Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion

Research output: Contribution to journalArticle

Abstract

Modeling and simulations are naturally augmented by extensive Uncertainty Quantification (UQ) and sensitivity analysis requirements in the nuclear reactor system design, in which uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. Historically, expert judgment has been used to specify the nominal values, probability density functions and upper and lower bounds of the simulation code random input parameters for the forward UQ process. The purpose of this paper is to replace such ad-hoc expert judgment of the statistical properties of input model parameters with inverse UQ process. Inverse UQ seeks statistical descriptions of the model random input parameters that are consistent with the experimental data. Bayesian analysis is used to establish the inverse UQ problems based on experimental data, with systematic and rigorously derived surrogate models based on Polynomial Chaos Expansion (PCE). The methods developed here are demonstrated with the Point Reactor Kinetics Equation (PRKE) coupled with lumped parameter thermal-hydraulics feedback model. Three input parameters, external reactivity, Doppler reactivity coefficient and coolant temperature coefficient are modeled as uncertain input parameters. Their uncertainties are inversely quantified based on synthetic experimental data. Compared with the direct numerical simulation, surrogate model by PC expansion shows high efficiency and accuracy. In addition, inverse UQ with Bayesian analysis can calibrate the random input parameters such that the simulation results are in a better agreement with the experimental data.

Original languageEnglish (US)
Pages (from-to)29-52
Number of pages24
JournalNuclear Engineering and Design
Volume313
DOIs
StatePublished - Mar 1 2017

Fingerprint

chaotic dynamics
Chaos theory
chaos
polynomials
reactors
Polynomials
expansion
simulation
Bayesian analysis
reactivity
Uncertainty analysis
nuclear reactors
uncertainty analysis
Direct numerical simulation
coolants
sensitivity analysis
coefficients
Nuclear reactors
probability density function
guy wires

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Nuclear Energy and Engineering
  • Materials Science(all)
  • Safety, Risk, Reliability and Quality
  • Waste Management and Disposal
  • Mechanical Engineering

Cite this

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title = "Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion",
abstract = "Modeling and simulations are naturally augmented by extensive Uncertainty Quantification (UQ) and sensitivity analysis requirements in the nuclear reactor system design, in which uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. Historically, expert judgment has been used to specify the nominal values, probability density functions and upper and lower bounds of the simulation code random input parameters for the forward UQ process. The purpose of this paper is to replace such ad-hoc expert judgment of the statistical properties of input model parameters with inverse UQ process. Inverse UQ seeks statistical descriptions of the model random input parameters that are consistent with the experimental data. Bayesian analysis is used to establish the inverse UQ problems based on experimental data, with systematic and rigorously derived surrogate models based on Polynomial Chaos Expansion (PCE). The methods developed here are demonstrated with the Point Reactor Kinetics Equation (PRKE) coupled with lumped parameter thermal-hydraulics feedback model. Three input parameters, external reactivity, Doppler reactivity coefficient and coolant temperature coefficient are modeled as uncertain input parameters. Their uncertainties are inversely quantified based on synthetic experimental data. Compared with the direct numerical simulation, surrogate model by PC expansion shows high efficiency and accuracy. In addition, inverse UQ with Bayesian analysis can calibrate the random input parameters such that the simulation results are in a better agreement with the experimental data.",
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