博碩士論文 102322003 詳細資訊




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姓名 呂柏邑(Po-I Lu)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 穩健設計於結構被動控制之應用
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摘要(中) 於工程實務中,設計參數往往因環境、施工等等因素而有不確定性,穩健設計是一種透過統計方式將不確定性因子考量進模型中的設計方法,希望可以降低不確定性因子的影響。本研究之目的即是將穩健設計應用於結構被動控制系統設計中,並期望結構性能表現可以滿足使用需求。研究中,結構性能表現是以結構受震反應為指標,希望穩健設計結果不僅可以降低不確定性因子的影響,同時可降低結構受震反應。因此本研究之穩健設計為多目標函數最佳化問題,分別為降低不確定性因子之影響與降低結構反應。
  研究中,多目標函數最佳化問題是將個別目標函數透過加權組合成為單目標函數,再以單目標最佳化演算法搜尋最佳解。基於傳統權重法無法有效搜尋非凸可行區之最佳解前緣(Pareto front),故本研究亦採用Normal Boundary Intersection(NBI)法來搜尋多目標函數之加權最佳解,並利用被動式調諧質量阻尼器之穩健設計討論其優點。研究結果顯示,在非凸問題上,NBI法確實較傳統權重法有效搜尋多目標函數最佳化問題的最佳解前緣。最後,本研究亦針對不等高橋墩隔震橋梁進行穩健設計,結果顯示考量不確定性因子後之設計結果,能有效降低不確定性因子之影響,並且降低結構反應。
摘要(英) Robust design is aimed to minimize the effect of uncertainty through statistical method. The purpose of this research is to apply robust optimal design method in structural design. While robust design is aimed to minimize the effect of uncertainty, to minimize response of structure is also essential for passive control structures. Thus robust design for structural design is multi-objective problem.
One way to solve a multi-objective problem is to convert the problem into a single-objective optimization problem by using the weighted sum method. However, the traditional weighted sum method cannot find the pareto front for a problem with nonconvex feasible domain. To resolve the difficulty, the normal boundary intersection (NBI) method is adopted in this research. The robust design results of a tuned-mass damper system by using the weight-sum method and the NBI method are compared. The results show that the NBI method is better than the weight-sum method for non-convex problems. Finally, the robust design of isolation system for a bridge with columns of irregular heights using the NBI method is then presented. The results show that the proposed robust design methodology can be effectively used to design the isolation system for the bridge such that the effects of parametric uncertainties and the responses of bridge structure can be minimized simultaneously.
關鍵字(中) ★ 穩健設計
★ 多目標最佳化
★ 被動調諧質量阻尼器
★ 不等高橋墩隔 震橋梁
關鍵字(英) ★ Robust design
★ Multi-objective optimization
★ Tuned-mass damper
★ Isolated bridge with columns of irregular heights
論文目次 摘要 I
Abstract II
誌 謝 III
目 錄 IV
表目錄 VIII
圖目錄 X
第一章 緒 論 1
1.1研究動機 1
1.2文獻回顧 4
1.3論文架構 9
第二章 研究方法 11
2.1穩健設計 11
2.1.1穩健設計之數學模型 11
2.1.2穩健設計之束制條件 13
2.2系統反應的平均值與標準差之計算方法 15
2.2.1具解析解之系統反應的平均值與標準差的計算方法 15
2.2.2不具解析解之系統反應的平均值與標準差的計算方法 16
2.3Latin-Hypercube取樣法 17
2.4多目標函數最佳化 18
2.5改良式布穀鳥演算法 25
第三章 TMD系統之穩健設計 29
3.1TMD系統模型及解析解 29
3.2TMD之穩健設計 31
3.2.1TMD穩健設計之不確定性因子 31
3.2.2訊號因子 34
3.2.3控制因子 34
3.2.4穩健最佳化設計之數學模式 34
3.2.4.1問題描述 34
3.2.4.2目標函數之數學模式 35
3.2.4.3TMD系統的多目標函數最佳化 36
3.3傳統TMD建議設計方法 37
3.4結果討論 38
3.4.1權重法之設計結果 38
3.4.2NBI法之設計結果 45
3.4.2.1NBI法不同取樣數之設計結果的比較 51
3.4.2.2取樣500次之設計結果 53
第四章 不等高橋梁之穩健設計 55
4.1橋梁結構之分析方法 55
4.1.1目標橋梁之細部資料 55
4.1.2目標橋梁之分析模型與構材受力變形關係 57
4.1.3數值方法 62
4.1.3.1Newmark-b法 62
4.1.3.2Runge-Kutta法 65
4.1.4求解運動方程式 66
4.1.5平行運算 68
4.2目標橋梁之穩健設計 70
4.2.1穩健設計之因子 70
4.2.1.1不確定性因子 70
4.2.1.2訊號因子 71
4.2.1.3控制因子(設計參數) 74
4.2.2目標橋梁穩健問題的數學模式 75
4.2.2.1穩健設計之數學模式 76
4.2.2.2目標函數之考量方式 76
4.2.2.3演算法參數設定 79
4.2.3修改MCS演算法之可靠性討論 79
4.2.4束制條件參數之討論 85
4.3設計結果討論 93
4.3.1單一震波之穩健設計結果 93
4.3.2三組實測震波之穩健設計結果 101
第五章 結論與建議 117
5.1結論 117
5.2建議 119
參考文獻 121
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指導教授 莊德興(Der-Shin Juang) 審核日期 2016-7-28
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