## 4 Health Prognostics
### Rul
#### 4.3.1 Degradation Model  
The physical degradation model simulates the degradation process through the nominal life model. The general application depends on the model understanding of the physical process and potential system degradation characteristics [153, 213]. The empirical degradation model is a data-driven model for statistical analysis through a large number of monitoring data. The advantages and disadvantages of these two methods are summarized and analyzed below.  
(1) Physical Degradation Models  
Based on the physical degradation model, the RUL prediction method needs to consider the different operation modes and environmental conditions. The physical meaning of equipment degradation and professional theory were used to create failure mode, which is employed to estimate the RUL [117, 152, 227]. When using this method, it is vital to understand the fundamental physical model of the system for calculating the damage rate and its accumulation process over time. The physical degradation model could obtain higher accuracy RUL prediction results when the equipment is relatively simple, and the degradation is caused by a single degradation factor.  
The common prediction based on the physical model is crack propagation modeling. [PERSON] et al. used lognormal random variables to establish a random defect propagation model based on the deterministic defect propagation rate model for RUL prediction [228]. [PERSON] et al. employed a physical model method based on Paris law to predict the residual life of gear fatigue cracks [229]. [PERSON] et al. established a detailed physical model of a centrifugal pump to describe its degradation process [230]. [PERSON] et al. established a life model based on the Forman crack propagation law of linear elastic fracture mechanics for machine RUL prediction [231].  
The main advantage of this method is to realize the RUL prediction from the dynamics of the equipment degradation mechanism. If the model parameters have a one-to-one mapping relationship with physical coefficients, better degradation description and accurate prediction results could be obtained [94]. Nevertheless, the degradation models vary with equipment or systems, so the application of the method is limited. The modeling process also involves much professional knowledge, and it may be necessary to use assumptions and expert knowledge when describing the operation process and estimating parameters. In addition, mathematical models are usually expressed by complex differential equations or partial differential equations, which require a powerful computational solver and high computational cost [224]. Moreover, the difference of internal materials, the complexity and diversity of the external working environment, and the interaction of various components result in difficulty fully understanding the actual physical process of degradation and es  
Figure 11: Summary of RUL prediction methods.  
tablishing an accurate physical model for RUL prediction [232; 233; 234; 235]. Therefore, the physical degradation model is mainly used for RUL prediction modeling of simple equipment such as fan, bearing, and pump in the practical application of MSAE.