應用支援向量機與類神經網路偵測與辨識多變量製程管制外訊號來源之研究

Detecting and classifying out-of-control signals in multivariate processes using support vector machines and neural networks

鄭慧萍(Hui-Ping Cheng)

指導教授 ： 鄭春生

元智大學/工程學院/工業工程與管理學系/博士(2008年)

摘要

管制圖為統計製程管制最重要的工具之一。在許多工業製程中必須同時監控具有兩個或多個相關之品質特性，因此傳統單變量管制圖並不適用。當管制外訊號出現時，我們必須找出變異來源，並且即時採取矯正措施以避免再度發生。在多變量管制法中，目前遭遇到最大的問題在於管制外信號之解釋，亦即當製程已發生變異時，我們必須確定管制外信號是由那個變量所引起的。
本研究之目的是利用支援向量機 (support vector machine, SVM) 與類神經網路 (artificial neural network, ANN) 建構一個能偵測與辨識多變量管制圖中管制外訊號的系統。主要分為多變量製程中之平均值偏移、變異數偏移與非隨機樣式之辨識系統三個部分。對於平均值偏移與變異數偏移的多變量製程，我們將管制外訊號之解釋視為一個分類問題。本系統包含一個偏移偵測器與一個分類器，傳統 管制圖與一般化變異數管制圖分別為平均值與變異數偏移的偵測器，一旦管制外訊號被偵測到，分類器將會確定此變異是來自於哪一個變量所產生。本研究採用支援向量機與類神經網路兩種分類器，並且研究兩個變量與三個變量的情形。此外，我們亦針對正偏、負偏與正負混和偏移的情況加以探討。本研究亦討論三個變量時，不同的共變異數矩陣變化的結果。傳統分解法 (decomposition method) 將作為比較的基準以比較不同分類法之分類結果，本研究採用正確分類率作為評估指標。
對於多變量管制圖非隨機樣式的辨識，本研究探討之非隨機樣式包括趨勢樣式 (trends)、偏移樣式 (sudden shifts)、混合樣式 (mixtures) 與週期性樣式 (cyclic patterns)，主要以支援向量機與類神經網路為基礎，建構多變量非隨機樣式辨識系統。傳統多變量區別分析 (discriminant analysis) 將作為比較的基準以比較不同分類器之分類結果。研究結果顯示支援向量機與類神經網路之辨識績效並無明顯差異，但皆較傳統多變量區別分析為佳。此外，本研究亦討論不同類型之非隨機樣式同時出現以及不同的共變異數矩陣變化的情形。
本研究亦提出兩種不同方式之辨識程序，用以改善非隨機樣式分類之效益。程序一為一個階段之系統架構，同時將正常數據與非隨機樣式進行分類。程序二則為兩階段之系統架構，其中包含了兩個分類器。第一個分類器用來判斷製程中是否出現非隨機樣式，第二個分類器則是將非隨機樣式進行分類。實驗結果顯示，本研究所提出之程序二可以對非隨機樣式有更佳之辨識能力。最後，在敏感度分析中，針對類神經網路與支援向量機之系統參數與訓練樣本進行測試。由實驗結果發現分類器對於參數的調整或訓練樣本結構之改變，都能夠呈現穩健的辨識績效。

關鍵字

多變量製程管制 ； 支援向量機 ； 類神經網路 ； 樣式辨識 ； 分解法 ； 區別分析

並列摘要

Process control charts are important tools for monitoring process mean shifts in manufacturing industries. There are many situations in which the simultaneous monitoring or control of two or more related quality characteristics is necessary. Out-of-control signals in multivariate charts may be caused by one or more variables or a combination of variables. One difficulty encountered with multivariate control charts is the interpretation of an out-of-control signal. That is, we have to determine which variable is responsible for the signal.
For mean shifts and variance shifts, a novel approach to identifying the sources of variation in multivariate process was presented. We formulated the interpretation of out-of-control signal as a classification problem. The proposed system included a shift detector and a classifier. The traditional T-square chart and the generalized variance chart worked as a mean and a variance shift detector, respectively. When an out-of-control signal is generated, a classifier will determine which variable is responsible for the shift. We considered two classifiers based on support vector machine (SVM) and artificial neural network (ANN). We investigated several shift types for p=2 and p=3 cases, that is, positive shifts, negative shifts, and mixed positive and negative shifts. In addition, we also studied the various covariance matrices with varying values of ’s for p=3. We propose using subgroup data and some extracted features as predictors. The performance of the proposed system is evaluated by computing its classification accuracy. We use traditional decomposition method as a baseline for comparison. Moreover, we explored a grid-search on C and of SVMs for mean and variance shift classifiers. The findings of this investigation showed that SVMs are quite robust against parameter selections.
For multivariate pattern recognition issue, we implemented two classifiers based on SVM and ANN to identify multivariate unnatural patterns. In this work, we investigated four types of unnatural patterns identified in the literature, namely, trends, sudden shifts, mixtures, cyclic patterns. We considered multivariate processes with various covariance matrices to cover the whole range of parameters for each pattern type. The discriminant analysis in multivariate statistics is regarded as a baseline. Furthermore, we also proposed a two-stage classification procedure to further improve the performance of the SVM-based classifier. Moreover, for p=3, we investigate the various covariance matrices with varying values of ’s for the case of concurrent (or mixed) patterns.
Results from simulation studies indicate that the SVM and ANN have similar classification performances. Both classifiers can perform significantly better than the traditional statistical method. The proposed method may facilitate the diagnosis of the out-of-control signal.

並列關鍵字

multivariate control charts ； support vector machines ； neural networks ； pattern recognition ； decomposition method ； discriminant analysis

參考文獻

Alt, F. B. (1985). Multivariate quality control. In S. Kotz, N. L. Johnson, and C. R. Read (Eds.), The Encyclopedia of Statistical Sciences, New York: Wiley, pp.110-122.

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Aparisi, F., Jabaloyes, J., and Carrion, A. (2001). Generalized variance chart design with adaptive sample sizes: The bivariate case. Communications in Statistics- Theory and Methods, 30, 931-948.

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Cheng, C. S. (1997). A neural network approach for the analysis of control chart patterns. International Journal of Production Research, 35, 667-697.