## 4 Case Study
### Results and Discussion  
In order to further demonstrate and validate the proposed method, RVM [23] and LSTM [29] were selected as comparison methods in this section. As shown in Figure 12, H1 is the prediction result obtained by the proposed method. H2 is realized by the LSTM prediction method. H3 uses the RVM method to build a reconstruction model to realize prediction.  
Figure 11: Change of system health condition for interference state.  
Figure 10: Hybrid prediction of system health condition.  
It can be seen from the prediction curve that the prediction time is within 500 h, and the three methods can achieve good prediction results. With the increase of prediction time, H2 and H3 deviate greatly from real life (after 1000 h). The method proposed in this paper can better extract the changes of characteristic data, and the prediction result T1 (5262 h) is closer to the real value (5300 h). According to Equation (16), the \(RMSE\) values used to measure the prediction effects of the different prediction methods can be obtained--the results were shown in Figure 13. From TTS to 500 h after the health condition prediction, the three methods could be used, and the error was relatively small. After 500 h, the prediction deviation was obviously large, and after 1000 h, the prediction result showed a large deviation. Through the evaluation index \(RMSE\), it could be seen that the proposed method had high prediction accuracy throughout the whole process.  
When predicting the health condition of a complex ship mechanical system, if the prediction time is too long, it will be affected by the internal and external uncertainties of the system, and the prediction result will be far from real life (as shown in T2 in Figure 11). The use of dynamically updating training data to track the health condition could achieve better prediction results. For the autonomous ship, the port mode was adopted for maintenance.  
Figure 12: Prediction effect of different methods.  
Figure 13: Comparison of prediction accuracy of different methods.  
In other words, in most cases, the whole lifecycle of a ship's system or equipment does not need to be predicted. According to the voyage and port characteristics, the phased prediction was made. As long as there was enough margin in the current voyage, it could meet the needs of unmanned navigation. If the voyage operation time is \(T\) (at present, the requirement for unmanned ships is \(T>500\)) hours, it is only necessary to predict the health of the system and make sure that its work could be guaranteed within these hours. In this way, advance maintenance or a specific port maintenance plan could be made according to the health allowance.  
For a high-reliability ship mechanical system, equipment self-healing and switching would greatly affect the life of the system. The integration method proposed in this paper can dynamically extract SHI according to the changes of data features and describe the health condition of the system more accurately. At the same time, the prediction process realizes adaptive prediction by decomposing SHI and using a hybrid prediction method, and the prediction result is closer to the real system health condition.