The semi-empirical nature of best-estimate models closing the balance equations of thermal-hydraulic (TH) system codes is well-known as a significant source of uncertainty for accuracy of output predictions. This uncertainty, called model uncertainty, is usually represented by multiplicative (log-)Gaussian variables whose estimation requires solving an inverse problem based on a set of adequately chosen real experiments. One method from the TH field, called CIRCE, addresses it. We present in the paper a generalization of this method to several groups of experiments each having their own properties, including different ranges for input conditions and different geometries. An individual (log-)Gaussian distribution is therefore estimated for each group in order to investigate whether the model uncertainty is homogeneous between the groups, or should depend on the group. To this end, a multi-group CIRCE is proposed where a variance parameter is estimated for each group jointly to a mean parameter common to all the groups to preserve the uniqueness of the best-estimate model. The ECME algorithm for Maximum Likelihood Estimation is adapted to the latter context, then applied to relevant demonstration cases. Finally, it is tested on a practical case to assess the uncertainty of critical mass flow assuming two groups due to the difference of geometry between the experimental setups.

翻译：最佳估算模型封闭热工水力系统代码平衡方程的半经验性质，是导致输出预测精度存在显著不确定性的公认原因。这种称为模型不确定性的不确定性，通常由乘性（对数）高斯变量表示，其估计需要基于一组适当选择的真实实验求解逆问题。来自热工水力领域的一种方法——CIRCE——可解决此问题。本文将该方法推广至多组实验场景，每组实验具有自身特性，包括不同的输入条件范围和不同几何构型。因此，对每一组分别估计独立的（对数）高斯分布，以探究模型不确定性在组间是否具有同质性，抑或应随组别变化。为此，提出多组CIRCE方法，其中为每组联合估计方差参数，并设置所有组共有的均值参数以保持最佳估算模型的唯一性。针对该新情境调整了用于极大似然估计的ECME算法，并将其应用于相关演示案例。最后，将该方法应用于实际案例：假设因实验装置几何构型差异而分为两组，评估临界质量流的不确定性。