System-level Modelling of Liquid Metal Loop using Time Series Analysis and Network Graph Laplacian

Operation and maintenance costs for nuclear reactors are high due to requirements for time-intensive operational checklists and procedures associated with start-up, shutdown, and power level changes. These O&M costs can be greatly reduced if these processes are automated using imaging and sensory information. Live monitoring of nuclear reactors using various sensors is vital to the understanding of plant behavior and adequate risk assessment. Time series analysis of a time signal or coupled time signals at a single location can be used to characterize various physical phenomena at that specific location. Nuclear reactors are complex plants, consisting of many interconnected components, where phenomena in one component can impact various behavior in all other components. It is for this reason that an accurate understanding of plant phenomena relies on a solid understanding of the connectivity of various components and the sensor signals at various locations within the plant. An accurate model which captures the connectivity between the spatial locations of the plant transients is necessary to accurately model various phenomena within the entire reactor. Graph theory, specifically network graph Laplacians, can be used along with probabilistic time series analysis to accurately model the interconnectivity of various reactor components, and the impact that one signal has on another. To validate this method, an established, scaled, liquid metal experimental loop using gallium as a surrogate fluid is modelled and validated using COMSOL, a commercial computational fluid dynamics (CFD) software. The CFD model is then used to generate thermal-hydraulic data signals at various spatial locations throughout the loop. The inter-connectivity of these points is described using the network graph Laplacian, which describes each point in the loop as a node, and then comprises a weighted matrix of connections between each of these nodes. The graph Laplacian and corresponding nodal sensing data is then used to train a kernel, which can inform the impact of various phenomena at one location in the plant on phenomena at other locations in the plant. The sensing data and graph network of these nodes are used to construct a surrogate model of the liquid metal loop. This model is then used to predict the behavior at certain nodes where the sensing data is not provided to the model. This predicted flow behavior is then validated against the provided CFD data. When provided sensing data from an actual reactor, this surrogate model can be used to provide a probabilistic framework for risk assessment and can be further be used for sensor optimization and global autonomous control of a reactor.