Artificial neural network surrogate development of equivalence models for nuclear data uncertainty propagation in scenario studies

Scenario studies simulate the whole fuel cycle over a period of time, fromextraction of natural resources to geological storage. Through the comparison of different reactor fleet evolutions and fuel management options, they constitute a decision-making support. Consequently uncertainty propagation studies, which are necessary to assess the robustness of the studies, are strategic. Amongnumerous types ofphysicalmodel in scenario computation that generate uncertainty, the equivalence models, built for calculating fresh fuel enrichment (for instance plutonium content in PWR MOX) so as to be representative of nominal fuel behavior, are very important. The equivalence condition is generally formulated in terms of end-of-cycle mean core reactivity. As this results from a physical computation, it is therefore associated with an uncertainty. A state-of-the-art of equivalence models is exposed and discussed. It is shown that the existing equivalent models implemented in scenario codes, such as COSI6, are not suited to uncertainty propagation computation, for the following reasons: (i) existing analytical models neglect irradiation, whichhasa strongimpactonthe resultandits uncertainty; (ii) current black-boxmodels are not suited to cross-section perturbations management; and (iii) models based on transport and depletion codes are too time-consuming for stochastic uncertainty propagation. Anewtype of equivalencemodel based on Artificial Neural Networks (ANN) has been developed, constructed with data calculated with neutron transport and depletion codes. Themodel inputs are the fresh fuel isotopy, the irradiation parameters (burnup, core fractionation, etc.), cross-sections perturbations and the equivalence criterion (for instance the core target reactivity inpcmat the end of the irradiation cycle). The model output is the fresh fuel content such that target reactivity is reached at the end of the irradiation cycle. Those models are built and then tested on databases calculated with APOLLO2 (for thermal spectra) and ERANOS (for fast spectra) reference deterministic transport codes. A short preliminary uncertainty propagation and ranking study is then performed for each equivalence models.