• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.10 s.241
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• pp.1139-1147
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• 2005

The shape optimal design of the plate-fin type heat sink with vortex generator is performed to minimize the pressure loss subjected to the desired maximum temperature numerically. Evaluation of the performance function, in general, is required much computational cost in fluid/thermal systems. Thus, global approximate optimization techniques have been introduced into the optimization of fluid/thermal systems. In this study, Kriging method Is used to obtain the optimal solutions associated with the computational fluid dynamics (CFD). The results show that when the temperature .rise is less than 40 K, the optimal design variables are $B_1=2.44\;mm,\;B_2=2.09\;mm$, and t=7.58 mm. Kriging method can dramatically reduce computational time by 1/6 times compared to SQP method so that the efficiency of Kriging method can be validated.

• Journal of The Korean Society of Agricultural Engineers
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• v.47 no.6
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• pp.3-14
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• 2005

Accurate estimation of the spatial distribution of rainfall is critical to the successful modeling of hydrologic processes. The objective of this study is to evaluate the applicability of spatially distributed rainfall data. Spatially distributed rainfall was calculated using Kriging method and Thiessen method. The application of spatially distributed rainfall was appreciated to the runoff response from the watershed. The results showed that for each method the coefficient of determination for observed hydrograph was $0.92\~0.95$ and root mean square error was $9.78\~10.89$ CMS. Ordinary Kriging method showed more exact results than Simple Kriging, Universal Kriging and Thiessen method, based on comparison of observed and simulated hydrograph. The coefncient of determination for the observed peak flow was 0.9991 and runoff volume was 0.9982. The accuracy of rainfall-runoff prediction depends on the extent of spatial rainfall variability.

• Journal of Information Processing Systems
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• v.11 no.1
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• pp.134-147
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• 2015

This paper presents the applications of Kriging spatial interpolation methods for meteorologic variables, including temperature and relative humidity, in regions of Vietnam. Three types of interpolation methods are used, which are as follows: Ordinary Kriging, Universal Kriging, and Universal Kriging plus Digital Elevation model correction. The input meteorologic data was collected from 98 ground weather stations throughout Vietnam and the outputs were interpolated temperature and relative humidity gridded fields, along with their error maps. The experimental results showed that Universal Kriging plus the digital elevation model correction method outperformed the two other methods when applied to temperature. The interpolation effectiveness of Ordinary Kriging and Universal Kriging were almost the same when applied to both temperature and relative humidity.

• Journal of Korean Society on Water Environment
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• v.26 no.2
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• pp.252-260
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• 2010

The point rainfall measurements need to be converted to the areal rainfall by means of mean areal precipitation (MAP) estimation methods. And it is not appropriate to evaluate the areal rainfall with constant drift because of the geomorphological influences to rainfall field. Non-stationarity should be applied to the estimation of the areal rainfall, therefore, to consider these effects. Kriging methods with special functional would be a suitable tool in this case. Generalized covariance Kriging method is the most developed one among different Kriging methods. From this point of view this study performs the analysis of its applicability to distributed runoff model. For these purpose, distributed rainfall was created by Thiessen and Kriging method. And distributed rainfall of each method was applied into HyGIS-GRM. The result of applying, Runoff was different in the rainfall data form. Therefore, To apply Kriging method with physical meaning is that it is the useful method as distributed rainfall-runoff model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.5
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• pp.381-389
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• 2017

The kernel density was determined based on sampling points obtained in a Markov chain simulation and was assumed to be an important sampling function. A Kriging metamodel was constructed in more detail in the vicinity of a limit state. The failure probability was calculated based on importance sampling, which was performed for the Kriging metamodel. A pre-existing method was modified to obtain more sampling points for a kernel density in the vicinity of a limit state. A stable numerical method was proposed to find a parameter of the kernel density. To assess the completeness of the Kriging metamodel, the possibility of changes in the calculated failure probability due to the uncertainty of the Kriging metamodel was calculated.

• 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.

• Structural Engineering and Mechanics
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• v.66 no.6
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• pp.677-691
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• 2018

Reliability assessment of complex structures using simulation methods is time-consuming. Thus, surrogate models are usually employed to reduce computational cost. AK-MCS is a surrogate-based Active learning method combining Kriging and Monte-Carlo Simulation for structural reliability analysis. This paper proposes three modifications of the AK-MCS method to reduce the number of calls to the performance function. The first modification is related to the definition of an initial Design of Experiments (DoE). In the original AK-MCS method, an initial DoE is created by a random selection of samples among the Monte Carlo population. Therefore, samples in the failure region have fewer chances to be selected, because a small number of samples are usually located in the failure region compared to the safe region. The proposed method in this paper is based on a uniform selection of samples in the predefined domain, so more samples may be selected from the failure region. Another important parameter in the AK-MCS method is the size of the initial DoE. The algorithm may not predict the exact limit state surface with an insufficient number of initial samples. Thus, the second modification of the AK-MCS method is proposed to overcome this problem. The third modification is relevant to the type of regression trend in the AK-MCS method. The original AK-MCS method uses an ordinary Kriging model, so the regression part of Kriging model is an unknown constant value. In this paper, the effect of regression trend in the AK-MCS method is investigated for a benchmark problem, and it is shown that the appropriate choice of regression type could reduce the number of calls to the performance function. A stepwise approach is also presented to select a suitable trend of the Kriging model. The numerical results show the effectiveness of the proposed modifications.

• 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.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.678-683
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• 2008

Moment-based reliability analysis is the method to calculate reliability using Pearson System with first-four raw moments obtained from simulation model. But it is too expensive to calculate first four moments from complicate simulation model. To overcome this drawback the MD(multiplicative decomposition) method which approximates simulation model to kriging metamodel and calculates first four raw moments explicitly with multiplicative decomposition techniques. In general, kriging metamodel is an interpolation model that is decomposed of global model and local model. The global model, in general, can be used as the constant global model, the 1st order global model, or the 2nd order global model. In this paper, the influences of global models on the accuracy and robustness of raw moments are examined and compared. Finally, we suggest the best global model which can provide exact and robust raw moments using MD method.

• 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.