## 2 Materials and Methods
### Using Dynamic Bayesian Networks to Model Complex Engineering Systems
Depending on the potential accidents that may impact the CES, different accident nodes will be needed to reflect different states that may not be mutually exclusive and occur at the same time;  
Figure 3: Theoretical DBN construct that indicates the relationships between event/accident data, system information from sensor data, the overall system diagnostics, and prognostics. Additional information about each node could then be used to infer posterior estimates of the other nodes. * **System Information/Sensor Data:** CESs generate a sizable amount of data of different types and in varying frequencies. These data can take the form of sensor readings, analytical measurements, and status and maintenance reports, and can either be continuous or discrete. Since data sources are frequently updated with new system information, these are the \"dynamic\" nodes of the DBN. The classification of data into discrete bins is dependent upon the nature of the data; however, a common bin distribution would be for \"normal operating conditions\", \"above operating conditions\", and \"below operating conditions\". This region is predominantly where additional model evidence is added to the DBN, as extra information can be used to make informed decisions about the nodes in the other regions;
* **System Prognostics:** this region of the model provides insight into potential failure modes that a CES might fail from given a particular accident. These are typically distinct from other prognostics techniques, which might indicate a remaining useful life of the system; rather than indicating whether a system will be healthy or faulty at a given point in time, these nodes indicate what will be the resulting failure of the system given the current system information and data. Examples may include \"metal cladding failure\" or \"short-circuit\" and are often expressed as a binary option (i.e., \"Yes/True\" and \"No/False\"). Each failure event state should be considered as a separate node;
* **System Diagnostics:** Based on the system prognostics estimate captured in the \"System Prognostics\" region, CES health can be assessed by whether or not the system will fail from another failure mode other than expected failures at the end of its life cycle. Unlike the other nodes, this region can be fully captured in a single node with a number of mutually exclusive states; depending on the CES's structure, this approach can be used on the subsystem level as well. An easy way of expressing this is through a simple OR gate-style node for overall system health. Examples of states may include \"Healthy\", \"Faulty\", or \"Inoperable\". Following Figure 4, information about the accident state as well as system or sensor data provide information about the current system diagnostics. An understanding of the current system health in conjunction with the system measurements can be used for system prognostics to identify potential  
Figure 4: The nodes within a DBN model designed to monitor CES health following an accident event can be classified into four information regions: accident state, system information and sensor data, system prognostics, and system diagnostics. The arrows drawn between the information regions reflect the directed relationships; the model is designed so that each node is fully connected to the child information region (i.e., each “Accident State” node is fully connected to every “System Information/Sensor Data” node and every “System Prognostics” node). causes of system failure. Because of the relationship arcs connecting the four different regions within a DBN, a model structured in this manner can be used to provide diagnostics and prognostics. From the information provided by the sensor and an understanding about the accident sequences, understanding about the current health of the system can be determined. Using the time-dependent relationships of each system as well, that information can be propagated backwards to adjust understanding of the system. This will in turn adjust the current understanding.