臺灣博碩士論文加值系統

中文摘要

本論文所設計的混合模糊建模主要是結合參數建模及歸屬函數建模各別的優點，建立一個建模精度及建模效率兼備的模糊系統。所謂混合建模就是依照不同的資料型態以不同的建模方式建模，首先將收集到的資料以競爭式學習法進行分類，然後利用參數建模快速的模擬出系統的趨勢，再藉由門檻植 ( mes值) 確認各群聚的資料形態，將資料型態分為 “整齊” 與 “混亂”兩大類，在資料分佈較為混亂的群聚則改用歸屬函數建模，以較準確的方式來描述該群聚的狀態，整齊的資料則維持參數建模的結果。
在論文中以一個非線性系統進行模擬測試，以競爭式學習法將資料分為3 ~ 6 群後，再各別利用參數建模、歸屬函數建模及混合模糊建模進行三種方式建模，將三種建模的輸出結果相互比較，混合模糊建模的建模精度相對於參數建模提升了46%；在建模效率方面，混和模糊建模所使用的模糊規則數量比歸屬函數建模減少55%，確實達到分析結果的精度與建模效率兼備的目的。
群聚分析的分群數量並非設定愈多愈好，在論文的模擬測試結果中，將分群數量設定為3~5群時所分析的結果較好，因此設定適當的分群數量才能得到較好的分析結果。
在實驗驗證的部份是以CMP製程的工程數據進行模擬，其數據包含Pad Counts、CMP研磨時間、薄膜厚度及實際研磨掉的厚度，取其中600筆當作訓練資料，另外取50筆作為輸入資料來驗證混合模糊建模的預測能力。而預測結果的mse值為2.2，預測值的趨勢也與實際值非常相近，證明了混合模糊建模預測的能力。

Abstract

In this thesis, a hybrid fuzzy modeling approach combining both the Takagi-Sugeno fuzzy model and the standard fuzzy model was proposed so that it possesses the properties of precision and of efficiency. To use this approach, the data are firstly grouped by competitive learning. Then, Takagi-Sugeno fuzzy models are established for each group of data. If the mean square error of a group of data is less than a predefined threshold, its Takagi-Sugeno fuzzy model is acceptable; otherwise, the standard fuzzy model must be used because the data are disordered and a more accurate model is needed.
For examining the hybrid fuzzy modeling approach, a simulation was performed in this study. Data of a nonlinear system were partitioned into 3 – 6 groups, respectively. Takagi-Sugeno fuzzy model, standard fuzzy model, and hybrid fuzzy model were then established. Comparing the results, the hybrid fuzzy model has better precision with 46% improvement against the Takagi-Sugeno fuzzy model. In addition, the hybrid fuzzy model needs less fuzzy rules than the standard fuzzy model for 55%. In conclusion, the hybrid fuzzy model has the advantages of precision and efficiency.
More groups do not guarantee better modeling result. In our example, 3 – 5 groups are suitable to give accurate fuzzy model. Obviously, appropriate grouping provides a good basis for accurate modeling.
Finally, this hybrid fuzzy modeling approach was implemented to CMP process. The considered parameters include pad counts, polishing time, thickness of thin film, and removal thickness. A total of 600 runs of data were used for training and the other 50 runs of data were utilized for testing the capability of model. The mean square error of fuzzy model is 2.2 and the predictions of fuzzy model are closed to the real values.

目錄

中文摘要……………………………………………………………I
英文摘要……………………………………………………………III
誌謝…………………………………………………………………V
目錄…………………………………………………………………VI
圖目錄………………………………………………………………VIII
表目錄………………………………………………………………XI
符號說明……………………………………………………………XII
第一章 緒論…………………………………………………………1
1-1 研究動機與目的…………………………………………………1
1-2 文獻回顧…………………………………………………………2
1-3 論文組織架構……………………………………………………5
第二章 相關理論與方法……………………………………………6
2-1 類神經網路………………………………………………………6
2-1-1 類神經網路介紹………………………………………………6
2-1-2 類神經網路系統架構…………………………………………7
2-1-3 學習演算法……………………………………………………9
2-1-4 競爭式學習演算法……………………………………………11
2-2 模糊理論…………………………………………………………13
2-2-1 模糊集合………………………………………………………14
2-2-2 模糊推論系統…………………………………………………18
2-2-3 模糊規則庫……………………………………………………19
2-2-4 模糊模式………………………………………………………20
2-2-5 解模糊化………………………………………………………22
第三章 系統設計……………………………………………………25
3-1 模糊系統架構說明………………………………………………25
3-2 群聚分析…………………………………………………………27
3-3 參數建模…………………………………………………………32
3-4 增加歸屬函數建模………………………………………………37
第四章 研究結果……………………………………………………44
4-1 模擬測試…………………………………………………………44
4-1-1 模擬測試方法…………………………………………………44
4-1-2 模擬結果討論…………………………………………………50
4-2 實驗結果與討論…………………………………………………54
第五章 結論…………………………………………………………59
參考文獻……………………………………………………………61



圖目錄

圖2.1 類神經網路系統架構…………………………………………8
圖2.2 監督式學習演算法……………………………………………9
圖2.3 非監督式學習演算法.…………………………………………10
圖2.4 神經元權重學習示意圖………………………………………11
圖2.5 競爭式學習演算法……………………………………………13
圖2.6 三角形函數……………………………………………………15
圖2.7 梯形歸屬函數…………………………………………………16
圖2.8 高斯歸屬函數…………………………………………………17
圖2.9 模糊推論系統…………………………………………………19
圖2.10 Mamdani推論模式示意圖……………………………………21
圖3.1 模糊系統架構圖………………………………………………26
圖3.2 競爭式學習法之聚類分析流程圖……………………………28
圖3.3 輸入參考資料點………………………………………………29
圖3.4 神經元權重向量的改變過程…………………………………31
圖3.5 高斯函數模糊化………………………………………………35
圖3.6 解模糊化過程…………………………………………………36
圖3.7 輸出模糊集合…………………………………………………36
圖3.8 歸屬函數的建模流程…………………………………………38
圖3.9 初始歸屬函數…………………………………………………39
圖3.10 第1回建模結果………………………………………………40
圖3.11 增加一條歸屬函數之模擬結果………………………………41
圖3.12增加歸屬函數建模過程………………………………………42
圖3.13 mse收斂圖……………………………………………………42
圖4.1 資料輸入輸出分佈圖…………………………………………45
圖4.2 聚類分析結果…………………………………………………46
圖4.3 參數建模結果(上)及mse值(下)………………………………47
圖4.4 混合模糊建模結果……………………………………………49
圖4.5 各種群聚數量以參數建模之結果……………………………50
圖4.6 各種群聚數量以歸屬函數建模之結果………………………51
圖4.7 各種群聚數量以混合模糊建模之結果.………………………52
圖4.8 聚類分析群聚重疊的現象……………………………………53
圖4.9 CMP設備示意圖………………………………………………55
圖4.10 CMP製程訓練資料(研磨時間與研磨厚度關係圖) …………56
圖4.11 CMP製程訓練資料(研磨墊使用次數與研磨厚度關係圖)…56
圖4.12 CMP製程訓練資料..…………………………………………56
圖4.13混合模糊建模預測結果(分3類)………………………………57
圖4.14混合模糊建模預測結果(分4類)………………………………57
圖4.15混合模糊建模預測結果(分5類)………………………………57




表目錄

表3.1 輸入參考資料點………………………………………………29
表3.1 調整神經元路徑表……………………………………………31
表4.1 群聚中心及表示符號…………………………………………45
表4.2 參數建模之mse值及模糊規則數量……………………………48
表4.3 混合模糊建模之平均誤差值(mse)……………………………49
表4.4 各種群聚數量以參數建模之結果……………………………50
表4.5 各種群聚數量以歸屬函數建模之結果………………………51
表4.6 各種群聚數量以混合模糊建模之結果………………………52
表4.7 混合模糊建模預測結果………………………………………58

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