不确定性智能系统的模式摄动和规则自动获取的研究
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摘要
不确定性普遍存在于主观和客观世界中,模糊性是它最重要的形式之一。不确定性人工智能是人工智能的深化和发展,现已经成为人工智能研究的热点和重大的前沿课题。而模糊逻辑系统和神经网络系统是不确定性人工智能的重要研究内容,在构建许多不确定性智能系统时,通常要为系统准备先验知识,比如模糊逻辑系统的已知规则和神经网络系统的训练模式。先验知识的不确定性引起了事物的复杂性和处理难度,这种不确定性从数学角度可以认为是一种误差,从动力学角度可以认为是一种摄动,有效获取先验知识以及评估和控制先验知识的误差对系统性能的影响已经成为不确定性智能系统的重要研究内容。有效获取先验知识已有很多工作,但始终没有关键突破;评估和控制先验知识的误差对系统性能的影响在传统模糊推理和模糊神经网络方面取得了一定的进展,但在一般神经网络还未开展,为此本文主要做了如下工作:
(1)研究了训练模式摄动对高斯型径向基函数网络性能的影响,指出了训练模式摄动的常见情形,建立了相关的定义和引理,接着从理论上严格证明了对某些模式摄动该网络的输出摄动幅度不放大,并用MATLAB编写了一个仿真实验应证了该理论证明的结果,该部分工作为径向基函数网络的性能分析提供了一个新的研究点,对训练模式的获取过程能提供警示和指导。
(2)提出了一种基于遗传算法的根据已知系统控制目标自动获取模糊控制规则的方法。该方法与其他多种方法相比较,具有能根据系统的控制目标,自动搜索获得最优(次优)模糊控制规则集的优点,并在倒立摆控制系统进行了仿真应用,具有较好的仿真效果。
最后本文对不确定性智能系统的一些研究问题进行了展望。
Uncertainty, one of whose most important forms is fuzziness, exists universally in the objective and subjective world. Artificial Intelligence with uncertainty, the advanced development of artificial intelligence, is a hot and important research topic now. And the fuzzy logic system and neural network system are the important research topics of artificial Intelligence with uncertainty. When we create many uncertain intelligent systems the transcendental knowledge, for example the known rules of the fuzzy logic systems and the training patterns of the neural network systems, should usually be prepared for the systems. The uncertainty of the transcendental knowledge, which can be thought of as errors from the viewpoint of mathematics and perturbation from dynamics, causes the complexity and solving difficulty of the things. Effective acquisition the transcendental knowledge, in which there has been much work but there is not pivotal breakthrough, and evaluation and controlling the errors of the transcendental knowledge impacting the performance of the systems, which has gotten some achievement in traditional fuzzy inference and fuzzy neural network but has not begun in universal neural network, have been two important research topics of the uncertain intelligent systems. The main work in this paper is as follows:
1. This paper studies the influence of the uncertainty of patterns perturbation on the performance of Gauss Radial Basis Function Neural Network. It gives interrelated definitions and lemmas, points the usual instances of the training patterns perturbation and then theoretically and strictly proves that the outputs perturbation of some patterns perturbation of the Gauss Radial Basis Function Neural Network is no bigger than the training patterns perturbation. Lastly it gives an experiment in MATLAB validating the validity of the theoretically inferred result. This part of work gives a new viewpoint in studying the performance of the Gauss Radial Basis Function Neural Network.
2. A method, which can automatically searches for the most or secondary optimized fuzzy control rules set according the controlling object of the systems, automatically acquiring fuzzy rules based on the genetic algorithm is proposed in this paper. An experiment illustrates the procedure of acquiring rules by genetic algorithm in pendulum system. The simulation results demonstrate the feasibility and effective-
(1)研究了训练模式摄动对高斯型径向基函数网络性能的影响,指出了训练模式摄动的常见情形,建立了相关的定义和引理,接着从理论上严格证明了对某些模式摄动该网络的输出摄动幅度不放大,并用MATLAB编写了一个仿真实验应证了该理论证明的结果,该部分工作为径向基函数网络的性能分析提供了一个新的研究点,对训练模式的获取过程能提供警示和指导。
(2)提出了一种基于遗传算法的根据已知系统控制目标自动获取模糊控制规则的方法。该方法与其他多种方法相比较,具有能根据系统的控制目标,自动搜索获得最优(次优)模糊控制规则集的优点,并在倒立摆控制系统进行了仿真应用,具有较好的仿真效果。
最后本文对不确定性智能系统的一些研究问题进行了展望。
Uncertainty, one of whose most important forms is fuzziness, exists universally in the objective and subjective world. Artificial Intelligence with uncertainty, the advanced development of artificial intelligence, is a hot and important research topic now. And the fuzzy logic system and neural network system are the important research topics of artificial Intelligence with uncertainty. When we create many uncertain intelligent systems the transcendental knowledge, for example the known rules of the fuzzy logic systems and the training patterns of the neural network systems, should usually be prepared for the systems. The uncertainty of the transcendental knowledge, which can be thought of as errors from the viewpoint of mathematics and perturbation from dynamics, causes the complexity and solving difficulty of the things. Effective acquisition the transcendental knowledge, in which there has been much work but there is not pivotal breakthrough, and evaluation and controlling the errors of the transcendental knowledge impacting the performance of the systems, which has gotten some achievement in traditional fuzzy inference and fuzzy neural network but has not begun in universal neural network, have been two important research topics of the uncertain intelligent systems. The main work in this paper is as follows:
1. This paper studies the influence of the uncertainty of patterns perturbation on the performance of Gauss Radial Basis Function Neural Network. It gives interrelated definitions and lemmas, points the usual instances of the training patterns perturbation and then theoretically and strictly proves that the outputs perturbation of some patterns perturbation of the Gauss Radial Basis Function Neural Network is no bigger than the training patterns perturbation. Lastly it gives an experiment in MATLAB validating the validity of the theoretically inferred result. This part of work gives a new viewpoint in studying the performance of the Gauss Radial Basis Function Neural Network.
2. A method, which can automatically searches for the most or secondary optimized fuzzy control rules set according the controlling object of the systems, automatically acquiring fuzzy rules based on the genetic algorithm is proposed in this paper. An experiment illustrates the procedure of acquiring rules by genetic algorithm in pendulum system. The simulation results demonstrate the feasibility and effective-
引文
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[5] 瞿东海,李力,靳蕃.基于模糊神经网络的非线性系统模型的辨识.计算机学报,2004,27(4):561-565
[6] 周 志 华 , 陈 世 福 . 神 经 网 络 规 则 抽 取 . 计 算 机 研 究 与 发 展 , 2002 ,39(4):398-405
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[8] 肖平,冯久超,余英林.多模式对模糊联想记忆网络的动态学习算法.计算机科学,1998,25(2):43-45
[9] 陈龙,王飞跃.一种新的神经模糊系统及其学习算法.模式识别与人工智能,2003,16(2):178-184
[10] 王立新.模糊系统与模糊控制.北京:清华大学出版社,2003,1:171-175
[11] 李 德 毅 , 刘 常 昱 , 韩 旭 等 . 不 确 定 性 人 工 智 能 , 软 件 学 报 ,2004, vol.15,No.11:1583-1594
[12] Mingsheng Ying.Perturbation of Fuzzy Reasoning.IEEE Transactions on Fuzzy systems,1999,7(5):625-629
[13] 袁和军,李骏. 模糊推理的摄动性. 模糊系统与数学,2001, 015(004):8-13
[14] 李永明,史忠植.连续状态模糊控制系统的鲁棒性稳定性分析.自动化学报,2002,28(4):654-657
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[17] 陈明.基于遗传算法 Fuzzy 规则自动获取.大连理工大学学报.1995,3(55):732-735
[18] 周小英.遗传算法在模糊控制规则优化中的实现.电子科技大学学报,2000,29(2):160-163
[19] 王晶.基于遗传算法的模糊系统优化设计方法. 控制理论与应用,1999,16(5):699-704
[20] Simon Haykin. Neural Networks.北京:机械工业出版社,2004:108-111
[21] Moody J ,Draken C. Fast Learning in Networks of Locally-tuned processing Units. Neural Computation, 1989,1(1):281-294
[22] 卢涛,陈德钊.径向基函数的研究进展和评述.计算机工程与应用,2005,15(4):60-62
[23] Lei Xu. Rival Penalized Competitive Learning for Clustering Analysis RBF Networks and Curve Detection.IEEE Trans on Neural Networks,1993,4 (4):636-649
[24] 王旭东. RBF 网络及其在过程控制中的应用.博士学位论文,上海交通大学,1997:1-3
[25] Chen S, Billings S A, Grant P M. Orthogonal Least Squares Learning Algorithm for Radial Basis Function Networks, IEEE Trans on Neural Networks, 1991, 2(2):302-309
[26] Chen S, Grant P M , Cowan C F N. Orthogonal Least Squares Learning Algorithm for training Multioutput. Radial Basis Function Networks, IEEE Proceedings F, 1992, 139(6):378-384
[27] Chen S, Billings S A, Grant P M. Recursive Hybrid Algorithm for nonlinear Identification using Radial Basis Function Networks, International Journal of Control, 1995, 55(5):1051-1070
[28] 刘文菊,郭景.RBF 神经网络中心选取 OLS 算法的研究.天津工业大学学报,2002,21(2):71-73
[29] B walczak, D L Massart. The Radial Basis Function-Partial Least Squares Approach as a Flexible Nonlinear Regression Technique. Analytical chemical Acta, 1996, 331:177-185
[30] B walczak, D L Massart. The Radial Basis Function-Partial Least Squares to Pattern Recognition Problem. Analytical chemical Acta,1996, 331:187-193
[31] 庄凌,陈德钊.RBF-CSR 方法及其应用于裂解装置建模的研究.高校化学工程学报,2002,16(1):64-69
[32] 赵伟祥,吴立德.基于 PLS 和 Gas 的径向基函数网络构造策略.软件学报,2002,13(8):1450-1455
[33] 徐蔚鸿,陈国平,杨静宇等.规则摄动时模糊蕴涵算子对模糊推理的鲁棒性的影响.计算机学报,2005,28(10):1700-1707
[34] 王士同,於东军.径向基函数神经网络的构造理论.华东船舶工业学院学报,1999,13(2):76-86
[35] Hearst M, Hirsh H. AI’s greatest trends and controversies.IEEE Intelligent Systems, 2000,15(1):8-17
[36] 何新贵.模糊知识处理的理论与技术.北京:国防工业出版社.1998:447-456
[37] 张 凯 , 钱 锋 , 刘 漫 丹 . 模 糊 神 经 网 络 技 术 综 述 . 信 息 与 控 制 , 2003, 32(5):431-435
[38] Zhou-Tian Fan, De-Fu Liu.On the power sequence of a fuzzy matrix in the sense of triangular norms.Fuzzy Sets and Systems 109(2000):409-417
[39] G.B.Stamou,S.G.Tzafestas.Neural fuzzy relational systems with a new learning algorithm.Mathematics and Computers in Simulation, 51(2000): 301-314
[40] 飞思科技产品研发中心.MATLAB 6.5 应用接口编程,北京:电子工业出版社,2003 年:126-131
[41] 施阳,李俊.MATLAB 语言工具箱.西安:西北工业大学出版社,1998 年:88-91
[42] 孙兆林.MATLAB 6.X 图像处理,北京:清华大学出版社,2002 年:142-145
[43] 缪绍纲.数字图像处理——活用 MATLAB.成都:西南交通大学出版社,2001年:34-37
[44] 王洪元,史国栋.人工神经网络技术及其应用.北京:中国石化出版社,2002年:156-160
[45] 姚俊,马松辉.基于 MATLAB 6.X Simulink 建模与仿真.西安:西安电子科技大学出版社,2002 年:110-114
[46] 飞思科技产品研发中心.MATLAB 6.5 辅助神经网络分析与设计,北京:电子工业出版社,2003 年:65-70
[47] 刘增良.模糊技术与应用选编(5).北京:北京航空航天大学,1997:84-87
[48] 徐宗本,张讲社.计算智能中的仿生学:理论与算法.北京:科学出版社,2003 年:146-150
[49] 孙增圻.智能控制理论与技术.北京:清华大学出版社.1997 年:221-226
[50] Zadeh L. Fuzzy sets. Inform Control,1965,8(3):338-353
[51] Kosko B. Neural Networks and Fuzzy Systems. New Jersy: pretice-Hall, 1992:54-60
[52] 张国良,曾静.模糊控制及其 MATLAB 应用.西安:西安交通大学出版社,2002:122-129
[53] 陈桂明,张明照,戚红雨等.应用 MATLAB 建模与仿真. 北京:科学出版社,2001:48-52
[54] 阎平凡,张长水.人工神经网络与模拟进化计算.北京:清华大学出版社,1999:119-123
[55] 王大中等.用于一节倒立摆中的模糊控制算法及其 FPGA 实现.微电子学,2003,23(1):29-32
[56] 黄忠霖.控制系统 MATLAB 计算及仿真. 北京:国防工业出版社,2001:146-158
[57] 苏金明,黄国明.MATLAB 与外部程序接口.北京:电子工业出版社,2004:79-85
[2] 孙霞,吴自勤.分形原理及其应用.合肥:中国科技大学出版社,2003:56-61
[3] 王俭,沈理.一种高效的模糊规则自动生成方法.计算机研究与发,1999,36(2):139-143
[4] 武妍,施鸿宝.一种基于 RoughSets 和模糊神经网络的规则获取方法.计算机工程与应用,1999,35(7):7-9
[5] 瞿东海,李力,靳蕃.基于模糊神经网络的非线性系统模型的辨识.计算机学报,2004,27(4):561-565
[6] 周 志 华 , 陈 世 福 . 神 经 网 络 规 则 抽 取 . 计 算 机 研 究 与 发 展 , 2002 ,39(4):398-405
[7] 梁怡,张文修.模糊规则的谐调度与矛盾规则的排除算法.计算机学报,1997,20(10):949-952
[8] 肖平,冯久超,余英林.多模式对模糊联想记忆网络的动态学习算法.计算机科学,1998,25(2):43-45
[9] 陈龙,王飞跃.一种新的神经模糊系统及其学习算法.模式识别与人工智能,2003,16(2):178-184
[10] 王立新.模糊系统与模糊控制.北京:清华大学出版社,2003,1:171-175
[11] 李 德 毅 , 刘 常 昱 , 韩 旭 等 . 不 确 定 性 人 工 智 能 , 软 件 学 报 ,2004, vol.15,No.11:1583-1594
[12] Mingsheng Ying.Perturbation of Fuzzy Reasoning.IEEE Transactions on Fuzzy systems,1999,7(5):625-629
[13] 袁和军,李骏. 模糊推理的摄动性. 模糊系统与数学,2001, 015(004):8-13
[14] 李永明,史忠植.连续状态模糊控制系统的鲁棒性稳定性分析.自动化学报,2002,28(4):654-657
[15] 顾 林 跃 , 干 萌 . 利 用 遗 传 算 法 自 动 生 成 模 糊 规 则 . 计 算 机 工程,1995,21(6):50-55
[16] 刘镇.用遗传算法优化模糊控制规则.贵州大学学报(自科),1999,28(5):7-11
[17] 陈明.基于遗传算法 Fuzzy 规则自动获取.大连理工大学学报.1995,3(55):732-735
[18] 周小英.遗传算法在模糊控制规则优化中的实现.电子科技大学学报,2000,29(2):160-163
[19] 王晶.基于遗传算法的模糊系统优化设计方法. 控制理论与应用,1999,16(5):699-704
[20] Simon Haykin. Neural Networks.北京:机械工业出版社,2004:108-111
[21] Moody J ,Draken C. Fast Learning in Networks of Locally-tuned processing Units. Neural Computation, 1989,1(1):281-294
[22] 卢涛,陈德钊.径向基函数的研究进展和评述.计算机工程与应用,2005,15(4):60-62
[23] Lei Xu. Rival Penalized Competitive Learning for Clustering Analysis RBF Networks and Curve Detection.IEEE Trans on Neural Networks,1993,4 (4):636-649
[24] 王旭东. RBF 网络及其在过程控制中的应用.博士学位论文,上海交通大学,1997:1-3
[25] Chen S, Billings S A, Grant P M. Orthogonal Least Squares Learning Algorithm for Radial Basis Function Networks, IEEE Trans on Neural Networks, 1991, 2(2):302-309
[26] Chen S, Grant P M , Cowan C F N. Orthogonal Least Squares Learning Algorithm for training Multioutput. Radial Basis Function Networks, IEEE Proceedings F, 1992, 139(6):378-384
[27] Chen S, Billings S A, Grant P M. Recursive Hybrid Algorithm for nonlinear Identification using Radial Basis Function Networks, International Journal of Control, 1995, 55(5):1051-1070
[28] 刘文菊,郭景.RBF 神经网络中心选取 OLS 算法的研究.天津工业大学学报,2002,21(2):71-73
[29] B walczak, D L Massart. The Radial Basis Function-Partial Least Squares Approach as a Flexible Nonlinear Regression Technique. Analytical chemical Acta, 1996, 331:177-185
[30] B walczak, D L Massart. The Radial Basis Function-Partial Least Squares to Pattern Recognition Problem. Analytical chemical Acta,1996, 331:187-193
[31] 庄凌,陈德钊.RBF-CSR 方法及其应用于裂解装置建模的研究.高校化学工程学报,2002,16(1):64-69
[32] 赵伟祥,吴立德.基于 PLS 和 Gas 的径向基函数网络构造策略.软件学报,2002,13(8):1450-1455
[33] 徐蔚鸿,陈国平,杨静宇等.规则摄动时模糊蕴涵算子对模糊推理的鲁棒性的影响.计算机学报,2005,28(10):1700-1707
[34] 王士同,於东军.径向基函数神经网络的构造理论.华东船舶工业学院学报,1999,13(2):76-86
[35] Hearst M, Hirsh H. AI’s greatest trends and controversies.IEEE Intelligent Systems, 2000,15(1):8-17
[36] 何新贵.模糊知识处理的理论与技术.北京:国防工业出版社.1998:447-456
[37] 张 凯 , 钱 锋 , 刘 漫 丹 . 模 糊 神 经 网 络 技 术 综 述 . 信 息 与 控 制 , 2003, 32(5):431-435
[38] Zhou-Tian Fan, De-Fu Liu.On the power sequence of a fuzzy matrix in the sense of triangular norms.Fuzzy Sets and Systems 109(2000):409-417
[39] G.B.Stamou,S.G.Tzafestas.Neural fuzzy relational systems with a new learning algorithm.Mathematics and Computers in Simulation, 51(2000): 301-314
[40] 飞思科技产品研发中心.MATLAB 6.5 应用接口编程,北京:电子工业出版社,2003 年:126-131
[41] 施阳,李俊.MATLAB 语言工具箱.西安:西北工业大学出版社,1998 年:88-91
[42] 孙兆林.MATLAB 6.X 图像处理,北京:清华大学出版社,2002 年:142-145
[43] 缪绍纲.数字图像处理——活用 MATLAB.成都:西南交通大学出版社,2001年:34-37
[44] 王洪元,史国栋.人工神经网络技术及其应用.北京:中国石化出版社,2002年:156-160
[45] 姚俊,马松辉.基于 MATLAB 6.X Simulink 建模与仿真.西安:西安电子科技大学出版社,2002 年:110-114
[46] 飞思科技产品研发中心.MATLAB 6.5 辅助神经网络分析与设计,北京:电子工业出版社,2003 年:65-70
[47] 刘增良.模糊技术与应用选编(5).北京:北京航空航天大学,1997:84-87
[48] 徐宗本,张讲社.计算智能中的仿生学:理论与算法.北京:科学出版社,2003 年:146-150
[49] 孙增圻.智能控制理论与技术.北京:清华大学出版社.1997 年:221-226
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