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研究生:蔡輔晃
研究生(外文):Fuhuang Tsai
論文名稱:反應曲面法與基底建構反應曲面法之研究
論文名稱(外文):A Comparison Study of Response Surface Methodology versus Basis Representation Methods
指導教授:王偉仲
指導教授(外文):Weichung Wang
學位類別:碩士
校院名稱:國立高雄大學
系所名稱:統計學研究所
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:113
中文關鍵詞:基底反應曲面法代理模型代理曲面計算機實驗最佳化基底函數字典均勻設計影像重現影像建構反應曲面法
外文關鍵詞:Basis-based response surface methodResponse surface methodologysurrogate surfacesurrogate modelcomputer experiment optimizationovercomplete basis functionsbasis functionsuniform designimage representation
相關次數:
  • 被引用被引用:18
  • 點閱點閱:3392
  • 評分評分:
  • 下載下載:430
  • 收藏至我的研究室書目清單書目收藏:1
針對解決最佳化的問題上,我們提出了一新的演算法,稱為基底建構反應曲面法。主要的策略是使用所有已知訊息在整個實驗區域內建構代理模型,再從代理模型中選擇可能的最佳點。我們將實驗區域分成多個格點,並僅考慮格點上的得到的反應值,使得能夠將問題視為一影像,進而應用一些影像處理技巧建構代理模型,其中Matching Pursuit演算法、Gabor function與均勻設計在我們提出的新演算法中有著重要的應用。我們針對平滑與不平滑與有多重極值點之反應曲面均進行一些測試,並且同時與傳統反應曲面法RSM進行比較。數值實驗結果也呈現了新演算法能夠有效率的搜尋到單一最佳點及同時搜尋多個最佳點。
Here we proposed a new algorithm named Basis-based response surface method(BRSM) that aiming at solving optimization problems arising in computer experiments. Techniques taken from experimental design, statistical approximation, and image representation are incorporated carefully in the proposed algorithm. The method iteratively construct surrogate surfaces over the whole experimental region by using overcomplete basis functions to predict possible optimum points and next experiments. We do test on some typical response surface and comparison between the RSM and the BRSM. Numerical result show that BRSM is quite efficient for finding single or multiple optima of smooth response surfaces.
目錄
中文摘要 ii
Abstract iii
1 前言 1
2 Basis-based Response Surface Method(BRSM) 3
2.1 BRSM演算法描述 4
2.2 Matching-Pursuit演算法 12
2.3 BRSM演算法的主要改進 18
2.4一個以Matching Pursuit法建構代理模型的例子 20
2.5一個詳細的BRSM實作過程 27
3 反應曲面法(RSM) 36
3.1 反應曲面法簡述 36
3.2 計算機實驗上之反應曲面法 39
3.3 最陡上升(或下降)過程 41
3.4 一個詳細的RSM實作例子 53
4 BRSM與RSM在一些例子上的數值實驗與比較 94
4.1 Smooth function with single extreme 94
4.2 Smooth function with two local extreme values 97
4.3 Oscillatory surface with multiple extreme values 100
5 討論 105
Appendix A : Basis Dictionary of Gabor function 107
Appendix B :在本篇文章中所用來供模擬之反應曲面 109
參考文獻 113
[1]Wang W. and Chen, R.B.(2004). Basis Representation Methodology for Response Surface. Technical report in Department of Applied Math. and Institute of Statistics, National University of Kaohsiung.
[2]Martin Buhmann(2003). Radial basis functions: theory and implementations. Cambridge; Cambridge University Press, 2003.New York:
[3]Devidas V. Pai, Hrushikesh N. Mhaskar.(2000). Fundamentals of approximation theory. Narosa Pub. House.
[4]Stapleton, James H.(1995). Linear statistical models. New York :Wiley,c1995.
[5]Myers, Raymond H. and Montgomery, Douglas C.(2002). Response surface methodology :process and product optimization using designed experiments(2nd ed.). New York :John Wiley & Sons.
[6]Box, George E. P. and Draper, Norman Richard.(1987). Empirical model-building and response surfaces. New York :Wiley.
[7]Box, G. E. P. and Wilson, K. B. (1951). On the Experimental Attainment of Optimum Conditions. Journal of he Royal Statistical Society, Ser. B, 13, 1-45.
[8]Stephane Mallat, Zhifeng Zhang.(1993). Matching Pursuit With Time-Frequency Dictionaries . IEEE Transactions on Signal Processing, 41:3397-3415.
[9]Bergeaud, F. and Mallat, S.(1995). Matching pursuit of images. 1995 International Conference on Image Processing, 1:53-56.
[10]Balkin, S.D. and Lin, D.K.J.(2000). Aneural network approach to Response surface methodology. Commun. Statist.-theory Meth., 29, 2215-2227
[11]Fang, K.T., Lin, D.K.J., Winker, P., and Zhang, Y. (2000). Uniform Design: theory and applications. Technometrics, 42: 237-248
[12]Arthur Pece and Nikolay Petkov.(2000). Fast atomic decomposition by the inhibition method. In Processing of the 15th International Conference on Pattern Recognition, Page 215-218.
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