• 한국환경과학회지
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• 제28권1호
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• pp.19-35
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• 2019

This study investigates the performance of four Bayesian methods, Random Walk Metropolis (RWM), Hit-And-Run Metropolis (HARM), Adaptive Mixture Metropolis (AMM), and Population Monte Carlo (PMC), for estimating the parameters and uncertainties of probability rainfall distribution, and the results are compared with those of conventional parameter estimation methods; namely, the Method Of Moment (MOM), Maximum Likelihood Method (MLM), and Probability Weighted Method (PWM). As a result, Bayesian methods yield similar or slightly better results in parameter estimations compared with conventional methods. In particular, PMC can reduce parameter uncertainty greatly compared with RWM, HARM, and AMM methods although the Bayesian methods produce similar results in parameter estimations. Overall, the Bayesian methods produce better accuracy for scale parameters compared with the conventional methods and this characteristic improves the accuracy of probability rainfall. Therefore, Bayesian methods can be effective tools for estimating the parameters and uncertainties of probability rainfall distribution in hydrological practices, flood risk assessment, and decision-making support.

• 대한산업공학회지
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• 제29권2호
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• pp.114-125
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• 2003

This paper proposes multivariate process capability indices (PCIs) for skewed populations using $T^2$rand modified process region approaches. The proposed methods are based on the multivariate version of a weighted standard deviation method which adjusts the variance-covariance matrix of quality characteristics and approximates the probability density function using several multivariate Journal distributions with the adjusted variance-covariance matrix. Performance of the proposed PCIs is investigated using Monte Carlo simulation, and finite sample properties of the estimators are studied by means of relative bias and mean square error.

• Nuclear Engineering and Technology
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• 제52권12호
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• pp.2733-2742
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• 2020

This paper presents an assessment of applicability of the multigroup cross sections generated with Monte Carlo tools to the fast reactor analysis based on transport calculations. 33-group cross section sets were generated for simple one- (1-D) and two-dimensional (2-D) sodium-cooled fast reactor problems using the SERPENT code and applied to deterministic steady-state and depletion calculations. Relative to the reference continuous-energy SERPENT results, with the transport corrected P₀ scattering cross section, the k-eff value was overestimated by 506 and 588 pcm for 1-D and 2-D problems, respectively, since anisotropic scattering is important in fast reactors. When the scattering order was increased to P₅, the 1-D and 2-D problem errors were increased to 577 and 643 pcm, respectively. A sensitivity and uncertainty analysis with the PERSENT code indicated that these large k-eff errors cannot be attributed to the statistical uncertainties of cross sections and they are likely due to the approximate anisotropic scattering matrices determined by scalar flux weighting. The anisotropic scattering cross sections were alternatively generated using the MC²-3 code and merged with the SERPENT cross sections. The mixed cross section set consistently reduced the errors in k-eff, assembly powers, and nuclide densities. For example, in the 2-D calculation with P3 scattering order, the k-eff error was reduced from 634 pcm to -223 pcm. The maximum error in assembly power was reduced from 2.8% to 0.8% and the RMS error was reduced from 1.4% to 0.4%. The maximum error in the nuclide densities at the end of 12-month depletion that occurred in ²³⁷Np was reduced from 3.4% to 1.5%. The errors of the other nuclides are also reduced consistently, for example, from 1.1% to 0.1% for ²³⁵U, from 2.2% to 0.7% for ²³⁸Pu, and from 1.6% to 0.2% for ²⁴¹Pu. These results indicate that the scalar flux weighted anisotropic scattering cross sections of SERPENT may not be adequate for application to fast reactors where anisotropic scattering is important.

• 전산구조공학
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• 제8권1호
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• pp.127-136
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• 1995

본 연구는 가중적분법을 이용한 추계론적 유한요소해석에 관한 것으로 구조계 내에 존재하는 재료상수와 기하학적 상수의 임의성을 해석에 고려하여 추계론적 해석을 수행하였으며 대상 구조로는 평판구조를 택하였다. 재료와 기하학적 해석인자의 임의성을 포함한 요소강성행렬의 유도를 위해서 임의장을 가장하였으며 임의장의 평균은 0이고 표준편차 값은 0.1을 사용하였다. 이러한 임의장의 특성은 auto-correlation 함수에 의해서 표현되었으며 이 함수는 반응변화도를 얻는 과정에 사용되었다. 본 연구에서는 평판의 두께에 대한 임의성을 고려하기 위해서 새로운 auto-correlation 함수가 유도되었다. 유도된 새로운 auto-correlation 함수는 재료탄성계수의 임의장 특성을 나타내는 기존의 함수와 임의장 분산 계수의 함수로 나타났다. 수치해석결과는 몬테카를로 시뮬레이션 결과와 비교되었으며 상호 잘 일치하는 좋은 결과를 나타내었고 이들 결과는 제시된 이론적인 수렴치와도 잘 일치하였다. 평판두께에 대한 해석의 경우 역시 Lawrence의 결과는 물론 몬테카를로 시뮬레이션과 제시된 이론치와도 잘 일치하였다.

• 한국전산구조공학회논문집
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• 제21권4호
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• pp.335-345
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• 2008

본 연구에서는 역학적 특성이 우수하여 다양한 구조에 적용되고 있는 복합적층판에 대한 추계론적 유한요소해석 정식화를 제안한다. 정식화의 제시는 추계론적 수치해석기법 중 그 정확도가 매우 높은 것으로 알려져 있는 가중적분법에 기초하였다. 공간적 불확실성을 가지는 인수로는 두 재료축에 대한 탄성계수와 면내 전단탄성계수가 고려되었다. 이들 재료인수들은 독립적인 추계장함수로 모델링 되었으며, 이들 추계장이 구조거동에 미치는 영향은 지수함수형태의 자기 및 상호상관함수를 적용하여 산정하였다. 수치예제를 통하여 복합적층판이 등방성 및 이방성의 재료에 의한 판 구조에 비하여 거동의 변동계수가 낮음을 보여주었으며, 제안된 해석법의 검증을 위하여 몬테카를로 해석을 동시에 수행하고 그 결과를 상호 비교하였다.

• 한국강구조학회 논문집
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• 제20권1호
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• pp.21-31
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• 2008

응답면기법(RSM, Response surface method)은 복잡한 구조물의 매우 작은 발생확률이나 신뢰성해 석에서 폭넓게 사용된다. MCS(Monte-Carlo Simulation)방법은 어떤 시스템의 평가에서도 사용될 수 있으나 해석시간이 파괴확률의 역수에 비례하게 되어 발생확률이 매우 희박한 시스템의 평가에 불리하다. 확률유한요소해석법은 이러한 MCS의 한계점을 해결해 줄 수 있는 대안이 될 수 있다. 그러나 이 방법은 평균과 표준편차 등이 모델링 (내부 프로그래밍)된 특별한 프로그램에서만 적용 가능하며 임의의 범용소프트웨어의 응답을 모델링하거나 임의의 프로그램의 특성을 이용할 수가 없다. RSM방법은 복잡한 구조시스템에서 응답에 대한 회귀모델을 구성하여 효율적인 해석단계를 통해 시간과 노력을 획기적으로 절감시킬 수 있다. 그러나 RSM의 정확도는 한계상태방정식의 선형성과 축점간의 거리에 영향을 받게 된다. 이런 단점을 해결하기 위해 한계상태방정식의 선형성과 무관하게 정확한 수렴해를 구하기 위한 개선된 적응적 응답면기법을 개발하고 선형과 2차형식의 응답면방정식에 대한 2가지 예를 들어 검증하였다. 검증결과 가장 효율적인 RSM기법을 결정하였다. 개발된 선형적응적가중응답 면기법 (linear adaptive weighted response surface method, LAW-RSM)은 비적응적이거나 비가중형식의 2차 RSM기법에 비해서 정해의 신뢰성지수에 가장 근접한 정확성과 수렴성을 나타낸다.

• Structural Engineering and Mechanics
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• 제20권4호
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• pp.477-493
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• 2005

In case of Mindlin plate, not only the bending deformation but also the shear behavior is allowed. While the bending and shear stiffness are given in the same order in terms of elastic modulus, they are in different order in case of plate thickness. Accordingly, bending and shear contributions have to be dealt with independently if the stochastic finite element analysis is performed on the Mindlin plate taking into account of the uncertain plate thickness. In this study, a formulation is suggested to give the response variability of Mindlin plate taking into account of the uncertainties in elastic modulus as well as in the thickness of plate, a geometrical parameter, and their correlation. The cubic function of thickness and the correlation between elastic modulus and thickness are incorporated into the formulation by means of the modified auto- and cross-correlation functions, which are constructed based on the general formula for n-th joint moment of random variables. To demonstrate the adequacy of the proposed formulation, a plate with various boundary conditions is taken as an example and the results are compared with those obtained by means of classical Monte Carlo simulation.

• 제어로봇시스템학회논문지
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• 제19권8호
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• pp.667-675
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• 2013

This paper presents vision-based techniques for underwater landmark detection, map-based localization, and SLAM (Simultaneous Localization and Mapping) in structured underwater environments. A variety of underwater tasks require an underwater robot to be able to successfully perform autonomous navigation, but the available sensors for accurate localization are limited. A vision sensor among the available sensors is very useful for performing short range tasks, in spite of harsh underwater conditions including low visibility, noise, and large areas of featureless topography. To overcome these problems and to a utilize vision sensor for underwater localization, we propose a novel vision-based object detection technique to be applied to MCL (Monte Carlo Localization) and EKF (Extended Kalman Filter)-based SLAM algorithms. In the image processing step, a weighted correlation coefficient-based template matching and color-based image segmentation method are proposed to improve the conventional approach. In the localization step, in order to apply the landmark detection results to MCL and EKF-SLAM, dead-reckoning information and landmark detection results are used for prediction and update phases, respectively. The performance of the proposed technique is evaluated by experiments with an underwater robot platform in an indoor water tank and the results are discussed.

• Communications for Statistical Applications and Methods
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• 제14권3호
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• pp.561-576
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• 2007

Five plotting positions are applied to the computation of probability weighted moments (PWM) on the parameters of the generalized logistic distribution. Over a range of parameter values with some finite sample sizes, the effects of five plotting positions are investigated via Monte Carlo simulation studies. Our simulation results indicate that the Landwehr plotting position frequently tends to document smaller biases than others in the location and scale parameter estimations. On the other hand, the Weibull plotting position often tends to cause larger biases than others. The plotting position (i - 0.35)/n seems to report smaller root mean square errors (RMSE) than other plotting positions in the negative shape parameter estimation under small samples. In comparison to the maximum likelihood (ML) method under the small sample, the PWM do not seem to be better than the ML estimators in the location and scale parameter estimations documenting larger RMSE. However, the PWM outperform the ML estimators in the shape parameter estimation when its magnitude is near zero. Sensitivity of right tail quantile estimation regarding five plotting positions is also examined, but superiority or inferiority of any plotting position is not observed.

• Journal of Ship and Ocean Technology
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• 제12권2호
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• pp.1-15
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• 2008

The main idea of this paper introduce stochastic structural parameters and random dynamic excitation directly into the dynamic functional variational formulations, and developed the nonlinear dynamic analysis of a stochastic variational principle and the corresponding stochastic finite element method via the weighted residual method and the small parameter perturbation technique. An interpolation method was adopted, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson-${\theta}$ Method was adopted to solve finite element equations. Numerical examples are compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.