• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2008년도 추계 학술발표회
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• pp.1296-1305
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• 2008

In this study, the spatial distribution of depth between alluvial soil and weathered soil of Song-do new city is analyzed using geostatistics. From analysis results, the boundary depth of north-east region is deeper than that of south-west region, and average depth of north-east region is 27.14m and average depth of south-west region is 23.25m. The boundary depth is estimated by ordinary kriging and inverse distance method, and estimated results are almost similarity. So, in Song-do new city, these two method can be used to estimate the boundary depth. The ordinary kriging method is a very useful tool because the more exact analysis of spatial continuity and distribution characteristic is possible.

• 한국산학기술학회논문지
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• 제7권4호
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• pp.684-689
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• 2006

강우자료는 수문시스템 해석에 있어 가장 기본이 되는 입력자료이며, 강우측정시에는 다양한 원인에 의해 결측이 발생하게 된다 따라서, 이러한 자료를 보정하기 위한 다양한 방법들이 제시되어 있으나 적용성이나 오차정도에 대한 평가 없이 사용되고 있는 실정이다. 본 연구에서는 기존에 사용중인 산술평균법, 정상연강우량법, 수정정상연강우량법, 역거릭법, 선형계획법, 크리깅방법 등의 강우량 보정방법을 비교 평가하였다.

• 한국항공우주학회지
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• 제33권2호
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• pp.32-38
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• 2005

본 연구에서는 근사모델을 이용하여 설계공간의 타당성을 높일 수 있는 방법을 제시하였다. 이때 설계공간을 이동시키기 위한 기준으로 Chebyshev Inequality를 사용하였다. 이를 공탄성을 고려한 항공기 익형 설계문제에 적용함으로써 타당성이 크게 향상됨을 확인하였으며 이렇게 구한 설계공간 내에서 최적화를 수행함으로써 보다 우수한 최적값도 얻을 수 있었다. 즉 설계공간 내에서 주어진 제약조건을 만족할 확률이 증가하였으며, 설계공간을 이동시킴으로써 보다 우수한 최적점이 설계공간 내에 포함되었다고 할 수 있다. 또한 이 과정에서 반응면 모델과 크리깅 모델, 두 가지 근사모델을 사용하여 정확성과 효율성, 실험점에 대한 강건성 등을 비교하였으며, 본 연구에서 설계한 문제의 경우 비교적 선형적인 특징으로 인해 반응면이 보다 우수한 결과를 보여줌을 확인하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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• pp.537-542
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• 2001

In recent engineering, the designer has become more and more dependent on computer simulation. But defining exact model using computer simulation is too expensive and time consuming in the complicate systems. Thus, designers often use approximation models, which express the relation between design variables and response variables. These models are called metamodel. In this paper, we introduce one of the metamodel, named Kriging. This model employs an interpolation scheme and is developed in the fields of spatial statistics and geostatistics. This class of interpolating model has flexibility to model response data with multiple local extreme. By reason of this multi modality, we can't use any gradient-based optimization algorithm to find global extreme value of this model. Thus we have to introduce global optimization algorithm. To do this, we introduce DE(Differential Evolution). DE algorithm is developed by Ken Price and Rainer Storn, and it has recently proven to be an efficient method for optimizing real-valued multi-modal objective functions. This algorithm is similar to GA(Genetic Algorithm) in populating points, crossing over, and mutating. But it introduces vector concept in populating process. So it is very simple and easy to use. Finally, we show how we determine Kriging metamodel and find global extreme value through two mathematical examples.

• Structural Engineering and Mechanics
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• 제78권2호
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• pp.209-218
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• 2021

For engineering, there are two major challenges in reliability analysis. First, to ensure the accuracy of simulation results, mechanical products are usually defined implicitly by complex numerical models that require time-consuming. Second, the mechanical products are fortunately designed with a large safety margin, which leads to a low failure probability. This paper proposes an efficient and high-precision adaptive active learning algorithm based on the Kriging surrogate model to deal with the problems with low failure probability and time-consuming numerical models. In order to solve the problem with multiple failure regions, the adaptive kernel-density estimation is introduced and improved. Meanwhile, a new criterion for selecting points based on the current Kriging model is proposed to improve the computational efficiency. The criterion for choosing the best sampling points considers not only the probability of misjudging the sign of the response value at a point by the Kriging model but also the distribution information at that point. In order to prevent the distance between the selected training points from too close, the correlation between training points is limited to avoid information redundancy and improve the computation efficiency of the algorithm. Finally, the efficiency and accuracy of the proposed method are verified compared with other algorithms through two academic examples and one engineering application.

• Geomechanics and Engineering
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• 제18권6호
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• pp.595-603
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• 2019

A modified model combining Kriging and Monte Carlo method (MC) is proposed for probabilistic estimation of tunnel face stability in this paper. In the model, a novel uniform design is adopted to train the Kriging, instead of the existing active learning function. It has advantage of avoiding addition of new training points iteratively, and greatly saves the computational time in model training. The kinematic approach of limit analysis is employed to define the deterministic computational model of face failure, in which the Hoek-Brown failure criterion is introduced to account for the nonlinear behaviors of rock mass. The trained Kriging is used as a surrogate model to perform MC with dramatic reduction of calls to actual limit state function. The parameters in Hoek-Brown failure criterion are considered as random variables in the analysis. The failure probability is estimated by direct MC to test the accuracy and efficiency of the proposed probabilistic model. The influences of uncertainty level, correlation relationship and distribution type of random variables are further discussed using the proposed approach. In summary, the probabilistic model is an accurate and economical alternative to perform probabilistic stability analysis of tunnel face excavated in spatially random Hoek- Brown media.

• Environmental Engineering Research
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• 제24권1호
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• pp.150-158
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• 2019

Soil contaminated with heavy metals from artisanal gold mining in Anka Local Government Area in Northwestern Nigeria was investigated to evaluate the human health risk as a result of heavy metals. Measured concentration of heavy metals and exposure parameters were used to estimate human carcinogenic and non-carcinogenic risk. GIS-based Kriging method was utilized to create a prediction maps of human health risks and probability maps of heavy metals concentrations exceeding their threshold limits. Hazard index calculation showed that 21 out of 23 locations are posing non-cancer risk for children. Adults and children are at high cancer risk in all locations as the total cancer risk exceeded $1{\times}10^{-6}$ (the lower limit CTR value). Kriging model showed that only a very small area in Anka has a hazard index of less than unity and cumulative target risk of less than $1{\times}10^{-4}$, indicating a significant carcinogenic and non-carcinogenic risks for children. The probability of heavy metals to exceed their threshold concentrations around the study area was also found to be high.

• 유체기계공업학회:학술대회논문집
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• 유체기계공업학회 2006년 제4회 한국유체공학학술대회 논문집
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• pp.543-544
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• 2006

Shape optimization of a transonic axial compressor rotor operating at the design flow condition has been performed using three-dimensional Navier-Stokes analysis and three different surrogate models: i.e.., Response Surface Method(RSM), Kriging Method, and Radial Basis Function(RBF). Three design variables of blade sweep, lean and skew are introduced to optimize the three-dimensional stacking line of the rotor blade. The object function of the shape optimization is selected as an adiabatic efficiency. Throughout the shape optimization of the rotor blade, the adiabatic efficiency is increased for the three different surrogate models. Detailed flow characteristics at the optimal blade shape obtained by different optimization method are drawn and discussed.

• Water Engineering Research
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• 제5권3호
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• pp.123-131
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• 2004

This paper describes the use of spatial interpolation for estimating seasonal crop potential evapotranspiration (PET) and irrigation water requirement in unmeasured evaporation gage stations within Edwards Aquifer, Texas using GIS. The Edwards Aquifer area has insufficient data with short observed records and rare gage stations, then, the investigation of data for determining of irrigation water requirement is difficult. This research shows that spatial interpolation techniques can be used for creating more accurate PET data in unmeasured region, because PET data are important parameter to estimate irrigation water requirement. Recently, many researchers are investigating intensively these techniques based upon mathematical and statistical theories. Especially, three techniques have well been used: Inverse Distance Weighting (IDW), spline, and kriging (simple, ordinary and universal). In conclusion, the result of this study (Table 1) shows the kriging interpolation technique is found to be the best method for prediction of unmeasured PET in Edwards aquifer, Texas.

• 환경영향평가
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• 제18권1호
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• pp.31-39
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• 2009

A lot of data which are used in environment analysis of air pollution have characteristics that are distributed continuously in space. In this point, the collected data value such as precipitation, temperature, altitude, pollution density, PM10 have spatial aspect. When geostatistical data analysis are needed, acquisition of the value in every point is the best way, however, it is impossible because of the costs and time. Therefore, it is necessary to estimate the unknown values at unsampled locations based on observations. In this study, spatial interpolation method such as local trend surface model, IDW(inverse distance weighted), RBF(radial basis function), Kriging were applied to PM10 annual average concentration of Seoul in 2005 and the accuracy was evaluated. For evaluation of interpolation accuracy, range of estimated value, RMSE, average error were analyzed with observation data. The Kriging and RBF methods had the higher accuracy than others.