• Title, Summary, Keyword: 크리깅 메타모델

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Sensitivity Validation Technique for Sequential Kriging Metamodel (순차적 크리깅 메타모델의 민감도 검증법)

  • Huh, Seung-Kyun;Lee, Jin-Min;Lee, Tae-Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.8
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    • pp.873-879
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    • 2012
  • Metamodels have been developed with a variety of design optimization techniques in the field of structural engineering over the last decade because they are efficient, show excellent prediction performance, and provide easy interconnections into design frameworks. To construct a metamodel, a sequential procedure involving steps such as the design of experiments, metamodeling techniques, and validation techniques is performed. Because validation techniques can measure the accuracy of the metamodel, the number of presampled points for an accurate kriging metamodel is decided by the validation technique in the sequential kriging metamodel. Because the interpolation model such as the kriging metamodel based on computer experiments passes through responses at presampled points, additional analyses or reconstructions of the metamodels are required to measure the accuracy of the metamodel if existing validation techniques are applied. In this study, we suggest a sensitivity validation that does not require additional analyses or reconstructions of the metamodels. Fourteen two-dimensional mathematical problems and an engineering problem are illustrated to show the feasibility of the suggested method.

Mean-Variance-Validation Technique for Sequential Kriging Metamodels (순차적 크리깅모델의 평균-분산 정확도 검증기법)

  • Lee, Tae-Hee;Kim, Ho-Sung
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.5
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    • pp.541-547
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    • 2010
  • The rigorous validation of the accuracy of metamodels is an important topic in research on metamodel techniques. Although a leave-k-out cross-validation technique involves a considerably high computational cost, it cannot be used to measure the fidelity of metamodels. Recently, the mean$_0$ validation technique has been proposed to quantitatively determine the accuracy of metamodels. However, the use of mean$_0$ validation criterion may lead to premature termination of a sampling process even if the kriging model is inaccurate. In this study, we propose a new validation technique based on the mean and variance of the response evaluated when sequential sampling method, such as maximum entropy sampling, is used. The proposed validation technique is more efficient and accurate than the leave-k-out cross-validation technique, because instead of performing numerical integration, the kriging model is explicitly integrated to accurately evaluate the mean and variance of the response evaluated. The error in the proposed validation technique resembles a root mean squared error, thus it can be used to determine a stop criterion for sequential sampling of metamodels.

Development of Computational Orthogonal Array based Fatigue Life Prediction Model for Shape Optimization of Turbine Blade (터빈 블레이드 형상 최적설계를 위한 전산 직교배열 기반 피로수명 예측 모델 개발)

  • Lee, Kwang-Ki;Han, Seung-Ho
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.34 no.5
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    • pp.611-617
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    • 2010
  • A complex system involves a large number of design variables, and its operation is non-linear. To explore the characteristics in its design space, a Kriging meta-model can be utilized; this model has replaced expensive computational analysis that was performed in traditional parametric design optimization. In this study, a Kriging meta-model with a computational orthogonal array for the design of experiments was developed to optimize the fatigue life of a turbine blade whose behavior under cyclic rotational loads is significantly non-linear. The results not only show that the maximum fatigue life is improved but also indicate that the accuracy of computational analysis is achieved. In addition, the robustness of the results obtained by six-sigma optimization can be verified by comparison with the results obtained by performing Monte Carlo simulations.

Shape Optimization of a CRT based on Response Surface and Kriging Metamodels (반응표면과 크리깅메타모델을 이용한 CRT 형상최적설계)

  • Lee, Tae-Hee;Lee, Chang-Jin;Lee, Kwang-Ki
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.27 no.3
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    • pp.381-386
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    • 2003
  • Gradually engineering designers are determined based on computer simulations. Modeling of the computer simulation however is too expensive and time consuming in a complicate system. Thus, designers often use approximation models called metamodels, which represent approximately the relations between design and response variables. There arc general metamodels such as response surface model and kriging metamodel. Response surface model is easy to obtain and provides explicit function. but it is not suitable for highly nonlinear and large scaled problems. For complicate case, we may use kriging model that employs an interpolation scheme developed in the fields of spatial statistics and geostatistics. This class of into interpolating model has flexibility to model response data with multiple local extreme. In this study. metamodeling techniques are adopted to carry out the shape optimization of a funnel of Cathode Ray Tube. which finds the shape minimizing the local maximum principal stress Optimum designs using two metamodels are compared and proper metamodel is recommended based on this research.

Optimization of a Train Suspension using Kriging Meta-model (크리깅 메타모델에 의한 철도차량 현수장치 최적설계)

  • Lee, Kwang-Ki;Lee, Tae-Hee;Park, Chan-Kyoung
    • Proceedings of the KSME Conference
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    • pp.339-344
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    • 2001
  • In recent engineering, the designer has become more and more dependent on the computer simulations such as FEM (Finite Element Method) and BEM (Boundary Element Method). In order to optimize such implicit models more efficiently and reliably, the meta-modeling technique has been developed for solving such a complex problems combined with the DACE (Design and Analysis of Computer Experiments). It is widely used for exploring the engineer's design space and for building meta-models in order to facilitate an effective solution of multi-objective and multi-disciplinary optimization problems. Optimization of a train suspension is performed according to the minimization of forty-six responses that represent ten ride comforts, twelve derailment quotients, twelve unloading ratios, and twelve stabilities by using the Kriging meta-model of a train suspension. After each Kriging meta-model is constructed, multi-objective optimal solutions are achieved by using a nonlinear programming method called SQP (Sequential Quadratic Programming).

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Sequential Feasible Domain Sampling of Kriging Metamodel by Using Penalty Function (벌칙함수 기반 크리깅메타모델의 순차적 유용영역 실험계획)

  • Lee Tae-Hee;Seong Jun-Yeob;Jung Jae-Jun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.6
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    • pp.691-697
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    • 2006
  • Metamodel, model of model, has been widely used to improve an efficiency of optimization process in engineering fields. However, global metamodels of constraints in a constrained optimization problem are required good accuracy around neighborhood of optimum point. To satisfy this requirement, more sampling points must be located around the boundary and inside of feasible region. Therefore, a new sampling strategy that is capable of identifying feasible domain should be applied to select sampling points for metamodels of constraints. In this research, we suggeste sequential feasible domain sampling that can locate sampling points likely within feasible domain by using penalty function method. To validate the excellence of feasible domain sampling, we compare the optimum results from the proposed method with those form conventional global space-filling sampling for a variety of optimization problems. The advantages of the feasible domain sampling are discussed further.

Reliability Estimation Using Kriging Metamodel (크리깅 메타모델을 이용한 신뢰도 계산)

  • Cho Tae-Min;Ju Byeong-Hyeon;Jung Do-Hyun;Lee Byung-Chai
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.30 no.8
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    • pp.941-948
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    • 2006
  • In this study, the new method for reliability estimation is proposed using kriging metamodel. Kriging metamodel can be determined by appropriate sampling range and sampling numbers because there are no random errors in the Design and Analysis of Computer Experiments(DACE) model. The first kriging metamodel is made based on widely ranged sampling points. The Advanced First Order Reliability Method(AFORM) is applied to the first kriging metamodel to estimate the reliability approximately. Then, the second kriging metamodel is constructed using additional sampling points with updated sampling range. The Monte-Carlo Simulation(MCS) is applied to the second kriging metamodel to evaluate the reliability. The proposed method is applied to numerical examples and the results are almost equal to the reference reliability.

A study of the correlation coefficients with respect to the degrees of the global models in the kriging metamodel (크리깅 메타모델에서 전역 모델에 따른 상관계수의 연구)

  • Cho, Su-Kil;Lee, Tae-Hee
    • Proceedings of the KSME Conference
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    • pp.701-705
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    • 2008
  • Design analysis and computer experiments (DACE) model is widely used to express efficiently the nonlinear responses in the field of engineering design. Kriging model, a DACE model, can approximately replace a simulation model that is very expensive or highly nonlinear. The kriging model is composed of the summation of a global model and a local model representing deviation from global model. The local model is determined by correlation coefficient of the pre-sampled points, where determination of the correct correlation coefficient has an effect on accuracy and robustness of the kriging model. Therefore, robustness of the correlation coefficient is explored with respect to degrees of the global model. Then we propose the range of correlation coefficient to make correct and robust kriging model and the influence of the correlation coefficients on the degrees of global model with respect to the nonlinearity of the pre-sampled responses.

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Reliability Estimation and RBDO Using Kriging Metamodel and Genetic Algorithm (크리깅 메타모델과 유전알고리즘을 이용한 신뢰도 계산 및 신뢰도기반 최적설계)

  • Cho, Tae-Min;Lee, Byung-Chai
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.11
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    • pp.1195-1201
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    • 2009
  • In this study, effective methods for reliability estimation and reliability-based design optimization(RBDO) are proposed using kriging metamodel and genetic algorithm. In our previous study, we proposed the accurate method for reliability estimation using two-staged kriging metamodel and genetic algorithm. In this study, the possibility of applying the previously proposed method to RBDO is investigated. The efficiency and accuracy of that method were much improved than those of the first order reliability method(FORM). Finally, the effective method for RBDO is proposed and applied to numerical examples. The results are compared to the existing RBDO methods and shown to be very effective and accurate.

Selection Method of Global Model and Correlation Coefficients for Kriging Metamodel (크리깅 메타모델의 전역모델과 상관계수 선정 방법)

  • Cho, Su-Kil;Byun, Hyun-Suk;Lee, Tae-Hee
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.8
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    • pp.813-818
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    • 2009
  • Design analysis and computer experiments (DACE) model is widely used to express efficiently nonlinear responses in the field of engineering design. As a DACE model, kriging model can approximately replace a simulation model that is very expensive or highly nonlinear. The kriging model is composed of the summation of a global model and a local model representing deviation from the global model. The local model is determined by correlation coefficient with the pre-sampled points, where the accuracy and robustness of the kriging model depends on the selection of proper correlation coefficients. Therefore, to achieve the robust kriging model, the range of the correlation coefficients is explored with respect to the degrees of the global model. Based on this study we propose the proper orders of the global model and range of parameters to make accurate and robust kriging model.