Inverse uncertainty quantification of input model parameters for thermal-hydraulics simulations using expectation–maximization under Bayesian framework

Rijan Shrestha, Tomasz Kozlowski

Research output: Contribution to journalArticle

Abstract

Quantification of uncertainties in code responses necessitates knowledge of input model parameter uncertainties. However, nuclear thermal-hydraulics code such as RELAP5 and TRACE do not provide any information on input model parameter uncertainties. Moreover, the input model parameters for physical models in these legacy codes were derived under steady-state flow conditions and hence might not be accurate to use in the analysis of transients without accounting for uncertainties. We present a Bayesian framework to estimate the posterior mode of input model parameters' mean and variance by implementing the iterative expectation–maximization algorithm. For this, we introduce the idea of model parameter multiplier. A log-normal transformation is used to transform the model parameter multiplier to pseudo-parameter. Our analysis is based on two main assumptions on pseudo-parameter. First, a first-order linear relationship is assumed between code responses and pseudo-parameters. Second, the pseudo-parameters are assumed to be normally distributed. The problem is formulated to express the scalar random variable, the difference between experimental result and base (nominal) code-calculated value as a linear combination of pseudo-parameters.

Original languageEnglish (US)
Pages (from-to)1011-1026
Number of pages16
JournalJournal of Applied Statistics
Volume43
Issue number6
DOIs
StatePublished - Apr 25 2016

Fingerprint

Uncertainty Quantification
Expectation Maximization
Hydraulics
Simulation
Model Uncertainty
Model
Parameter Uncertainty
Multiplier
Framework
Uncertainty
Quantification
Expectation-maximization Algorithm
Physical Model
Iterative Algorithm
Categorical or nominal
Linear Combination
Express
Random variable
Scalar
Transform

Keywords

  • Gaussian
  • expectation–maximization
  • maximum a posteriori

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "Quantification of uncertainties in code responses necessitates knowledge of input model parameter uncertainties. However, nuclear thermal-hydraulics code such as RELAP5 and TRACE do not provide any information on input model parameter uncertainties. Moreover, the input model parameters for physical models in these legacy codes were derived under steady-state flow conditions and hence might not be accurate to use in the analysis of transients without accounting for uncertainties. We present a Bayesian framework to estimate the posterior mode of input model parameters' mean and variance by implementing the iterative expectation–maximization algorithm. For this, we introduce the idea of model parameter multiplier. A log-normal transformation is used to transform the model parameter multiplier to pseudo-parameter. Our analysis is based on two main assumptions on pseudo-parameter. First, a first-order linear relationship is assumed between code responses and pseudo-parameters. Second, the pseudo-parameters are assumed to be normally distributed. The problem is formulated to express the scalar random variable, the difference between experimental result and base (nominal) code-calculated value as a linear combination of pseudo-parameters.",
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