Comparison of Critical Benchmark Experiment Similarity and Dissimilarity Measures in Application

Critical benchmark experiments are important basis for validation of nuclear criticality calculations, criticality safety assessment, validation of neutron transport methods and nuclear data validation. At present, there are about 5 000 critical benchmark experiments in ICSBEP handbook. In applications such as validation of nuclear criticality calculations and critical safety assessment, critical benchmark experiments are generally selected according to the characteristics of the nuclear assembly to be validated. With the development of sensitivity & uncertainty analysis methods, critical benchmark experiments suitable for specific applications can be selected according to the similarity of their sensitivity vectors. Several similarity and dissimilarity measures have been proposed to be used to assess the similarity or dissimilarity between two critical benchmark experiments. However, there is no clear criterion to choose which similarity measure or dissimilarity measure to be used in specific application. Three parts of work were done to provide recommendations for selecting similarity or dissimilarity measures in applications. First, a brief analysis was conducted on the similarity and dissimilarity measures of the critical benchmark experiments which were used widely, and their preliminary numerical characteristics and physical meanings were obtained. The similarity and dissimilarity measures were analyzed include E, G, C, Euclidean distance, and nuclear data covariance weighted Euclidean distance (F). Second, the above similarity and dissimilarity measures were applied in hypothetical examples to demonstrate the characteristics of these similarity and dissimilarity measures. Finally, these similarity and dissimilarity measures were applied in the Pu-Met-Fast classification of critical benchmark experiments in ICSBEP handbook, and the reasons for their different performances were analyzed. Based on the analysis, the similarity or dissimilarity measures used in specific application were recommended. There are significant differences in the results between similarity or dissimilarity measures that use nuclear data covariance as weights (C and F) and similarity or dissimilarity measures that do not use nuclear data covariance (E, G and Euclidean distance). The main reason is that when using the nuclear data covariance as weights, the influence of the cross sections with large uncertainty will be highlighted. In validations of nuclear data, and in applications where nuclear data is the main source of uncertainty, it is recommended to use measures weighted by nuclear data covariance. When measuring the intrinsic similarity between two critical benchmark experiments, it is recommended to use a measure that does not use nuclear data covariance as a weight. It is recommended to use F dissimilarity measure in measures weighted by nuclear data covariance. The main reason is that the F similarity measure has a clear physical meaning, which can measure the difference between the calculated biases of two critical benchmark experiments. For measures that do not use nuclear data covariance as weights, it is recommended to use Euclidean distance, and its physical meaning is also clear. The E similarity measure only measures the similarity between two experiments through the angle between the sensitivity vectors, which performs poorly in some examples and is not recommended.