Virtual sensing by grey-box modelling within an importance sampling Monte Carlo dynamic event tree framework for risk monitoring of small modular reactors

Small Modular Reactors (SMRs) integrate advanced safety features. However, the compactness of their core design renders it difficult to position measurement devices, for operation and risk monitoring. To address this issue, we develop a Grey-Box (GB) modelling framework that ensembles White-Box (WB) physics-based and Black-Box (BB) data-driven models to enable virtual sensing of in-core safety-critical variables. The BB model is trained with condition monitoring data to perform multi-step ahead estimation of measurable variables; the estimates are fed to a physics-based WB model to estimate the non-measurable variables. The GB model developed is embedded within a risk monitoring module that builds on an Importance Sampling Monte Carlo Dynamic Event Tree (IS-MCDET) to provide the risk profile of the SMR. The method is tested on the Small Modular Dual Fluid Reactor (SMDFR), a new-generation SMR whose developed GB model for risk monitoring consists in a zero-dimensional Thermal Hydraulic (TH) WB model and a Bi-directional Long-Short Term Memory (Bi-LSTM) BB model. The developed GB model is shown to comply with the regulatory requirements and explainable response to support risk-informed decision making.