基于粗糙集与神经网络的水质评价模型研究
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摘要
三峡库区水环境保护问题一直是国家重点关注的问题,关系到国家的经济建设和长治久安。而三峡库区由于其水文环境复杂,进行水质评价时评价因子较多,且存在冗余信息,所以在进行水质评价的时候既要保证建立正确评价模型,又要考虑到降低模型的复杂性,增强模型的可理解性。
本论文工作主要来源于三峡库区水污染重大事件科学决策关键技术研究项目下的一个子课题:三峡库区水环境安全综合信息分析系统。在分析三峡库区水环境各项数据的基础上,依据数据的特点,采用粗糙集和人工神经网络相结合的方法来建立水质评价模型。
粗糙集方法在不需要先验知识的情况下能够去除冗余信息,依据属性重要度挑选出适合进行最终评价的评价因子。人工神经网络以其具有自学习、自组织、较好的容错性和优良的非线性逼近能力,已在水质评价方面广泛应用。粗糙集和人工神经网络结合的方式有多种,本文主要分析了粗糙集用于数据预处理,作为处理器前端的结合方式和粗糙元神经网络这两种结合方式,以及将这两种结合方式再进行结合的粗糙集作为处理器前端,粗糙元神经网络作为处理器后端的评价模型。
粗糙集用于数据预处理,作为处理器前端的结合方式主要是指用粗糙集方法对数据进行约简,去除冗余信息,减少评价指标,将处理好后得到的评价指标作为人工神经网络的输入,再用BP神经网络进行建模评价。该结合方式减小了数据集的规模,一方面提高了数据的代表性,减少了噪声的干扰,从而使训练出来的神经网络不容易出现“过拟合”现象,另一方面减少了训练数据,使训练时间得以减少,提高了效率。
粗糙元神经网络主要是指针对输入的数据是不确定的、非精确值或范围值的时候,改造神经网络的传统神经元为由一对上下神经元组成的粗糙神经元,由此构成的神经网络处理能力更强,在处理范围值时能够得到更高的精度。
本文以三峡库区水环境数据为背景,将两种结合方法应用到实际系统中,实验对比了这两种结合方法,得出结论为:在实际系统中,粗糙集作为处理器前端,粗糙元神经网络作为评价模型的结合方式既能在提高运行效率基础上得到正确的结果,又能得到影响水质评价的指标因子集合,提高了系统的正确性和可理解性。所以最终在三峡库区水环境安全系统中选用该结合方式进行水质评价。
The water resources pollution problem in the Three Gorges area of the Yangtze River has drawn great attention from the outside and inside. The water environment is complicated, it also contains many factors and redundancy data in its evaluation. Both set up correct evaluation model and decrease complication of the model are what we supposed.
The work of this dissertation is derived from a research project named Three Gorges Dam Area Water Pollution and Counter. Through the analyses of the dam area data, we set up the water evaluation model in a combined method which contains rough set theory and artificial neural networks theory.
Rough sets is a kind of mathematical tool that is based upon math’s conception methods, which can be used to select the right evaluation factors set without any preliminary expert knowledge. Artificial neural networks have been applied in water evaluation area successfully because of its abilities of self-learning, self-organization, fault-tolerant and nonlinear- approximation. There are several combination strategies based on rough sets and artificial neural networks, two of them are discussed in this dissertation, one is using rough set method to preprocess the data and the other is a rough neural networks which contains rough neuron. At last, we also discussed the evaluation model combined of above two combination strategies, rough set method is used to preprocess the data and rough neural networks is used to evaluate the water.
The main purpose of the data preprocessing by using rough sets is clean the noisy data and reduce the evaluation factors. After preprocessing, the reduced data will be as the input of artificial neural networks, and then the evaluation model will be set up by using BP neural networks. The advantages of this combination strategy are not only clean the noisy data and decrease the probability of over-fitting in trained neural networks, but also reduce the training data which save the training time and improve the efficiency.
In rough neural networks, each rough neuron denotes an upper and lower boundary of a pattern, and rough neurons provide a capability on analyzing rough data. It is applied to deal with the data whose input and output are interval number.
In this dissertation, the two combination strategies are compared with each other in the experiment of Three Gorges Dam Area water data. The result is that the strategy which uses rough set as the data preprocessing unit and rough neurons networks as the evaluation model unit is better than the other strategies. In real evaluation system, using rough sets to preprocess the data can improve the efficiency and get the set of evaluation factors which are important or indispensable for the evaluation, and this also improve the comprehension of evaluation model. At last, we applied the method in the real system.
本论文工作主要来源于三峡库区水污染重大事件科学决策关键技术研究项目下的一个子课题:三峡库区水环境安全综合信息分析系统。在分析三峡库区水环境各项数据的基础上,依据数据的特点,采用粗糙集和人工神经网络相结合的方法来建立水质评价模型。
粗糙集方法在不需要先验知识的情况下能够去除冗余信息,依据属性重要度挑选出适合进行最终评价的评价因子。人工神经网络以其具有自学习、自组织、较好的容错性和优良的非线性逼近能力,已在水质评价方面广泛应用。粗糙集和人工神经网络结合的方式有多种,本文主要分析了粗糙集用于数据预处理,作为处理器前端的结合方式和粗糙元神经网络这两种结合方式,以及将这两种结合方式再进行结合的粗糙集作为处理器前端,粗糙元神经网络作为处理器后端的评价模型。
粗糙集用于数据预处理,作为处理器前端的结合方式主要是指用粗糙集方法对数据进行约简,去除冗余信息,减少评价指标,将处理好后得到的评价指标作为人工神经网络的输入,再用BP神经网络进行建模评价。该结合方式减小了数据集的规模,一方面提高了数据的代表性,减少了噪声的干扰,从而使训练出来的神经网络不容易出现“过拟合”现象,另一方面减少了训练数据,使训练时间得以减少,提高了效率。
粗糙元神经网络主要是指针对输入的数据是不确定的、非精确值或范围值的时候,改造神经网络的传统神经元为由一对上下神经元组成的粗糙神经元,由此构成的神经网络处理能力更强,在处理范围值时能够得到更高的精度。
本文以三峡库区水环境数据为背景,将两种结合方法应用到实际系统中,实验对比了这两种结合方法,得出结论为:在实际系统中,粗糙集作为处理器前端,粗糙元神经网络作为评价模型的结合方式既能在提高运行效率基础上得到正确的结果,又能得到影响水质评价的指标因子集合,提高了系统的正确性和可理解性。所以最终在三峡库区水环境安全系统中选用该结合方式进行水质评价。
The water resources pollution problem in the Three Gorges area of the Yangtze River has drawn great attention from the outside and inside. The water environment is complicated, it also contains many factors and redundancy data in its evaluation. Both set up correct evaluation model and decrease complication of the model are what we supposed.
The work of this dissertation is derived from a research project named Three Gorges Dam Area Water Pollution and Counter. Through the analyses of the dam area data, we set up the water evaluation model in a combined method which contains rough set theory and artificial neural networks theory.
Rough sets is a kind of mathematical tool that is based upon math’s conception methods, which can be used to select the right evaluation factors set without any preliminary expert knowledge. Artificial neural networks have been applied in water evaluation area successfully because of its abilities of self-learning, self-organization, fault-tolerant and nonlinear- approximation. There are several combination strategies based on rough sets and artificial neural networks, two of them are discussed in this dissertation, one is using rough set method to preprocess the data and the other is a rough neural networks which contains rough neuron. At last, we also discussed the evaluation model combined of above two combination strategies, rough set method is used to preprocess the data and rough neural networks is used to evaluate the water.
The main purpose of the data preprocessing by using rough sets is clean the noisy data and reduce the evaluation factors. After preprocessing, the reduced data will be as the input of artificial neural networks, and then the evaluation model will be set up by using BP neural networks. The advantages of this combination strategy are not only clean the noisy data and decrease the probability of over-fitting in trained neural networks, but also reduce the training data which save the training time and improve the efficiency.
In rough neural networks, each rough neuron denotes an upper and lower boundary of a pattern, and rough neurons provide a capability on analyzing rough data. It is applied to deal with the data whose input and output are interval number.
In this dissertation, the two combination strategies are compared with each other in the experiment of Three Gorges Dam Area water data. The result is that the strategy which uses rough set as the data preprocessing unit and rough neurons networks as the evaluation model unit is better than the other strategies. In real evaluation system, using rough sets to preprocess the data can improve the efficiency and get the set of evaluation factors which are important or indispensable for the evaluation, and this also improve the comprehension of evaluation model. At last, we applied the method in the real system.
引文
[1]高千红.概率神经网络在三峡进坝水域水质评价中的应用研究[D].南京.河海大学工程硕士论文. 2006.
[2]王海霞.模糊神经网络在水质评价中的应用[D].重庆.重庆大学硕士论文. 2002.
[3]刘进涛.模糊神经网络在水质评价中的应用[D].北京.首都师范大学硕士论文. 2006.
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[21]徐立中,王慧斌,杨锦堂.基于粗糙集理论的图像增强方法[J].仪器仪表学报. 2000, 21(5): 514-515, 524.
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[28]王珏,王任,苗夺谦等.基于Rough sets理论的”数据浓缩”[J].计算机学报. 1998, 21(5):393-400.
[29] Hu X H. and Nick C. Learning in relational databases: a rough set approach[J]. International Journal of Computational Intelligence. 1995, 11(2):323-338.
[30]徐德友,胡寿松.一种基于粗糙集的近似质量求取属性约简的决策算法[J].控制与决策, 2003,18(3):313-316.
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[32]叶东毅,陈昭炯.一个新的差别矩阵及其求核方法[J].电子学报. 2002, 30(7): 1086-1088.
[33]杨明.一种基于改进差别矩阵的核增量式更新算法[J].计算机学报. 2006, 29(3): 407-413.
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[2]王海霞.模糊神经网络在水质评价中的应用[D].重庆.重庆大学硕士论文. 2002.
[3]刘进涛.模糊神经网络在水质评价中的应用[D].北京.首都师范大学硕士论文. 2006.
[4] Pawlak Z. Rough sets-theoretical aspects of reasoning about data[M]. Dordrecht: Kluwer Academic Publishers. 1991, 9-30.
[6] Dubois D. and Prade H. Rough fuzzy sets and fuzzy rough sets[J]. International Journal of General Systems. 1990, 17(2):191-209.
[7]祝峰,何华灿.粗集的公理化[J].计算机学报. 2000, 23(3): 330-333.
[8]米据生,吴伟志等.粗糙集的构造与公理化方法[J].模式识别与人工智能. 2002, 15(3): 280-284.
[9] Pawan Lingras. Comparison of neofuzzy and rough neural networks[J]. Information Sciences. 1998, 110: 207-215.
[10] Nguyen H S. From optimal hyperplanes to optimal decision tree[C]. Proceedings of the IV International Workshop on Rough Sets, Fuzzy Sets and Machine Discovery, RSFD'96, Nov.6-8, 1996, Tokyo, Japan, 82-88.
[11] Wu Zhaocong and Li Deren. Neural networks based on rough sets and its application to remote sensing image classification[J]. Geo-Spatial Information Science, 2002, 5(2): 17-21.
[5] Ziarko W. Variable precision rough set model[J]. Journal of computer and system sciences, 1993, 46(1): 39-59.
[12]苗夺谦,胡桂荣.知识约简的一种启发式算法[J].计算机研究与发展. 1999, 36(6): 681-684.
[13] Shan N and Ziarko W. An incremental learning algorithm for constructing decision rules[C]. In: Kluwer R S, ed. Rough Sets, Fuzzy Sets and Knowledge Discovery. Springer-Verlag, 1994, 326-334.
[14] Muraszkieqicz M. and Ryhinski J. Towards a parallel rough sets computer[C]. In: Ziarko, W, ed. Rough Sets. Fuzzy Sets and Knowledge Discovery. Springer-Verlag, 1994, 434-443.
[15]陈文林,郝丽娜,徐心和.粗糙集—神经网络—专家系统混合系统及其应用[J].计算机工程. 2003, 29(9): 147-148,178.
[16] Ziarko W. Methodology for stork market analysis is utilizing rough set theory[C]. Proceedings of IEEE/IAFE Conference on Computational Intelligence for FinancialEngineering. 1995, 32~40.
[17] Surnoto T T. Automated discovery of media expert system rules from clinical data bases based on rough sets[C]. Proceedings of Second International Conference on Knowledge Discovery and Data Mining, USA. 1996, 63-72.
[18] Teghe M. Use of rough sets method to draw Premonitory factors for earthquakes by emphasizing gas geochemistry[M]. Intelligent Decision Support-Handbook of applications and Advances of the Rough Sets Theory. Dordrecht: Kluwer Academic Publishers.1992, 165~179.
[19] Rafal Deja. Conflict model with negotiations[R]. Institute of Computer Science Reports. Warsaw University of Technology .Warsaw, 1995.
[20]刘泓.基于粗糙集理论的车牌识别系统的研究与实现[D].合肥.合肥工业大学博士论文. 2003.
[21]徐立中,王慧斌,杨锦堂.基于粗糙集理论的图像增强方法[J].仪器仪表学报. 2000, 21(5): 514-515, 524.
[22]胡静,曹先彬,王煦法.基于相容粗糙集的图形图像信息预检索[J].计算机辅助设计与图形学学报. 2002, 14(3):33-37.
[23] Nejman D. A rough set based method of handwritten numerals classification[R]. Institute of Computer Science Reports. Warsaw University of Technology, Warsaw, 1994.
[24] Sienkiewiez J. Rough sets and rough function approaches to the control algorithm reconstruction[R]. Institute of Computer Science Reports. Warsaw University of Technology, Warsaw, 1996.
[25] Plonka L M. A rule-based stabilization of the inverted pendulum[J]. Computational Intelligence. 1995,Ⅱ(2):348-356.
[26] Mrozek A. Rough sets and dependency analysis among attributes in computer implementations of expert’s inference models[J]. International Journal of Man-Machine Studies.1989, 30(4):456-475.
[27]谭天乐.基于粗糙集的过程建模、控制与故障诊断[D].杭州.浙江大学博士学位论文. 2003.
[28]王珏,王任,苗夺谦等.基于Rough sets理论的”数据浓缩”[J].计算机学报. 1998, 21(5):393-400.
[29] Hu X H. and Nick C. Learning in relational databases: a rough set approach[J]. International Journal of Computational Intelligence. 1995, 11(2):323-338.
[30]徐德友,胡寿松.一种基于粗糙集的近似质量求取属性约简的决策算法[J].控制与决策, 2003,18(3):313-316.
[31] Skowron A. and Rauszer C.. The discernibility matrices and functions in information systems[M]. Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory,1992, PartⅢ, Chapter 2.
[32]叶东毅,陈昭炯.一个新的差别矩阵及其求核方法[J].电子学报. 2002, 30(7): 1086-1088.
[33]杨明.一种基于改进差别矩阵的核增量式更新算法[J].计算机学报. 2006, 29(3): 407-413.
[34] McCulloch W S. and Pitts W. Bulletin of Mathematical Biophysics[M]. 1943, 115-133.
[35] Hebb D O. The organization of behavior[M]. John Wiley, 1949, 1120-1223.
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