在工業製程中，為了確保化學工廠的安全及高效率的生產與運行，多變數統計製程監測(Multivariate Statistical Process Monitoring, MSPM)的地位變得愈來愈重要，其中隔離故障變數是了解故障發生根源的關鍵步驟。故障檢測的方法已廣泛被研究，但對於故障隔離的研究則是相對有限，尤其在統計檢測上分析多變數之間的影響是困難的。貢獻圖(Contribution Plots)是用於故障隔離的熱門技術，使用方式簡單，但常受限於模糊效應(Smearing Effect)的影響而導致錯誤的結果。重構分析是另一種類型的隔離方法，需沿著有可能發生錯誤的已知故障方向對製程變數進行重構，計算重構變數的統計量判斷是否回歸至管制限，但當樣本中含有大量變數時重構分析之計算量會過於繁重，因此並不適用於工業製程中。分支界定算法(Branch and Bound)是藉由求解組合性的優化問題以解決故障隔離問題，然而該方法的計算仍過於龐大。
在一般製程中，依據製程的方式可分為連續製程與批次製程，由於以不同的製程方式所獲得的數據存在著不同的特性，因此為了解決上述現有方法的問題，在本文中提出了基於懲罰項之判別分析的故障隔離方式，並且針對連續製程與批次製程加以分析。故障隔離的目的在於找出影響製程的關鍵變數，而該變數可用來辨別正常或故障操作，因此在某種意義上說，隔離故障變數相當於識別兩類的判別問題並且進行變數選擇；在正常操作下的數據視為一個類別，檢測到故障的數據視屬於另一類別。故本文主要想法為基於兩類的判別問題，利用加入懲罰項之判別分析來達到變數選擇的效果，該方法能提供故障變數的建議及關於過程變數對製程重要性的信息且有效避免龐大計算負擔，藉此能利於故障隔離的後續研究。
最後，分別以連續製程：田納西伊士曼製程(Tennessee Eastman Process)與批次製程：射出成型數據做為案例研究，驗證此方法的有效性。結果表明，相較於現有的方法，基於懲罰項的判別分析方法能夠提供依據對製程影響性由高至低的排序的故障變數且能減少計算負擔，故能有效的幫助工程師在製程中找出故障變數。

Isolating faulty variables is play an important role in multivariate statistical process monitoring (MSPC), which discover the source of the detected fault and ensure the safe and efficient operation of manufacturing and chemical industries.　 However, the MSPM is difficult to analyze the influences of multiple variables on monitoring statistics and relatively limited to isolate faulty variables.　The most popular technique for fault isolation is contribution plots. Although easy to use, contribution plots often suffer from “smearing” effect and yield misleading results. Reconstruction analysis is another type of isolation method, which re-calculates the values of process variables and monitoring statistics along certain candidate “faulty directions”. Such method requires the candidate “faulty directions” to be known, which may not be satisfied in industrial applications. A branch and bound (BAB) algorithm was proposed to address the fault isolation problem by solving a combinatorial optimization problem. However, the computational burden of BAB is heavy. In addition, reconstruction analysis may lead to inaccurate results when the number of variables is large, as shown in this paper.
To solve the mentioned problems of the existing methods, this paper proposes to conduct fault isolation via penalized discriminant analysis. In industrial processes,　the process can be divided into a continuous process and batch process, and each process have unique characteristics. According to the process method, we propose two kind of fault isolation method, respectively, for a continuous process and batch process. The basic idea is as follows. The goal of fault isolation is to identify variables responsible for the detected process abnormality. In other words, the variables to be isolated are those discriminating the normal process measurements and the fault samples. In a sense, isolating faulty variables is equivalent to identifying discriminating variables in a two-class problem, with the normal operation data regarded as belonging to one class and the data corresponding to the detected fault as belonging to the other class. Added a penalty term of discriminant analysis can reach the effect of variables selection. Since the proposed method can be solved efficiently using state-of-the-art algorithms, the problem of computational burden is avoided. Instead of just offering a suggested set of faulty variables, the proposed method provides more information on the relevance of process variables to the detected fault, which facilitates the subsequent root cause diagnosis step after isolation.
The benchmark Tennessee Eastman (TE) process and injection molding process are used as a case study to illustrate the effectiveness of the proposed method. The results show that, comparing to the existing methods, the penalized discriminant analysis method is more information-rich and easier to calculate.

摘要 I
Abstract III
目錄 VI
圖目錄 VIII
表目錄 X
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 7
1.4 文章架構 10
第二章 研究理論 11
2.1 連續製程之故障隔離 11
2.1.1 線性判別分析 11
2.1.2 線性判別分析與迴歸分析之關係 16
2.1.3 具有懲罰項之迴歸模型 19
2.1.4 具體分析方法之步驟介紹 22
2.2 批次製程之故障隔離 24
2.2.1 批次數據之展開 24
2.2.2 部分最小平方法 26
2.2.3 部分最小平方法與判別分析之關係 28
2.2.4 稀疏性部分最小平方法 30
2.2.5 具體分析方法之步驟介紹 32
第三章 初步成果 34
3.1 連續製程：田納西伊士曼製程 34
3.1.1 穩定狀態之故障隔離 39
3.1.2 過渡狀態之故障隔離 47
3.1.3 含有高度相關性變數之故障隔離 51
3.2 批次製程：射出成型 58
3.2.1 已完成之批次數據 61
3.2.2 未完成之批次數據 78
第四章 結論 90
第五章 參考文獻 92

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