Inverse Uncertainty Quantification by Hierarchical Bayesian Modeling and Application in Nuclear System Thermal-Hydraulics Codes

In nuclear Thermal Hydraulics (TH) system codes, a significant source of input uncertainty comes from the Physical Model Parameters (PMPs), and accurate uncertainty quantification in these input parameters is crucial for validating nuclear reactor systems within the Best Estimate Plus Uncertainty (BEPU) framework. Inverse Uncertainty Quantification (IUQ) method has been used to quantify the uncertainty of PMPs from a Bayesian perspective. This paper introduces a novel hierarchical Bayesian model for IUQ which aims to mitigate two existing challenges: the high variability of PMPs under varying experimental conditions, and unknown model discrepancies or outliers causing over-fitting issues for the PMPs. The proposed hierarchical model is compared with the conventional single-level Bayesian model based on the PMPs in TRACE using the measured void fraction data in the Boiling Water Reactor Full-size Fine-mesh Bundle Test (BFBT) benchmark. A Hamiltonian Monte Carlo Method - No U-Turn Sampler (NUTS) is used for posterior sampling in the hierarchical structure. The results demonstrate the effectiveness of the proposed hierarchical structure in providing better estimates of the posterior distributions of PMPs and being less prone to over-fitting. The proposed hierarchical model also demonstrates a promising approach for generalizing IUQ to larger databases with a broad range of experimental conditions and different geometric setups.