Nuclear Engineering and Technology

Korean Nuclear Society (한국원자력학회)
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Theoretical approach for uncertainty quantification in probabilistic safety assessment using sum of lognormal random variables

  • Song, Gyun Seob (Department of Energy Systems Engineering, Chung-Ang University) ;
  • Kim, Man Cheol (Department of Energy Systems Engineering, Chung-Ang University)
  • Received : 2021.06.29
  • Accepted : 2021.12.25
  • Published : 2022.06.25
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Abstract

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.

Keywords

Acknowledgement

This work was supported by the Nuclear Safety Research Program of the Korea Foundation of Nuclear Safety, granted financial resource from the Multi-Unit Risk Research Group (MURRG), with funding by the Korean government's Nuclear Safety and Security Commission [grant number 1705001] and the Nuclear Research & Development Program of the National Research Foundation of Korea, funded by the Korean government's Ministry of Science and ICT [grant number NRF-2017M2B2B1071973].

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