可靠度最佳化設計可分為最佳化及可靠度兩方面來探討。最佳化分析包括整體設計的概念，使其最終結果符合所需；可靠度則是評估整體產品或系統品質的指標。若需求設定為考慮設計參數變異性的設計（Reliability-Based Design Optimization），簡稱RBDO，將設計參數的變異性考慮在最佳化的設計流程裡，藉著每次可靠度的分析評估，再利用最佳化來改善整體表現，依此重覆、持續的分析處理，直到達成最終最佳化設計，並符合設定之可靠度需求。 在處理可靠度最佳化的問題，必須分別處理可靠度與最佳化。其本質為一雙迴圈法(Double loop)，雙迴圈法有一個很大的缺點，就是計算時間很長，計算量很大。因此為了有效率的去處理結構最佳化問題分析，本研究以雙層系統(the Bi-level system)的概念為出發點，希望利用上層和下層的雙層系統建立協同最佳化模式，並建立協調中心，負責整合最佳化與可靠度分析的結果，使兩者在同一時間裡進行計算，如此可靠度分析將無須等候最佳化之分析結果，接著以現有的商業套裝軟體，呈現其3D圖形之最佳化結果。文末以一個例題來說明，不但具有快速的計算效率，同時亦達到設計給定的可靠度指標。 This study presents a concurrent approach to evaluate the Reliability-Based Design Optimization (RBDO). The proposed approach prevents the RBDO from conducting the inherited double-loop calculation. Thus, the computational efficiency of performing a RBDO is improved. To concurrently perform a RBDO, the RBDO problem is reformulated as a system with a bi-level structure, which consists of upper and lower levels. The upper level has one sub-system, while the lower level includes two sub-systems. The sub-system in the upper level aims to minimize the discrepancy between results obtained from the two sub-systems in the lower level. The two major calculations in a RBDO problem, which are the reliability analysis (RA) and deterministic optimization (DO), are decomposed via two sets of linking variables. RA and DO serve as the two sub-systems in the lower level. The linking variables, which are "copies" of the design variables (DVs) and random design variables (RVs), connect the upper and lower levels to make three sub-systems as a whole. Once the RBDO is reformulated, the objective of the upper level is to minimize the difference of the linking variables obtained from each sub-system in the lower level. The main tasks in the lower level are to execute the deterministic optimization and reliability analysis. In the proposed method, the optimization and reliability analysis need not to be conducted sequentially. Instead, these two analyses are executed simultaneously to accelerate the RBDO process and to reduce the computational cost. Details of a RBDO solved by the bi-level algorithm is revealed through a numerical example provided in this study
