• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.135-140
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• 2007

In this paper, an Improved Dimension Reduction(IDR) method is proposed for uncertainty quantification that employes Kriging interpolation technic. It has been acknowledged that the DR method is accurate and efficient for assessing statistical moments and reliability due to the sensitivity free feature. However, the DR method has a number of drawbacks such as instability and inaccuracy for problems with increased nonlineality. In this paper, improved DR is implanted by three steps. First, the Kriging interpolation method is used to accurately approximate the responses. Second, 2N+1 and 4N+1 ADOEs are proposed to maintain high accuracy of the method for UQ analysis. Third, numerical integration scheme is used with accurate but free response values at any set of integration points of the surrogated model.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.870-875
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• 2004

Current trend of design technologies shows engineers to objectify or automate the given decision-making process. The numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, the robust design strategy is developed based on the DACE and the global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the system. The robustness is determined by the DACE model to reduce the real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.

• Interaction and multiscale mechanics
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• v.2 no.4
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• pp.353-374
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• 2009

A new seamless multiscale simulation was developed for coupling the continuum model with its molecular dynamics. Kriging-based Finite Element Method (K-FEM) is employed to model the continuum base of the entire domain, while the molecular dynamics (MD) is confined in a localized domain of interest. In the coupling zone, where the MD domain overlaps the continuum model, the overall Hamiltonian is postulated by contributions from the continuum and the molecular overlays, based on a quartic spline scaling parameter. The displacement compatibility in this coupling zone is then enforced by the Lagrange multiplier technique. A multiple-time-step velocity Verlet algorithm is adopted for its time integration. The validation of the present method is reported through numerical tests of one dimensional atomic lattice. The results reveal that at the continuum/MD interface, the commonly reported spurious waves in the literature are effectively eliminated in this study. In addition, the smoothness of the transition from MD to the continuum can be significantly improved by either increasing the size of the coupling zone or expanding the nodal domain of influence associated with K-FEM.

• Communications for Statistical Applications and Methods
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• v.27 no.5
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• pp.547-568
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• 2020

Modeling the statistical autocorrelations in spatial data is often achieved through the estimation of the variograms, where the selection of the appropriate valid variogram model, especially for small samples, is crucial for achieving precise spatial prediction results from kriging interpolations. To estimate such a variogram, we traditionally start by computing the empirical variogram (traditional Matheron or robust Cressie-Hawkins or kernel-based nonparametric approaches). In this article, we conduct numerical studies comparing the performance of these empirical variograms. In most situations, the nonparametric empirical variable nearest-neighbor (VNN) showed better performance than its competitors (Matheron, Cressie-Hawkins, and Nadaraya-Watson). The analysis of the spatial groundwater dataset used in this article suggests that the wave variogram model, with hole effect structure, fitted to the empirical VNN variogram is the most appropriate choice. This selected variogram is used with the ordinary kriging model to produce the predicted pollution map of the nitrate concentrations in groundwater dataset.

• 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).

• Asian Pacific Journal of Cancer Prevention
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• v.17 no.10
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• pp.4587-4590
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• 2016

Background: In many countries gastric cancer has the highest incidence among the gastrointestinal cancers and is the second most common cancer in Iran. The aim of this study was to identify and map high risk gastric cancer regions at the county-level in Iran. Methods: In this study we analyzed gastric cancer data for Iran in the years 2003-2010. Area-to-area Poisson kriging and Besag, York and Mollie (BYM) spatial models were applied to smoothing the standardized incidence ratios of gastric cancer for the 373 counties surveyed in this study. The two methods were compared in term of accuracy and precision in identifying high risk regions. Result: The highest smoothed standardized incidence rate (SIR) according to area-to-area Poisson kriging was in Meshkinshahr county in Ardabil province in north-western Iran (2.4,SD=0.05), while the highest smoothed standardized incidence rate (SIR) according to the BYM model was in Ardabil, the capital of that province (2.9,SD=0.09). Conclusion: Both methods of mapping, ATA Poisson kriging and BYM, showed the gastric cancer incidence rate to be highest in north and north-west Iran. However, area-to-area Poisson kriging was more precise than the BYM model and required less smoothing. According to the results obtained, preventive measures and treatment programs should be focused on particular counties of Iran.

• Korean Journal of Soil Science and Fertilizer
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• v.17 no.4
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• pp.319-324
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• 1984

Spatial variability of sand, silt, and clay contents on Hwadong SiCL and Jungdong SL was studied by using geostatistical concept. The measurements were made within a $33{\times}14m^2$ area at the nodes of 2 by 2m grids. The validity of all assumptions (stationarity, variogram models, etc.) was proved by Jack-knifing procedure and frequency distribution performed on the original data grids. The variogram of sand content on Hwadong SiCL was different from the linear model and that of clay content of Jungdong SL the linear and the spherical model in calculation of both kriged values and kriged variances in identification of its choice for simplicity.

• Journal of Korean Society of Transportation
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• v.32 no.4
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• pp.380-388
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• 2014

Annual average daily traffic(AADT) serves as important basic data in the transportation sector. AADT is used as design traffic which is the basic traffic volume in transportation planning. Despite of its importance, at most locations, AADT is estimated using short term traffic counts. An accurate AADT is calculated through permanent traffic counts at limited locations. This study dealt with estimating AADT using various models considering both the spatial correlation and time series data. Kriging models which are commonly used spatial statistics methods were applied and compared with each model. Additionally the External Universal kriging model, which includes explanatory variables, was used to assure accuracy of AADT estimation. For evaluation of various kriging methods, AADT estimation error, proposed using national highway permanent traffic count data, was analyzed and their performances were compared. The result shows the accuracy enhancement of the AADT estimation.

• Economic and Environmental Geology
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• v.29 no.5
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• pp.575-587
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• 1996

The purpose of this study is to develop geostatistical methods for selection of prospective areas of polymetallic nodule deposits in KODOS (Korea Deep Ocean Study) area of the North-East Pacific Ocean. In this study $110{\times}165$ grid system was used, and each node represents the center of an estimated block of $1km{\times}1km$. The ordinary kriging was applied to SeaBeam2000 data in order to evaluate the bathymetry. A structural analysis (variogram) of the bathymetry data was carried out for constructing digital terrain model (DTM) and the maximum slopes of the bathymetry were calculated by DTM data. The above method can be used to solve the problem that is resulted from the lack of theory of a change of support model for the maximum slope of the bathymetry. The ordinary kriging and the indicator kriging were used to evaluate the nodule abundance, and the different two kriging methods were compared to evaluate the accuracy for the estimation of the nodule abundance. It has been shown that indicator kriging was better estimation tool than the ordinary kriging. The overlay map is presented for the selection of potentially minable sites by combining the two indicator maps of the nodule abundance and the maximum slope of bathymetry. This overlay map could be utilized to establish follow-up survey and to investigate the potentially minable sites in the KODOS area.

• Environmental Analysis Health and Toxicology
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• v.29
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• pp.12.1-12.8
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• 2014

Objectives Cohort studies of associations between air pollution and health have used exposure prediction approaches to estimate individual-level concentrations. A common prediction method used in Korean cohort studies is ordinary kriging. In this study, performance of ordinary kriging models for long-term particulate matter less than or equal to $10{\mu}m$ in diameter ($PM_{10}$) concentrations in seven major Korean cities was investigated with a focus on spatial prediction ability. Methods We obtained hourly $PM_{10}$ data for 2010 at 226 urban-ambient monitoring sites in South Korea and computed annual average $PM_{10}$ concentrations at each site. Given the annual averages, we developed ordinary kriging prediction models for each of the seven major cities and for the entire country by using an exponential covariance reference model and a maximum likelihood estimation method. For model evaluation, cross-validation was performed and mean square error and R-squared ($R^2$) statistics were computed. Results Mean annual average $PM_{10}$ concentrations in the seven major cities ranged between 45.5 and $66.0{\mu}g/m^3$ (standard deviation=2.40 and $9.51{\mu}g/m^3$, respectively). Cross-validated $R^2$ values in Seoul and Busan were 0.31 and 0.23, respectively, whereas the other five cities had $R^2$ values of zero. The national model produced a higher cross-validated $R^2$ (0.36) than those for the city-specific models. Conclusions In general, the ordinary kriging models performed poorly for the seven major cities and the entire country of South Korea, but the model performance was better in the national model. To improve model performance, future studies should examine different prediction approaches that incorporate $PM_{10}$ source characteristics.