• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.3A
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• pp.193-200
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• 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
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• 2009.04a
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• pp.101-104
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• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.5
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• pp.413-419
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• 2008

Deterministic design optimization (DO) does not explicitly deal with a variety of factors from inherent randomness and uncertainties. Reliability based design optimization(RBDO) is necessary to use in engineering systems in order to guarantee quality and performance of product. In this paper, design variables are considered as random variables. Standard deviation according to change of design variables have changed as much as coefficient of variation. And, if the standard deviation is error of manufacturing, standard deviation-mean relation is concave form. We obtain reliability index using advanced first order second moment method(AFOSM). This paper is examined by solving two examples and the results are compares with DO, RBDO and suggested RBDO.

• Proceedings of the Korean Nuclear Society Conference
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• 1995.05a
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• pp.596-601
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• 1995

신뢰도 분석 방법을 이용하여 습식 사용후핵연료 중간저장시설의 냉각계통에 대한 최적 설계조건을 도출하기 위한 연구를 수행하였다. 먼저 고장수목 분석을 통한 설계 취약점을 평가하여 21개의 설계대안을 도출하였고, 최종적으로 설계대안에 대한 건설비 용, 계통신뢰도 분석 및 확률론적 안전기준을 고려한 비용효과 분석을 실시하였다. 설계 대안들 중에서 100% 루프 다중설계, 루프당 한 개의 펌프 사용, 안전등급 부여 및 주 루프에서 정화계통이 분리된 경우가 최적설계안으로 나타났다. 여기서 적용된 방법론은 유사시설의 최적설계에 유용하게 응용될 수 있을 것으로 사료된다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.6
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• pp.649-653
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• 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
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• v.23 no.2
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• pp.62-67
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• 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.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.11
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• pp.1067-1074
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• 2010

In this study, RBDO(Reliability Based Design Optimization) was performed for a supersonic double-wedge inlet. By considering uncertainty of design with given design space, the pressure recovery was transformed into the probabilistic constraint while the inlet drag was considered as a deterministic objective function. To save computational analysis cost and to search good design space, Latin-Hypercube design of experiment and the Kriging model were incorporated and then RBDO was performed. Monte-Carlo simulation was performed to verify the accuracy of AFORM(Advanced First Order Reliability Method). It was found that AFORM result agreed very well with the Monte-Carlo simulation result. The system reliability was guaranteed by considering uncertainty of the design variables. In case of considering diverse uncertainty of system design, RBDO was found to be useful.

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

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

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