## 4 Case Study
### System Failure Prognostics  
#### 4.2.1 System Health Prediction Based on Degradation  
When the system was in normal production operation, the function of the system was mainly affected by the state of the filter. After cleaning, the system recovered some function, and the health state was characterized by local self-healing. According to the TTS setting method, when the health value reached the trigger condition, the training samples were constructed, and the prediction end point was set according to the threshold. Data set A was selected to verify the effectiveness of the method. The calculation steps of the health condition prediction were as follows:  
(1) A dynamic feature extraction algorithm was used to achieve feature extraction. The system presented different state features in the life cycle, so the dynamic feature extraction algorithm could capture the dynamic features of the system more accurately to represent the health state. DKPCA was used to extract the features of the data, and the calculation steps were as follows. Step 1: The size of the data matrix was limited. According to the analysis requirements for the operation of the unmanned ship (>500 h), the matrix size had to be larger than the unmanned running time, so the number of samples was selected as \(N=520\), and the data matrix was \(X\in R^{520\times 9}\). To reduce the impact of the data amplitude differences, the matrix needed to be standardized. Step 2: According to experimental experience, the selected value of the interval time is 1 (\(\Delta=1\)). Then Equations (1)-(3) were applied to obtain the lag time \(l_{opt}=3\) of the reconstruction matrix, and the reconstruction matrix was \(\widetilde{X}\in R^{(N-3)\times 36}\). Using Equation (4) to obtain the mapping data matrix gives \(G_{N_{D}}=\left\{ \begin{matrix}k\\ l\end{matrix} \right\}_{k=1}^{N_{D}}\). Step 3: After obtaining the mapping matrix, the \(\lambda^{p}\geq 10^{-5}\)\(p=1,2,3\ldots,N_{D}\) condition was applied to filter \(G_{N_{D}}\), and the matrix \(G_{p}\) was obtained. Step 4: The correlation dimension was used to solve the number of principal components of the matrix. The result is shown in Figure 7. It can be seen from the figure that the number of pivotal elements of the data in different time periods of the data was constantly changing, and this was not unique. As depicted in Figure 7, the 13 features could describe the system state in the initial state. When the system fluctuated, the number of features increased to 14. With the system state in the transition processes, the number of features varied from 12 to 13. Finally, when the system was in the late degradation stage the number of features was stable at 13. Different mapping matrices \(G_{\gamma}\) were constructed according to the principal components shown in Figure 7. These matrices contained the dynamic structure of the original data that could effectively reduce the influence of the cross-correlation between the data on the analysis results, which was beneficial to the construction of the SHI. Figure 7: The number of features varying with time. (2) SHI construction  
Suitable fuel usually includes pressure, viscosity, and flow to meet the functional requirements of a main engine. During the working process, the viscosity was affected by the state of the HE, so this parameter was used as the characteristic parameter to describe the health condition of the system. The flow rate was mainly affected by the power of the main engine, which could be reflected by the pressure characteristics. Therefore, the main engine fuel oil inlet pressure could be used as the functional indicator of the system to judge whether the system SHI met the function requirements. The SHIs of different feature fusion methods are shown in Figure 8. H1 was directly obtained with the PCA method [12], H2 was constructed by the proposed SAE fusion method. The number of network layers was 3, and the number of neurons in each network was 4, 4, and 1.