• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.30 no.3A
• /
• pp.193-200
• /
• 2010

Structural design requires simultaneously to ensure safety by considering quantitatively uncertainties in the applied loadings, material properties and fabrication error and to maximize economical efficiency. As a solution, system reliability-based design optimization (SRBDO), which takes into consideration both uncertainties and economical efficiency, has been extensively researched and numerous attempts have been done to apply it to structural design. Contrary to conventional deterministic optimization, SRBDO involves the evaluation of component and system probabilistic constraints. However, because of the complicated algorithm for calculating component reliability indices and system reliability, excessive computational time is required when the large-scale finite element analysis is involved in evaluating the probabilistic constraints. Accordingly, an algorithm for SRBDO exhibiting improved stability and efficiency needs to be developed for the large-scale problems. In this study, a more stable and efficient SRBDO based on the performance measure approach (PMA) is developed. PMA shows good performance when it is applied to reliability-based design optimization (RBDO) which has only component probabilistic constraints. However, PMA could not be applied to SRBDO because PMA only calculates the probabilistic performance measure for limit state functions and does not evaluate the reliability indices. In order to overcome these difficulties, the decoupled algorithm is proposed where RBDO based on PMA is sequentially performed with updated target component reliability indices until the calculated system reliability index approaches the target system reliability index. Through a mathematical problem and ten-bar truss problem, the proposed method shows better convergence and efficiency than other approaches.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2009.04a
• /
• pp.101-104
• /
• 2009

최적설계는 설계자가 요구하는 제한조건을 만족시키는 범위에서 목적함수가 최소가 되는 설계점을 찾는 방법이다. 그러나 기존의 최적설계는 불확실성의 영향을 고려하지 않아 최적해가 제한조건의 경계에 위치하고 이것은 모델링과정이나 가공 등으로 인한 오차에 대한 영향을 고려하지 않는 문제점이 있다. 신뢰성 기반 최적설계는 불확실성을 정량화하면서 신뢰도를 계산하는 신뢰도 해석과정과 최적설계과정을 포함한다. 일반적으로 신뢰성 해석은 크게 추출법, 급속 확률 적분법, 모멘트 기반 신뢰성해석이 있다. 가장 널리 사용되는 급속 확률 적분법 중 최대 손상 가능점(MPP) 방법은 많은 MPP점이 존재하는 경우 수치적 비용이 증가하는 문제점과 표준 정규분포 공간으로 변환하는 과정에서 제한조건의 비선형성을 증가시켜 큰 오차를 발생시키는 문제점이 있다. 본 논문에서는 RBDO를 수행하기에 앞서 선행되어야 할 신뢰성해석 방법으로 곱분해기법을 사용하였고 이로부터 민감도 정보를 유도하여 기울기 기반 최적화 알고리즘을 적용하였다.

• Proceedings of the KIEE Conference
• /
• 2007.07a
• /
• pp.571-573
• /
• 2007

본 논문에서는 전력계통의 신뢰도를 확률적인 관점에서 접근하고 평가 할 수 있는 신뢰도평가 시스템의 기본 개념과 설계를 소개한다． 확률기반 신뢰도 평가시스템은 Enumeration 기반，Cumulant 기반， Monte-Carlo 시뮬레이션 기반의 세 가지 기법을 사용하여 신뢰도를 평가하도록 설계하였다．

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.38 no.6
• /
• pp.649-653
• /
• 2014

Although many reliability analysis and reliability-based design optimization (RBDO) methods have been developed to estimate system reliability, many studies assume the uncertainty of the design variable to be constant. In practice, because uncertainty varies with the design variable's value, this assumption results in inaccurate conclusions about the reliability of the optimum design. Therefore, uncertainty should be considered variable in RBDO. In this paper, we propose an RBDO method considering variable uncertainty. Variable uncertainty can modify uncertainty for each design point, resulting in accurate reliability estimation. Finally, a notable optimum design is obtained using the proposed method with variable uncertainty. A mathematical example and an engine cradle design are illustrated to verify the proposed method.

• Journal of the Korean Magnetics Society
• /
• v.23 no.2
• /
• pp.62-67
• /
• 2013

This paper introduces an effective methodology for reliability-based design optimization of electromagnetic products, where a performance measure approach is adopted to accurately assess probabilistic constrains. Two design problems consisting of a loudspeaker and a superconducting magnetic energy storage system are considered. The efficiency of the proposed method in evaluating the failure probability of performances during the optimization process are compared with the existing method based on the reliability index approach. Moreover, in term of the accuracy of probability failure values, optimized design results are examined with reference values obtained from the Monte Carlo simulation.

• Proceedings of the Korean Reliability Society Conference
• /
• 2002.06a
• /
• pp.211-216
• /
• 2002

실제적인 문제에서 신뢰성 기반 최적 설계(RBDO)를 구현하기 위해서는 유한요소 모델을 해석하기 위한 상용 프로그램과 설계한 것에 대한 신뢰성을 산정할 수 있는 프로그램을 통합하고 최적화 알고리듬을 적용하여야 최적화를 수행하여야만 한다. 또한 최적화 과정에서 최적상태에서 제약조건이 비활성 영역에서 놓이게 되는 것을 방지하기 위해서 제약조건 최적화 문제를 비제약 조건 최적화 문제로 바꾸어 주는 장애 함수를 사용하여 최적화를 수행하였다. 그리고 이 방법론을 기존의 신뢰성기반 최적화 방법론, 즉 신뢰도지수 접근방법과 목표성능치 접근방법과의 비교를 하였다.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.22 no.4
• /
• pp.299-306
• /
• 2009

Design optimization is a method to find optimum point which minimizes the objective function while satisfying design constraints. The conventional optimization does not consider the uncertainty originated from modeling or manufacturing process, so optimum point often locates on the boundaries of constraints. Reliability based design optimization includes optimization technique and reliability analysis that calculates the reliability of the system. Reliability analysis can be classified into simulation method, fast probability integration method, and moment-based reliability method. In most generally used MPP based reliability analysis, which is one of fast probability integration method, if many MPP points exist, cost and numerical error can increase in the process of transforming constraints into standard normal distribution space. In this paper, multiplicative decomposition method is used as a reliability analysis for RBDO, and sensitivity analysis is performed to apply gradient based optimization algorithm. To illustrate whole process of RBDO mathematical and engineering examples are illustrated.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.29 no.1A
• /
• pp.45-52
• /
• 2009

In conventional structural design, deterministic optimization which satisfies codified constraints is performed to ensure safety and maximize economical efficiency. However, uncertainties are inevitable due to the stochastic nature of structural materials and applied loads. Thus, deterministic optimization without considering these uncertainties could lead to unreliable design. Recently, there has been much research in reliability-based design optimization (RBDO) taking into consideration both the reliability and optimization. RBDO involves the evaluation of probabilistic constraint that can be estimated using the RIA (Reliability Index Approach) and the PMA(Performance Measure Approach). It is generally known that PMA is more stable and efficient than RIA. Despite the significant advancement in PMA, RBDO still requires large computation time for large-scale applications. In this paper, A new reliability-based design optimization (RBDO) method is presented to achieve the more stable and efficient algorithm. The idea of the new method is to integrate a response surface method (RSM) with PMA. For the approximation of a limit state equation, the moving least squares (MLS) method is used. Through a mathematical example and ten-bar truss problem, the proposed method shows better convergence and efficiency than other approaches.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2004.05b
• /
• pp.961-965
• /
• 2004

본 연구에서는 상수관망의 신뢰도 기반 최적화설계에서 시스템 구성물의 기계적 고장의 영향뿐만이 아니라 관로의 수리학적 능력과 절점수요에서의 불확실성이 결합되어 인식할 수 있는 새로운 방법을 제시하였다. 수질과 연관된 신뢰도 문제는 고려하지 않았고 단지 수량의 항으로 수요자들의 요구량을 충족시키기 위해 급수관망의 공급능력을 고려하였다. 수량의 관점에서 관망의 신뢰도의 측정은 절점 수요량들이 항상 만족되어진다고 가정한 상태에서 불충분한 수두의 정도를 이용한다. 따라서 절점신뢰도는 공급되는 절점수두가 미리 규정된 최소수두를 상외하거나 충족시키는 확률로 정의되어진다. 이 모형에 의해 설계된 상수관망은 정상관망 상태구성(구성물의 고장이 발생하지 않았을 경우)와 미리 정해진 고장 시나리오의 범위와 연관된 관망의 악화된 구성상태 모두에서 절점에서의 임의의 수요량과 임의의 수리학적 능력하에서 상수공급량의 항으로 규정된 수준의 서어비스의를 제공할 수 있다. 본 모형은 다양한 관망구성에 내해 상수관망의 신뢰도의 정도를 결정하기 위해서 Monte-Carlo 모의를 이용하였다. 실제 상수관망에 내해 본 인구모형을 이용하여 신뢰도 및 최적화 해석이 수행되었다. 해석결과 본 모형은 합리적으로 관망 전체에 대해 합리적인 범위의 신뢰도를 유지하면서 관망의 건설비용의 치적화가 수행될 수 있었다.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.2
• /
• pp.163-168
• /
• 2011

Robust optimization or reliability-based design optimization are some of the methodologies that are employed to take into account the uncertainties of a system at the design stage. For applying such methodologies to solve industrial problems, accurate and efficient methods for estimating statistical moments and failure probability are required, and further, the results of sensitivity analysis, which is needed for searching direction during the optimization process, should also be accurate. The aim of this study is to employ the function approximation moment method into the sensitivity analysis formulation, which is expressed as an integral form, to verify the accuracy of the sensitivity results, and to solve a typical problem of reliability-based design optimization. These results are compared with those of other moment methods, and the feasibility of the function approximation moment method is verified. The sensitivity analysis formula with integral form is the efficient formulation for evaluating sensitivity because any additional function calculation is not needed provided the failure probability or statistical moments are calculated.