• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.422-427
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• 2008

This study is to illustrate the usefulness of Kriging Dimension Reduction Method(KDRM), which is to construct probability distribution of response function in the presence of the physical uncertainty of input variables. DRM has recently received increased attention due to its sensitivity-free nature and efficiency that considerable accuracy is obtained with only a few number of analyses. However, the DRM has a number of drawbacks such as instability and inaccuracy for functions with increased nonlinearity. As a remedy, Kriging interpolation technique is incorporated which is known as more accurate for nonlinear functions. The KDRM is applied and compared with MCS methods in a compression coil spring design problem. The effectiveness and accuracy of this method is verified.

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

• 한국수자원학회논문집
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• 제39권8호
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• pp.669-676
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• 2006

수문 인자, 특히 강우량의 공간 분포 해석은 수자원 분야에서 중요한 관심사 중 하나이다. 기존의 티센법(Thiessen), 역거리법, 등우선법이 공간적 연속성과 지형 특성을 고려하지 못하는 한계를 가지고 있는데, 본 연구에서는 일강우량에 대한 강우 공간분포 해석의 정확도 향상을 위해 월평균 자료와 평년 강우량 자료를 산출하여, 이들과 수집한 일강우량 자료간의 상관성 분석하였으며 이를 근거로 지구통계학적 분석방법인 코크리깅(Co-kriging) 기법의 이차변수로 적용하여 공간 분포 해석을 실시하였으며, 기존의 역거리법과 단순 크리깅 기법에 의한 분석결과와 비교하였다. 구축한 강우량 자료간의 상관성을 조사한 결과, 일강우량은 당 해의 월평균 강우량 및 전체 자료기간의 월평균 강우량 자료와 높은 상관성을 가지는 것으로 나타났으며, 이 자료들을 Co-kriging 기법에 적용한 결과, 강우 공간 분포의 해석 정확도가 향상되었으며, 향후 다른 기상 상관 인자를 적용함으로서 강우량을 비롯한 수문인자의 공간 분포해석상 문제가 되는 불확실성을 줄일 수 있을 것이다.

• 한국항공우주학회지
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• 제47권8호
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• pp.541-548
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• 2019

본 논문은 Flush Air Data Sensing(FADS) 시스템의 방빙에 요구되는 열량을 예측하였다. 설계 초기 단계에서 효과적으로 요구 열량을 예측하기 위해 handbook 기법을 적용하였다. 이를 위해 비행환경에 따른 대표 물리량들을 입력하면 handbook 기법의 수식을 통해 열량을 예측하는 프로그램을 개발하였다. 이때 예측 값의 신뢰도를 높이기 위하여 handbook 기법에서 핵심적인 변수인 충돌효율계수를 CFD 해석을 통해 계산해 내었다. 액적 충돌 판정을 효과적으로 수행하기 위해 Kriging 기법을 적용하여 물체 형상에 대한 등고면 DB를 구축하였다. 또한 액적 궤적 예측을 위해 마찬가지로 Kriging 기법을 적용하여 속도장 DB를 구축하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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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).

• International Journal of Aeronautical and Space Sciences
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• 제17권4호
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• pp.491-500
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• 2016

This paper presents a highly efficient aeroelastic optimization method based on a surrogate model; the model is verified by considering the case of a high-aspect-ratio composite wing. Optimization frameworks using the Kriging model and genetic algorithm (GA), the Kriging model and improved particle swarm optimization (IPSO), and the back propagation neural network model (BP) and IPSO are presented. The feasibility of the method is verified, as the model can improve the optimization efficiency while also satisfying the engineering requirements. Moreover, the effects of the number of design variables and number of constraints on the optimization efficiency and objective function are analysed in detail. The accuracy of two surrogate models in aeroelastic optimization is also compared. The Kriging model is constructed more conveniently, and its predictive accuracy of the aeroelastic responses also satisfies the engineering requirements. According to the case of a high-aspect-ratio composite wing, the GA is better at global optimization.

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

• 전기학회논문지
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• 제62권2호
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• pp.177-183
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• 2013

We describe a new method for selecting design variables for shape optimization of high-voltage gas circuit breaker using a Kriging meta-model and a genetic algorithm. Firstly we sample balance design variables using the Latin Hypercube Sampling. Secondly, we build meta-model using the Kriging. Thirdly, we search the optimal design variables using a genetic algorithm. To obtain the more exact design variable, we adopt the boundary shifting method. With the proposed optimization frame, we can get the improved interruption design and reduce the design time by 80%. We applied the proposed method to the optimization of multivariate optimization problems as well as shape optimization of a high - voltage gas circuit breaker.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.57-76
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• 2007

Kriging is a nonparametric regression method used in geostatistics for estimating curves and surfaces for spatial data. It may come as a surprise that the Kriging estimator, normally derived as the best linear unbiased estimator, is also the solution of a particular variational problem. Thus, Kriging estimators can also be interpreted as generalized smoothing splines where the roughness penalty is determined by the covariance function of a spatial process. We build off the early work by Silverman (1982, 1984) and the analysis by Cox (1983, 1984), Messer (1991), Messer and Goldstein (1993) and others and develop an equivalent kernel interpretation of geostatistical estimators. Given this connection we show how a given covariance function influences the bias and variance of the Kriging estimate as well as the mean squared prediction error. Some specific asymptotic results are given in one dimension for Matern covariances that have as their limit cubic smoothing splines.

• Structural Engineering and Mechanics
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• 제70권5호
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• pp.513-524
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• 2019

This study proposed an improved particle swarm optimization (IPSO) method ensemble with kriging model for model updating. By introducing genetic algorithm (GA) and grouping strategy together with elite selection into standard particle optimization (PSO), the IPSO is obtained. Kriging metamodel serves for predicting the structural responses to avoid complex computation via finite element model. The combination of IPSO and kriging model shall provide more accurate searching results and obtain global optimal solution for model updating compared with the PSO, Simulate Annealing PSO (SimuAPSO), BreedPSO and PSOGA. A plane truss structure and ASCE Benchmark frame structure are adopted to verify the proposed approach. The results indicated that the hybrid of kriging model and IPSO could serve for model updating effectively and efficiently. The updating results further illustrated that IPSO can provide superior convergent solutions compared with PSO, SimuAPSO, BreedPSO and PSOGA.