• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.4A
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• pp.677-687
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• 2006

Kriging interpolation is one of the generally used interpolation techniques in Geostatistics field. This technique includes the experimental and theoretical variograms and the formulation of kriging interpolation. In contrast to the conventional least square method for stress recovery, kriging interpolation is based on the weighted least square method to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by variogram modeling for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In addition to this, the p-level is increased non-uniformly or selectively through a posteriori error estimation based on SPR (superconvergent patch recovery) technique, proposed by Zienkiewicz and Zhu, by auto mesh p-refinement. The cut-out plate problem under tension has been tested to validate this approach. It also provides validity of kriging interpolation through comparing to existing least square method.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.14-14
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• 2015

공간보간기법은 미계측지역의 강수예측을 위해 통상적으로 사용되는 방법 중의 하나이다. 이 연구에서는 기상청에서 제공하고 있는 RCP 8.5 시나리오에 의한 남한상세 강수자료 중 지형이 복잡한 도서지역에서 제공되지 않는 데이터 누락격자에 대하여 최적의 공간보간기법을 선정하여 강수자료를 생성할 수 있도록 하였다. 적합한 보간기법을 선정하기 위해 데이터 누락지역에 대한 분석을 수행하였고, 최신 행정구역도에 맞추어 $1km{\times}1km$ 격자를 한반도 전체지역에 맞추어 생성된 격자를 사용하였다. ESRI사의 ArcGIS 프로그램을 이용하여 공간보간기법을 적용하였다. 사용된 보간법은 역거리가중치법(IDW), 정규크리깅(Ordinary Kriging), 보편크리깅(Universal Kriging), 스플라인(Spline)이며 가장 적합한 공간보간기법을 선정하기 위해 기후변화시나리오에 의한 데이터 중 해안선 주변 특정격자에서의 값을 누락시켜 공간보간기법을 통해 생성된 값과 기후변화 시나리오에 의한 값을 정량적으로 비교하였다. 공간보간기법의 적합도 평가를 위해 MAE(Mean Absolute Error), MSE(Mean Squared Error), PBIAS(Percent of BIAS), G(goodness of prediction) 분석을 수행하였고, 산점도 분석을 통해 실제값과 보간값의 오차율 평가를 병행하여 최적 공간보간기법을 결정하였다. 사용된 강수데이터는 RCP 8.5 시나리오에서 2015~2019년 중 강수가 높게 나타난 8월 자료를 이용하였다. 해안선 지역의 강수량 추정시 역거리 가중치법과 크리깅방법은 일부 지점에서 과다 추정되는 경향이 있고, 스플라인 방법이 전체적인 총 강수량이 기후변화시나리오에 의한 실제값과 유사한 것으로 나타났다. 실제값과 보간값의 교차검증을 수행한 결과 정규크리깅 기법이 가장 높은 정확도를 보였으며, 전체적으로 실제값과 유사한 범위내의 강수량이 생성되는 것으로 나타났다.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.9 no.1
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• pp.63-73
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• 1991

The data type of the echo sounding for the contouring of coastal chart is continuous profiles, and there are no data between the profiles. In this study, at first, the depths of the regular grid along the sounding line were interpolated by linear equation. After that the depths of the regular grid located between the profiles were interpolated by kriging. The semivariogram contributes to the weight of interpolation. After comparison with the conventional Moving Average and Kriging, it turns out that this algorithm shows merits in the field of the accuracy and computing time.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.23 no.1
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• pp.39-47
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• 2005

In this study, three-dimensional information of submarine topography acquired by assembling DGPS method and echo sounder which mainly used in the marine survey. Moreover, the hopper dredging capacity in harbor public affair has been calculated by utilizing kriging, radial basis function and nearest neighbor interpolation. Also, utilization of DGPS/Echo sounder method in calculation of the dredging capacity have been confirmed by comparing and analyzing the hopper dredging capacity and the actual one as per each interpolation. According to this comparison result, in case of applying kriging interpolation, some 1.89% of error rate has been shown as difference of the contents is 15,364 ㎥ and in case of applying radial basis function interpolation and nearest neighbor interpolation, 3.9% and 4.4% of error rates have respectively shown. In case the study for application of the proper interpolation as per characteristics of submarine topography, is preceded in calculation of the dredging capacity relevant to harbor public affairs, it is expected that more speedy and correct calculation for the dredging capacity can be made.

• Journal of the Korean Association of Geographic Information Studies
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• v.13 no.3
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• pp.29-41
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• 2010

In this study, the prediction errors of various spatial interpolation methods used to model values at unmeasured locations was compared and the accuracy of these predictions was evaluated. The root mean square (RMS) was calculated by processing different parameters associated with spatial interpolation by using techniques such as inverse distance weighting, kriging, local polynomial interpolation and radial basis function to known elevation data of the east coastal area under the same condition. As a result, a circular model of simple kriging reached the smallest RMS value. Prediction map using the multiquadric method of a radial basis function was coincident with the spatial distribution obtained by constructing a triangulated irregular network of the study area through the raster mathematics. In addition, better interpolation results can be obtained by setting the optimal power value provided under the selected condition.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.21 no.3
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• pp.295-304
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• 2008

This paper comprises two specific objectives. The first is to examine the applicability of Ordinary Kriging interpolation(OK) to finite element method that is based on variogram modeling in conjunction with different allowable limits of separation distance. The second is to investigate the accuracy according to theoretical variograms such as polynomial, Gauss, and spherical models. For this purpose, the weighted least square method is applied to obtain the estimated new stress field from the stress data at the Gauss points. The weight factor is determined by experimental and theoretical variograms for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. The validity of the proposed approach has been tested by analyzing two numerical examples. It is noted that the numerical results by Gauss model using 25% allowable limit of separation distance show an excellent agreement with theoretical solutions in literature.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.23 no.3
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• pp.251-260
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• 2005

The Development of CCD has contributed to great advancement in mapping technology with giving benefits to research community of photogrammetry. The purpose of this paper is to find the best selection of interpolation method for creating a terrain model form close range digital photogrammetry. T-test as a kind of statistical analysis was conducted to analyze the similarity of hydraulic model with close range digital photogrammetry and trigonometric leveling. Also, many interpolation methods such as inverse distance, kriging, nearest neighbor and TIN about the hydraulic model interpolation were conducted to compare the results for computer to display actual terrain an optimum interpolation of the digital elevation model form close range digital photogrammetry. The results revealed that kriging and TIN interpolation were efficient methods to judge the hazard interpolation law by analyzing geometric similarity of hydraulic model against hydraulic model application.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.4 s.74
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• pp.429-440
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• 2006

This paper comprises two specific objectives. The first is to examine the applicability of ordinary kriging interpolation(OK) to the p-adaptivity of the finite element method that is based on variogram modeling. The second objective Is to present the adaptive procedure by the hierarchical p-refinement in conjunction with a posteriori error estimator using the modified S.P.R. (superconvergent patch recovery) method. The ordinary kriging method that is one of weighted interpolation techniques is applied to obtain the estimated exact solution from the stress data at the Gauss points. The weight factor is determined by experimental and theoretical variograms for interpolation of stress data apart from the conventional interpolation methods that use an equal weight factor. In the p-refinement, the analytical domain has to be refined automatically to obtain an acceptable level of accuracy by increasing the p-level non-uniformly or selectively. To verify the performance of the modified S.P.R. method, the new error estimator based on limit value has been proposed. The validity of the proposed approach has been tested with the help of some benchmark problems of linear elastic fracture mechanics such as a centrally cracked panel, a single edged crack, and a double edged crack.

• Journal of the Korean Association of Geographic Information Studies
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• v.16 no.3
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• pp.147-163
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• 2013

The purpose of this study is to compare precipitation distributions in precipitation data sets over South Korea produced by three interpolation methods. The differences of precipitation caused by interpolation methods is an important information when the interpolated precipitation data sets were used in researches such as ecological and hydrological modeling as well as regional climate impact studies. In this study, the precipitation data sets were produced by IDW(Inverse Distance Weighting) and Cokriging in this study and the PRISM(Precipitation-elevation Regressions on Independent Slopes Model) data set obtained from Climate Change Information Center of Korea. The spatial resolution of the precipitation data is 1km. As a result, there was a great precipitation difference caused by interpolation methods in data of mountainous watersheds in general. Especially the difference of monthly precipitation was 10~20% or more in the mountainous watersheds near the Military Demarcation Line dividing North and South Korea, Mt. Sobaik, Mt. Worak, Mt. Deogyu, Mt. Jiri and Taeback Mountain Range. It means that a final result of a research can be affected by adopted interpolation method when an interpolated precipitation data set is used in the research for the these study sites.

• 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.