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

Highlights: • Inverse uncertainty quantification is implemented using MLE and MAP formulations. • Effect of boundary conditions on physical models' uncertainties was investigated. • A bias term related to BCs was added to the mathematical framework of MLE and MAP. • Implementation was for RSTART code based on the BFBT benchmark. • Improvement in results with bias term was observed without no data overfitting. - 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.