臺灣博碩士論文加值系統

實驗設計法與替代模型兩種方法近來被廣泛的使用在電腦模擬試驗中，其主要原因為採用實驗設計法可以降低計算的次數，而利用替代模型取代原本複雜的模型則可減少計算的時間。這兩者結合使用可以大幅度縮短電腦實驗的時間，但當取樣點數被限制時，何種實驗設計方式運用於替代模型時有較可靠的預測結果，是本研究探討的重點。
本研究使用兩個輸入變數與一個輸出變數的熱液動潤滑模型進行研究，以拉丁立方取樣(Latin Hypercube Sampling)、均勻設計(Uniform Design)與網格取樣(Regular Meshing)三種實驗設計方式與四種取樣數目(分別為16、36、64及100點)，以類神經網路(Artificial Neural Network)為替代模型，進行實驗設計法的比較。替代模型測試採用均方根誤差與最大絕對誤差百分比為標準，並可藉此分析與判斷在相同取樣點時取樣方式的優劣。
本研究之電腦實驗結果顯示，與其他兩種取樣法比較，均勻設計在取樣點數較少時，有較準確的預測結果，並在各種不同的類神經網路架構下，有著最低的誤差平均值。本研究並歸納出單/雙隱藏層之類神經網路架構與不同取樣方式和取樣數目之間的關係，能提供後續類似研究的參考。

Design of experiments and metamodels are used extensively in computer-based simulations for providing useful information with less effort. Usually a metamodel can provide an efficient and accurate substitute for the original numerical model. Thus, the combination of design of experiments and metamodels can reduce the execution time in many applications. In some cases, for example the sample size is limited, the effect of design of experiments on the performance of a metamodel can become a dominant factor. The effect of sampling technique is the main focus of this study.
In this study, a Thermohydrodynamic model is substituted by a metamodel, artificial neural network. Three experimental designs (Latin Hypercube, Uniform Design and Regular Meshing) and four sample sizes (16, 36, 64 and 100) were used to examine the accuracy of the metamodel. The model has two input variables and one output variable. Root mean square error and maximum absolute error were used for assessing the metamodel.
The results of the computer experiments show that for a small sample size the uniform design provides better prediction and has minimum average error in a variety of networks. This study provides a reference for the researchers who are interested in the application of artificial neural network, the design of experiments and the sampling techniques.

第一章 簡介
1.1 前言
1.2 研究動機
1.3 文獻回顧第二章 實驗設計法
2.1 拉丁立方取樣 (Latin Hypercube Sampling, LHS)
2.1.1 總均值模型 (Overall Mean Model)
2.1.2 LHS的特性
2.1.3 LHS的佈點步驟
2.2 均勻設計 (Uniform Design, UD)
2.2.1 均勻設計表
2.2.2 均勻設計表之構造 (優良格點法)
第三章 替代模型
第四章 研究方法
4.1 熱液動潤滑模型
4.2 拉丁立方取樣設計
4.3 均勻設計法取樣設計
4.4 網格取樣法設計
第五章 實驗結果與討論
5.1 100個取樣點之結果
5.2 64個取樣點之結果
5.3 36個取樣點之結果
5.4 16個取樣點之結果
5.5 結果與討論
第六章 結論與建議
參考文獻

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