• International Journal of Automotive Technology
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• v.8 no.1
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• pp.93-102
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• 2007

The frontal crash optimization of an engine room member using the response surface method was studied. The engine room member is composed of the front side member and the sub-frame. The thicknesses of the panels on the front side member and the sub-frame were selected as the design variables. The purpose of the optimization was to reduce the weight of the structure, under the constraint that the objective quantity of crash energy is absorbed. The response surface method was used to approximate the crash behavior in mathematical form for optimization procedure. To research the effect of the regression method, two different methodologies were used in constructing the response surface model, the least square method and the moving least square method. The optimum with the two methods was verified by the simulation result. The precision of the surrogate model affected the optimal design. The moving least square method showed better approximation than the least square method. In addition to the deterministic optimization, the reliability-based design optimization using the response surface method was executed to examine the effect of uncertainties in design variables. The requirement for reliability made the optimal structure be heavier than the result of the deterministic optimization. Compared with the deterministic optimum, the optimal design using the reliability-based design optimization showed higher crash energy absorption and little probability of failure in achieving the objective.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.4
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• pp.67-71
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• 1990

This study is concerned with the optimum design of stiffened cylindrical members frequently found in floating offshore platforms with constraints on reliability. Minimised is the expected total cost which is composed of the structural cost and the expected failure cost. Some design requirements drawn from variotus design codes are also considered as constraints. Reliability of critical component in a structure only is considered in this paper and the system failure is discarded since the probability of system failure is in general much smaller than the probability of component failure and it is very difficult to evaluate the cost due to system failure. Ultimate strength only is considered and not the fatigue strength. Several parametric studies are illustrated and the optimum solutions for different strength models which are now in use for the design of stiffened cylinders are derived to show the optimum designs against different strength models for the same type of structural component. The present results lead to the important conclusions relating to the posibility of more cost saving in the design of such structure through the reliability-based optimisation process.

• Structural Engineering and Mechanics
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• v.70 no.1
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• pp.81-96
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• 2019

In this paper, a hybrid uncertain model is applied to system reliability based design optimization (RBDO) of trusses. All random variables are described by random distributions but some key distribution parameters of them which lack information are defined by variation intervals. For system RBDO of trusses, the first order reliability method, as well as monotonicity analysis and the branch and bound method, are utilized to determine the system failure probability; and Improved (${\mu}+{\lambda}$) constrained differential evolution (ICDE) is employed for the optimization process. System reliability assessment of several numerical examples and system RBDO of different truss structures are proposed to verify our results. Moreover, the effect of different classes of interval distribution parameters on the optimum weight of the structure and the reliability index are also investigated. The results indicate that the weight of the structure is increased by increasing the uncertainty level. Moreover, it is shown that for a certain random variable, the optimum weight is more increased by the translation interval parameters than the rotation ones.

• 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.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 Magnetics
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• v.17 no.1
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• pp.46-50
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• 2012

A reliability-based optimization method for electromagnetic design is presented to take uncertainties of design parameters into account. The method can provide an optimal design satisfying a specified confidence level in the presence of uncertain parameters. To achieve the goal, the reliability index approach based on the firstorder reliability method is adopted to deal with probabilistic constraint functions and a double-loop optimization algorithm is implemented to obtain an optimum. The proposed method is applied to the TEAM Workshop Problem 22 and its accuracy and efficiency is verified with reference of Monte Carlo simulation results.

• Journal of computational fluids engineering
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• v.11 no.1 s.32
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• pp.21-28
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• 2006

Reliability Based Design Optimization(RBDO) is one of the optimization methods that minimize the product failure due to small changes of operating conditions or process errors. It searches the optimum that satisfies the safety margin of each constraint, and it gives stable and reliable designs. However, RBDO requires many times oj computational efforts compared with the conventional deterministic optimization(DO) to evaluate the probability of failure about each constraint, therefore it is hard to apply directly to large-scaled problems such as a flexible wing shape design optimization. For the efficient reliability analysis, the approximate reliability analysis method with the two-point approximation(TPA) is proposed In this study, the lift-to-drag ratio maximization designs are performed with 3-dimensional Navier-Stokes analysis and NASTRAN structural analysis, and the optimization results about the deterministic, FORM and SORM are compared.

• Computational Structural Engineering
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• v.6 no.1
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• pp.77-89
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• 1993

Current Bridge foundation design is based on Working Stress Design(WSD), but Load Factor Based on Optimum Reliability(LFBOR) design method is more rational than the WSD. For this reason, this study proposes a reliability based design criteria for the bridge foundation, which is most common type of bridge foundation(Shallow, Pile and Caission), and also proposes the theoretical basis of nominal safety factors of stability analysis by introducing the reliability theory. The limit state equations of stability analysis of bridge foundation and the uncertainty measuring algorithms of each equation are also derived by Cornell's MFOSM(Mean First Order 2nd Moment Methods)using the stability analysis fourmula Highway Bridge Design Codes.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1992.04a
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• pp.134-139
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• 1992

This study introduces simple derivation of optimum load factors based on both cornell's MFOSM (Mean First Order End Moment) methods and Lind - Hasofers AFOSM (Advanced First Order 2nd Moment) methods and demonstrates the relationship between the optimum reliability, the load factors, the probability distributions selected to model the load, and a measure of relative failure cost. Although some of the cost parameters cannot be evaluated accurately and the upper tail characteristics of the distributions of the random loads remain uncertainty, this optimum reliability formulation provides insight on which Parameters are most significant in selecting appropriate load criteria for structure design.

• Structural Engineering and Mechanics
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• v.31 no.1
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• pp.11-24
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• 2009

In China, the oil and natural gas resources of Bohai Bay are mainly marginal oil fields. It is necessary to build both ice-resistant and economical offshore platforms. However, risk is involved in the design, construction, utilization, maintenance of offshore platforms as uncertain events may occur within the life-cycle of a platform under the extreme ice load. In this study, the optimum design model of the expected life-cycle cost for ice-resistant platforms based on cost-effectiveness criterion is proposed. Multiple performance demands of the structure, facilities and crew members, associated with the failure assessment criteria and evaluation functions of costs of construction, consequences of structural failure modes including damage, revenue loss, death and injury as well as discounting cost over time are considered. An efficient approximate method of the global reliability analysis for the offshore platforms is provided, which converts the implicit nonlinear performance function in the conventional reliability analysis to linear explicit one. The proposed life-cycle optimum design formula are applied to a typical ice-resistant platform in Bohai Bay, and the results demonstrate that the life-cycle cost-effective optimum design model is more rational compared to the conventional design.