本研究以進階新型三點近似法為基礎，改善最佳化過程中可能會遇到的奇異點，引入移位技術作為中介變數，發展加強進階新型三點近似法數學模型，並可滿足目前參考點及另兩參考點的函數值與靈敏度值，提升最佳化求解的準確性及穩健性。針對加強進階新型三點近似函數進行數值測試，並與進階新型三點近似法做比較，討論其誤差性及準確性。研擬定序列近似最佳化策略，其中包括參
考點的選取及收斂策略，以及探討求解的合理性與有效性。
    接著應用在工程設計例題，以加強進階新型三點近似法求解，證明加強三點近似法的求解過程，能有效避免在最佳化過程中可能發生的奇異點，得到較準確的最佳化結果。本研究應用有限元素分析軟體ANSYS及最佳化數值工具Visual Doc結合，並用來求解光學檢測結構最佳化，並與參考文獻做比較。本文提出的近似方法及求解策略，能以較少的數值迭代次數得到最佳化收斂結果，驗證近似法於最佳化設計的有效性與實用性。同時進一步對體積及位移雙目標最佳化設計，得到距離理想點最靠近的平衡解，以達到光學檢測機構的設計需求。

On the basis of the advanced new three-point approximation method, this thesis presents a shifting level technique combined the advanced new three-point approximation applying on structural optimization problems.  Numerical examples show that the singularity can be effectively avoided by shifting level technique during optimization process.  From the examination, it is verified that fewer iterations is required than other approximation optimization.  The numerical error and the numbers of convergence can be reduced as well.  The completed optimization process including moving region are re-examined and proposed in the thesis.  
A large-scale optical inspection structure for modern wafer manufacture is presented in the thesis.  To promote the precision of quality measurement and inspection, it is necessary to increase the structural stiffness and to optimize the structural behavior control.  In the beginning, the finite element analysis must be successfully applied to the correct model, and then an appropriate optimization model must can be proposed.  Thus, to minimize the structural weight and minimize critical deflection are two design objectives are assigned in the numerical optimization process.  Consequently, the proposed enhanced three-point approximation optimization is applied to the solution process.  A satisfactory result can be obtained in proposed approximated design optimization process.

目錄	
致謝	I
中文摘要	II
英文摘要	III
目錄	V
圖目錄	VII
表目錄	IX
符號說明	X
第一章 緒論	1
	1.1 研究動機與目的	1
	1.2 研究背景	3
	1.3 本文架構	7
第二章 加強進階新型三點近似法原理及模型	9
	2.1處理奇異點的方法	9
	2.1.1修正倒數近似法	9
	2.1.2兩點修正倒數近似法	10
	2.1.3加強兩點近似法	11
	2.2三點近似法簡介	15
	2.3加強進階新型三點近似法(EAnTPA)	17
第三章 加強進階新型三點近似法數值分析	25
	3.1 EAnTPA的性能分析	25
	3.2應用EAnTPA的最佳化流程	29
	3.4結合ANSYS與Visual Doc	35
第四章 加強進階新型三點近似法最佳化	37
	4.1應用EAnTPA於彈簧最佳化設計	37
	4.2檢驗EAnTPA於焊接結構最佳化設計	54
第五章 光學檢測結構最佳化設計	66
	5.1光學檢測結構有限元分析	67
	5.2應用EAnTPA於光學檢測結構最佳化	73
	5.3應用EAnTPA於光學檢測結構雙目標最佳化	88
	5.4雙目標最佳化結果驗證	95
第六章 結論	97
	6.1綜和討論與結論	97
	6.2未來展望	99
參考文獻	100



圖目錄
圖3-1 例題1 AnTPA及EAnTPA相對誤差曲線圖	27
圖3-2 例題2 AnTPA及EAnTPA相對誤差曲線圖	28
圖3-3 三點近似法最佳化流程	29
圖3-4 加強進階新型三點近似法最佳化流程	34
圖3-5 ANSYS與Visual DOC流程圖	36
圖4-1 線圈彈簧	37
圖4-2 彈簧重量最小化結果	50
圖4-3 限制條件 的相對誤差曲線圖 53
圖4-4為懸臂焊接樑結構	54
圖4-5 焊接樑成本最小化目標函數迭代情形	64
圖5-1光學檢測儀結構	70
圖5-2 X-樑最佳化設計的負載及邊界條件示意圖	70
圖5-3 光學量測儀有限元分析結果	71
圖5-4 SOLID95元素	71
圖5-5 X-樑的設計變數	74
圖5-6 X-樑體積最小化結果	79
圖5-7檢測單元位移最小化結果	84
圖5-8文獻[32]X-樑體積最小化結果	87
圖5-9文獻[32] 檢測單元位移最小化之結果	87
圖5-10統一目標函數迭代過程	93
圖5-11 X-樑體積迭代過程	94
圖5-12檢測單元位移量迭代過程	94

表目錄
表3-1 本文近似法最佳化初始策略	32
表4-1 進階新型三點近似法彈簧重量最小化結果	50
表4-2 加強進階新型三點近似彈簧重量最小化結果	51
表4-3彈簧最小化結果比較	51
表4-4 EAnTPA 焊接樑成本最小化結果	64
表4-5焊接樑成本最小化結果比較	65
表5-1 AOI各部零件材料性質[33]	72
表5-2 X-樑體積最小化結果	79
表5-3檢測組位移最小化結果	84
表5-4 X-樑體積最小化結果比較	86
表5-5檢測單元位移最小化結果比較	86
表5-6 雙目標最佳化結果	93

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