## 2 PHM: Reference Methodologies, Frameworks, and Architectures
### Prognostic Assessment Function  
Prognostics concerns the future behavior of a system and aims to anticipate the occurrence of a failure and predict its Remaining Useful Life (RUL). The RUL is a measure of the time left before machinery loses its operational ability and serves to avoid undesired or even catastrophic consequences. Prognostics can be conducted at three levels [69]: existing failure mode prognostics, future failure mode prognostics, and post-action prognostics. At the first level, the RUL and its confidence limits are computed for each failure mode identified in the previous diagnostics step. At the second level, interactions between different failure modes are considered and models describing such secondary failures are developed to build the worst-case scenario for the component under analysis. At the third level, relationships between the developed models and the maintenance actions that have been/could be undertaken to prevent failures are evaluated.  
The degradation process identification and the RUL estimation are carried out by resorting to three approaches: physics-based, data-driven, and hybrid.  
Physics-based approaches build mathematical models that quantitatively describe the degradation process based on failure mechanisms or first principles of damage. They use the CM data to identify model parameters and predict future behavior. The fundamental hypothesis of this approach is the existence of a physical model describing the degradation evolution. If so, then the future behavior is determined by progressing the degradation model in the future.  
Data-driven approaches only rely on historical data collected by sensors to identify the degradation evolution and predict the future trend. These approaches build mathematical models, whose coefficients are estimated and updated based on the training data (previous usage conditions), that represent the relationships between input variables (the HI) and the output (the degradation state). The prediction is based on the estimated coefficients and the mathematical model. Data-driven models for prognostics can be classified into statistical and stochastic models [70, 71], such as the Wiener Process [72] and Markov models [73], Machine Learning models, such as ANNs [74] and SVM [75], and Deep Learning models [76].  
The main advantage of physic-based approaches lies in the direct physical meaning of the model output. They outperform data-driven models, since they achieve highly accurate RUL estimation, especially for long-term predictions [77]. Although data-driven models are easy and fast to implement, they heavily depend on the availability of a large amount of robust data. In addition, a huge storage capacity is required, and the correlation between the extrapolated trend and a specific failure is not guaranteed [78]. The obtained results from data-driven models are not easy to interpret since they are not related to any physical phenomena and are usually less precise and more computationally expensive than physics-based models. On the other hand, physics-based models are hard to build, especially for complex systems.  
Hybrid approaches combine physics-based models and data-driven models, improving prediction accuracy. Furthermore, hybrid approaches guarantee a reliable prognostic at both component and system levels. A review on typical hybrid approaches for prognostics and RUL prediction can be found in [79].