Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/2723
標題: 回應表面法在最佳化設計之應用
Applications of Response Surface Methodology in Optimum Designs
作者: 李弦政
Lee, Shing-Cheng
關鍵字: Response Surface Methodology;回應表面法;Optimum Design;stepwise regression methods;face center cube;最佳化設計;逐步迴歸分析;面中心立方體佈點方式
出版社: 機械工程學系
摘要: 
本文應用回應表面的方法來取代有限元素分析或實驗,以快速取得一近似的結構分析或是實驗值,利用此一近似的目標函數和限制函數的值求取最佳化問題的最佳解。回應表面是利用統計和數學的方法在一設計空間中利用選定的設計點建立起設計變數和回應值的顯函數關係,因此可利用此種顯函數快速進行系統回應值計算和靈敏度分析求得最佳解。
應用回應表面的方法最重要的是能利用最少的設計點模擬出準確度尚佳的近似函數,為了提升回應表面的準確性本文提出兩種縮減設計空間的方法增加回應表面式的準確性,第一種方法是將原始設計空間縮小一半,分二階段搜尋最佳解。第二種方法是將設計變數空間縮小一半,然後分階段搜尋最佳解。本文並且利用面中心立方體的佈點方式使用最少的設計點以提高計算效率。除了縮減設計空間外如果將輸入值和回應值做數據轉換也能取得較正確的回應表面式,因此本文將輸入值取自然對數和使用Box-Cox所提出的回應次方轉換法對回應值做轉換。最後使用逐步迴歸的方法來建構最適當的回應表面式。運用上述方法建構出回應表面式後,再以商用軟體DOT/DOC來求得各範例的最佳解。
本文將前述方法應用於切削最佳化和結構最佳化實例中,建立回應表面預測模式求得最佳值,並且與數學式或文獻所求得的最佳化結果比較。

In order to quickly obtain approximation results of structural analyses or experimental data, this research employs response surface method to replace finite element analyses and experiments. The optimum solutions of the design or experimental problems are sought using response surfaces for the objective and constraint functions. The response surface method is a statistical approach to create an approximate explicit function of design variables in a given design space. Therefore it is easy to compute the function values and sensitivities using response surfaces and the optimum solution can be obtained quickly.
The most important concern using response surface is to generate a response function with maximum accuracy while using minimum number of design points. To increase the accuracy of response surfaces, this thesis proposes two approaches to achieve the goal. One is to reduce the original design space to its half initially and then construct response surfaces in this reduced region to find optimum solution. After locating the optimum solution, a new design region centered on the found optimum solution is created and the final solution is searched in this new region. The other approach is similar to the previous one except the reduction of design space is made on each design variable by a given reduction ratio. The design or experimental points used to construct response surfaces are determined by central composite design. In addition to reduce the design space , the transformation of input and output data will also greatly improve the accuracy of the approximations. The input and output data are transformed by taking natural logarithm and power transformation, respectively. The step wise regression technique is finally used to select the most appropriate design variables in the model. DOT/DOC software is used to solve optimum design problems in this thesis.
Several examples including metal cutting experiments and structural designs are illustrated. The optimum solutions obtained by response surface are compared with known solutions.
URI: http://hdl.handle.net/11455/2723
Appears in Collections:機械工程學系所

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