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。 ;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.
