適應性核獨立成份分析(KICA)於非線性流程之監控

Fault Detection of Non-Linear Processes Using Adaptive Kernel Independent Component Analysis

郭學哲(Hsueh-Che Kuo)

指導教授 ： 許俊欽

朝陽科技大學/理工學院/工業工程與管理系碩士在職專班/碩士(2011年)

摘要

Francis 和 Michael 於2002年發展核獨立成份分析法(Kernel Independent Component Analysis; KICA)於非線性化學流程之監控。雖然，傳統KICA能有效監控非線性、非高斯流程，但針對資料具有動態(dynamic)特性時仍無法有效監控。此外，傳統KICA監控統計量僅考慮目前觀測值之變動大小(magnitude)，而忽略先前觀測值之變動。因此，僅適用於監測大幅度之流程變動，而無法有效偵測小幅度流程變動。然偵測小幅度流程變動以及早採取矯正行動對於某些流程是重要的，如化學流程。
基於上述，本研究擬發展適應性(adaptive)管制圖用以提升KICA之異常偵測能力。本研究方法，首先加入延遲變數(lagged variables)用以擴充原始資料矩陣，其目的在於考慮流程動態特性。之後，將擴充矩陣(angmented matrix)透過核函數(kernel funtion)投影至較高維度之空間，隨後利用傳統ICA演算法擷取出較低維度之獨立成份(Independent Components;ICs)。接下來利用指數加權移動平均法(Exponentially Weighted Moving Average;EWMA)預測ICs，其目的在於記錄過往觀測值之資訊。最後，將所得之EWMA預測值與ICs進行整合發展出適應性監控統計量。所提之監控統計量，因其母體分配未知，所以本研究將利用無母數核密度估計法(kernel density estimation;KDE)決定管制圖界限。
本研究使用兩個實證研究來驗證方法之有效性，其中，第一個案例為模擬兩個非線性流程，主要針對所提方法進行敏感度分析。第二個案例為田納西伊士曼流程案例，主要用以比較傳統ICA、KICA與所提方法之監測能力。實驗結果顯示所提之方法能有效提升傳統KICA之偵測能力。

關鍵字

主成份分析 ； 獨立成份分析 ； 核獨立成份分析 ； 指數加權移動平均法

並列摘要

Kernel Independent Component Analysis is developed to deal with a non-linear dataset by Francis and Michael in 2002. In order to ensure the plant safety and produce high quality product, on-line process monitoring of a chemical process is an important issue. A chemical process usually behaves properties of non-Gaussian, non-linear and dynamics. Even though KICA can handle non-linear process, it fails to monitor dynamics process(i.e. autocorrelation).
Besides, the traditional KICA used Mahalanobis distance to monitor the process. It implies only the recent observation is used, but previous observations are ignored. Thus, KICA may fail to monitor small process shifts.
In order to overcome these drawbacks, this study will present an adaptive statistic to monitor a non-Gaussian, non-linear and dynamic process which is common encounted in a chemical process. At first, the collected data matrix is augmented by adding lagged variables. This preprocessing step is used to deal with the autocorrelation property of the chemical process. After that, the augmented matrix is then projected into a higher dimensional space (i.e. feature space) in order to take non-linear property into consideration. In the aftermath, the Exponentially Weighted Moving Average (EWMA) is used to extracted ICA components to store the information of past observations. Finally, the adaptive statistic is then developed by integrating EWMA and ICA extracted components. We will show the traditional ICA monitoring statistic is a special case of the proposed one.
The efficiency of the proposed method will be verified by implementing two examples. For the first example, a simulation example is used for sensitivity analysis of the proposed statistic. After that, the Tennessee Eastman (TE) process is used for comparing traditional monitoring methods (i.e. ICA and KICA) and proposed method. Results indicate the proposed statistic is superior for monitoring small process shifts when compare with traditional methods.

並列關鍵字

Kernel Independent Component Analysis ； Exponentially Weighted Moving Average ； Independent Component Analysis ； Principal Component Analysis

參考文獻

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