本文以基因病變的程度模擬限制條件的違反量，將總違反量轉換為第二個設計目標。將原目標函數做為第一個設計目標，使用多目標策略的非支配排序法，同時最小化這兩個目標，求得柏拉圖解(Pareto)；此時的限制條件將會收斂至零，只保留原目標函數的值。本文將敘述此方法的過程及最佳化程序，並以數值例題及結構設計問題來驗證此方法的效率性及收斂性，並與文獻結果進行比較。
    現今微致動器大都用於微小量測及用於生物醫學工程等方面，本研究以最大化致動器工作端的位移量當做主要目標，又考慮實際應用而加入了溫度的限制條件，利用ANSYS進行分析，並結合本研究所發展的限制條件處理方法進行最佳化設計。本文所探討的微致動器分為兩大類：第一類為單熱臂型式，包含等長度模型，等寬度模型及可變長度及寬度模型。第二類為雙熱臂型式。可變長度及可變寬度模型為本研究所發展的創新設計，結果顯示在有限制條件時，雙熱臂設計的位移量，皆高於其他單熱臂模型。雙熱臂模型可以得到最大的位移量，但是相對需要較多的材料使用量。本文研究的另一個特色可以求解得到在最大化位移量時的最佳電壓輸入值。

The quantity of violation in constraints is simulated to the concept of gene pathological change in biological system. The violation of all constraints is transformed to an artificially second design objective required to be minimized simultaneously. Consequently, the original objective integrated with such artificial objective to construct a two-objective in design optimization problem. A unique Pareto point can be sequentially obtained in which the value of second objective will converge to zero. This thesis presents the complete numerical algorithm and process in dealing with such a genetic revolution based optimization method. Some illustrative problems are solved and compared with that in published papers.
    Another topic in this thesis is the development for the optimization of electro-thermal microactuator and the application using constrained GA presented in this thesis.  The design objective is the maximization of the deflection on a working point that corporate with a upper temperature limitation.  Four models of electro-thermal microactuator are explored. The first category contains three models of single hot arm: constant length model, constant width model, and variable length/width model.  The fourth model is double hot-arm model. The structural material volume, design deflection, and temperature influence are primary study items.  Each model has its own feature that can be applied on particular situation. The optimum operating voltage can be obtained during the proposed solution process.  In general, double hot-arm model results in the largest expected displacement; however, it requires a larger amount material than other model.

目錄
中文摘要……………………………………………………………..II
英文摘要……………………………………………………………..IV
目錄…………………………………………………………………..VI
圖目錄………………………………………………………………..VIII
表目錄…………………………………………………………………XI
符號說明………………………………………………………………XIV
第一章	緒論…………………………………………………………1
1.1	研究動機與目的………………………………………....1
1.2	文獻回顧……………………………………………………3
1.3	本文架構……………………………………………………6
第二章	以多目標技術處理限制條件的基因演算法………………7
2.1	基本基因演算法……………………………………………8
2.2	非支配排序法原理…………………………………………14
2.3	多目標技術處理限制條件的基因演算最佳化……………16
2.4	含限制條件的數值最佳化…………………………………24
第三章	單熱臂電熱式微致動器最佳化設計……………………..52
3.1	有限元素結構分析…………………………………………53
3.2	等長度微致動器最佳化設計………………………………68
3.3	等寬度微致動器最佳化設計………………………………74
3.4	可變長度及可變寬度微致動器最佳化設計………………79
3.5      考慮彈性臂的修正探討……………………………………85
第四章	雙熱臂電熱式微致動器最佳化設計………………………87
4.1	有限元素結構分析…………………………………………87
4.2	雙熱臂微致動器最佳化設計………………………………91
第五章	結論…………………………………………….…….……97
5.1	綜合討論與結論……………………………………………97
5.2	未來展望……………………………………………………99
參考文獻………………………………………………………………100

圖目錄
圖2.1 基本基因演算法流程圖……………………………………13
圖2.2 非支配解示意圖……………………………………………14
圖2.3 Pareto front示意圖………………………………………….15
圖2.4 非支配排序法於限制條件最佳解收斂圖…………………19
圖2.5非支配排序於限制條件的簡要流程圖…………………….19
圖2.6 含限制條件遺傳演算最佳化流程圖………………………21
圖2.7數值例題一二維函數圖形………………………………….25
圖2.8數值例題一最佳解迭代圖…………………………………..28
圖2.9數值例題二最佳解迭代圖……………………………….…32
圖2.10數值例題三最佳解迭代圖…………………………………….36
圖2.11數值例題三最佳解迭代圖………………………….…………40
圖2.12 10桿桁架結構圖……………….……………..………………42
圖2.13本文方法求解10桿迭代圖………………..………..……….42
圖2.14 空間25桿桁架結構圖…………………………………….....49
圖3.1 等長度電熱式微致動器示意圖……………………………56
圖3.2仿做(深色線段)Design B[7]的比較電壓與位移圖…..…57
圖3.3等寬度電熱式微致動器示意圖………………………….….59
圖3.4仿做(深色線段)Design A[7]的比較電壓與位移曲線圖……60
圖3.5 可變長度及可變寬度微致動器示意圖…………………….61
圖3.6可變長度及可變寬度結果並比較的電壓與位移曲線圖….64
圖3.7 非支配排序的基因演算法結合ANSYS分析流程圖……...67
圖3.8等長度電熱式微致動器最佳化設計圖………………………61
圖3.9等長度不含限制條件電壓與位移量曲線圖…………………..63
圖3.10等長度最佳化電壓與溫度曲線……………………………..64
圖3.11等長度最佳化位移與溫度曲線…………………………….65
圖3.12含溫度限制的等長度電熱式微致動器的最大位移圖…….70
圖3.13含溫度限制的等長度電熱式微致動器迭代圖…………….70
圖3.14等寬度電熱式微致動器最佳化設計圖…………………….72
圖3.15等寬度不含限制條件電壓與位移量曲線圖……………….67
圖3.16等寬度最佳化電壓與溫度曲線………………..………….…67
圖3.17等寬度最佳化位移與溫度曲線…..…………………………68
圖3.18含溫度限制的等寬度電熱式微致動器的最大位移圖………73
圖3.19含溫度限制的等寬度電熱式微致動器迭代圖…......…….…73
圖3.20可變長度及可變寬度電熱式微致動器最佳化設計圖..…….77
圖3.21三種模型不含限制條件電壓與位移量曲線圖……………....80
圖3.22可變長度及可變寬度最佳化電壓與溫度曲線………………81
圖3.23可變長度及可變寬度最佳化位移與溫度曲線………………82
圖3.24溫度限制可變長度及可變寬度微致動器的最大位移圖…….87
圖3.25結合長短臂與粗細臂微致動器迭代收斂圖………………….87
圖4.1雙熱臂電熱式微致動器示意圖……………………………….88
圖4.2仿做(實心小圓點)文獻[19]的電壓與位移比較圖………..90

表目錄
表2.1數值例題一分析結果表….…………….………….…………...27
表2.2數值例題二最佳化分析結果表1..………….……..…………..30
表2.3數值例題二最佳化分析結果表2………………..……………31
表2.4數值例題三最佳化分析結果表1………………………..……34
表2.5數值例題三最佳化分析結果表2…………………………..…35
表2.6數值例題三最佳化分析結果表1……………………………..39
表2.7數值例題三最佳化分析結果表2……………………...……39
表2.8 10桿最佳化分析結果表……………………..……………….44
表2.9 10桿桁架設計變數結果表……….…………..………………44
表2.10 10桿桁架應力限制結果表…………………………………....45
表2.11 10桿桁架位移限制結果表……………………………………46
表2.12空間25桿桁架結構受力表(單位：lbf)….…………………..50
表2.13空間25桿桁架結構求解結果表…………………………….51
表3.1多晶矽材料性質[7]……………………….…………………..56
表3.2 Design B(等長度)電熱式微致動器[7]……………………57
表3.3 Design A(等寬度)電熱式微致動器[7]………………..…59
表3.4參考可變長度及可變寬度電熱式微致動器[7]………………...63
表3.5單晶矽材料性質[19]…………………………………………....68
表3.6多晶矽等長度電熱式微致動器不同電壓結果表………………71
表3.7單晶矽等長度電熱式微致動器不同電壓結果表………………71
表3.8含溫度限制多晶矽等長度模型操作電壓與位移表……………73
表3.9含溫度限制單晶矽等長度模型操作電壓與位移表……………73
表3.10多晶矽等寬度電熱式微致動器不同電壓結果表………….…76
表3.11單晶矽等寬度電熱式微致動器不同電壓結果表…………….76
表3.12含溫度限制多晶矽等寬度模型操作電壓與位移表....…….…78
表3.13含溫度限制單晶矽等寬度模型操作電壓與位移表.....………78
表3.14可變長寬電熱式微致動器不同電壓結果表………………….80
表3.15可變長寬電熱式微致動器不同電壓結果表………………….80
表3.16含溫度限制多晶矽可變長寬模型操作電壓與位移………….83
表3.17含溫度限制單晶矽可變長寬模型操作電壓與位移………….83
表3.18三種模型使用多晶矽材料含溫度限制的效能比較……….…84
表3.19三種模型使用單晶矽材料含溫度限制的效能比較………….84
表3.20彈性臂修正後的等長度模型及可變長度模型比較………….86
表4.1雙臂電熱式微致動器[19]………...…………………………….89
表4.2單晶矽雙熱臂電熱式微致動器不同電壓結果表…...……..…..93
表4.3多晶矽雙熱臂電熱式微致動器不同電壓結果表…………...….93
表4.4含溫度限制單晶矽雙熱臂模型操作電壓與位移表……………95
表4.5含溫度限制多晶矽雙熱臂模型操作電壓與位移表…………....95
表4.6可變長寬模型與雙熱臂模型的最佳效能比較…..…………….96

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