• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2008년도 추계학술대회A
• /
• pp.701-705
• /
• 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.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2008년도 추계학술대회A
• /
• pp.1016-1021
• /
• 2008

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 examined. The accuracy of that method is much improved than the first order reliability method with similar efficiency. 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.

• 대한기계학회논문집A
• /
• 제30권8호
• /
• pp.985-992
• /
• 2006

Many methods for reliability analysis have been studied and one of them, a moment method, has the advantage that it doesn't require sensitivities of performance functions. The moment method for reliability analysis requires the first four moments of a performance function and then Pearson system is used for the probability of failure where the accuracy of the probability of failure greatly depends on that of the first four moments. But it is generally impossible to assess them analytically for multidimensional functions, and numerical integration is mainly used to estimate the moment. However, numerical integration requires many function evaluations and in case of involving finite element analyses, the calculation of the first fo 따 moments is very time-consuming. To solve the problem, this research proposes a new method of approximating the first four moments based on kriging metamodel. The proposed method substitutes the kriging metamodel for the performance function and can also evaluate the accuracy of the calculated moments adjusting the approximation range. Numerical examples show the proposed method can approximate the moments accurately with the less function evaluations and evaluate the accuracy of the calculated moments.

• Journal of Mechanical Science and Technology
• /
• 제20권8호
• /
• pp.1169-1182
• /
• 2006

Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.

• 대한기계학회논문집A
• /
• 제30권6호
• /
• pp.691-697
• /
• 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.

• 대한기계학회논문집A
• /
• 제33권12호
• /
• pp.1464-1470
• /
• 2009

RBDO approach based on a sampling method with the Kriging metamodel and Constraint Boundary Sampling (CBS), which is sequential sampling method to generate metamodels is proposed. The major advantage of the proposed RBDO approach is that it does not require Most Probable failure Point (MPP) which is essential for First-Order Reliability Method (FORM)-based RBDO approach. The Monte Carlo Sampling (MCS), most well-known method of the sampling methods for the reliability analysis is used to assess the reliability of constraints. In addition, a Cumulative Distribution Function (CDF) of the constraints is approximated using Moving Least Square (MLS) method from empirical distribution function. It is possible to acquire a probability of failure and its analytic sensitivities by using an approximate function of the CDF for the constraints. Moreover, a concept of inactive design is adapted to improve a numerical efficiency of the proposed approach. Computational accuracy and efficiency of the proposed RBDO approach are demonstrated by numerical and engineering problems.

• 대한기계학회논문집A
• /
• 제34권5호
• /
• pp.541-547
• /
• 2010

메타모델의 정확도를 엄밀하게 검증하는 것은 메타모델링에서 중요한 연구주제이다. k 점 선택교차검증기법이 많은 계산시간을 요구하면서도 메타모델의 정확도를 정략적으로 측정하지 못한다. 최근들어, 평균 $_0$ 기준이 메타모델의 정확도를 정량적으로 제공하기 위하여 제안되었다. 그러나 평균 $_0$ 검증 기준은 크리깅 메타모델이 부정확함에도 불구하고 일찍 수렴하는 경향이 있다. 따라서 본 연구에서는 최대엔트로피를 이용한 순차적 실험계획에서 크리깅모델의 평균과 분산을 이용한 정확도 평가기법을 제안한다. 이 제안한 기법은 평균 및 분산을 계산할 때 수치해석으로 구하는 것이 아니라 크리깅메타모델을 직접 적분하여 구하기 때문에 k 점 선택교차검증기법보다 효율적이며 정확하다. 제안한 기준은 실제 응답의 평균제곱오차의 경향과 매우 유사하여 순차적 실험계획의 수렴기준으로 사용할 수 있다.

• Geomechanics and Engineering
• /
• 제30권2호
• /
• pp.187-199
• /
• 2022

Kriging metamodel, as a flexible machine learning method for approximating deterministic analysis models of an engineering system, has been widely used for efficiently estimating slope reliability in recent years. However, the autocorrelation function (ACF), a key input to Kriging that affects the accuracy of reliability estimation, is usually selected based on empiricism. This paper proposes an adaption of the Kriging method, named as Genetic Algorithm optimized Whittle-Matérn Kriging (GAWMK), for addressing this issue. The non-classical two-parameter Whittle-Matérn (WM) function, which can represent different ACFs in the Matérn family by controlling a smoothness parameter, is adopted in GAWMK to avoid subjectively selecting ACFs. The genetic algorithm is used to optimize the WM model to adaptively select the optimal autocorrelation structure of the GAWMK model. Monte Carlo simulation is then performed based on GAWMK for a subsequent slope reliability analysis. Applications to one explicit analytical example and two slope examples are presented to illustrate and validate the proposed method. It is found that reliability results estimated by the Kriging models using randomly chosen ACFs might be biased. The proposed method performs reasonably well in slope reliability estimation.

• 한국전산유체공학회지
• /
• 제9권1호
• /
• pp.34-40
• /
• 2004

Recently with growth in the capability of super computers and Parallel computers, shape design optimization is becoming easible for real problems. Also, Computational Fluid Dynamics(CFD) techniques have been improved for higher reliability and higher accuracy. In the shape design optimization, analysis solvers and optimization schemes are essential. In this work, the Roe's 2nd-order Upwind TVD scheme and DADI time march with multigrid were used for the flow solution with the Euler equation and FDM(Finite Differenciation Method), GA(Genetic Algorithm) and Kriging were used for the design optimization. Kriging were applied to 2-D airfoil design optimization and compared with FDM and GA's results. When Kriging is applied to the nonlinear problems, satisfactory results were obtained. From the result design optimization by Kriging method appeared as good as other methods.

• 대한기계학회논문집A
• /
• 제33권11호
• /
• pp.1225-1232
• /
• 2009

This study suggests a structural design process for the upper control arm installed at a vehicle. Static strength and durability are the most important responses in the structural design of a control arm. This study considers the static strength in the optimization process. The inertia relief method for FE analysis is utilized to simulate the static loading conditions. According to the classification of structural optimization, the structural design of a control arm is included in the category of shape optimization. In this study, the metamodel technique using the kriging method is adopted to obtain the minimum weight satisfying the strength constraint. Then, the final design is suggested by considering the durability criteria. The durability assessment is obtained by the index of fatigue durability called the SWT (Smith-Watson-Topper) index. The final optimum shape has been proposed by trial and error method.