• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.65-75
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• 2012

In setting an experimental design for the prediction outside the experimental region (extrapolation design), it is natural for the experimenter to be very careful about the validity of the model for the design because the experimenter is not certain whether the model can be extended beyond the design region or not. In this paper, a hybrid constrained type approach was adopted in dealing model uncertainty as well as the prediction error using the three basic principles available in literature, maxi-min, constrained, and compound design. Furthermore, the effect of the distance of the extrapolation design point from the design region is investigated. A search algorithm was used because the classical exchange algorithm was found to be complex due to the characteristic of the problem.

• The Korean Journal of Applied Statistics
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• v.28 no.3
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• pp.561-571
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• 2015

When we consider an optimal design to predict the response corresponding to the point outside the design region, we are extremely careful about choosing the design criteria for selecting the support points. The assumed model and its accompanying error structure should be assumed to extend beyond the design region for the selected design criteria to be valid. Thus, we modify the existing design criteria such as extrapolation-optimality to be suited to those situations. We propose some maximin approaches in this paper. Simple and quadratic regression models are tested to find the basic characteristics of such maximin approaches. Some main findings are discussed in the conclusion.

• Journal of the Optical Society of Korea
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• v.18 no.5
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• pp.507-516
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• 2014

We present a hybrid method for spectral reflectivity recovery, using 3D extrapolation as a supplemental method for 3D interpolation. The proposed 3D extrapolation is an extended version of 3D interpolation based on the barycentric algorithm. It is faster and more accurate than the conventional spectral-recovery techniques of principal-component analysis and nonnegative matrix transformation. Four different extrapolation techniques (based on nearest neighbors, circumcenters, in-centers, and centroids) are formulated and applied to recover spectral reflectivity. Under the standard conditions of a D65 illuminant and 1964 $10^{\circ}$ observer, all reflectivity data from 1269 Munsell color chips are successfully reconstructed. The superiority of the proposed method is demonstrated using statistical data to compare coefficients of correlation and determination. The proposed hybrid method can be applied for fast and accurate spectral reflectivity recovery in image processing.

• Smart Structures and Systems
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• v.17 no.6
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• pp.995-1015
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• 2016

In the design and condition assessment of bridges, it is usually necessary to take into consideration the extreme conditions which are not expected to occur within a short time period and thus require an extrapolation from observations of limited duration. Long-term structural health monitoring (SHM) provides a rich database to evaluate the extreme conditions. This paper focuses on the extrapolation of extreme traffic load effects on bridges using long-term monitoring data of structural strain. The suspension Tsing Ma Bridge (TMB), which carries both highway and railway traffic and is instrumented with a long-term SHM system, is taken as a testbed for the present study. Two popular extreme value extrapolation methods: the block maxima approach and the peaks-over-threshold approach, are employed to extrapolate the extreme stresses induced by highway traffic and railway traffic, respectively. Characteristic values of the extreme stresses with a return period of 120 years (the design life of the bridge) obtained by the two methods are compared. It is found that the extrapolated extreme stresses are robust to the extrapolation technique. It may owe to the richness and good quality of the long-term strain data acquired. These characteristic extremes are also compared with the design values and found to be much smaller than the design values, indicating conservative design values of traffic loading and a safe traffic-loading condition of the bridge. The results of this study can be used as a reference for the design and condition assessment of similar bridges carrying heavy traffic, analogous to the TMB.

• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.693-703
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• 2014

When setting up an experiment for extrapolation at multiple points outside the design space, we often face a difficulty in which point we should emphasize even if the polynomial model under consideration is given. In this paper we propose various methods under two possible scenarios that deal with extrapolations. One considered in this paper is the situation when the model assumed can be extended beyond the design space. In this setting, the many classical methods(including various approaches the authors proposed before) were revisited in the context of extrapolation. But the real problem arises when there is an uncertainty concerning the validity of the assumed model. Therefore, the second scenario is to develop an appropriate procedure when we have limited information about model. Consequently, a hybrid approach is suggested to deal with this issue of how to handle the multiple extrapolating under model uncertainty. A search algorithm was implemented because the classical exchange algorithm was found difficult to handle the complexity of the problem.

• Wind and Structures
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• v.7 no.6
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• pp.373-392
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• 2004

This paper presents a methodology for spatial extrapolation of wind-induced pressure time series from a corner bay to roof locations on a low building away from the corner through the application of proper orthogonal decomposition (POD). The approach is based on the concept that pressure time series in the far field can be approximated as a linear combination of a series of modes and principal coordinates, where the modes are extracted from the full roof pressure field of an aerodynamically similar building and the principal coordinates are calculated from data at the leading corner bay only. The reliability of the extrapolation for uplift time series in nine bays for a cornering wind direction was examined. It is shown that POD can extrapolate reasonably accurately to bays near the leading corner, given the first three modes, but the extrapolation degrades further from the corner bay as the spatial correlations decrease.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.273-278
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• 1988

This paper represents the computer application techniques of initial and modification machining for dies with 3-dimensional scluptured surfaces. All procedures from die design to die machining and measurement are covered. The component of modelling is data management and modification (extrapolation and smoothing), surface modelling, and nc program preparation. Also this paper introduces the utility for successful and efficient operation of system such as map generation, data communication, tool path verification, contour map generation, graphic processing of extrapolation and smoothing results, and CAD/CAM system interface. Examples are given to illustrate the modelling.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.433-442
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• 1995

For the line search of a multi-variable optimization, an efficient algorithm is presented. The algorithm sequentially employs several polynomial approximations such as 2-point quadratic interpolation, 3-point cubic interpolation/extrapolation and 4-point cubic interpolation/extrapolation. The order of polynomial function is automatically increased for improving the accuracy of approximation. The method of approximation (interpolation or extrapolation) is automatically switched by checking the slope information of the sample points. Also, for selecting the initial step length along the descent vector, a new approach is presented. The performance of the proposed method is examined by solving typical test problems such as mathematical problems, mechanical design problems and dynamic response problems.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.31 no.3
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• pp.146-151
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• 2018

In this study, we compared the threshold-voltage extraction methods of accumulation-type JLDG (junctionless double-gate) MOSFETs (metal-oxide semiconductor field-effect transistors). Threshold voltage is the most basic element of transistor design; therefore, accurate threshold-voltage extraction is the most important factor in integrated-circuit design. For this purpose, analytical potential distributions were obtained and diffusion-drift current equations for these potential distributions were used. There are the ${\phi}_{min}$ method, based on the physical concept; the linear extrapolation method; and the second and third derivative method from the $I_d-V_g$ relation. We observed that the threshold-voltages extracted using the maximum value of TD (third derivatives) and the ${\phi}_{min}$ method were the most reasonable in JLDG MOSFETs. In the case of 20 nm channel length or more, similar results were obtained for other methods, except for the linear extrapolation method. However, when the channel length is below 20 nm, only the ${\phi}_{min}$ method and the TD method reflected the short-channel effect.