臺灣博碩士論文加值系統

批次製程在現代化工產業所扮演的角色已越來越重要，諸如半導體、生化及製藥工業等都大量應用批次製程技術。批次製程的特性可由原始數據的分析來得到，而運用這些製程資訊將使得製程能夠達到所需的產率及品質要求。由於批次製程數據包含了批次，變數及時間的三種維度，因此在本論文中，我們將應用PARAFAC（Parallel Factor analysis）三維數據分析方式，從過去的量測數據萃取出系統的特性，發展線上即時批次製程的監控技術。
在發展線上即時監控PARAFAC前，以系統的方式說明異常的變異量下，PARAFAC較MPCA更容易偵測出異常的變動。此變異量分析主要是以兩個一次微分項來計算，當異常加入系統後所產生的變異量，而從這分析的結果我們得知PARAFAC的韌性度較MPCA為高。隨後本論文將發展含動態特性的線上即時DPARAFAC及Tri-DPLS方法，其概念主要是結合以時間作為視窗平移的技術，使得數據包含所有變數與時間的關係，加強系統的動態特性，就如同我們過去所發展的BDPCA及BDPLS。
本論文針對批次製程所提出的DPARAFAC及Tri-DPLS方法，比過去所提出的MPCA更為靈敏，將更容易在系統發生異常時有效的偵測出異常情形。最後，我們將使用幾個例子作為本理論的驗證，並和過去所發展的線上即時監控策略做比較。

Batch production processes play an important role in chemical industries. Pharmaceuticals, biochemicals, semiconductors and polymers, for example, often utilize batch production. Batch processes are characterized by prescribed processing of raw materials into products within finite duration. The profiles as the fingerprint of the batch operations provide vital information characteristics of the operation of the batch. They can be used to identify if the current operating condition is successful. In this research, an online batch process monitoring based on the three-way data analysis is developed because the data in the batch operation are usually arranged in a three-way matrix with batch, measurements and their time profiles. Based on parallel factor analysis (PARAFAC), the developed technique extracts the state of the system via applications of mathematical and statistical methods from the big volume of the past historical database.
Before the on-line PARAFAC model is developed, a systematic derivation explains why PARAFAC is chosen over MPCA. The variance of the abnormal data based on the estimated model is derived. It is not necessary to carry out the derivation for the abnormal profile estimates. The variance of the abnormal data can be expressed into two Jacobians terms to capture the amount of the abnormal variations. The issues of the detection of the abnormal variance suffered from the number of components are presented. From this analysis, it can clearly indicate PARAFAC is more robust than MPCA. Then on-line batch monitoring methods, referred to as DPARFAC and Tri-DPLS, are developed. They integrate the time-lagged windows of the process dynamic behavior with PARAFAC and tri-PLS respectively. They deal with dynamic relationships; that is, the measured variables at one time instant have the serial correlation within variable series at the past time instances. Like our previously developed BDPCA and BDPLS, DPARAFAC and Tri-DPLS models only collect the previous data during the batch run without expensive computations to anticipate the future measurements. This leads to simple monitoring charts, easy tracking of the progress in each batch run and monitoring the occurrence of the observable upsets. Several examples are used to investigate the potential applications of the proposed methods and make a comparison with the previous on-line methods.

摘要I
AbstractII
目錄IV
圖目錄VI
表目錄VIII
第一章 前言1
1-1 文獻回顧1
1-2 研究動機3
第二章：靜態管制分析－量測變數為基礎的管制方式5
2-1 批次製程的數據結構5
2-2 MPCA離線偵測6
2-2-1 MPCA離線偵測原理6
2-2-2 MPCA離線管制9
2-3 PARAFAC離線偵測10
2-3-1 PARAFAC離線偵測原理10
2-3-2 PARAFAC離線管制17
2-4 MPCA與PARAFAC的比較18
2-4-1 過去比較PARAFAC與MPCA的文獻回顧18
2-4-2 異常數據變動大小的變動原理24
附錄：式（2-46）∼式（2-49）的推導36
第三章 即時偵測分析－量測變數為基礎的管制方式41
3-1 MPCA線上即時偵測41
3-1-1 MPCA批次監控原理41
3-1-2 MPCA線上即時監控技術42
3-1-3 異常數據變動大小的比較44
3-2共變異係數矩陣討論55
3-3 PARAFAC數據排列動態特性討論56
3-4 DPARAFAC線上即時偵測58
3-4-1 DPARAFAC批次監控原理58
3-4-2 DPARAFAC數據排列的動態特性60
3-4-3 DPARAFAC線上即時監控技術63
3-5 MPCA、PARAFAC、BDPCA與DPARAFAC線上即時偵測的比較67
第四章：靜態管制分析－品質變數為基礎的管制方式71
4-1 MPLS離線偵測71
4-1-1 MPLS離線偵測原理71
4-1-2 MPLS離線管制75
4-2 Tri-PLS離線偵測77
4-2-1 Tri-PLS離線偵測原理77
4-2-2 Tri-PLS離線管制79
4-3 討論81
第五章：即時偵測分析－品質變數為基礎的管制方式84
5-1 MPLS線上即時偵測84
5-1-1 MPLS批次監控原理84
5-1-2 MPLS線上即時監控技術86
5-2 Tri-DPLS 線上即時偵測88
5-2-1 Tri-DPLS批次監控原理88
5-2-2 Tri-DPLS線上即時監控技術90
5-3 討論93
第六章 結論97
符號說明105
參考文獻107

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