在工業製程中，為了提升製程良率，品質，和安全，品質管制、缺陷檢測、故障診斷等議題受到重視，而基於數據的統計方法逐漸成為提供工業製程中突破及解決問題的重要技術。而圖論對於拓撲學、群論、矩陣論有著密切關係，在圖中，資料關係中的連通性常用以描述變數間的某種特定關係。由於近代工業的複雜度日漸提升，本文將由兩個研究應用主題展示基於數據的統計方法與圖中連通性間的關係之應用與改善。
於第一部分中，應用了多變數線性分析方法–主成分分析（Principle Component Analysis, PCA），於非破壞性檢測中之熱影像缺陷特徵提取。研究中通過考慮現有網絡中熱成像圖像像素的連通性來增強負荷值的稀疏性，進一步提升提出方法的可行性和有效性。案例研究使用古鑲嵌物和碳纖維增強聚合物（Carbon Fiber Reinforced Polymer, CFRP）作為主動熱成像技術實施目標。藉由不同的實驗樣品條件與多種參數設定，演示表面缺陷表徵的實驗結果。
研究第二部分中，利用概率分布統計的方法所得出時間序列之因果性的方法–傳遞熵，研究工業製程中之變數因果關係。在研究中提出利用管制圖為概念的符號傳遞熵(Symbolic Transfer Entropy, STE)應用，研究針對不同的離散化方法於製程應用的實踐性。通過管制圖概念符號化的序列能夠提供更準確及高解釋力的訊息，從而減少因背景雜訊或擾動帶來偏差的結果。並通過田納西伊士曼程序(Tennessee Eastman process)IDV1演示提出方法之解釋性與準確性提升，生成有向圖。
文章將分成兩個獨立部分，除目錄及參考文獻外，文獻回顧、研究方法等架構都將分開撰寫。

In industrial processes, great attentions have been paid to quality control, defect detection, fault diagnosis, etc. for ensuring yield, product quality, and process safety, whereas data-driven statistical methods have become an important breakthrough technology to solve these problems. Graph theory, which closely relates to topology, group theory, and matrix theory, is a potentially useful tool in these fields. In a graph, the relationship between variables can be described with the connectivity between nodes. This research work will discuss the utilizationof the graph theory in industrial applications and illustrate the advantages with two different applications.
In the first part of this thesis, the multivariate linear analysis method, Principal Component Analysis (PCA), was applied to extract the defect features contained in thermal images for non-destructive testing. Different from the conventional PCA, the connectivity between pixels was considered in this work and described with a graph to enhance the interpretability of the loading vectors. Hence, the defect identification performance was enhanced. The feasibility and effectiveness of the proposed method was illustrated with two case studies, including the active thermography tests of an ancient marquertry sample and a carbon fiber reinforced polymer (CFRP) sample.. The results were analyzed under different test conditions and various parameter settings.
In the second part of this work, variable causality in industrial processes was investigated by using an improved transfer entropy method for root cause fault diagnosis of industrial processes. Transfer entropy is often used for generate the causal map in a system. In my research, a symbolic transfer entropy (STE) method based on a control chart was proposed for root cause diagnosis, whiledifferent discretization methods was studied. The results showed that by symbolizing the time series of process variables based on a control chart, the diagnosis results become more robust to noise and more accurate. The case study of the Tennessee Eastman process (TEP), showed the feasibility of the proposed method. More accurate signed directed graphs were generated to show the causality in the process.

摘要 II
Abstract III
目錄 V
圖目錄 VIII
表目錄 X
第一部分 XI
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 3
1.3 研究動機與目的 6
1.4 文章架構 7
第二章 熱影像數據處理 7
2.1 前言 7
2.2 主成分熱成像分析法(PCT) 10
2.3 稀疏主成分熱成像分析法(SPCT) 12
2.4 節點連結稀疏主成分熱成像分析法(ESPCT) 15
第三章 樣本與實驗介紹 18
3.1實驗樣品 18
3.1.1. 古鑲嵌物 18
3.1.2. 碳纖維增強複合材料(Carbon Fiber Reinforced Polymer) 20
3.2實驗儀器 22
3.3實驗步驟 24
3.4數據結構與預處理 26
第四章 實驗數據與討論 28
4.1原始熱影像 28
4.2古鑲嵌物 30
4.1.1主成分熱影像分析法(PCT) 30
4.2.2稀疏主成分熱影像分析法(SPCT) 31
4.2.3節點連結稀疏主成分熱影像分析法(ESPCT) 32
4.3碳纖維增強複合材料(CFRP) 34
4.3.1主成分熱影像分析法(PCT) 34
4.3.2稀疏主成分熱影像分析法(SPCT) 35
4.3.3節點連結稀疏主成分熱影像分析法(ESPCT) 36
第五章 小結 42
第二部分 43
第一章 緒論 44
1.1 前言 44
1.2 研究背景(文獻與動機) 45
1.3 文章結構 49
第二章 研究理論 50
2.1 訊息理論(Information Theory) 50
2.2傳遞熵(Transfer Entropy) 52
2.2.1 條件傳遞熵(Conditional transfer entropy) 52
2.2.2 符號化傳遞熵(Symbolic Transfer Entropy, STE) 53
2.2.2.1 TE的離散版本 53
2.2.2.2 全域符號化(global symbolization) 54
2.3 管制圖(Contrl Chart) 55
2.3.1 X－Rm管制圖(Individuals and Moving-Range Charts) 55
2.3.2 指數加權移動平均管制圖(EWMA) 56
2.4 顯著水準估計 57
2.5 指標 59
2.6 研究方法 60
2.7 最小生成樹(Minimum Spanning Tree) 64
第三章 非線性案例討論 66
3.1田納西伊士曼程序(Tennessee Eastman process) 66
3.2參數設定 73
3.2.1 IDV 1(A/C feed ratio, B composition constant) 73
3.2.2 資料符號化處理 74
3.1結果討論 80
第四章 小結 93
結論 94
參考文獻 95

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