• The KSFM Journal of Fluid Machinery
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• v.16 no.6
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• pp.32-39
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• 2013

In the present study, three-dimensional aerodynamic optimization of high pressure turbine nozzle for turbofan engine was performed. For this, Kriging surrogate model was built and refined iteratively by supplying additional experimental points until the surrogate model and CFX result has effective difference on objective function. When the surrogate model satisfied this reliability condition and developed enough, optimum point was investigated. Commercial program PIAnO was used for optimization process and evolutionary algorithm was used for searching optimum point. As a result, difference between estimated value from Kriging surrogate model and CFD result converges within 0.01% and the optimized nozzle shape has 0.83% improved aerodynamic efficiency.

• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.923-930
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• 2006

A Kriging model is a sort of approximation model and used as a deterministic model of a computationally expensive analysis or simulation. Although it has various advantages, it is difficult to assess the accuracy of the approximated model. It is generally known that a mean square error (MSE) obtained from the kriging model can't calculate statistically exact error bounds contrary to a response surface method, and a cross validation is mainly used. But the cross validation also has many uncertainties. Moreover, the cross validation can't be used when a maximum error is required in the given region. For solving this problem, we first proposed a modified mean square error which can consider relative errors. Using the modified mean square error, we developed the strategy of adding a new sample to the place that the MSE has the maximum when the MSE is used for the assessment of the kriging model. Finally, we offer guidelines for the use of the MSE which is obtained from the kriging model. Four test problems show that the proposed strategy is a proper method which can assess the accuracy of the kriging model. Based on the results of four test problems, a convergence coefficient of 0.01 is recommended for an exact function approximation.

• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.155-160
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• 2006

In this paper, we propose a spatial filtering scheme using factorial kriging, one of geostatistical filtering methodin order to separate regional and residual gravity anomaly. This scheme is based on the assumption that regional anomalies have longer distance relation and residual anomalies have effected on smaller range. We decomposed gravity anomalies intotwo variogram models with long and short effectiveranges by means of factorial kriging. And decomposed variogram models produced the regional and residual anomalies. This algorithm was examined using by a synthetic gravity data, and applied to a real microgravity data to figure out abandoned mineshaft.

• Journal of the Korean Association of Geographic Information Studies
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• v.15 no.1
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• pp.16-33
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• 2012

The aim of this study is to estimate aboveground biomass carbon stocks using ordinary kriging(OK) which is the most commonly used type of kriging and regression kriging(RK) that combines a regression of the auxiliary variables with simple kriging. The analysis results shows that the forest carbon stock in Danyang is estimated at 3,459,902 tonC with OK and 3,384,581 tonC with RK in which the R-square value of the regression model is 0.1033. The result of RK conducted with sample plots stratified by forest type(deciduous, conifer and mixed) shows the lowest estimated value of 3,336,206 tonC and R-square value(0.35 and 0.18 respectively) is higher than that of when all sample plots used. The result of leave-one-out cross validation of each method indicates that RK with all sample plots reached the smallest root mean square error(RMSE) value(22.32 ton/ha) but the difference between the methods(0.23 ton/ha) is not significant.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.6
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• pp.391-398
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• 2023

In this paper, a penalized maximum likelihood estimation (PMLE) method that applies a penalty to increase the accuracy of a basis-screening-based Kriging model (BSKM) is introduced. The maximum order and set of basis functions used in the BSKM are determined according to their importance. In this regard, the cross-validation error (CVE) for the basis functions is employed as an indicator of importance. When constructing the Kriging model (KM), the maximum order of basis functions is determined, the importance of each basis function is evaluated according to the corresponding maximum order, and finally the optimal set of basis functions is determined. This optimal set is created by adding basis functions one by one in order of importance until the CVE of the KM is minimized. In this process, the KM must be generated repeatedly. Simultaneously, hyper-parameters representing correlations between datasets must be calculated through the maximum likelihood evaluation method. Given that the optimal set of basis functions depends on such hyper-parameters, it has a significant impact on the accuracy of the KM. The PMLE method is applied to accurately calculate hyper-parameters. It was confirmed that the accuracy of a BSKM can be improved by applying it to Branin-Hoo problem.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.6 no.1
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• pp.71-77
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• 2007

In case of the welding process, a conventional production method of gate valve, it has a merit of light weight, but also a demerit of high production cost and an impossibility in mass production due to work by hand. However, in case of the forging process, it has economic merits and can take a mass production process, too. The main focus of this paper is the optimization of preform in the forging process. This paper proposed an optimal design to improve the mechanical efficiency of gate valve made by forging method instead of welding. the optional design is conducted as application of real response model to Kriging model using computer simulation. Also, from verification of the response model with optimized results we were confirmed that the applications of Kriging method to structural optimum design using finite element analysis and equation are useful and reliable.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.14 no.6
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• pp.125-131
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• 2005

The purpose of this study is an optimization of gate valve made by forging method instead of welding method. In this study, we propose an optimal shape design to improve the mechanical efficiency of gate valve. In order to optimize more efficiently and reliably, the meta-modeling technique has been developed to solve such a complex problems combined with the DACE (Design and Analysis of Computer Experiments). The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the function. Also, we prove reliability of the DACE model's application to gate valve by computer simulations using FEM(Finite Element Method).

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.985-992
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• 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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.6
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• pp.864-870
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• 2003

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 approximation 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 model of a train suspension. After each Kriging model is constructed, multi -objective optimal solutions are achieved by using a nonlinear programming method called SQP(Sequential Quadratic Programming).