• Title/Summary/Keyword: Optimality criteria

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Multi-Optimal Designs for Second-Order Response Surface Models

  • Park, You-Jin
    • Communications for Statistical Applications and Methods
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    • v.16 no.1
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    • pp.195-208
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    • 2009
  • A conventional single design optimality criterion has been used to select an efficient experimental design. But, since an experimental design is constructed with respect to an optimality criterion pre specified by investigators, an experimental design obtained from one optimality criterion which is superior to other designs may perform poorly when the design is evaluated by another optimality criterion. In other words, none of these is entirely satisfactory and even there is no guarantee that a design which is constructed from using a certain design optimality criterion is also optimal to the other design optimality criteria. Thus, it is necessary to develop certain special types of experimental designs that satisfy multiple design optimality criteria simultaneously because these multi-optimal designs (MODs) reflect the needs of the experimenters more adequately. In this article, we present a heuristic approach to construct second-order response surface designs which are more flexible and potentially very useful than the designs generated from a single design optimality criterion in many real experimental situations when several competing design optimality criteria are of interest. In this paper, over cuboidal design region for $3\;{\leq}\;k\;{\leq}\;5$ variables, we construct multi-optimal designs (MODs) that might moderately satisfy two famous alphabetic design optimality criteria, G- and IV-optimality criteria using a GA which considers a certain amount of randomness. The minimum, average and maximum scaled prediction variances for the generated response surface designs are provided. Based on the average and maximum scaled prediction variances for k = 3, 4 and 5 design variables, the MODs from a genetic algorithm (GA) have better statistical property than does the theoretically optimal designs and the MODs are more flexible and useful than single-criterion optimal designs.

Topology Design of a Structure with a Specified Eigenfrequency (주어진 고유주파수를 갖는 구조물의 위상최적설계)

  • Lee, Jong-Hwan;Min, Seung-Jae
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.7
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    • pp.1210-1216
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    • 2003
  • Topology optimization is applied to determine the layout of a structural component with a specified frequency by minimizing the difference between the specified structural frequency and a given frequency. The homogenization design method is employed and the topology design problem is solved by the optimality criteria method. The value of a weighting factor in the optimality criteria plays an important role in this topology design problem. The modified optimality criteria method approximated by using the binomial expansion is suggested to determine the suitable value of the weighting factor, which makes convergence stable. If a given frequency is set as an excited frequency, it is possible to avoid resonance by moving away the specified structural frequency from the given frequency. The results of several test problems are compared with previous works and show the validity of the proposed algorithm.

Optimum Design of Plane Frames Subject to Displacement and Stress Constraints (처짐과 응력제약(應力制約)을 받는 평면(平面) 뼈대의 최적설계(最適設計))

  • Chung, Young Shik;Lee, Jae Whane
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.7 no.1
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    • pp.23-31
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    • 1987
  • This work presents an optimality criteria method which gives accurate solution to the structural optimization problem of plane frames subject to displacement and stress constraints. The method is made efficient, as well as rigorous, by including only the lateral displacement of the top floor in the set of behavioral constraints. The bending stresses of members are treated as side constraints based on the concept of fully-stressed-design, but the optimality of the final design is tested by treating them as behavioral constraints and examining if the design satisfies this new optimality criteria. Worked examples show the superiority of the rigorous opimality criteria in spite of its being simple and efficient.

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Study on the Optimality of 2-level Resolution V Minimal Fractional Factorial Designs (2-수준계 Resolution V 최소 부분실험법의 최적성에 관한 연구)

  • Kim Sang Ik
    • Journal of Korean Society for Quality Management
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    • v.32 no.3
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    • pp.234-243
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    • 2004
  • In this paper, we study the optimality of 2-level resolution V minimal fractional factorial designs which can be constructed by using a partially balanced array. Moreover the relative efficiencies of such designs are compared in the sense of three optimality criteria such as determinant(D)-optimality, trace(A)-optimality, and eigenvalue(E) -optimality criterion.

Preliminary Hull Form Generation by Form Parameter Method using GA (GA를 이용한 Form parameter 방법에 의한 초기선형 생성)

  • Kim, Su-Young;Shin, Sung-Chul;Shin, KYoung-Yup
    • Journal of the Korean Institute of Intelligent Systems
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    • v.12 no.1
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    • pp.44-51
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    • 2002
  • In order to generate hull form, fairness criteria applies to object function, B-spline curve vertices are considered as design variables, optimization is proceeded with satisfying geometric constraint conditions. GA(Genetic Algorithm) and optimality criteria apply to optimization process in this study.

A Study on Form Parameter Method by Optimum Vertex Point Search (조정점 최적탐색에 의한 Form Parameter 방법에 관한 연구)

  • 김수영;신성철;김덕은
    • Journal of the Society of Naval Architects of Korea
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    • v.39 no.4
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    • pp.60-65
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    • 2002
  • In order to generate hull form, we introduced optimization process. Fairness criteria is applied to object function, B-Spline control vertices are considered as design variables, optimization is proceeded with satisfying geometric constraint conditions. GA(Genetic Algorithm) and optimality criteria are applied to optimization process in this study.

Optimality in Designs of Experiment

  • Choi Kuey-Chung
    • Proceedings of the Korean Reliability Society Conference
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    • 2005.06a
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    • pp.109-113
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    • 2005
  • Optimality for block designs have received much attention in the literature. Here we review these criteria and present results showing their A,D and E connection. Also we acquainted with the mathematical methods of designing optimal experiments. In this paper, we will to do work about optimality in experimental designs.

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Design of Step-Stress Accelerated Degradation Test based on the Wiener Process and D-Optimality Condition (Wiener Process 및 D-Optimality 조건 하에서 계단형 가속열화시험 설계)

  • Kim, Heongil;Park, Jaehun;Sung, Si-Il
    • Journal of Applied Reliability
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    • v.17 no.2
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    • pp.129-135
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    • 2017
  • Purpose: This article provides step-stress accelerated degradation test (ADT) plans based on the Wiener process. Method: Step-stress levels and the stress change times are determined based on the D-optimality criteria to develop test plans. Further, a simple grid search method is provided for obtaining the optimal test plan. Results: Based on the solution procedure, ADT plans which include the stress levels and change times are developed for conducting the reliability test. Conclusion: Optimal step-stress ADT plans are provided for the case where the number of measurements is small.

A Study on the Topology Optimization of Electric Vehicle Cross beam using an Optimality Criteria Method in Determination of Arranging Hole( I ) (원공배열 결정에 최적기준법에 의한 전동차 크로스 빔의 위상최적화에 관한 연구( I ))

  • 전형용
    • Journal of the Korean Society for Precision Engineering
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    • v.19 no.11
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    • pp.137-145
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    • 2002
  • Electric vehicle body has to be subjected to uniform load and requires auxiliary equipment such as air pipe and electric wire pipe. Especially, the cross beam supports the weight of passenger and electrical equipments. a lightweight vehicle body is salutary to save operating costs and fuel consumption. Therefore this study is to perform the size and the shape optimization of crossbeam for electric vehicle using the method of topology optimization to introduce the concept of homogenization based on optimality criteria method which is efficient for the problem having the number of design variables and a few boundary condition. this provides the method to determine the optimum position and shape of circular hole in the cross beam and then can achieve the optimal design to reduce weight.

Topology Optimization using an Optimality Criteria Method (최적조건법에 의한 위상 최적화 연구)

  • 김병수;서명원
    • Transactions of the Korean Society of Automotive Engineers
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    • v.7 no.8
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    • pp.224-232
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    • 1999
  • Topology optimization has evolved into a very efficient concept design tool and has been incorporated into design engineering processes in many industrial sectors. In recent years, topology optimization has become the focus of structural design community and has been researched and applied widely both in academia and industry. There are mainly tow approaches for topology optimization of continuum structures ; homogenization and density methods. The homogenization method is to compute is to compute an optimal distribution of microstructures in a given design domain. The sizes of the micro-calvities are treated as design variables for the topology optimization problem. the density method is to compute an optimal distribution of an isotropic material, where the material densities are treated as design variables. In this paper, the density method is used to formulate the topology optimization problem. This optimization problem is solved by using an optimality criteria method. Several example problems are solved to show the usefulness of the present approach.

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