1. 模糊模型規則庫自動建立之演算法 An improved approach to automatically build fuzzy model rules 王乃堅 (Nai-Jian Wang) 台灣科技大學電機系 中華民國九十年十月二十日 地點：政大經濟系

2. 2 Outline Motivations The concept of system identification The improved algorithm Simulations and Discussions Conclusions and Future Works

3. 3 Motivation Only I/O data Model construction I/O relation Modification

4. 4 The concept of system identification Structure Identification I a: Input candidates b: Input variables Structure Identification II a: Number of rules b: Partition of input space Parameter Identification

5. 5 Takagi and Sugeno’s model

6. 6 Sugeno and Yasukawa’s model

7. 7 Fuzzy modeling

8. 8 To decide the number of rules

9. 9 Fuzzy C-means clustering

10. 10 To determine the number of rules

11. 11 Coarse fuzzy modeling Fuzzy C-Regression Model (FCRM) Premise parameters generation Consequent parameters generation

12. 12 Fuzzy C-Regression Model (1)

13. 13 Fuzzy C-Regression Model (2)

14. 14 Premise parameters generation (1)

15. 15 Premise parameters generation (2)

16. 16 Premise parameters generation (3)

17. 17 Premise parameters generation (4)

18. 18 Consequent parameters generation

19. 19 Fine tuning

20. 20 The steepest decent method

21. 21 The gradient of objective function (1)

22. 22 The gradient of objective function (2)

23. 23 The gradient of objective function (3)

24. 24 Stop condition

25. 25 Example 1 (1) Rule 3.0953.201 3.518-0.249-0.265 1.4771.511 2.7512.406 6.504-0.672-0.469 2.0722.156 2.8282.437 4.842-0.381-0.421 1.8311.839 2.6672.805 4.136-0.387-0.357 1.0261.369 2.8972.544 5.052-0.559-0.243 2.0051.924

26. 26 Example 1 (2) Rule 3.8062.842 5.165-1.094-0.224 0.9571.471 2.7671.853 4.741-1.117-1.072 1.0800.657 2.0232.682 3.671-0.572-0.884 0.5901.323 2.9733.221 3.447-0.317-0.551 0.9511.120 2.8942.363 8.415-0.376-0.785 1.9842.230 The optimal parameters

27. 27 Example 1 (3)

28. 28 Example 2 (1)

29. 29 Example 2 (2)

30. 30 Example 3 (1)

31. 31 Example 3 (2)

32. 32 Conclusions and Future Works 架構精簡，彈性大 易於在電腦上實現 不錯的運算效率和較佳的近似結果 有較佳的能力去描述未知系統 改進 FCM 方法不足之處 以其他的最佳化方法取代最陡坡降法

33. 33 Least-squares estimator