多元系統(Multidisciplinary system)常見於工程的實際問題。在實務設計或最佳化的過程中，納入設計參數的不確定性(uncertainty)，已成為優質工程設計(Quality engineering)的趨勢。至今，多元系統的最佳化(Multidisciplinary design optimization, MDO)及以可靠度為基礎的最佳化(Reliability-based design optimization, RBDO)，已有許多研究成果發表於文獻中。然而，現今的研究較少著墨於以可靠度為基礎的多元系統的最佳化(Reliability-based multidisciplinary design optimization, RBMDO)；基於此類問題最接近實際的工程應用，因此具有高度的研究價值，故為本計畫之研究主題。 RBMDO在本質上是一個三個疊層的分析(tri-level)；最外層為肯定(deterministic)的最佳化分析，中間層為可靠度分析(reliability analysis)，而最內層為多元系統的系統分析(system analysis)。由此可見，RBMDO 是一個相當複雜且費時的計算。為減輕計算上的負擔，本計畫將研究並提出另一種分析的分法(algorithm)：藉由一系列(sequential)的分析取代原有的三個疊層的分析。其概略的觀念為: 1.利用逆可靠度分析(inverse reliability analysis)的結果，去除原問題(RBMDO)中最佳化與可靠度分析之間的結合關係(coupled)。 2.運用Analytical Target Cascading (ATC)的技術將多元系統的系統分析轉變為多個單一系統的分析。如此，原本的三個疊層的分析，將轉為一個接一個的單一分析(最佳化、可靠度或單一系統的分析)；因而減輕原本大量的繁重計算。 在所建議的方法中，有幾個關鍵點，需更多的研究加以驗證或開發；1.許多研究顯示，去除RBDO中最佳化與可靠度分析之間的結合關係，仍有很大的改善空間(執行期間：第一年)。2.多元系統的逆可靠度分析，目前沒有已發展完整的理論可供使用(執行期間：第二年)。3. 結合逆可靠分析與ATC的概念並應用於多元系統，仍有待研究(執行期間：第三年)。基於上述三點中，均存有眾多可供研究的議題；是以提出一個為期三年的研究計畫，循序漸進地，每年執行其中的一個主題。最終，整合為一完整的RBMDO的綜合研究。 The objective of this study is to investigate an efficient approach for reliability-based design multidisciplinary optimization (RBMDO). RBMDO has drawn more attention recently in quality engineering because a system level analysis is usually needed in industrial applications and, in most cases; variability is existed in design variables. There are many researches have been focused on the study of reliability-based design optimization (RBDO) and multidisciplinary design optimization (MDO). However, few of them have paid attention on the topic of RBMDO. Therefore, there is of interest to investigate the potential efficient way for RBMDO and this is the major goal of this proposal. The RBMDO is inherently a tri-level analysis: the first level is the deterministic optimization. The second level is the reliability analysis at each design trial. The third level is the system analysis in a multidisciplinary system. Therefore, the computational cost of RBMDO is unaffordable in most situations. To lessen the computational burden, we propose a new approach which is a sequential process to replace the original tri-level analysis. Two key concepts are listed as follows: 1. we utilize the concept of inverse reliability to decouple the reliability analysis and optimization. 2. the original problem is decomposed hierarchically at multiple levels using Analytical Target Cascading (ATC). Thus, RBMDO becomes a series of reliability analysis, deterministic optimization and individual sub-system analysis. Through above process, the computational time can be reduced significantly. Previous researches have shown that: 1. there are many rooms of improving the results of decoupling techniques. 2. no matured model for the inverse reliability analysis of a multidisciplinary system. 3. the concept of combining ATC and inverse reliability analysis needs to be verified. Since many important issues shown above need to be investigated, we propose a three-year plan and each year will execute one of the above unsolved topics sequentially. At the end of the project, the completed study of RBMDO will be finished and documented.
