### Abstract

In the framework of BEPU (Best Estimate plus Uncertainty) methodology, the uncertainties involved in simulations must be quantified to prove that the investigated design is reasonable and acceptable. The uncertainties in predictions are usually calculated by propagating input uncertainties through the simulation model, which requires prior knowledge of the model or code input uncertainties. However, in thermal-hydraulics (TH) best estimate codes like TRACE, some parameters called physical model parameters in empirical correlations may have large uncertainties and their distributions are unknown to code users. Inverse Uncertainty Quantification (IUQ), also called Bayesian Calibration or Data Assimilation, aims at inversely quantifying the uncertainties associated with input parameters that are consistent with experimental data, and thus replacing the ad-hoc “expert judgment” or “user self-assessment”. Previous IUQ work in the field of nuclear engineering mainly use Markov Chain Monte Carlo (MCMC) algorithms to calculate the posterior distributions of certain parameters, however, they are mostly limited to relatively small datasets. The calculated posterior distributions are only valid for the selected experimental cases and may vary given different datasets. This paper introduces a Hierarchical Bayesian Inference approach in the IUQ framework to account for the variability of TRACE physical model parameters in different experimental conditions. The hierarchical model provides a more stable framework so that outliers will not have significant influence on the calculation results. The hierarchical model introduces more parameters in the sampling process so a gradient-based sampling methods called No-U-Turn Sampler (NUTS) is used for this high-dimensional MCMC sampling problem. This framework is applied to TRACE physical model parameters based on steady-state void fraction data in BFBT benchmark and the posterior distributions obtained will be meaningful for future forward uncertainty analysis.

Original language | English (US) |
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Pages | 4795-4807 |

Number of pages | 13 |

State | Published - Jan 1 2019 |

Event | 18th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2019 - Portland, United States Duration: Aug 18 2019 → Aug 23 2019 |

### Conference

Conference | 18th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2019 |
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Country | United States |

City | Portland |

Period | 8/18/19 → 8/23/19 |

### Fingerprint

### Keywords

- BFBT benchamrk
- Hierarchical Bayesian inference
- Inverse uncertainty quantification
- MCMC

### ASJC Scopus subject areas

- Nuclear Energy and Engineering
- Instrumentation

### Cite this

*Inverse uncertainty quantification by hierarchical Bayesian inference for TRACE physical model parameters based on BFBT benchmark*. 4795-4807. Paper presented at 18th International Topical Meeting on Nuclear Reactor Thermal Hydraulics, NURETH 2019, Portland, United States.

**Inverse uncertainty quantification by hierarchical Bayesian inference for TRACE physical model parameters based on BFBT benchmark.** / Wang, Chen; Wu, Xu; Kozlowski, Tomasz.

Research output: Contribution to conference › Paper

}

TY - CONF

T1 - Inverse uncertainty quantification by hierarchical Bayesian inference for TRACE physical model parameters based on BFBT benchmark

AU - Wang, Chen

AU - Wu, Xu

AU - Kozlowski, Tomasz

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In the framework of BEPU (Best Estimate plus Uncertainty) methodology, the uncertainties involved in simulations must be quantified to prove that the investigated design is reasonable and acceptable. The uncertainties in predictions are usually calculated by propagating input uncertainties through the simulation model, which requires prior knowledge of the model or code input uncertainties. However, in thermal-hydraulics (TH) best estimate codes like TRACE, some parameters called physical model parameters in empirical correlations may have large uncertainties and their distributions are unknown to code users. Inverse Uncertainty Quantification (IUQ), also called Bayesian Calibration or Data Assimilation, aims at inversely quantifying the uncertainties associated with input parameters that are consistent with experimental data, and thus replacing the ad-hoc “expert judgment” or “user self-assessment”. Previous IUQ work in the field of nuclear engineering mainly use Markov Chain Monte Carlo (MCMC) algorithms to calculate the posterior distributions of certain parameters, however, they are mostly limited to relatively small datasets. The calculated posterior distributions are only valid for the selected experimental cases and may vary given different datasets. This paper introduces a Hierarchical Bayesian Inference approach in the IUQ framework to account for the variability of TRACE physical model parameters in different experimental conditions. The hierarchical model provides a more stable framework so that outliers will not have significant influence on the calculation results. The hierarchical model introduces more parameters in the sampling process so a gradient-based sampling methods called No-U-Turn Sampler (NUTS) is used for this high-dimensional MCMC sampling problem. This framework is applied to TRACE physical model parameters based on steady-state void fraction data in BFBT benchmark and the posterior distributions obtained will be meaningful for future forward uncertainty analysis.

AB - In the framework of BEPU (Best Estimate plus Uncertainty) methodology, the uncertainties involved in simulations must be quantified to prove that the investigated design is reasonable and acceptable. The uncertainties in predictions are usually calculated by propagating input uncertainties through the simulation model, which requires prior knowledge of the model or code input uncertainties. However, in thermal-hydraulics (TH) best estimate codes like TRACE, some parameters called physical model parameters in empirical correlations may have large uncertainties and their distributions are unknown to code users. Inverse Uncertainty Quantification (IUQ), also called Bayesian Calibration or Data Assimilation, aims at inversely quantifying the uncertainties associated with input parameters that are consistent with experimental data, and thus replacing the ad-hoc “expert judgment” or “user self-assessment”. Previous IUQ work in the field of nuclear engineering mainly use Markov Chain Monte Carlo (MCMC) algorithms to calculate the posterior distributions of certain parameters, however, they are mostly limited to relatively small datasets. The calculated posterior distributions are only valid for the selected experimental cases and may vary given different datasets. This paper introduces a Hierarchical Bayesian Inference approach in the IUQ framework to account for the variability of TRACE physical model parameters in different experimental conditions. The hierarchical model provides a more stable framework so that outliers will not have significant influence on the calculation results. The hierarchical model introduces more parameters in the sampling process so a gradient-based sampling methods called No-U-Turn Sampler (NUTS) is used for this high-dimensional MCMC sampling problem. This framework is applied to TRACE physical model parameters based on steady-state void fraction data in BFBT benchmark and the posterior distributions obtained will be meaningful for future forward uncertainty analysis.

KW - BFBT benchamrk

KW - Hierarchical Bayesian inference

KW - Inverse uncertainty quantification

KW - MCMC

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M3 - Paper

AN - SCOPUS:85073749986

SP - 4795

EP - 4807

ER -