本研究以流形學習（Manifold Learning）和局部信息之概念對非線性製程變數進行監測、分析以及診斷。在無故障訊息的情況下，傳統上使用的非線性製程監測方法為Kernel Principal Component Analysis (KPCA)，而流形學習方法最大方差展開（Maximum Variance Unfolding, MVU）利用保持局部信息的特性建立一全局模型，改善了KPCA無法很好保持潛在流形的特性，但MVU有個缺陷是模型只適用於訓練樣本，因此本文以非線性投影方法Gaussian Process Regression (GPR)逼近MVU之輸入以及輸出空間，發展出一種擴展的最大方差展開方法（Extended Maximum Variance Unfolding, EMVU），GPR的另個優點是其參數能自動學習，而KPCA的核參數選擇問題卻仍未有一個較明確的解決方案，在線上監測中，EMVU不只以傳統的T2和SPE指標監測模型之距離及擬合度，並加入輸出預測變異量作為一新指標，能夠更大的顯示輸入空間中測試樣本與訓練樣本的差異性。在有故障數據的情形下，常用分類方法建立模型，其中，支持向量機是近年來最被廣泛使用的一種分類方法。本研究基於局部模型可能趨向線性或模型非線性複雜度較全局模型低的概念，以即時學習（Just In Time Learning, JITL）的方式，在新樣本採集時即時以鄰近點建立局部多分類支持向量機（Multiclass Support Vector Machines, MSVM）模型、即時監測，因此將之命名為JITL-MSVM，而每個模型建立時皆採用快速的留一交叉驗證法（Fast Leave One Out, FLOO）自動選擇模型參數，以符合”即時”的目的。本研究最後使用田納西伊士曼程序（Tennessee Eastman process process）模擬一連續非線性製程進行分析並與傳統方法比較。

目錄 I
圖目錄 II
表目錄 III
第一章 緒論 1
1.1前言 1
1.2文獻回顧 2
1.3研究動機 6
1.3.1擴展最大方差展開法 6
1.3.2即時學習-多分類支持向量機方法 7
第二章 研究方法 8
2.1核主成分分析 8
2.2擴展最大方差展開法 10
2.2.1最大方差展開 10
2.2.2高斯程序迴歸 12
2.2.3擴展最大方差展開監測方法 14
2.2.4錯誤判定方法 – 重構 15
2.2.5擴展最大方差展開建模方法及監測流程 17
2.3利用局部信息與即時學習於非線性製程監測 18
2.3.1最小二乘支持向量機及1對1多分類支持向量機 18
2.3.2一次性求解多分類支持向量機 19
2.3.3快速留一交叉驗證法 21
2.3.4利用局部信息與即時學習於非線性製程建模方法及監測流程 23
2.4田纳西-伊斯曼製程 23
第三章 研究成果 30
3.1擴展最大方差展開研究成果 30
3.1.1非線性映射 30
3.1.2擴展最大方差展開於數學例子效果展示 33
3.1.3建模階段及參數選擇 40
3.1.5錯誤判定 49
3.2利用局部信息與即時學習於非線性製程監測研究成果 53
3.2.1建模階段及參數選擇 53
3.2.2即時學習-多分類支持向量機方法結果 54
第四章 結論 57
第五章 參考文獻 58

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