本文探討可靠度基的設計最佳化(Reliability Based Design Optimization ,RBDO)含不確定的統計資訊，以變異球體來描述相關聯性的分佈狀態，及以逆可靠度分析，應用到RBDO及全面穩健設計最佳化，發展設計流程及技術。 在不考慮可靠度之結構最佳化設計時，雖然可以得到夠強度的結構設計，但是此結果的可靠度機率可能偏低，亦不是穩健的設計結果。所以在設計之時，同時考慮提高滿足設計限制的合理性，減少目標性能之變異，最大化系統可靠度及最佳化原有設計之性能目標值，稱為全面穩健最佳化設計。 為了達到全面穩健最佳化設計，需先訂定極限狀態函數，使用逆可靠度分析進行RBDO。再觀察不合理的限制條件，使用變異球體模態的方法來進行合理化修正求解，接著探討最小化目標性能變異之設計，再結合修正不合理的限制條件，進行RBDO，即完成全面穩健最佳化設計。工程結構例題說明本文所提設計方法技術之正確及實用。 In general, a reliability-based design optimization (RBDO) problem contains the system reliability consideration of optimizing design goal subject to design constraints. Due to the uncertainty of random variables and/or random parameters, the final design may have a low possibility of satisfying constraints. In other word, once the design closes to constrained boundary (means active constraint), it may have a high possibility in infeasible region. This thesis applies a variation sphere transformation that moves the feasibility boundary to promote the feasibility of active constraints. The complete design process is called the RBDO considering feasibility robustness (RBDO-FR). Due to the uncertainty of random variables and/or random parameters, the final design may also have a wide distribution of design goal performance. In other word, the larger deviation of performance is not a result of robust performance. This thesis applies a variation sphere transformation, two-level factorial experiment and Takuchi three-point approximation to estimate the variation. We minimize the performance variation so that the complete design process is called the RBDO considering performance robustness (RBDO-PR). Base on the consideration of RBDO-FR and RBDO-PR, it is obviously to take into account a RBDO problem simultaneously contain both feasibility robustness and performance robustness. Thus, a RBDO with total robustness (RBDO-TR) is the main development in this thesis. The whole integrated design process of RBDO-TR is presented with some illustrative examples and engineering design. In the development, the performance measure approach (PMA) is applied for the structural reliability analysis.
