Determination of Bias, Bias Uncertainty, and Coverage using Data Assimilation

摘要

Integral critical experiments, constructed in support of model validation, are employed to calculate adjustments for the nuclear cross-sections via a Bayesian Estimation approach, often referred to as Data Assimilation (DA). The premise of DA is that the adjusted cross-sections will improve the agreement between the measured and predicted responses for the integral experiments as well as other operating conditions, which have not been included in the assimilating procedure, such as hot full power reactor conditions. Although DA has been adopted in many scientific fields, its application for nuclear engineering applications in the US has been heavily debated over the past forty years. The main concern is that the adjustments are over-compensating for the unknown sources of uncertainties, often referred to as modeling uncertainties or errors. We do not intend to contribute to this debate; however we show that DA results can be used to construct biases for the model responses, e.g. performance metrics such as eigenvalue and reactivity coefficients. More importantly, uncertainties of the biases can be calculated to serve as confidence measures of their applicability at hot operating conditions. We adopt this approach because biasing code responses is a more traditional and accepted engineering practice than adjusting the basic input model parameters, such as cross-sections in neutronics calculations. Finally, we introduce a coverage metric that measures how much of the uncertainties at hot operating conditions are represented by the uncertainties captured in the cold integral experiments. If modeling uncertainties are not properly accounted for, the proposed coverage metric behaves erratically indicating potential flaw in the DA procedure.