臺灣博碩士論文加值系統

主成份分析法 (Principal Component Analysis, PCA) 已被廣泛應用於多變量流程失效之監控。當觀測值之間為獨立時，傳統 PCA 能有效地偵測流程異常。然而，許多實際流程數據往往呈現自相關 (autocorrelation) 之特性。因此 Ku, Storer 與 Georgakis (1995) 建議引入延遲變數藉以擴充原始矩陣進而發展出動態主成份分析法 (Dynamic PCA, DPCA) 來監控自相關流程。然而 Rato 和 Reis (2013) 進一步研究發現 DPCA 的監控統計量 (T^2與 Q) 仍存在高度之自相關性。為解決此議題，Rato 與 Reis (2013) 發展去相關殘差動態主成份分析法 (Dynamic PCA based on Decorrelated Residuals, DPCA-DR) 藉以降低監控統計量之自相關性。
雖然 DPCA-DR 可降低監控統計量之自相關性，但 T^2 與 Q 還是存在某種程度之自相關性，此將影響最終的監控結果。此外 T^2 與 Q 的監控統計量僅利用目前觀測值來計算馬氏距離，而忽略了先前觀測值之資訊，因此只能偵測大幅度變動之流程偏移，而無法有效地偵測出小幅度之偏移。
基於上述，本研究將發展 DPCA-DR-GLR 方法，目的在於能有效地同時偵測大、小幅度之流程異常偏移。所提方法中，DPCA-DR 主要用於變數維度刪減並降低 T^2 與 Q 之自相關性；GLR (Generalized Likelihood Ratio) 統計量因考量目前及以往觀測值資訊，因此本研究擬用以作為監控統計量。本研究所提 DPCA-DR-GLR 方法之優點在於：（1）可同時偵測大、小幅度偏移；（2）可估計異常變動時間點做為異常診斷之資訊；（3）監控過程中不需額外給定任何參數值。所提方法之有效性將應用三個案例來進行驗證，包含自相關流程模擬案例，田納西伊士曼流程 (Tennessee Eastman Process) 及白酒檢測案例。實驗結果顯示所提方法能有效偵測多變量自相關之流程失效。

Principal Component Analysis (PCA) has been widely used for multivariate process fault detection. PCA can effectively detect process faults under the premise of independent observations. However, the acquired data from a real process usually exhibits autocorrelation characteristics. Therefore, Ku, Storer and Georgakis (1995) suggested to introduce lagged variables into original data matrix and then apply the traditional PCA algorithm to the augmented matrix, they called this method as Dynamic PCA (DPCA). Moreover, Rato and Reis (2013) discovered the T^2 and Q monitoring statistics calculated from DPCA still present autocorrelation. To tackle this issue, Rato and Reis (2013) developed a Dynamic PCA based on Decorrelated Residuals (DPCA-DR) method in an attempt to reduce the autocorrelation of T^2 and Q.
Even though the implementation of DPCA-DR can lower the autocorrelation of monitoring metrics, the autocorrelation cannot be exterminated. Furthermore, T^2 and Q are essentially calculated from Mahalanobis distance in which only recent observation was taken into consideration, leading to an ineffective detection of a small process change.
According to abovementioned, this study will develop a DPCA-DR-GLR in an effort to detect a wide range of process changes. The DPCA-DR-DR was used to reduce data dimensionality and reduce the autocorrelation of T^2 and Q. The Generalized Likelihood Ratio (GLR) is adopted as the monitoring statistic due to the simultaneous consideration of recent observation and past observations. The advantages of the proposed method includes : 1) can detect a wide range of process changes; 2) can estimate the process change point that will provide practitioner the fault diagnosed information; 3) no further parameters to be given during monitoring. The efficiency of the proposed method will be verified via three examples : a simulated multivariate autocorrelated process, Tennessee Eastman process and White-wine inspection. Result demonstrated that the proposed method can effectively detect multivariate autorrelated process faults.

目錄
中文摘要……………………………………………………………………………... I
Abstract………………………………………………………………………………III
誌謝…………………………………………………………………………………...V
目錄…………………………………………………………………………………..VI
表目錄………………………………………………………………………………..IX
圖目錄………………………………………………………………………………...X
第一章 緒論…………………………………………………………………………1
1.1 研究背景與動機……………………………………………………….…………1
1.2 研究目的………………………………………………………………………….3
1.3 研究架構………………………………………………………………………….5
第二章 文獻探討……………………………………………………………………7
2.1 多變量管制圖回顧………………………………………………………….7
2.2 PCA監控方法……………………………………....………………….......11
2.3 DPCA監控方法……………………………………………………………13
2.4 DPCA-DR監控方法……………………………………………………….14
2.5 廣義概似比管制圖………………………………………………………...15
第三章 研究方法…………………………………………………………………..17
3.1 Offline training……………………………………………………………...17
3.2 Online monitoring…………………………………………………………..18
3.3 方法流程圖………………………………………………………………...19
第四章 實例驗證……………………………………………………………………20
4.1 操作介面介紹……………………………………………………………...20
4.2 模擬案例…………………………………………………………………...22
4.2.1流程說明…………………………………………………………….22
4.2.2監控結果…………………………………………………………….23
4.3 田納西伊士曼流程 (Tennessee Eastman)………………………………...30
4.3.1 流程說明……………………...…………………………………….30
4.3.2 監控結果……………………………...…………………………….34
4.4 白酒品質檢測（Wine Quality）………………………………………….64
4.4.1 流程說明……………………………………………………………64
4.4.2 監控結果……………………………………………………………66
第五章 結論與未來研究……………………………………………………………71
5.1 結論………………………………………………………………………...71
5.2 未來研究…………………………………………………………………...72
參考文獻……………………………………………………………………………..73
 
表目錄
表1.1 GLR計算範例…………………………………………………………………3
表4.1 非高斯製程類型設定………………………………………………………..23
表4.2 四種方法監控模擬流程之假警訊…………………………………………..29
表4.3 四種方法監控模擬流程之偵測率…………………………………………..29
表4.4 田納西伊士曼流程之監控變數……………………………………………..32
表4.5 田納西伊士曼流程之流程異常模式………………………………………..33
表4.6 四種方法監控TE流程之假警訊…………………………………………...61
表4.7 四種方法監控TE流程之偵測率…………………………………………...62
表4.8 各方法偵測率之 T 檢定……………………………………………………63
表4.8 白酒之變數…………………………………………………………………..65
表4.9 四種方法監控白酒之假警訊………………………………………………..70
表4.10 四種方法監控白酒之偵測率………………………………………………70
 
圖目錄
圖1.1 修華特管制圖之監控結果……………………………………………………4
圖1.2 GLR 管制圖之監控結果……………………………………………………...4
圖1.2 研究流程圖……………………………………………………………………6
圖3.1 DPCA-DR-GLR方法之流程圖……………………………………………...19
圖4.1 MATLAB操作介面………………………………………………………….20
圖4.2 模擬案例之自相關圖………………………………………………………..25
圖4.3 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 之假警訊…………………..26
圖4.4 PCA、DPCA、DPCA-DR、DPCA-DR-GLR偵測 Fault1 之結果……….27
圖4.5 PCA、DPCA、DPCA-DR、DPCA-DR-GLR偵測 Fault2 之結果……….28
圖4.6 田納西伊士曼流程 (Jong-Min Lee et al., 2004)……………………………31
圖4.7 Fault15 之自相關圖………………………………………………………….39
圖4.8 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X1 之結果………….40
圖4.9 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X2 之結果………….41
圖4.10 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X3 之結果………...42
圖4.11 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X4 之結果………...43
圖4.12 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X5 之結果………...44
圖4.13 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X6 之結果………...45
圖4.14 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X7 之結果………...46
圖4.15 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X8 之結果………...47
圖4.16 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X9 之結果………...48
圖4.17 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X10 之結果……….49
圖4.18 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X11 之結果……….50
圖4.19 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X12 之結果……….51
圖4.20 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X13 之結果……….52
圖4.21 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X14 之結果……….53
圖4.22 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X15 之結果……….54
圖4.23 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X16 之結果……….55
圖4.24 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X17 之結果……….56
圖4.25 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X18 之結果……….57
圖4.26 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X19 之結果……….58
圖4.27 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X20 之結果……….59
圖4.28 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測 X21 之結果……….60
圖4.29 白酒之自相關圖……………………………………………………………67
圖4.30 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 之假警訊…………………68
圖4.31 PCA、DPCA、DPCA-DR、DPCA-DR-GLR 偵測白酒之結果…………69

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中文部分
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