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. The framework is applied to the case study of a generic Passive Safety System (PSS) for Decay Heat Removal (DHR) designed for advanced Nuclear Power Plants (NPPs). The PSS operation is modelled through a time-demanding Thermal-Hydraulic (T-H) model and the pressure selected for characterizing the PSS response to accidental conditions shows a strong non-smooth and multimodal behavior. A comparison with an alternative approach of literature relying on the use of Support Vector Classifier (SVC) to cluster the output domain is presented to support the framework as a valid approach in challenging CRs characterization.