## 4 Health Prognostics
### HS Division
#### 4.2.1 Degradation Stage  
According to the changing trend of HIs, the degradation processes of MSAE could be divided into different HSs. HS can intuitively show the degradation process of the system, which is helpful to guide the selection of RUL prediction methods. At present, there are mainly three different forms of degradation for dividing HS in most literature, namely single stage, two stages, and multi-stages, as shown in Figure 10.  
Figure 10a shows only a single gradually increasing trend from health to failure, indicating only a single HS in the degradation process. Therefore, it can be modeled with a single degradation model, and RUL prediction can be realized.  
Figure 10: Different HSs: (**a**) one stage of specific equipment and (**b**) two stages of some systems and (**c**) three stages of bearings.  
The degradation trend in Figure 10b shows two different stages, the HS at the beginning of the operation and the fault stage after a period of operation. At present, the HS of most MSAE can be divided according to this type. According to the delay time concept, [PERSON] et al. defined a two-stage fault process: steady development and rapid increase, and studied the method of identifying the starting point of defects [188]. [PERSON] et al. applied a two-stage degradation method to distinguish between health data and degraded data to avoid the interference of health data on RUL prediction accuracy [189]. [PERSON] et al. detected fault occurrence according to a two-stage alarm threshold combined with the AR model and Kalman filter [190]. [PERSON] et al. improved the accuracy of two-stage division by using the method of adaptive alarm threshold [191]. Through the division of two-stage health status, we can see that the data in the HS does not show the trend related to degradation. The fault and RUL prediction analysis shall be carried out when the system and equipment begin to fail. Therefore, a series of unnecessary modeling and calculation for the analysis of HS data can be avoided. Because of the situation, HS is used to detect the initial machinery degradation and define it as the first prediction time (FPT) to guide the start of the RUL prediction process.  
The two-stage division is only applicable to the case where the trend of machinery in the degradation stage is consistent and can be represented by a single degradation model. However, changes in operating conditions or failure modes will affect the degradation trend of machinery, so it may be necessary to further divide it into three or more HSs according to the degradation. As shown in Figure 10c, the HS is divided into three stages: health, degradation, and critical. [PERSON] et al. divided the degradation process of bearings into several different stages [192; 193]. [PERSON] et al. defined four HSs for generator bearing: excellent, good, alert, and dangerous according to the degree of deterioration [194]. [PERSON] et al. determined four different degradation stages according to the confidence value (CV) of health state and the change rate of CV and developed different prediction models according to different HSs [195]. In addition, the clustering algorithm [196; 197; 198] and the AI classification method [199; 200; 201; 202; 203] are also applicable to the division of different HSs and have achieved good results. A single model is not enough to express its degradation process when performing failure analysis and RUL prediction on equipment with three or more HSs. It is necessary to establish corresponding models according to the different degradation characteristics of each stage.