基于粗集与聚类的神经模糊建模
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摘要
在现代复杂工业控制中，由于被控对象通常具有多变量、严重的非线性、强耦合、大滞后、分布参数、时变以及种类繁多的干扰，使得基于精确数学模型的常规控制方法已无法获得满意的动静态控制效果。近年来，基于神经网络和模糊逻辑的神经模糊控制得到了广泛的应用。在众多的神经模糊建模方法中，数Jang于1994年提出的ANFIS-自适应神经模糊建模方法最为突出，它的自适应性质使得它几乎可直接应用于自适应控制和学习控制；事实上，它可以替代控制系统的任意神经元网络并执行同样的功能。然而它和绝大多数神经模糊建模一样总是不可避免地存在着这样一个难题，即结构辨识问题，也就是如何合适地划分输入输出空间，如何从观测数据中提取出较为简化的模糊规则库，避免规则库爆炸问题。
由Z.Pawlak提出的粗糙集理论是一种刻划不完整性和不确定性的又一个强有力的数学工具，能有效地分析不精确(imprecise)、不一致(inconsistent)、不完整(incomplete)等各种不完备的信息，还可以对数据进行分析和推理，从中发现隐含的知识,揭示潜在的规律。
本文在学习已有文献的基础上，结合作者三年来的学习与实践，利用聚类算法较好的数据组织与分类能力以及粗集理论强大的数据分析与分类能力，分别提出了两种从系统的观测数据中提取模糊规则的方法，构造类似于ANFIS模型的SCANFIS模型和RSANFIS模型，使得规则库的规模不再随系统的输入维数呈指数增长，一定程度上解决了维数灾难问题，为复杂的多输入系统的建模提出了一种切实有效的建模方法。具体的仿真试验表明这两种建模方法对于复杂的多输入系统的建模，在效率与精度上比ANFIS模型及其他模型都要好。
In the control of complicated modern industrial plants,because most of the plants have many input variables,high non-linearity,tight coupling,serious transmission lag,distributed parameters,time -varying and many kinds of disturbances,the conventional control methods based on the exact mathematical model can not achieve both approving dynamic and static results. Recently,Neuro-fuzzy Control base on the Neural Network Theory and Fuzzy Logic System was used widely and successfully. In most of these Neuro-fuzzy modeling methods,the ANFIS (Adaptive -Network-based Fuzzy Inference Systems) method which was proposed by Jang in 1993 is the most prominent one,its adaptive property made it possible to be used in adaptive control and learning control directly. In fact,it can replace any Neural Network of the control systems and carry out the same function. However,it has the same problem as most of the Neuro-fuzzy systems - rule explosion problem. It is a difficult problem relates to the structure identification of the
system and concerns with the partition of the input and output space and the rule generation of the raw sample data.
Rough set theory,introduced by Zdzislaw Pawlak in the early 1980s,is another new powerful mathematical tool to deal with vagueness and uncertainty. It can analyze the imprecise,inconsistent and incomplete information effectively,find out the connotative knowledge and detect the potential rule of the system under consideration.
In this paper,combine with what the author learned and studied during the three years,using the Cluster Algorithm and the Rough Set Theory,the author propos two new rule generation methods and put forward two new Neuro-fuzzy modeling methods with the T-S type of rule consequent,which named SCANFIS and RSANFIS respectively. Both methods can get over the rule explosion problem and confine the size of the rule base to a reasonable one. They give effective solutions to the modeling of the complicate multi-input systems. The simulation results show that both methods are more powerful than ANFIS method in modeling complicate multi-input systems concerning with efficiency and precision of the model.
由Z.Pawlak提出的粗糙集理论是一种刻划不完整性和不确定性的又一个强有力的数学工具，能有效地分析不精确(imprecise)、不一致(inconsistent)、不完整(incomplete)等各种不完备的信息，还可以对数据进行分析和推理，从中发现隐含的知识,揭示潜在的规律。
本文在学习已有文献的基础上，结合作者三年来的学习与实践，利用聚类算法较好的数据组织与分类能力以及粗集理论强大的数据分析与分类能力，分别提出了两种从系统的观测数据中提取模糊规则的方法，构造类似于ANFIS模型的SCANFIS模型和RSANFIS模型，使得规则库的规模不再随系统的输入维数呈指数增长，一定程度上解决了维数灾难问题，为复杂的多输入系统的建模提出了一种切实有效的建模方法。具体的仿真试验表明这两种建模方法对于复杂的多输入系统的建模，在效率与精度上比ANFIS模型及其他模型都要好。
In the control of complicated modern industrial plants,because most of the plants have many input variables,high non-linearity,tight coupling,serious transmission lag,distributed parameters,time -varying and many kinds of disturbances,the conventional control methods based on the exact mathematical model can not achieve both approving dynamic and static results. Recently,Neuro-fuzzy Control base on the Neural Network Theory and Fuzzy Logic System was used widely and successfully. In most of these Neuro-fuzzy modeling methods,the ANFIS (Adaptive -Network-based Fuzzy Inference Systems) method which was proposed by Jang in 1993 is the most prominent one,its adaptive property made it possible to be used in adaptive control and learning control directly. In fact,it can replace any Neural Network of the control systems and carry out the same function. However,it has the same problem as most of the Neuro-fuzzy systems - rule explosion problem. It is a difficult problem relates to the structure identification of the
system and concerns with the partition of the input and output space and the rule generation of the raw sample data.
Rough set theory,introduced by Zdzislaw Pawlak in the early 1980s,is another new powerful mathematical tool to deal with vagueness and uncertainty. It can analyze the imprecise,inconsistent and incomplete information effectively,find out the connotative knowledge and detect the potential rule of the system under consideration.
In this paper,combine with what the author learned and studied during the three years,using the Cluster Algorithm and the Rough Set Theory,the author propos two new rule generation methods and put forward two new Neuro-fuzzy modeling methods with the T-S type of rule consequent,which named SCANFIS and RSANFIS respectively. Both methods can get over the rule explosion problem and confine the size of the rule base to a reasonable one. They give effective solutions to the modeling of the complicate multi-input systems. The simulation results show that both methods are more powerful than ANFIS method in modeling complicate multi-input systems concerning with efficiency and precision of the model.
引文
1. R. Jang. "ANFIS: Adaptive-Network-based Fuzzy Inference System." IEEE Trans. On Systems, Man & Cybernetics, may 1993.
2. Jyh-Shing R.Jang," Fuzzy Modeling Using Generalized Neural Networks and Kalman Filter Algorithm ".
3. T. Takagi and M. Sugeno. "Fuzzy identification of systems and its application to modeling and control." IEEE Trans. On Systems, Man & Cybernetics, vol. 15. pp.116-132. 1985.
4. M.Sugeno and G.T. Kang, "Structure Identification of Fuzzy Model". Fuzzy Sets and Systems 28(1988),p15-33.
5. J.S.R. Jang, C. T. Sun, E.Mizutani. "Neuro-Fuzzy and Soft Computing A Computional Approach to Learning and Machine Intelligence". Publish by Prentice Hall. 1997.
6. R.R. Yager and D. P. Filev. "Approximate clustering via the mountain method." IEEE Trans. On systems, man & Cybernetics, 24:1279-1284,1992.
7. R.R. Yager and D. P. Filev. "Generation of fuzzy rules by mountain clustering." Joumal of Intelligent and Fuzzy Systems, 2:209-219, 1994.
8. Ronald R. Yager and Dimitar P. Filev. "Essentials of fuzzy modeling and control.", John Wilwy & Sons, Inc,1994.
9. J.-S. Roger Jang. "Structure determination in fuzzy modeling: a fuzzy CART approach", In proceedings of IEEE International conference on Fuzzy Systems, Orlando,Florida, June 1994.
10. Stephen L. Chiu, "A Cluster Estimation Method with Extension to Fuzzy Model Identification" IEEE Trans.1994.
11. Ken Nozaki, Hisao Ishibuchi, Hideo Tanaka. "A simple but powerful heuristic method for generating fuzzy rules from numerical data." Fuzzy Sets and Systems 86 (1997) 251-270.
12. Ching-Chang Wang, Hung-Ren Lai, "Generating Fuzzy Control Rules by a Clustering Algorithm Based on a Grey Relational Measure ", IEEE international Fuzzy Systems Conference Proceedings, 1999.
13. Ken Nozaki, Hisao Ishibuchi, Hideo Tanaka, "A simple but powerful heuristic method for generating fuzzy rules from numerical data ", Fuzzy Sets and Systems 86(1997) 251-270.
14. Frank Klawonn,Rudolf Kruse, "Constructing a fuzzy controller from data", Fuzzy Sets and Systems 85(1997) 177-193.
15. Howard Demuth, Mark Beale, "Neural Network Toolbox For Use with MATLAB User's Guide Version 3.0"
16. MathWork, "Fuzzy Logic Toolbox For Use with MATLAB--User's Guide Version 2".
17. Jung-heum Yon, "Structure Optimization of Fuzzy-Neural Network Using Rough Set Theory". IEEE international Fuzzy Systems Conference Proceedings, August 22-25,1999.
18. PawlakZ. "Rough set". International Journal of Computer and Information Sciences, 1982, 11(5), p341-356.
19. Pawlak, Z. "Rough Sets: Theoretical Aspects of Reasoning About Data". Kluwer Academic Publisher, 1994.
20. B. Walczak, D.L. Massart, "Rough sets theory", Chemometrics and intelligent laboratory systems 47(1999), p1-16.
21. A Mrozek, "Use of rough sets and decision tables for implementing rule-based control of industrial process".Bull polish Acad Scitech, 1986,34, p357-364.
22. W Ziarko, T Areiszewski, S Hoda. "Urban rail corridor control through machine learning. An intelligent Vehicle-Highway System Approach ", 1994,1453,p91-97.
23. Plokanl, A. Mrozek. "Rule-based stabilization of the inverted pendulum". Computational Intelligence, 1995,
24. Slowinski R. "Rough Classification of HSV Patients. Intelligent Decision Support". Kluwer, Roman Slowinski, 1992, p77-94.
25. HuXH, Cercone N. "Learning in relational databases: A rough set approach". Inter. J.of Computational Intelligence, 1992,11(2), p323-338.
26. Lenarcik A, Piasta A. "Discretization of Condition Attributes Space". Intelligent Decision Support. Kluwer,Roman Slowinski, 1992, p373-389.
27．王立新，《自适应模糊系统与控制-设计与稳定性分析》，国防工业出版社，1995。
28．孙增圻等，《智能控制理论与技术》，清华大学出版社，广西科学技术出版社 1997．4。
29．李士勇，《模糊控制·神经控制和智能控控制论》，哈尔滨工业大学出版社，1996．10。
30．王士同，《神经模糊系统及其应用》，北航出版社，1998．6。
31．陈国良、韩文廷，“人工神经网络理论研究进展”，电子学报，1996年02期。
32．倪春木，蔡志峰等，“模糊神经网络在辨识小车摆系统中的应用”，厦门大学学报增刊。
33．丛爽，《面向MATLAB工具葙的神经网络理论与应用》，中国科学技术大学出版社，1998．11。
34．曾黄麟，《粗集理论及其应用——关于数据推理的就方法》，重庆大学出版社，1996．9。
35．张文修等，《粗糙集理论与方法》，科学出版社，2001．7。
36．王钰、苗夺谦、周育健，“关于Rough Set理论与应用综述”，模式识别与人工智能，1996，9(4)，p337—344。
37．谢克明、杨静，“粗糙集合及其在智能控制领域的应用前景”，太原理工大学学报，Vol．30,No．4,July 1999。
38．吴福保、李奇、宋文忠，“基于粗集理论知识表达系统的一种归纳学习方法”，控制与决策，(1999)No．3，p206—211。
39．赵卫东等，“基于粗集理论的一种归纳学习算法”，管理工程学报，Vol．14，No．4，2000。
40．王亚英等，“基于粗集理论的规则知识获取技术”，上海交通大学学报，Vol．34．No．5．May 2000。
41．苗夺谦、胡贵荣，“知识约简的一种启发式算法．计算机研究与发展”，1999，36(6)，p681—684。
42．苗夺谦，“Rough Set理论中连续属性的离散化方法”，自动化学报，Vol．27．No3．May 2001。
43．黎明、张化光，“基于粗糙集的神经网络建模方法研究”，自动化学报，Vol．28．No．1．Jan．2002。
44．李永敏、朱善君、孙增圻等，“根据粗糙集理论进行BP网络设计的研究”，系统工程理论与实践，No．4，1999．04。
45．李文等，“一种建立模糊型的粗糙集方法：，控制理论与应用，Vol．18,No．1,Feb．,2001。
46. Zdzislaw Pawlak, "Rough Set Theory", Akluelles Schlagwort, 3/01-3/02。
47. A.Skowron. "The rough sets theory and evidence theory", Fundamental Informaticae, 1990.68-162。
48. Li-Xin Wang, "Analysis and design of hierarchical fuzzy systems", Fuzzy Systems, IEEE Transactions on, Vol.7, Issue: 5, Oct. 1999, p: 617-624。
49．陈道德，“Rough Set神经网络智能系统及其应用”，模式识别与人工智能，12(1)，p1-5，1999。
50．李莉，“基于可变精度粗集模型的增量式归纳学习”，计算机科学，(1999)No．1，p55—58。
2. Jyh-Shing R.Jang," Fuzzy Modeling Using Generalized Neural Networks and Kalman Filter Algorithm ".
3. T. Takagi and M. Sugeno. "Fuzzy identification of systems and its application to modeling and control." IEEE Trans. On Systems, Man & Cybernetics, vol. 15. pp.116-132. 1985.
4. M.Sugeno and G.T. Kang, "Structure Identification of Fuzzy Model". Fuzzy Sets and Systems 28(1988),p15-33.
5. J.S.R. Jang, C. T. Sun, E.Mizutani. "Neuro-Fuzzy and Soft Computing A Computional Approach to Learning and Machine Intelligence". Publish by Prentice Hall. 1997.
6. R.R. Yager and D. P. Filev. "Approximate clustering via the mountain method." IEEE Trans. On systems, man & Cybernetics, 24:1279-1284,1992.
7. R.R. Yager and D. P. Filev. "Generation of fuzzy rules by mountain clustering." Joumal of Intelligent and Fuzzy Systems, 2:209-219, 1994.
8. Ronald R. Yager and Dimitar P. Filev. "Essentials of fuzzy modeling and control.", John Wilwy & Sons, Inc,1994.
9. J.-S. Roger Jang. "Structure determination in fuzzy modeling: a fuzzy CART approach", In proceedings of IEEE International conference on Fuzzy Systems, Orlando,Florida, June 1994.
10. Stephen L. Chiu, "A Cluster Estimation Method with Extension to Fuzzy Model Identification" IEEE Trans.1994.
11. Ken Nozaki, Hisao Ishibuchi, Hideo Tanaka. "A simple but powerful heuristic method for generating fuzzy rules from numerical data." Fuzzy Sets and Systems 86 (1997) 251-270.
12. Ching-Chang Wang, Hung-Ren Lai, "Generating Fuzzy Control Rules by a Clustering Algorithm Based on a Grey Relational Measure ", IEEE international Fuzzy Systems Conference Proceedings, 1999.
13. Ken Nozaki, Hisao Ishibuchi, Hideo Tanaka, "A simple but powerful heuristic method for generating fuzzy rules from numerical data ", Fuzzy Sets and Systems 86(1997) 251-270.
14. Frank Klawonn,Rudolf Kruse, "Constructing a fuzzy controller from data", Fuzzy Sets and Systems 85(1997) 177-193.
15. Howard Demuth, Mark Beale, "Neural Network Toolbox For Use with MATLAB User's Guide Version 3.0"
16. MathWork, "Fuzzy Logic Toolbox For Use with MATLAB--User's Guide Version 2".
17. Jung-heum Yon, "Structure Optimization of Fuzzy-Neural Network Using Rough Set Theory". IEEE international Fuzzy Systems Conference Proceedings, August 22-25,1999.
18. PawlakZ. "Rough set". International Journal of Computer and Information Sciences, 1982, 11(5), p341-356.
19. Pawlak, Z. "Rough Sets: Theoretical Aspects of Reasoning About Data". Kluwer Academic Publisher, 1994.
20. B. Walczak, D.L. Massart, "Rough sets theory", Chemometrics and intelligent laboratory systems 47(1999), p1-16.
21. A Mrozek, "Use of rough sets and decision tables for implementing rule-based control of industrial process".Bull polish Acad Scitech, 1986,34, p357-364.
22. W Ziarko, T Areiszewski, S Hoda. "Urban rail corridor control through machine learning. An intelligent Vehicle-Highway System Approach ", 1994,1453,p91-97.
23. Plokanl, A. Mrozek. "Rule-based stabilization of the inverted pendulum". Computational Intelligence, 1995,
24. Slowinski R. "Rough Classification of HSV Patients. Intelligent Decision Support". Kluwer, Roman Slowinski, 1992, p77-94.
25. HuXH, Cercone N. "Learning in relational databases: A rough set approach". Inter. J.of Computational Intelligence, 1992,11(2), p323-338.
26. Lenarcik A, Piasta A. "Discretization of Condition Attributes Space". Intelligent Decision Support. Kluwer,Roman Slowinski, 1992, p373-389.
27．王立新，《自适应模糊系统与控制-设计与稳定性分析》，国防工业出版社，1995。
28．孙增圻等，《智能控制理论与技术》，清华大学出版社，广西科学技术出版社 1997．4。
29．李士勇，《模糊控制·神经控制和智能控控制论》，哈尔滨工业大学出版社，1996．10。
30．王士同，《神经模糊系统及其应用》，北航出版社，1998．6。
31．陈国良、韩文廷，“人工神经网络理论研究进展”，电子学报，1996年02期。
32．倪春木，蔡志峰等，“模糊神经网络在辨识小车摆系统中的应用”，厦门大学学报增刊。
33．丛爽，《面向MATLAB工具葙的神经网络理论与应用》，中国科学技术大学出版社，1998．11。
34．曾黄麟，《粗集理论及其应用——关于数据推理的就方法》，重庆大学出版社，1996．9。
35．张文修等，《粗糙集理论与方法》，科学出版社，2001．7。
36．王钰、苗夺谦、周育健，“关于Rough Set理论与应用综述”，模式识别与人工智能，1996，9(4)，p337—344。
37．谢克明、杨静，“粗糙集合及其在智能控制领域的应用前景”，太原理工大学学报，Vol．30,No．4,July 1999。
38．吴福保、李奇、宋文忠，“基于粗集理论知识表达系统的一种归纳学习方法”，控制与决策，(1999)No．3，p206—211。
39．赵卫东等，“基于粗集理论的一种归纳学习算法”，管理工程学报，Vol．14，No．4，2000。
40．王亚英等，“基于粗集理论的规则知识获取技术”，上海交通大学学报，Vol．34．No．5．May 2000。
41．苗夺谦、胡贵荣，“知识约简的一种启发式算法．计算机研究与发展”，1999，36(6)，p681—684。
42．苗夺谦，“Rough Set理论中连续属性的离散化方法”，自动化学报，Vol．27．No3．May 2001。
43．黎明、张化光，“基于粗糙集的神经网络建模方法研究”，自动化学报，Vol．28．No．1．Jan．2002。
44．李永敏、朱善君、孙增圻等，“根据粗糙集理论进行BP网络设计的研究”，系统工程理论与实践，No．4，1999．04。
45．李文等，“一种建立模糊型的粗糙集方法：，控制理论与应用，Vol．18,No．1,Feb．,2001。
46. Zdzislaw Pawlak, "Rough Set Theory", Akluelles Schlagwort, 3/01-3/02。
47. A.Skowron. "The rough sets theory and evidence theory", Fundamental Informaticae, 1990.68-162。
48. Li-Xin Wang, "Analysis and design of hierarchical fuzzy systems", Fuzzy Systems, IEEE Transactions on, Vol.7, Issue: 5, Oct. 1999, p: 617-624。
49．陈道德，“Rough Set神经网络智能系统及其应用”，模式识别与人工智能，12(1)，p1-5，1999。
50．李莉，“基于可变精度粗集模型的增量式归纳学习”，计算机科学，(1999)No．1，p55—58。