A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System

In the safety analyses of passive systems for nuclear energy applications, computationally demanding models can be substituted by fast-running surrogate models coupled with adaptive sampling techniques; for speeding up the exploration of the components and system state-space and the characterization of the conditions leading to failure (i.e., the system Critical failure Regions, CRs). However, in some cases of non-smoothness and multimodality of the state-space, the existing approaches do not suffice. In this paper, we propose a novel methodological framework, based on Finite Mixture Models (FMMs) and Adaptive Kriging (AK-MCS) for CRs characterization in case of non-smoothness and/or multimodality of the output. The framework contains three main steps: 1) dimensionality reduction through FMMs to tackle the output non-smoothness and multimodality, while focusing on its clusters defining the system failure; 2) adaptive training (AK-MCS) of the metamodel on the reduced space to mimic the time-demanding model and, finally, 3) use of the trained metamodel provide the output for new input combinations and retrieve information about the CRs.