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：逆不确定性量化方法已被广泛用于量化核热工水力系统中物理模型参数的不确定性。本文提出了一种新颖的分层贝叶斯模型，旨在缓解逆不确定性量化面临的两大挑战：物理模型参数在不同实验条件下呈现的高变异性，以及未知模型偏差或异常值导致的过拟合问题。采用TRACE程序与BFBT基准题中实测空泡份额数据，将所提分层模型与传统单层贝叶斯模型进行对比。后验采样采用哈密顿蒙特卡洛方法中的无U型抽样器。结果表明，所提分层模型能有效提供更优的物理模型参数后验分布估计，且更不易出现过拟合。该方法也为将逆不确定性量化推广至涵盖广泛实验条件的更大规模数据库提供了可行途径。