networks. 1989,2:359-366.
[81] Honik K. Approximation Capabilities of Multilayer Feedforward Networks Neural[J]. Neural Network, 1991,4: 551-557.
[82] 陈天平. 神经网络及其在系统识别应用中的逼近问题[J]. 中国科学(A辑), 1994,24 (1): 1-7.
[83] 董聪. 前向网络全局最优化问题研究[J].中国科学基金, 1997,1:23-29.
[84] 懂聪. 人工神经网络: 当前的进展与问题[J]. 科技导报,1999,7:26-30.
[85] 懂聪, 郭晓华. 计算智能中若干热点问题的研究与进展[J]. 控制理论与应用, 2000, 17(5):691-697.
[86] Tom M. Mitchell著. 机器学习[M]. 曾华军, 张银奎等译. 北京: 机械工业出版社. 2003, 1.
[87] 金龙著. 神经网络预报建模理论方法与应用[M]. 北京: 气象出版社. 将于2004年出版.
[88] 王成名, 余鑫辉等编著. 应用概率统计[M]. 广西: 广西师范大学出版社. 1994, 3.
[89] 杨善朝, 张军舰编著. SPSS统计软件应用基础[M]. 广西: 广西师范大学出版社. 2001, 9.
[90] 苏金明, 张莲花, 刘波等编著. Matlab工具箱应用[M]. 北京: 电子工业出版社. 2004, 1.
[91] 张志涌等编著. 精通Matlab6.5版. 北京: 北京航空航天大学出版社. 2003, 5.