## 2 PHM: Reference Methodologies, Frameworks, and Architectures
Regarding the architecture's design, in [7], a functional architecture is defined as an iterative process that consists of four steps: (1) identification and decomposition of system functions and a definition of their hierarchy; (2) identification of functional elements and interfaces; (3) the description of the functional architecture through graphic tools; (4) verification of the quality and completeness of system functions and validation of the compliance with stakeholder's requirements. The system functions defined in that study are Data Acquisition (DA), Data Processing (DP), Fault Diagnosis Assessment (FDA), Prognostic Assessment (PA), and Health Management (HM). The DA module has the capabilities of acquiring data and temporarily storing them for further analysis. The DP model includes the data manipulation and the data transmission to the next module. In the FDA module, fault detection, isolation, and identification are performed; further, a state assessment sub-function is also included, whose results are transmitted to the HM module for decision making. The PA module consists of the sub-functions of health state estimation, RUL prediction, and health assessment, whose results will also be sent to the HM module. Finally, the HM module collects and integrates the information from the outcomes of FDA and PA modules to provide recommended maintenance advisories to an external maintenance management system. From the architecture point of view, there are two common approaches for the PHM of components and systems, as illustrated in Figure 2. Both start with the data collection. Then, the first approach suggests performing the DP function, which corresponds with the extraction of relevant features, revealing different health conditions of the machinery. These features represent the input for diagnostics that correspond to the FDA function. The goal is to find the relationship between the extracted features and the health condition of the equipment. Finally, the PA function corresponds to prognostics, which deal with the degradation trend modeling for future behavior estimation and Remaining Useful Life (RUL) prediction of the machinery [4]. The second approach is similar to the first one. It includes Health Indicator (HI) construction, the Health Stage (HS) division, and the RUL prediction [25]. The HI is a monotone function that is extracted from raw signals and reveals the component degrada  
Figure 2: Existing functional architectures (application level). tion. Then, the approach suggests dividing the component's life into more HS divisions corresponding to different severity levels of the failure. Finally, the HI future values are predicted according to a pre-built degradation model; the RUL is computed as the difference between the time in which the HI is expected to overcome a pre-fixed Failure Threshold (FT) and the current time. Thus, as the authors state, the main difference between the two approaches lies in the variable time. Indeed, in the first approach, the diagnostic deals with the identification of the fault pattern and severity of machinery at a single time point, in the second approach, the HS division aims to divide the continuous degradation processes of machinery into different HSs according to the varying trends of HI in each HS. In the following sections, techniques and models for performing the DP, FDA, and PA functions are briefly reviewed. Note that these sections do not aim for a complete review of the existing literature. Rather, the aim is to describe how the PHM system functions can be performed, with a particular focus on the needed input of each technique, their strengths, weaknesses, and use cases.