An Efficient Metamodel-based Exploration Framework for Characterizing the Critical Failure Regions of a Nuclear Passive Safety System

Passive Safety Systems (PSSs) are increasingly employed in advanced Nuclear Power Plants (NPPs) since they are considered, in general, more reliable than active systems. Their safety performance is evaluated through computationally expensive Thermal-Hydraulic (T-H) simulations models and the identification of the operational conditions which lead to unsafe conditions (the so-called Critical failure Regions, CRs) may be challenging. In this view, the computationally expensive T-H models simulating the PSSs behavior can be replaced by fast-running surrogate models (also called metamodels), coupled with adaptive sampling techniques for speeding up the exploration and efficiently focusing the analysis on the most interesting regions of the domain, i.e., the CRs boundary (limit surface). However, when the PSS state-space also shows a non-smooth and/or multimodal nature, even the previously mentioned metamodel-based approaches may not suffice. In such cases, suitable techniques, like Finite Mixture Models (FMMs) or clustering methods, should be sought and effectively combined to tackle these issues. In the present thesis, a passive Decay Heat Removal (DHR) system of a NPP is considered and its CRs are characterized with respect to two safety-critical variables of interest (used to evaluate the success of the PSS operation): the amount of energy exchanged by the PSS and the maximum pressure value reached inside the pressure vessel. A time-demanding Best-Estimate Thermal-Hydraulic (BE-TH) code is employed to simulate the PSS operation. In the analysis of the energy exchanged, which shows a smooth trend, the well-known Adaptive Kriging Monte Carlo Sampling (AK-MCS) is employed. This methodology is based on a fast-running Kriging regression model, iteratively constructed and progressively refined in proximity of the PSS CR boundary by means of an adaptive sampling technique. The results show that a satisfactory level of accuracy (estimation error around 2%) can be reached with less than 200 BE-TH.simulations. Thus, the Kriging metamodel can be exploited to accurately explore the CRs in few minutes, instead of directly using the BE-TH which takes some hours for each simulation. On the other side, in the analysis of the maximum vessel pressure, which shows a non-smooth and multimodal behavior, a novel methodological framework is proposed, combining Finite Mixture Models (FMMs) and AK-MCS. In particular, 1) FMMs are employed to reduce the dimensionality of the non-smooth and multimodal PSS state-space, while identifying “prototypical clusters” of PSS functional failure configurations; 2) a metamodel (namely, AK-MCS) is adaptively trained on the reduced space to mimic the time-demanding T-H model; and, finally, 3) the trained metamodel is used to evaluate new PSS configurations and retrieve information about CRs. Finally, a comparison with an alternative approach of literature based on the use of a classifier to cluster the output domain is presented to support the framework as a valid approach in challenging CRs characterization. The results show that the FMM-based framework allows overcoming the issue of PSS state-space non-smoothness and multimodality, indeed, a satisfactory metamodel accuracy (estimation error < 0.5%) is reached with only 300 BE-TH simulations. Moreover, the proposed framework always outperforms the alternative technique with the classifier if an equal number of BE-TH simulations is used.