The evolution and release of fission gas impacts the performance of UO2 nuclear fuel. We have created a Bayesian framework to calibrate a novel model for fission gas transport that predicts diffusion rates of uranium and xenon in UO2 under both thermal equilibrium and irradiation conditions. Data sets are taken from historical diffusion, gas release, and thermodynamic experiments. These data sets consist invariably of summary statistics, including a measurement value with an associated uncertainty. Our calibration strategy uses synthetic data sets in order to estimate the parameters in the model, such that the resulting model predictions agree with the reported summary statistics. In doing so, the reported uncertainties are effectively reflected in the inferred uncertain parameters. Furthermore, to keep our approach computationally tractable, we replace the fission gas evolution model by a polynomial surrogate model with a reduced number of parameters, which are identified using global sensitivity analysis. We discuss the efficacy of our calibration strategy, and investigate how the contribution of the different data sets, taken from multiple sources in the literature, can be weighted in the likelihood function constructed as part of our Bayesian calibration setup, in order to account for the different number of data points in each set of data summaries. Our results indicate a good match between the calibrated diffusivity and non-stoichiometry predictions and the given data summaries. We demonstrate a good agreement between the calibrated xenon diffusivity and the established fit from Turnbull et al. (1982), indicating that the dominant uranium vacancy diffusion mechanism in the model is able to capture the trends in the data.

翻译：裂变气体的演化和释放影响UO2核燃料的性能。我们建立了一个贝叶斯框架，用于校准一个新颖的裂变气体输运模型，该模型可预测铀和氙在UO2中热平衡及辐照条件下的扩散速率。数据集取自历史上的扩散、气体释放及热力学实验。这些数据集均由汇总统计量（包括测量值及其相关不确定度）构成。我们的校准策略采用合成数据集来估计模型参数，使得模型预测结果与所报告的汇总统计量一致。通过这种方式，报告中的不确定度被有效反映在推断出的不确定性参数中。此外，为保持计算可行性，我们采用参数数量缩减的多项式代理模型替代裂变气体演化模型，并通过全局灵敏度分析确定关键参数。我们讨论了校准策略的有效性，并探究了如何通过贝叶斯校准框架中构建的似然函数，对取自文献中多个来源的不同数据集进行加权，以考虑每组数据汇总中不同数量的数据点。结果表明，校准后的扩散率及非化学计量比预测与给定数据汇总吻合良好。我们展示了校准后的氙扩散率与Turnbull等人（1982）建立的经典拟合结果高度一致，表明模型中占主导的铀空位扩散机制能够捕捉数据趋势。