發展適應性管制圖以提升傳統ICA監控方法

Developing an Adaptive Chart to Enhance Traditional ICA Based Monitoring Method

李政毅(Cheng-Yi Li)

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(2009年)

摘要

主成份分析(Principal Component Analysis; PCA)方法可將高維度之原始變數轉換為較具低維度之空間，因此PCA常被用於多變量分析之資料前處理的工具。然PCA進行變數轉換時僅考慮共變異數矩陣(Covariance matrix)，因此只能去除變數間之相關性，而不能使變數間具獨立之特性。此外，利用PCA進行流程監控時必須假設所得之主成份符合高斯分配(Gaussian distribution)。然從現實流程所收集之數據經PCA轉換後所得之主成份常違反高斯分配之假設。
近來，獨立成份分析(Independent Component Analysis; ICA)方法被發展用於處理非高斯分配之資料。不同於PCA，ICA轉換原始變數考慮較高階次之統計量並試圖使變數間具獨立之特性。傳統上，以ICA為基礎之流程監控方法，常利用馬氏距離做為監控統計量，然此統計量只考慮目前觀測值之變動大小(magnitude)，而忽略先前觀測值之變化。因此，傳統ICA流程監控方法僅適用於偵測大幅度之流程變動，而針對小幅度之流程變動並無法有效的進行偵測。
基於上述，本研究擬發展ㄧ適應性管制圖用以提升傳統ICA監控方法之異常偵測能力。本研究首先利用ICA擷取獨立成份(Independent Components; ICs)，之後利用指數加權移動平均(Exponentially Weighted Moving Average; EWMA)法預測流程平均值之變動，最後結合所擷取之ICs與所預測之EWMA值發展出適應性統計量。此外，本研究利用所提之統計量進一步發展線上流程監控架構。
本研究所提之方法將應用於四個不同流程之監控。其中，第一個案例為一線性流程之監控。第二個案例為一非線性流程之監控。第三個案例為田納西伊士曼(Tennessee Eastman；TE)流程之監控。最後一案例為台灣電力公司火力發電廠之流程監控。所提方法之有效性，將與傳統監控方法進行驗證比較。實驗結果顯示所提之方法能有效提升傳統ICA之偵測能力。

關鍵字

多變量統計流程監控 ； 主成份分析 ； 指數加權移 ； 獨立成份分析

並列摘要

PCA (Principal Component Analysis; PCA) can handle high dimensional of the original variables onto a lower dimensional subspace, so PCA is often used for multivariate analysis as the data pre-processing tool. PCA imposes independency up to second ordered statistic (i.e. mean and variance) and hence can only decorrelate variables but not to make variables to be independent. For PCA based process monitoring, the extracted components are assumed to follow Gaussian distribution. However, the collected data from practical processes such as chemical, food, pharmaceutical and so forth usually exhibit the extracted PCA components rarely conform to the Gaussian assumption.
Recently, Independent Component Analysis (ICA) has been developed to deal with the non-Gaussian dataset. Different from the PCA, ICA considers higher order statistics and aims to impose variables to be independent. ICA is further used for monitoring non-Gaussian processes. However, the traditional ICA based monitoring scheme considers only the magnitude of recent observation but ignores the information of previous observations. Thus, the traditional ICA based monitoring method is not sensitive to detect small changed disturbance.
As mentioned above, in order to enhance the detectability of ICA based monitoring method, an adaptive chart based on ICA will be developed. The basic idea of proposed method utilizes the Exponentially Weighted Moving Average (EWMA) to predict the changing direction of process mean and then the estimated values are integrated with the extracted ICA components.
The adaptive chart will be implemented to monitor four different processes: linear process, non-linear process, a real case study of Tennessee Eastman (TE) process and a thermal power plant case. The efficiency of adaptive chart will be verified by comparing to several conventional monitoring schemes. The experiment results show the proposed method can efficiently enhance the detectability for traditional ICA monitoring method. Besides, the adaptive chart processes superior performance than alternative methods.

並列關鍵字

EWMA ； ICA ； PCA ； MSPM

參考文獻

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