• Nuclear Engineering and Technology
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• v.54 no.6
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• pp.2084-2093
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• 2022

Probabilistic safety assessment is widely used to quantify the risks of nuclear power plants and their uncertainties. When the lognormal distribution describes the uncertainties of basic events, the uncertainty of the top event in a fault tree is approximated with the sum of lognormal random variables after minimal cutsets are obtained, and rare-event approximation is applied. As handling complicated analytic expressions for the sum of lognormal random variables is challenging, several approximation methods, especially Monte Carlo simulation, are widely used in practice for uncertainty analysis. In this study, a theoretical approach for analyzing the sum of lognormal random variables using an efficient numerical integration method is proposed for uncertainty analysis in probability safety assessments. The change of variables from correlated random variables with a complicated region of integration to independent random variables with a unit hypercube region of integration is applied to obtain an efficient numerical integration. The theoretical advantages of the proposed method over other approximation methods are shown through a benchmark problem. The proposed method provides an accurate and efficient approach to calculate the uncertainty of the top event in probabilistic safety assessment when the uncertainties of basic events are described with lognormal random variables.

• Proceedings of the Korean Nuclear Society Conference
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• 2003.10a
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• pp.131-131
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• 2003

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1804-1812
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• 2022

The aim of this paper is to assess the reliability and accuracy of the PSI standard method, used in many previous works, for the quantification of ND uncertainties in the SPERT-III RIA transient, by quantifying the discrepancy between the actual inserted reactivity and the original static reactivity worth and their associated uncertainties. The assessment has shown that the inherent S3K neutron source renormalization scheme, introduced before starting the transient, alters the original static reactivity worth of the transient CR and reduces the associated uncertainty due to the ND perturbation. In order to overcome these limitations, two additional methods have been developed based on CR adjustment. The comparative study performed between the three methods has showed clearly the high sensitivity of the obtained results to the selected approach and pointed out the importance of using the right procedure in order to simulate correctly the effect of ND uncertainties on the overall parameters in a RIA transient. This study has proven that the approach that allows matching the original static reactivity worth and starting the transient from criticality is the most reliable method since it conservatively preserves the effect of the ND uncertainties on the inserted reactivity during a RIA transient.

• Steel and Composite Structures
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• v.44 no.5
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• pp.651-676
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• 2022

Most of the experimental, theoretical, and numerical studies on the stability of functionally graded composites are deterministic, while there are full of complex interactions of variables with an inherently probabilistic nature, this paper presents a non-intrusive framework to investigate the stochastic nonlinear buckling behaviors of porous functionally graded cylindrical shells exposed to inevitable source-uncertainties. Euler-Lagrange equations are theoretically derived based on the three variable refined shear deformation theory. Closed-form solutions for the shell buckling loads are achieved by solving the deterministic eigenvalue problems. The analytical results are verified with numerical results obtained from finite element analyses that are conducted in the commercial software ABAQUS. The non-intrusive framework is completed by integrating the Monte Carlo simulation with the verified closed-form solutions. The convergence studies are performed to determine the effective pseudorandom draws of the simulation. The accuracy and efficiency of the framework are verified with statistical results that are obtained from the first and second-order perturbation techniques. Eleven cases of individual and compound uncertainties are investigated. Sensitivity analyses are conducted to figure out the five cases that have profound perturbative effects on the shell buckling loads. Complete probability distributions of the first three critical buckling loads are completely presented for each profound uncertainty case. The effects of the shell thickness, volume fraction index, and stochasticity degree on the shell buckling load under compound uncertainties are studied. There is a high probability that the shell has non-unique buckling modes in stochastic environments, which should be known for reliable analysis and design of engineering structures.

• Journal of Soil and Groundwater Environment
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• v.18 no.1
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• pp.94-101
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• 2013

It is well known that uncertainty associated with soil sampling is bigger than that with analysis. In this research, uncertainties for soil sampling when assessing TPH and BTEX concentration in soils were quantified based on actual field data. It is almost impossible to assess exact contamination of the site regardless how carefully devised for sampling. Uncertainties associated with sample reduction for further chemical analysis were quantified approximately 10 times larger than those associated with core sampling on site. Bigger uncertainties occur when contamination level is low, sample quantity is small, and soil particle is coarse. To minimize the uncertainties on field, homogenization of soil sample is necessary and its procedures are proposed in this research as well.

• Journal of Korean Society for Atmospheric Environment
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• v.34 no.4
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• pp.610-615
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• 2018

A filter-based optical technique is one of the representative ways for the measurement and quantification of black carbon (BC). Since the filter-based technique adopts a simple principle, it is easy to put into practical use and instrumental products have already been commercialized. In this study, however, the absorption coefficients of BC after the correction process was estimated to be approximately 3 times lower than those before the correction process. In addition, the difference between before and after corrections was also evident for the trend of increasing and decreasing absorption coefficient. When BC concentration is low, uncertainty may increase regardless of corrections due to the artifacts of filter. In this sense, techniques without using a filter are required, and uncertainties will be minimized if these techniques are used to further complement the filter-based black carbon measurements. Finally, this study is believed to help understand the uncertainty and correction of filter-based black carbon measurements.

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1902-1908
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• 2022

In many of the complex systems modeled in the field of nuclear engineering, it is often useful to use linear regression-based analyses to analyze relationships between model parameters and responses of interests. In cases where the response of interest is calculated by a simulation which uses Monte Carlo methods, there will be some uncertainty in the responses. Further, the reduction of this uncertainty increases the time necessary to run each calculation. This paper presents some discussion on how the Monte Carlo error in the response of interest influences the error in computed linear regression coefficients. A mathematical justification is given that shows that when performing linear regression in these scenarios, the error in regression coefficients can be largely independent of the Monte Carlo error in each individual calculation. This condition is only true if the total number of calculations are scaled to have a constant total time, or amount of work, for all calculations. An application with a simple pin cell model is used to demonstrate these observations in a practical problem.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.29-29
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• 2023

To mitigate the damaging impacts of floods, accurate prediction of runoff, streamflow and flood inundation is needed. Conventional approach of simulating hydrology and hydraulics using loosely coupled models cannot capture the complex dynamics of surface and sub-surface processes. Additionally, the scarcity of data in ungauged basins and quality of data in gauged basins add uncertainty to model predictions, which need to be quantified. In this presentation, first the role of integrated modeling on creating accurate flood simulations and inundation maps will be presented with specific focus on urban environments. Next, the use of machine learning in producing streamflow predictions will be presented with specific focus on incorporating covariate shift and the application of theory guided machine learning. Finally, a framework to quantify the uncertainty in flood models using Hierarchical Bayesian Modeling Averaging will be presented. Overall, this presentation will highlight that creating accurate information on flood magnitude and extent requires innovation and advancement in different aspects related to hydrologic predictions.

• Nuclear Engineering and Technology
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• v.46 no.3
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• pp.291-298
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• 2014

This paper concerns estimating uncertainties of the core neutronics design parameters of power reactors by direct sampling method (DSM) calculations based on the two-step McCARD/MASTER design system in which McCARD is used to generate the fuel assembly (FA) homogenized few group constants (FGCs) while MASTER is used to conduct the core neutronics design computation. It presents an extended application of the uncertainty propagation analysis method originally designed for uncertainty quantification of the FA FGCs as a way to produce the covariances between the FGCs of any pair of FAs comprising the core, or the covariance matrix of the FA FGCs required for random sampling of the FA FGCs input sets into direct sampling core calculations by MASTER. For illustrative purposes, the uncertainties of core design parameters such as the effective multiplication factor ($k_{eff}$), normalized FA power densities, power peaking factors, etc. for the beginning of life (BOL) core of Yonggwang nuclear unit 4 (YGN4) at the hot zero power and all rods out are estimated by the McCARD/MASTER-based DSM computations. The results are compared with those from the uncertainty propagation analysis method based on the McCARD-predicted sensitivity coefficients of nuclear design parameters and the cross section covariance data.

• Journal of Environmental Science International
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• v.20 no.12
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• pp.1541-1551
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• 2011

This study applied the Bayesian method for the quantification of the parameter uncertainty of spatial linear mixed model in the estimation of the spatial distribution of probability rainfall. In the application of Bayesian method, the prior sensitivity analysis was implemented by using the priors normally selected in the existing studies which applied the Bayesian method for the puppose of assessing the influence which the selection of the priors of model parameters had on posteriors. As a result, the posteriors of parameters were differently estimated which priors were selected, and then in the case of the prior combination, F-S-E, the sizes of uncertainty intervals were minimum and the modes, means and medians of the posteriors were similar to the estimates using the existing classical methods. From the comparitive analysis between Bayesian and plug-in spatial predictions, we could find that the uncertainty of plug-in prediction could be slightly underestimated than that of Bayesian prediction.