本文探討工業製程中的預測問題，並分為兩個部份，第一部分為批次製程終點預測及敏感度分析，第二部分為高斯過程回歸之模型遷移。
第一部份是批次製程終點預測的研究。批次製程是工業界常使用的方法，但由於批次間的變異性，每個批次的結束時間都不同，可能會導致在操作上的額外成本，如果能預測出每個批次的終點將能提供操作者有用的資訊，像是後續的排程、減少閒置的機台。本文運用機率主成分分析在有缺失數據的情況下能估計主成分的特性，預測出批次未來變數的走向，並以敏感度分析對預測結果加以解釋。回顧過去對終點預測的方法只能提供點預測，而主成分分析不僅提供了對終點的點預測，還能預測每個採樣時間的均值以及變異數而推出預測終點的置信區間，操作者可利用這些機率相關的資訊改善機台使用以及後續的排程。
第二部分則是利用模型遷移預測產品品質，工業中，為了達到市場及消費者的需求，常需要改變操作條件以製造不同規格的產品，重新建立一個品質預測模型需要蒐集多組實驗的數據，非常耗費成本與時間，而只用有限的新製程數據點建模，模型的預測效果較差，因此有學者提出模型遷移的方法，但此方法只能在新舊製程輸入變數個數相同的情形下使用。而本文針對新舊製程輸入變數個數不同的問題進行模型遷移，預測結果顯示模型遷移能從原始模型中獲取資訊，以少量的新製程數據點達到較佳的預測效果。

The prediction problems in industrial processes are investigated in this work. This thesis is divided into two parts. First, the end-point prediction problem in batch processes is discussed. Then, Bayesian model migration between processes with different number of variables is studied.
Batch process is a widely used manufacturing method in industry. However, due to the inter-batch variation, the end time of batch varies, which may cause additional cost in operation scheduling. The capability of predicting batch end time offers valuable information to help the operators make decisions, which may lead to improved capacity utilization, reduced expected workload, and overall reduced operating cost. This article proposes applying a probabilistic model, i.e. probabilistic principal component analysis (PPCA), for predicting the completion time of batch processes and explain the results by sensitivity analysis. PPCA can provide not only the point estimation of the end time, but also provides useful information to evaluate the prediction uncertainty, based on which operators can improve the capacity utilization and scheduling.
In the second part of this thesis, the model migration problem with changing number of process parameters is studied. In industry, process modeling often requires a large number of experimental data which are usually difficult to obtain with a limited cost of time and money. It is natural to consider model migration which aims to build a reliable process model with a small number of data of the current process and an available model of a similar process. However, in previous research, it often requires that the current process has the same group of parameters as the past process. In this study, the model migration method is revised and extended to the applications that the number of process parameters changes. The feasibility of the proposed methods are illustrated with two case studies.

第一章 緒論 1
1.1 前言 1
1.2文章架構 2
2.1 文獻回顧與研究動機 3
2.2.1 機率主成分分析 5
2.2.2 敏感度分析 10
2.3 案例分析與討論 12
2.3.1 啤酒發酵製程 12
2.3.2 快速重力過濾器(rapid gravity filter) 21
第三章 高斯過程回歸之模型遷移 28
3.1 文獻回顧與研究動機 28
3.2 研究方法 29
3.2.1 高斯過程回歸 29
3.2.2 模型遷移 30
3.4 案例分析與討論 32
3.4.1 實驗室等級CSTR→ 工業等級CSTR 32
3.4.2 CSTR→ PFR 35
第四章 結論 38
參考文獻 40

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