## 2 Materials and Methods  
The use of sensors to monitor the health of strategic system components has led to an increase in the availability of data regarding the system's current performance. These data have the potential to provide diagnostic information about the current health of the overall system, as well as a prognostic assessment of the future state of the system given its current health status. Understanding the current and potential future health states of a system allows its operators and maintainers to make more informed critical operating or maintenance decisions to prolong a system's operating life before it loses critical functionality. This is a priority for systems that are mission-critical, expensive to repair or replace from a failed state, or pose a safety risk to humans and other associated systems if not fully operable. This process of converting data and expert knowledge from CESs into informed diagnostic and prognostic decisions is illustrated in Figure 1.  
Previous PHM research has focused predominantly on smaller components and subsystems. This is in part due to the increased availability of life data for these smaller systems. Additionally, it is easier to assume independence when identifying potential interactions that lead to system or component failure. These prognostic techniques often rely on data coming from a single sensor or sensor type. In his literature review, [PERSON] [2] states that there are three categories for the different approaches to  
Figure 1: Modeling complex engineering systems (CESs), such as power plants and large maritime vessels, with causal-based models such as dynamic Bayesian networks, provides system operators and maintainers improved diagnostic and prognostic awareness. This causal knowledge about the system is particularly important following an accident event when action is needed to mitigate system damage and loss of functionality. converting system data into a future system health assessment: data-driven, expert-based (often in the form of a physics-based relationship), or a hybrid compilation of the two. Monitoring CES health, however, is more difficult. These systems have multiple integrated hardware, software, and human components functioning together. The subsystems within the platform provide a complicated network of dependencies and common-cause failures. Data from a single data sensor is not sufficient for providing an accurate depiction of system health, and, as a result, prognostic techniques for complex systems require the fusion of data of various types and sources. In their work, [PERSON] et al. [3] found that data fusion in prognostics takes place in three different approaches based on the data, features, and decisions. Despite these challenges, PHM is an important capability for system operations as many of these CESs are critical to maintain, costly, and potentially harmful if not functioning correctly. This is shown by [PERSON] et al. [4] as their prognosis model was designed to support large industrial maintenance. Because of the additional hurdles associated with the system health monitoring of complex engineering systems, there have been many different approaches towards generating PHM for complex engineering systems (PACES). An initial approach was identifying relationships within the subsystems and expanding them to the system level. [PERSON] and [PERSON] [5] modeled the reliability of complex systems with an object-oriented approach. Over time, PHM strategies continued to incorporate more data from various sources [6]. In 2020, [PERSON] et al. [7] created a systematic methodology for defining and designing PHM for aircraft maintenance. While some methods rely on machine learning to take advantage of the large amount of system data available, others adopt a fundamentally different tactic relying on expert knowledge. For example, [PERSON] and [PERSON] [8] approached dynamic failure scenarios through fuzzy on-line estimations of the remaining useful life (RUL) of nuclear plants.