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 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 developed in \cite{Celeux10} is extended to the latter context, then applied to a demonstration case. Finally, it is implemented on two experimental setups that differ in geometry to assess uncertainty of critical mass flow.

翻译：最佳估算模型在半经验性质上闭合热工水力系统代码的平衡方程，这被认为是导致输出预测精度不确定性的重要来源。此类不确定性称为模型不确定性，通常通过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——专门处理此问题。本文将该方法推广至多组实验场景，每组实验具有独特属性（包括不同的输入条件范围和几何结构）。因此，为每组分别估计独立的高斯分布，以探究模型不确定性在各组间是否同质，或是否应根据组别而异。为此，提出一种多组CIRCE方法，其中为每组联合估计方差参数，同时保留所有组共有的均值参数以确保最佳估算模型的唯一性。本文将文献\cite{Celeux10}中开发的基于ECME算法的极大似然估计扩展至上述背景，并应用于演示案例。最后，该方法被实施于两种几何结构不同的实验装置，以评估临界质量流的不确定性。