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오목한 성능함수에서 공액경사도법을 이용한 단일루프 단일벡터방법의 수렴성 개선
정성범(Seong-Beom Jeong),이세정(Se-Jung Lee),Gyung-Jin Park(박경진) 대한기계학회 2012 大韓機械學會論文集A Vol.36 No.7
신뢰성 기반 최적설계의 효과적인 수행을 위하여 개발된 단일루프 단일벡터 방법은 신뢰성 해석의 계산과정을 제거함으로써 최적설계 시 발생하는 과도한 계산비용을 줄일 수 있다. 하지만 성능함수의 오목한 정도가 심할 경우, 수렴을 하지 못하고 발산하는 경향을 보인다. 때문에 일반적인 단일루프 단일벡터 방법은 낮은 수렴성과 부정확성 문제를 내포하고 있다. 본 연구에서는 공액경사도법을 이용한 단일루프 단일벡터 방법을 제안한다. 공액경사도법은 이전 반복과정의 최대가능손상점에서 계산된 방향벡터들을 이용하여 현재 설계점에서의 최대가능손상점을 산출하기 위한 새로운 방향벡터를 구하고 이 방향벡터를 이용하여 현재점에서의 최적화를 수행한다. 이를 다양한 수학예제에 적용하고 다른 방법들과 수치적 성능 비교를 통해 제안한 방법의 유용성을 검증한다. 공액경사도법을 이용한 단일루프 단일벡터 방법은 성능함수 특성에 크게 영향을 받지 않으며 수렴성을 크게 향상시킬 수 있다. The reliability based design optimization (RBDO) approach requires high computing cost to consider uncertainties. In order to reduce the design cost, the single loop single vector (SLSV) approach has been developed for RBDO. This method can reduce the cost in calculating deign sensitivity by elimination of the nested optimization process. However, this process causes the increment of the instability or inaccuracy of the method according to the problem characteristics. Therefore, the method may not give accurate solution or the robustness of the solution is not guaranteed. Especially, when the function is concave, the process frequently diverges. In this research, the concept of the conjugate gradient method for unconstrained optimization is utilized to develop a new single loop single vector method. The conjugate gradient is calculated with gradient directions at the most probable points (MPP) of previous cycles. Mathematical examples are solved for the verification of the proposed method. The numeri cal performances of the obtained results are compared to those of other RBDO methods. The SLSV approach using conjugate gradient is not greatly influenced by the problem characteristics and improves its convergence capability.
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최상현,이광원,이익진 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.7
The single-loop method (SLM) for reliability-based design optimization (RBDO) can be inaccurate when constraint functions are highly nonlinear because it uses gradient information calculated at the approximated most probable point (MPP) of the previous iteration. To overcome this limitation, this paper presents a new adaptive SLM (ASLM) that can automatically select the gradient at the approximate MPP of the previous iteration or the design point of the current iteration. If the design movement is large, the normalized gradient is calculated at the current design point, and the approximate MPP is calculated using the mean value method, and if small, the gradient is calculated at the approximate MPP of the previous iteration. In this study, a post optimization (PO) technique using constraint boundary sampling (CBS) is also proposed to improve the accuracy of ASLM. In the proposed method, ASLM is performed first, and then PO is applied to find a more accurate RBDO optimum using the Kriging model generated by samples accumulated during ASLM and sequentially added by CBS when the Kriging model is not accurate enough. Numerical studies show that the proposed ASLM is more efficient than the existing RBDO methods and the proposed PO improves its accuracy.
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Hong-Zhong Huang,Xudong Zhang,Yu Liu,Debiao Meng,Zhonglai Wang 대한기계학회 2012 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.26 No.7
Reliability-based design optimization (RBDO) has been receiving increasing attention for achieving high safety and reliability in engineering design. Sequential optimization and reliability assessment (SORA), as one of the efficient single-loop methods, decouples an RBDO problem into sequential deterministic optimization and reliability analysis. An enhanced SORA (ESORA) method is proposed with the aim of further improving the computational efficiency for RBDO, considering both cases of constant and varying variances of random design inputs while keeping the single-loop framework. Vehicle side impact example is used to test and compare the efficiency of the proposed method with existing approaches.
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K & C 특성의 신뢰성 향상을 위한 차량 현가장치의 최적설계
최병렬(Byung-Lyul Choi),최진호(Jin-Ho Choi),최동훈(Dong-Hoon Choi) 한국자동차공학회 2004 한국자동차공학회 춘 추계 학술대회 논문집 Vol.- No.-
This study introduces the Reliability-Based Design Optimization(RBDO) to enhance the kinematic and compliance (K & C) characteristics of automotive suspension system. In previous studies, the deterministic optimization has been performed to enhance the K & C characteristics. Unfortunately, uncertainties in the real world have not been considered in the deterministic optimization. In the design of suspension system, design variables with the uncertainties, such as the bushing stiffness, have a great influence on the variation of the suspension performances. There is a need to quantify these uncertainties and to apply the RBDO to obtain the design, satisfying the target reliability level. In this research, design variables including uncertainties are dealt as random variables and reliability of the suspension performances, which are related the K & C characteristics, are quantified and the RBDO is performed. The RBD-optimum is compared with the deterministic optimum to verify the enhancement in reliability. Thus, the reliability of the suspension performances is estimated and the RBD-optimum, satisfying the target reliability level, is determined.
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