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.

翻译：在核热工水力（TH）系统程序中，输入不确定性的重要来源之一是物理模型参数（PMPs），在最佳估算加不确定性（BEPU）框架下，准确量化这些输入参数的不确定性对于验证核反应堆系统至关重要。逆不确定性量化（IUQ）方法已从贝叶斯视角用于量化PMPs的不确定性。本文提出一种新颖的分层贝叶斯模型用于IUQ，旨在缓解两个现有挑战：不同实验条件下PMPs的高变异性，以及未知的模型偏差或异常值导致PMPs出现过拟合问题。基于TRACE程序中的PMPs，利用沸水反应堆全尺寸细网格棒束测试（BFBT）基准中的实测空泡份额数据，将所提分层模型与传统单层贝叶斯模型进行了比较。在分层结构中采用哈密顿蒙特卡洛方法——无U-turn采样器（NUTS）进行后验采样。结果表明，所提分层结构能有效提供更优的PMPs后验分布估计且不易出现过拟合。该分层模型还展示了一种将IUQ推广至涵盖广泛实验条件与不同几何构型的大型数据库的有效途径。