## 2 Materials and Methods
### Case Study: Transient Overpower Event (TOP) in a Sodium Fast Reactor (SFR)
#### 2.3.2 DBN Construction  
For this study, a simplified model was constructed to cover the primary elements of the SFR that are relevant for scramming failures in the event of a transient overpower. As previously mentioned, automatic scram action occurs when the power-to-flow ratio, the reactor's inlet and outlet temperature, or overall reactor pressure are measured above a certain threshold. Designing a DBN model to help operators identify current system health status and potential failure modes, as shown in Figure 5, therefore requires nodes in the accident state, system and sensor information, system diagnostics, and system prognostics information regions. The temporal loops included for the system information nodes (Power-to-flow, Pressure, Inlet and Outlet Temperature) indicate a distinct dependency on previous parameter values, unlike the other nodes which have static conditional probabilities (i.e., a prediction of the current scram state is not dependent upon the scram state prediction from a previous measurement). This model's conditional probability tables are trained with operational data provided from scenarios that resulted in three distinct outcomes: failure due to clad melting; failure due to thermal relocation; and a successful model outcome. The model's objective is identifying the current health state of the reactor as well as the likelihood of a certain outcome based on current data from the system's sensors. Data received from the system will be used as evidence for an improved determination of the state of the reactor's scram and trip mechanism. The DBN model is constructed using the GeNIE software; conditional probability table (CPT) elements are calculated using the Python programming language. As CESs generate a multitude of data, there are large amounts of readily available data that can be used to inform the model's quantification of the conditional probability tables. The information provided for this model was carried out in multiple simulations over different time period measurements. For example, nuclear reactor data from the SAS4A-SASSYS-1 code was collected more rapidly at the beginning of the accident simulation, at a rate of 0.1 simulation seconds, and slowed down to a collection frequency of 100 s. On the other hand, new information from the PRIMAR4 code was provided approximately every nine seconds. This is similar to real-world scenarios in which measurements and sensor readings occur over different frequencies. As such, operators are dealing with a mixture of newer and older information and need to consider these respectively. In order to capture as much relevant information as possible, an operational timeline was created to consolidate both model readings into one sequence of events. As illustrated in Figure 6, relevant information was identified from both models. The available data were then sorted based on the simulation time at which the data were received. When new data were acquired from a sensor, that entry would replace the measurement from the previous timing; however, the \"current\" information from other system sensors would remain as new data have not yet been provided. Using the simulated data generated from the reactor and infrastructure models, a sample set of conditional probability tables, which reflects how the health of the nuclear reactor system progresses over time, was quantified. The CPTs provide insight into the transformation of the different nodes across the model and describe the causal relationships within the nodes. For this DBN structure, there are three types of CPT that are reflective of different structures in the nodes: static CPTs for the static nodes and initialization and temporal CPTs for the dynamic nodes.