Passive systems failure probability estimation by the meta-AK-IS² algorithm

Highlights: • Many future nuclear reactor concepts rely on passive safety systems. • Uncertainties in physical behavior may give rise to functional failures. • Passive system failures are rare events difficult to estimate by crude Monte Carlo. • We propose a kriging-based importance sampling for estimating failure probabilities. • We compare the results with other variance reduction-based methods of literature. - Abstract: Simplicity of design and independence from external inputs make passive safety systems very attractive both from the economical and safety points of view, for the development of future nuclear reactor concepts. On the other hand, concerns arise due to the not fully understood physical phenomena underlying their (passive) functioning and the scarce operating experience to characterize them, which can give rise to functional failures due to deviations from their modeled, expected behavior. The estimation of the probabilities of these failures requires the propagation of uncertainties in the passive systems functions models, which can be done by classical, crude Monte Carlo schemes. However, the passive system design is such that failure is a rare event, which renders these approaches often impractical due to the computational efforts involved in the repetition of runs of the computer codes numerically encoding the system model. In order to overcome this problem, in this paper we propose to apply the meta-AK-IS² algorithm, previously introduced by the authors for obtaining improved computational efficiencies by coupling a kriging-based metamodel to an MC-based importance sampling strategy. The method is developed and demonstrated with reference to a case study of a natural convection-based cooling system of a gas-cooled fast reactor, operating under a post-loss-of-coolant accident (LOCA). A comparison is made with respect to other variance reduction-based methods of literature