Inverse Uncertainty Quantification (IUQ) method has been widely used to quantify the uncertainty of Physical Model Parameters (PMPs) in nuclear Thermal Hydraulics (TH) systems. This paper introduces a novel hierarchical Bayesian model which aims to mitigate two existing challenges in IUQ: the high variability of PMPs under varying experimental conditions, and unknown model discrepancies or outliers causing over-fitting issues. The proposed hierarchical model is compared with the conventional single-level Bayesian model using TRACE code and the measured void fraction data in the BFBT benchmark. A Hamiltonian Monte Carlo Method - No U-Turn Sampler (NUTS) is used for posterior sampling. The results demonstrate the effectiveness of the proposed hierarchical model in providing better estimates of the posterior distributions of PMPs and being less prone to over-fitting. The proposed method also demonstrates a promising approach for generalizing IUQ to larger databases with broad ranges of experimental conditions.

翻译：逆不确定性量化（IUQ）方法已被广泛应用于量化核热工水力（TH）系统中物理模型参数（PMPs）的不确定性。本文提出了一种新颖的层次贝叶斯模型，旨在缓解IUQ中存在的两个挑战：不同实验条件下PMPs的高变异性，以及未知模型偏差或异常值导致的过拟合问题。通过TRACE程序与BFBT基准测试中的实测空泡份额数据，将该层次模型与传统单层贝叶斯模型进行了比较。采用汉密尔顿蒙特卡洛方法-无U型转折采样器（NUTS）进行后验采样。结果表明，所提出的层次模型能更有效地估计PMPs的后验分布，并且不易发生过拟合。该方法也为将IUQ推广至涵盖广泛实验条件的大型数据库提供了一条有前景的途径。