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

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：35

、訪客IP：18.119.167.237

姓名

詹薏蓁(Yi-Chen Chan) 查詢紙本館藏

畢業系所

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)

相關論文

★ 應用失效模式效應分析於產品研發時程之改善	★ 服務品質因子與客戶滿意度關係研究-以汽車保修廠服務為例
★ 家庭購車決策與行銷策略之研究	★ 計程車車隊派遣作業之研究
★ 電業服務品質與服務失誤之探討-以台電桃園區營業處為例	★ 應用資料探勘探討筆記型電腦異常零件-以A公司為例
★ 車用配件開發及車主購買意願探討(以C公司汽車配件業務為實例)	★ 應用田口式實驗法於先進高強度鋼板阻抗熔接條件最佳化研究
★ 以層級分析法探討評選第三方物流服務要素之研究-以日系在台廠商為例	★ 變動良率下的最佳化批量研究
★ 供應商庫存管理架構下運用層級分析法探討供應商評選之研究-以某電子代工廠為例	★ 台灣地區快速流通消費產品銷售預測模型分析研究–以聯華食品可樂果為例
★ 競爭優勢與顧客滿意度分析以中華汽車為例	★ 綠色採購導入對電子代工廠的影響-以A公司為例
★ 以德菲法及層級分析法探討軌道運輸業之供應商評選研究–以T公司為例	★ 應用模擬系統改善存貨管理制度與服務水準之研究-以電線電纜製造業為例

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

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

[1] Ankenman, B., Nelson, B. L., Staum, J. "Stochastic Kriging for Simulation Metamodeling. " Operations Research, 58(2), pp. 371–382, 2010.
[2] Banks, J., J. S. Carson II, B. L. Nelson, D. M. Nicol. "Discrete-Event System Simulation (5th ed.). " Pearson Prentice Hall, 2009.
[3] Barton, R. R., Nelson, B. L., Xie, W. "Quantifying Input Uncertainty via Simulation Confidence Intervals. " INFORMS Journal on Computing, 26(1), pp. 74–87, 2014.
[4] Barton, Russell R. "Simulation metamodels." 1998 Winter Simulation Conference. Proceedings (Cat. No. 98CH36274), 1998.
[5] Barton, Russell R., Meckesheimer M. "Metamodel-based simulation optimization." Handbooks in operations research and management science, 13, pp. 535-574, 2006.
[6] Bartz-Beielstein, T., Zaefferer, M. "Model-based methods for continuous and discrete global optimization." Applied Soft Computing, 55, pp. 154-167, 2017.
[7] Chen, X., Ankenman, B. E., Nelson, B. L. "The effects of common random numbers on stochastic kriging metamodels." ACM Transactions on Modeling and Computer Simulation (TOMACS) , 22(2) , pp. 1-20, 2012.
[8] Chen, X., Ankenman, B. E., Nelson, B. L. "Enhancing stochastic kriging metamodels with gradient estimators." Operations Research , 61(2) , pp. 512-528, 2013.
[9] Chen, X., Ankenman, B., Nelson, B. L. "Common random numbers and stochastic kriging." Proceedings on the 2010 Winter Simulation Conference, 2010.
[10] Chen, X., Kim, K.-K. "Stochastic kriging with biased sample estimates." ACM Transactions on Modeling and Computer Simulation (TOMACS) , 24(2) , pp. 1-23, 2014.
[11] Cressie, N. "Aggregation in geostatistical problems." Geostatistics Troia’92. Springer, pp. 25-36, 1993.
[12] Fang, K. T., R. Li, Sudjianto, A. "Design and Modeling for Computer Experiments Chapman & Hall." CRC, 304, 2006.
[13] Gupta, A., Ding, Y., Xu, L., Reinikainen, T. "Optimal parameter selection for electronic packaging using sequential computer simulations." Journal of Manufacturing Science and Engineering, 128(3), pp. 705-715, 2006.
[14] Huang, D., Allen, T. T., Notz, W. I., Zeng, N. "Global optimization of stochastic black-box systems via sequential kriging meta-models." Journal of global optimization, 34(3), pp. 441-466, 2006.
[15] Kleijnen, J. P. C. "Design and analysis of simulation experiments, second edition." Springer, 2015.
[16] Kleijnen, J. P. C. "Kriging metamodeling in simulation: A review." European journal of operational research , 192(3) , pp. 707-716, 2009.
[17] Kleijnen, J. P. C. "Simulation Optimization through Regression or Kriging Metamodels." High-Performance Simulation-Based Optimization. Springer, pp.115-135, 2020.
[18] Li, Y. F., Ng, S. H., Xie, M., Goh, T. N. "A systematic comparison of metamodeling techniques for simulation optimization in decision support systems." Applied Soft Computing, 10(4), pp.1257-1273, 2010.
[19] Pham, T., Wagner, M. "Filtering noisy images using kriging." ISSPA′99. Proceedings of the Fifth International Symposium on Signal Processing and its Applications (IEEE Cat. No. 99EX359), 1999.
[20] Qu, H., Fu, M. C. "Gradient extrapolated stochastic kriging." ACM Transactions on Modeling and Computer Simulation (TOMACS), 24(4) , pp.1-25, 2014.
[21] Quan, N., Yin, J., Ng, S. H., Lee, L. H. "Simulation optimization via kriging: a sequential search using expected improvement with computing budget constraints." IIE Transactions, 45(7), pp.763-780, 2013.
[22] Roshan, U., Livesay, D. R. "Probalign: multiple sequence alignment using partition function posterior probabilities." Bioinformatics , 22(22), pp. 2715-2721, 2006.
[23] Sacks, J., Welch, W. J., Mitchell, T. J., Wynn, H. P. "Design and analysis of computer experiments." Statistical science, pp. 409-423, 1989.
[24] Sakata, S., F. Ashida, M. Zako. "On applying Kriging-based approximate optimization to inaccurate data." Computer methods in applied mechanics and engineering, pp.2055-2069, 2007.
[25] Sargent, R. "Verification and validation of simulation models." Journal of simulation ,7(1), pp.12-24, 2013.
[26] Shen, H., Hong, L. J., Zhang, X. "Enhancing stochastic kriging for queueing simulation with stylized models." IISE Transactions, 50(11), pp.943-958, 2018.
[27] Shi, X., Tong, C., Wang, L. "Evolutionary optimization with adaptive surrogates and its application in crude oil distillation." 2016 IEEE Symposium Series on Computational Intelligence, pp.1-8, 2016.
[28] Simpson, T. W., Poplinski, J. D., Koch, P. N.,Allen, J. K. "Metamodels for computer-based engineering design: survey and recommendations." Engineering with computers, 17(2), pp.129-150, 2001.
[29] Staum, J. "Better simulation metamodeling: The why, what, and how of stochastic kriging." Proceedings of the 2009 Winter Simulation Conference (WSC), pp.119-113, 2009.
[30] Stein, M. L. "Interpolation of spatial data: some theory for kriging." Springer Science & Business Media, 2012.
[31] Tew, J.D., Wilson, J.R. "Estimating simulation metamodels using combined correlationbased variance reduction techniques." IIE Transactions, 26(3), pp.2-16, 1994.
[32] Xie, W., Nelson, B. L., Barton, R. R. "A Bayesian framework for quantifying uncertainty in stochastic simulation." Operations Research, 62(6), pp.1439-1452, 2014.
[33] Yin, J., Ng, S. H., Ng, K. M. "A study on the effects of parameter estimation on Kriging model′s prediction error in stochastic simulations." Proceedings of the 2009 Winter Simulation Conference (WSC), 2009.
[34] Yin, J., Ng, S. H., Ng, K. M. "Kriging metamodel with modified nugget-effect: The heteroscedastic variance case." Computers & Industrial Engineering, 61(3), pp.760-777, 2011.
[35] Zou, L., Zhang, X. "Stochastic kriging for inadequate simulation models." arXiv preprint arXiv:1802.00677, 2018.

指導教授

葉英傑(Ying-Chieh Yeh)

審核日期

2020-7-29

推文