- 學位論文
利用隱藏馬可夫樹模式以提昇製程監控效能
Improving Performance of Process Monitoring Using Hidden Markov Tree Model
摘要
我們利用基於小波轉換發展的隱藏式馬可夫樹模型（Hidden Markov tree models, HMT），去改善傳統製程監控上只針對時間面的統計製程管制（statistical process control）。HMT不但可從不同尺度的時間與頻率上分析量測數據，且能在這些尺度中獲取真實量測的系統行為，前者比起傳統的過濾方式有較佳的去雜訊能力和較少的失真訊號；後者可從不可說明的動態擾動萃取出系統特徵，如實際數據的聚集和持續性，這是SPC所忽略的。我們將分別發展基於HMT的SPC和MSPC（multivariate SPC）監控系統，首先從正常操作數據經小波轉換訓練出HMT模式，此模式參數的訓練是靠著反覆的EM（expectation maximization）演算法，利用過去操作資訊建模之後，其監控方法的原理與傳統的SPC相似，建立簡單的監控管制圖，容易追蹤和監控製程錯誤的發生。本研究比較現有的SPC方法來說明以HMT結合SPC監控方法的優點：當不可說明的擾動序列有很強的關聯性時，它呈現出較精確的結果。在本文中將以實際工廠所提供的數據進行監控，幫助讀者探索內容並驗證本方法的效能。
關鍵字
隱藏式馬可夫樹模型並列摘要
Wavelet-based hidden Markov tree (HMT) models is proposed to improve the conventional time-scale only statistical process model (SPC) for process monitoring. HMT in the wavelet domain can not only analyze the measurements at multiple scales in time and frequency but also capture the statistical behavior of real world measurements in these different scales. The former can provide better noise reduction and less signal distortion than conventional filtering methods; the latter can extract the statistical characteristics of the unmeasured dynamic disturbances, like the clustering and persistence of the practical data which are not considered in SPC. Based on HMT, a univariate and a multivariate SPC are respectively developed. Initially, the HMT model is trained in the wavelet domain using the data obtained from the normal operation regions. The model parameters are trained by the expectation maximization algorithm. After extracting the past operating information, the proposed method, like the philosophy of the traditional SPC, can generate simple monitoring charts, easily tracking and monitoring the occurrence of observable upsets. The comparisons of the existing SPC methods that explain the advantages of the properties of the newly proposed method are shown. They indicate that the proposed method can lead to more accurate results when the unmeasured disturbance series are getting strong correlation. Data from the monitoring practice in the industrial problems are presented to help readers delve into the matter.