### Abstract

The documentation of most nuclear thermal-hydraulics codes does not provide sufficient information on uncertainty of physical models (e.g. interfacial heat transfer coefficients). These models were derived based on experimental data and implemented as empirical correlations in the computational code. The uncertainty quantification for the relevant output quantity (e.g. Peak Cladding Temperature)requires estimation of the Probability Density Functions (PDFs)of the code inputs, such as physical models. In this paper, we investigate the effect of boundary conditions (outlet pressure, inlet liquid temperature, and inlet flow rate)on the uncertainty of two physical models (the interfacial friction coefficient and the wall to liquid friction coefficient). The boundary conditions effect was accounted for by adding a bias term to the mathematical framework of two existing methods for Inverse Uncertainty Quantification (IUQ): the Maximum Likelihood Estimation (MLE)method and the Maximum A Posterior (MAP)method. The two methods were demonstrated using the BFBT benchmark, experimental data was compared to code predictions of the RSTART thermal-hydraulics code for two different cases: without and with bias term. The results show an evident improvement in code prediction when the bias term is used. Finally, a validation set of experimental data was used to investigate the possibility of data overfitting, and the proposed methodology showed absence of overfitting when bias terms are used.

Original language | English (US) |
---|---|

Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | Annals of Nuclear Energy |

Volume | 133 |

DOIs | |

State | Published - Nov 2019 |

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### Keywords

- BFBT
- Bias terms
- Inverse uncertainty quantification
- Maximum A Posterior estimation
- Maximum Likelihood Estimation

### ASJC Scopus subject areas

- Nuclear Energy and Engineering

### Cite this

**Estimation of probability Density Functions for model input parameters using inverse uncertainty quantification with bias terms.** / Abu Saleem, Rabie A.; Kozlowski, Tomasz.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Estimation of probability Density Functions for model input parameters using inverse uncertainty quantification with bias terms

AU - Abu Saleem, Rabie A.

AU - Kozlowski, Tomasz

PY - 2019/11

Y1 - 2019/11

N2 - The documentation of most nuclear thermal-hydraulics codes does not provide sufficient information on uncertainty of physical models (e.g. interfacial heat transfer coefficients). These models were derived based on experimental data and implemented as empirical correlations in the computational code. The uncertainty quantification for the relevant output quantity (e.g. Peak Cladding Temperature)requires estimation of the Probability Density Functions (PDFs)of the code inputs, such as physical models. In this paper, we investigate the effect of boundary conditions (outlet pressure, inlet liquid temperature, and inlet flow rate)on the uncertainty of two physical models (the interfacial friction coefficient and the wall to liquid friction coefficient). The boundary conditions effect was accounted for by adding a bias term to the mathematical framework of two existing methods for Inverse Uncertainty Quantification (IUQ): the Maximum Likelihood Estimation (MLE)method and the Maximum A Posterior (MAP)method. The two methods were demonstrated using the BFBT benchmark, experimental data was compared to code predictions of the RSTART thermal-hydraulics code for two different cases: without and with bias term. The results show an evident improvement in code prediction when the bias term is used. Finally, a validation set of experimental data was used to investigate the possibility of data overfitting, and the proposed methodology showed absence of overfitting when bias terms are used.

AB - The documentation of most nuclear thermal-hydraulics codes does not provide sufficient information on uncertainty of physical models (e.g. interfacial heat transfer coefficients). These models were derived based on experimental data and implemented as empirical correlations in the computational code. The uncertainty quantification for the relevant output quantity (e.g. Peak Cladding Temperature)requires estimation of the Probability Density Functions (PDFs)of the code inputs, such as physical models. In this paper, we investigate the effect of boundary conditions (outlet pressure, inlet liquid temperature, and inlet flow rate)on the uncertainty of two physical models (the interfacial friction coefficient and the wall to liquid friction coefficient). The boundary conditions effect was accounted for by adding a bias term to the mathematical framework of two existing methods for Inverse Uncertainty Quantification (IUQ): the Maximum Likelihood Estimation (MLE)method and the Maximum A Posterior (MAP)method. The two methods were demonstrated using the BFBT benchmark, experimental data was compared to code predictions of the RSTART thermal-hydraulics code for two different cases: without and with bias term. The results show an evident improvement in code prediction when the bias term is used. Finally, a validation set of experimental data was used to investigate the possibility of data overfitting, and the proposed methodology showed absence of overfitting when bias terms are used.

KW - BFBT

KW - Bias terms

KW - Inverse uncertainty quantification

KW - Maximum A Posterior estimation

KW - Maximum Likelihood Estimation

UR - http://www.scopus.com/inward/record.url?scp=85065173913&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065173913&partnerID=8YFLogxK

U2 - 10.1016/j.anucene.2019.05.005

DO - 10.1016/j.anucene.2019.05.005

M3 - Article

AN - SCOPUS:85065173913

VL - 133

SP - 1

EP - 8

JO - Annals of Nuclear Energy

JF - Annals of Nuclear Energy

SN - 0306-4549

ER -