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研究生:林育民
研究生(外文):Yu-Min Lin
論文名稱:以奇異值調整法簡化模糊類神經網路
論文名稱(外文):Simplification of Fuzzy Neural Network via Singular Value Regulation
指導教授:王啟旭
指導教授(外文):Chi-Hsu Wang
學位類別:碩士
校院名稱:國立交通大學
系所名稱:電機與控制工程系所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:94
語文別:英文
論文頁數:46
中文關鍵詞:模糊類神經網路奇異值
外文關鍵詞:Fuzzy neural networkSingular value
相關次數:
  • 被引用被引用:1
  • 點閱點閱:231
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  • 下載下載:23
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摘要      
本論文提供一種縮減規則庫的方法來提升模糊類神經網路的效能。其核心理論為藉由調整由輸入輸出向量構成之模糊類神經網路矩陣的奇異值來改變輸入輸出之間的關係。我們稱此方法奇異值調整法。此方法可避免隨著輸出情況的高度複雜化而來之規則庫增加的問題。因此模糊類神經網路將有更好的效率。另外,因為模糊類神經網路是以小的規則庫來運作,其對應到規則庫的權重值可以很容易地以最小平方法得到。因此,模糊類神經網路對於輸出情況的變化將有更迅速的反應。我們藉由幾個例子來分析其誤差。所得到的結果證實由簡化過的規則庫仍可將精確度維持在很高的水平,因而大幅提升了模糊類神經網路的效率。
ABSTRACT
The main purpose of this paper is to enhance the efficiency of a fuzzy neural network (FNN) by proposing a new training methodology with rule reduction. The core of this methodology is to modify the input-output relations by updating the singular value set associated with the FNN matrix, which is composed of the rule vectors and desired output vectors. We name it for Singular Value Regulation (SVR). By adopting this method, the FNN can have a better efficiency owing to it is free from extension of rule base, which often accompanies with high complexity of the situation described by the desired output. In addition, updating the weighting factor set associated with the rule base can be easily determined using least square method since the FNN often performs with a small size of rule base. Therefore, the FNN can have an instant response of the alternation of the output situation. Error analysis has been performed with illustrated examples. The outcome shows that the precision can be well maintained with the simplified rule base so that the efficiency of FNN is greatly enhanced.
Contents
摘要 …………………………………………………… 3
Abstract …………………………………………………… 4
致謝 …………………………………………………… 5
Chapter 1 Introduction……………………………………… 9
Chapter 2 Problem Formulation…………………………….. 11
Chapter 3 Singular Value Regulation (SVR)……………….. 15
3.1 Singular Value Decomposition (SVD)……………... 15
3.2 Singular Value Regulation (SVR)………………….. 16
3.3 Improved training strategy…………………………. 21
Chapter 4 Reduction of Rule Base………………………….. 29
Chapter 5 Illustrative Examples………………………….…. 32
Conclusion …………………………………………………………… 45
Reference …………………………………………………………… 46





List of Figures
Figure 1 Configuration of Fuzzy neural network……………….……………. 3
Figure 2 Vector space distribution in the case with large error...….….. 4
Figure 3 Vector space distribution in the case with small error……….. 5
Figure 4 Vector space distribution in the ideal case……………………... 5
Figure 5 Rule base transformed by regulating singular value.…….……..…. 10
Figure 6(a) Feasible paths for navigation……………………….…………...…... 16
Figure 6(b) Output training pattern for the navigated object……………… 17
Figure 6(c) Membership functions for controlling the turning angle and speed 17
Figure 6(d) Configuration of fuzzy neural network in two different cases.. .17
Figure 7(a) Outcome of the generated paths in case1……………………….. 19
Figure 7(b) Outcome of the generated paths in case1…………………….……... 19
Figure 8 A feasible path for car navigation…………………………………... 24
Figure 9 Membership functions defined for generating the feasible
Paths…………………………………………………………………..
25
Figure 10 Paths generated by twenty-seven rules…………………….……. 27
Figure 11 Paths generated by reduced rule base…..………………………. 29
Figure 12 Two general cases for car navigation………….………………… 30
Figure 13 (a) Paths generated from the reduced rule base without tuning… 30
Figure 13 (b) Paths generated from the reduced rule base tuned by removing
Singular value………….…….……………………………………….
31
Figure 14 Comparison of navigated paths generated from tuned rule base and the original rule base….…………………………………………
31
Figure 15 Advantage of tuning rule base………………….…………………… 33
Figure 16 System identified by reduced rule base……………..………………. 36
Figure 17 Step response of the identified system…………………………… 36

List of Tables
Table 1 Weighting factor set obtained from different algorithms……….. 26
Table 2 Comparison of errors obtained from different algorithms……… 28
Table 3 Singular Values of the FNN matrix associated with the car navigation problem…………………………………………………
33
Table 4 Rule base set for car navigation problem 34
Table 5 The corresponding weighting factors associated with rules for car navigation……………………………………………………….
35
Table 6 Correlations between rules and desired outputs associated with the special case………………………………………………………
40
Table 7 Fuzzy sets associated with system identification of the plant model…………………………………………………………………
42
Table 8 The corresponding weighting factors associated with rules for system identification problem…………………………………..….
42
Reference
[1] C. H. Wang, W. Y. Wang, and T. T. Lee, “Fuzzy B-Spline membership function (BMF) and its application in fuzzy-neural control,” IEEE Trans. System, Man, Cybernetics”, Vol.25, pp.841-851, 1995.
[2] T. Sudkamp, A Knapp, and J. Knapp, “Model generation by domain refinement and rule reduction,” IEEE Trans. System, Man, Cybernetics – Part B: Cybernetics”, Vol.33, Issue.1. pp.45-55, Feb.2003.
[3] R. Thawonmas, and S. Abe, “A novel approach to vector selection based on analysis of class regions”, IEEE Trans. System, Man, Cybernetics– Part B: Cybernetics, Vol.27, No. 2, pp. 196-207, April 1997.
[4] Y. Yam, P.Baranyi, and C. T. Yang, “Reduction of fuzzy rule base via singular value decomposition,” IEEE Trans. Fuzzy System, Vol.7, pp.120-132, April 1999.
[5] C. W. Tao, “A Reduction Approach for Fuzzy Rule Bases of Fuzzy Controllers,” IEEE Trans. System, Man, Cybernetics - part B: Cybernetics, Vol. 32, pp, 1-7, 2002.
[6] Simon Haykin, “Neural network”, Hamilton, Ontario, Canada: Prentice Hall, 2nd ed, 1999.
[7] C. H Wang, H. Lei, and C. T. Lin, “Dynamical optimal learning rates of a certain class of fuzzy neural network and its application with genetic algorithm,” IEEE Trans. System, Man, Cybernetics – Part B: Cybernetics, Vol. 3, pp. 467-475, June 2001.
[8] Edwin K.P Chong, and Stanislaw H. Zak, “An introduction to optimization” John Wiley, 2001.
[9] L. I. Smith, “A tutorial on principal component analysis”, handout. February 26, 2002.
[10] K .I. Diamantaras and S. Y Kung, “Principal Component Neural Networks Theory and Applications” John Wiley & Sons Inc. 1996
[11] Agresti Alan,“Categorical data analysis” John Wiley & Sons. 1990
[12] Lewis Paul J,“Multivariate data analysis in industrial practice” Research Studies Press 1982.
[13] Pavlidis, Theodosios, T. Pavlidis,“Structural pattern recognition”Springer-Verlag, 1977
[14] Batchelor, Bruce G., edited by Bruce G.. Batchelor.“Pattern recognition: idea in practice, Plenum Press, 1978.
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