Monte Carlo Analysis of Nuclear Reactor Fluctuation Models

Abstract The integrity of a component in a safety critical industry is determined by carrying out Engineering Critical Assessments (ECA). These are designed to provide a conservative estimate of the life of a component based on conservative inputs/methodology. It is becoming increasingly apparent that for many applications these methods are overly conservative. The only physical way to really assess the reliability of a component is by producing many thousands, if not millions of a specific component and calculating a failure probability based on testing/OPEX. This is simply not feasible for the components in, for example, a nuclear reactor, and probabilistic techniques are becoming increasingly important as a means to understand the reliability of a component. This information can then be used to assess risk and inform inspection programmes. Typically a probabilistic method relies on assigning distributions to various input parameters and evaluating a probability integral, usually by Monte-Carlo analysis. A previous PVP paper developed Monte Carlo methods using the R6 fracture mechanics procedure. Although providing good insight into the likelihood of failure, these analyses were simplified and not readily applied to realistic plant situations. Further development would enable much more of the technology contained within R6 to be applied within probabilistic software. The following new features of the software are presented in this paper: • the latest K and limit load solutions from R6 for through wall circumferential defects • Simplified V factor approach to account for secondary stresses • two phase flow (water) based on the latest SQUIRT methodology • global bending, through wall bending, weld residual stress This enables a full probabilistic leak detection calculation for circumferential through wall cracks in pipes. Examples of probabilistic Leak-before-Break calculations for PWR pipework are presented in the paper.

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Facing Challenges for Monte Carlo Analysis of Full PWR Cores : Towards Optimal Detail Level for Coupled Neutronics and Proper Diffusion Data for Nodal Kinetics

SNA + MC 2013 - Joint International Conference on Supercomputing in Nuclear Applications + Monte Carlo ◽

10.1051/snamc/201402202 ◽

2014 ◽

Author(s):

A. Nuttin ◽

N. Capellan ◽

S. David ◽

X. Doligez ◽

C. El Mhari ◽

...

Keyword(s):

Monte Carlo ◽

Monte Carlo Analysis ◽

Diffusion Data

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Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

Methods of Information in Medicine ◽

10.1055/s-0038-1634534 ◽

1998 ◽

Vol 37 (03) ◽

pp. 235-238 ◽

Cited By ~ 1

Author(s):

M. El-Taha ◽

D. E. Clark

Keyword(s):

Monte Carlo ◽

Decision Trees ◽

Computer Algebra ◽

Taylor Series ◽

Computer Algebra System ◽

Random Variable ◽

Monte Carlo Analysis ◽

Normal Random Variable ◽

Medical Decision ◽

Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

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