在限制計算成本下異質性隨機克利金元模型與迴歸元模型之比較

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詹薏蓁(Yi-Chen Chan) 查詢紙本館藏

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工業管理研究所

論文名稱

在限制計算成本下異質性隨機克利金元模型與迴歸元模型之比較
(Comparison of Stochastic Kriging Metamodel and Regression Metamodel in Simulation：The Heteroscedastic Variance Case with Constraint Computing Budget)

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至系統瀏覽論文 (2025-7-25以後開放)

摘要(中)

元模型為解釋模型的模型，透過執行隨機模擬，模擬模型其輸出值提供了元模型所需的估計值。在隨機模擬實驗中，多項式迴歸與隨機克利金法皆為常見元模型建模方法。其中迴歸是找一個函數，使此函數盡量符合已知點的資料，此函數稱作迴歸函數；而隨機克利金法是為隨機模擬實驗開發的一種元建模方法，在克利金法的基礎上開發新的模型設計。隨機克利金法將模型輸出性能的不確定性與隨機模擬中固有的取樣不確定性區分開來，因此隨機克利金模型既要描述隨機模擬中原有的固有不確定性，又要考慮未知輸出的外部不確定性。
本篇論文比較了隨機克利金元模型與迴歸兩種元模型，在限制其計算成本的條件下，具異質性變異數輸出的模擬模型，不需經過複雜的轉換運算使其變異數趨於相似，便可直接用以建立元模型。在這項研究中，通過模擬實驗的設計和分析，經過共計100次的實驗，透過數據分析的結果，證明所提出的隨機克利金元模型相對於競爭方法，在限制條件下其模型估計性能更優於迴歸元模型。

摘要(英)

Ｍetamodel is a model for explaining the model. By running a stochastic simulation, we can know the number specified by the random model but cannot be analyzed and calculated. The output value of the simulation model provides the estimated value required by the metamodel. Polynomial Regression and stochastic kriging are both common metamodeling methods in stochastic simulation experiments. Regression method is to find a function that could match the known data as much as possible, this function called regression function. Another method is a metamodeling method developed for random simulation experiments named stochastic kriging. The design of the model is based on the kriging method, this method characterized both the intrinsic uncertainty inherent in a stochastic simulation and the extrinsic uncertainty about the unknown response surface.
In this study, we compared two different metamodels, stochastic kriging metamodel and regression metamodel. Under the condition of limiting calculation budget, the simulation model with heterogeneous variable output does not need to undergo complex conversion operations to make the variation tend to be similar. It can be used directly to build a metamodel. Through the design and analysis of simulation experiments, after a total of one hundred experiments, and through the results of data analysis, it is proved that stochastic kriging metamodel has the better performance of estimated.

關鍵字(中)

★ 多項式迴歸
★ 克利金法
★ 隨機克利金法
★ 元模型

關鍵字(英)

★ Polynomial Regression
★ Kriging Model
★ Stochastic Kriging
★ Metamodel

論文目次

中文摘要 i
ABSTRACT ii
目錄 iii
圖目錄 v
表目錄 vi
第一章、緒論 1
1-1　研究背景與動機 1
1-2　研究目的 4
1-3　研究架構 6
第二章、文獻探討 7
2-1　元模型（Metamodel） 7
2-2　隨機場（Random　Fields） 8
2-3　迴歸（Regression） 9
2-4　克利金法（Kriging　Method） 10
2-5　隨機克利金法（Stochastic　Kriging） 14
第三章、研究方法 19
3-1　模型假設 19
3-1-1　迴歸元模型 19
3-1-2　隨機克利金元模型 21
3-2　參數估計 25
3-2-1　迴歸元模型參數 25
3-2-2　隨機克金元模型參數 26
第四章、數值分析 27
4-1　環境設計 27
4-2　第一階段實驗 28
4-2-1　迴歸元模型 28
4-2-2　隨機克利金元模型 29
4-2-3　第一階段實驗結果 30
4-3　第二階段實驗 31
4-3-1　迴歸元模型 31
4-3-2　隨機克利金元模型 32
4-3-3　第二階段實驗結果 33
第五章、結論 36
5-1　結論 36
5-2　未來展望 36
參考文獻 38
附錄一 42
附錄二 44
附錄三 47
附錄四 49

參考文獻

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指導教授

葉英傑(Ying-Chieh Yeh)

審核日期

2020-7-29

推文