不考慮設計參數（變數）變異性的最佳化過程稱為定然式最佳化（Deterministic Optimization），簡稱DO，定然式最佳化設計，經常非常接近設計的約束條件，若將設計參數的變異性考慮進去，最佳化設計的結果，將會有很大的機率，落在約束條件之外的不允許範圍，是失敗機率很高的設計。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進去。最佳化設計的可靠度可以依設計者自行設計，來避免過高的失敗機率。RBDO在本質在為一雙迴圈法(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。ESORA (Efficient Sequential Optimization and Reliability Assessment, ESORA)為其中一種克服雙迴圈法缺點的方法，此演算法是結合現存幾個演算法形成新的演算法，將RBDO的問題去偶合(decouple)成一個單迴圈(Single loop)的定然式最佳化問題，此方法已在文獻中證明其效率比雙迴圏還快，克服計算量很大的缺點，同時能保有最佳化結果的精準性。本文依據ESORA的精神並稍加修改後，計算方法大致分成三部份：(1)對原結構進行逆可靠度分析，求得Most Probable Point (MPP)；(2)因為該MPP點隱含需求可靠度的相關訊息，因此，以該值取代原最佳化問題中的隨機參數，並執行定然式的最佳化；(3)對所得之最佳化結構進行逆可靠度分析，求得下一個MPP點，反覆演算步驟(1)及(2)直到最佳化結果（或MPP點）收斂為止。 此去偶合單迴圈技術已在許多RBDO的文獻中，證明其效率與精確性。但很少運用在考慮設計參數不確定性的拓樸最佳化上(Reliability-Based Topology Optimization, RBTO)。拓樸最佳化結果因可提供設計者最佳初始設計，因此其最終的拓樸便顯得十分重要，RBTO相較於DTO應可提供更理想的初步設計輪廓。RBTO需要克服與RBDO相同的問題就是計算量很大的缺點，而且在RBTO上更為困難的是因為其設計變數數量很大。本研究將其去偶合技術運用在RBTO上，將問題去偶合成定然式的拓樸最佳化，即使設計變數很多，在例題中能證明依然可以提升計算效率，也不失其精確性。 在這幾年期間，拓樸最佳化技術與可靠度分析，已有很多研究單位研究出更有效率、更精確的演算法，也發展出商業的套裝軟體。本研究後面的例題，將去偶合單迴圈法，應用在現有的套裝軟體，並達到預期的實用效果。 Reliability-Based Topology Optimization (RBTO) has been recognized can present an enhanced starting design point for engineers. A typical RBTO is inherently a double-loop procedure due to the probabilistic constraints; therefore, the computational cost is usually expensive and becomes one of the major concerns. The single-loop algorithm has been well developed and used in Reliability-Based Design Optimization (RBDO) to low the analysis cost for a long time, but only few of researches has put their attention on the application of this technique to the problem of RBTO. The primary idea of the single-loop approach is to decouple the optimization and reliability analysis, the key point is using the Most Probable Point (MPP) obtained from inverse reliability analysis to formulate an equivalent deterministic optimization corresponding to the original RBDO. Because the formulation of RBDO and RBTO are similar and it is believed the success of the single-loop in RBDO can be extended to RBTO. The suitability of the single-loop approach for RBTO is therefore investigated thoroughly in this study. Several numerical examples have been shown that the single-loop RBTO can produce similar topology as the double-loop RBTO but with much less calculation. Further, the single-loop RBTO is successfully incorporated with the existing software to create a more pleasant working procedure to practical engineers.
