## 1 Introduction  
The newest generation of artificial intelligence technology has promoted the process of ship autonomy and unmanned operation. Ship mechanical systems should make full use of new technology to achieve scientific O&M based on improving safety, reliability, and efficiency [1; 2]. The main research focus of ship O&M includes all-round state perception, real-time condition monitoring and evaluation, health condition prognostics, independent decision-making [3], and other technologies. More and more academic researchers and O&M engineers have been involved in machinery failure prognostics. For single-component equipment, some research has shown that incorporating prognostic information helps make more reasonable O&M decisions [4; 5]. Modern merchant vessels are complex systems constructed from numerous subsystems, with equipment and components provided by multiple different suppliers and integrated by a shipyard. There are often one or more types of economic, structural, and stochastic interactions between components. Intelligent O&M usually needs to consider the whole-system health condition in order to optimize system-level and even plant-level decision making [6; 7; 8]. The existence of these interdependencies makes the single-equipment prognostic model no longer applicable. At present, system-level failure prediction mainly includes two main problems, one is to establish a suitable SHI that can accurately describe the health condition of the system, the other is to select an appropriate prediction method according to the HI to realize the failure prediction [8]. Ship systems are complex mechanical systems designed to complete specific functions and lack the dominant physical characteristics which can directly represent their health condition. Therefore, it is necessary to use all kinds of sensor data to extract valuable data. Thus, the concept of a health indicator (HI) is introduced. A suitable HI is expected to simplify prognostic modeling and produce accurate prediction results. [PERSON] et al. (2019) use the improved radar chart method for constructing a system HI to produce the system condition evaluation. [PERSON] et al. (2019) employ composite HI to realize complex systems RUL prediction based on condition-monitoring signals. Through these HI construction methods, the multi-dimensional data from the sensors is defined as a virtual SHI that may be able to describe the health condition of a system. For ship mechanical systems, the construction of physical HIs is relatively complex, so virtual SHIs are the best choice. Some researchers constructed virtual SHIs based on principal-component analysis (PCA) ([PERSON] et al., 2019; [PERSON] et al., 2020), self-organizing maps ([PERSON] et al., 2019), Mahalanobis distance ([PERSON] et al., 2019), and stacked autoencoders (SAE) ([PERSON] et al., 2020). SAE is an effective unsupervised, feature-extraction network, which is very suitable for adaptive and online extraction of HI in multi-parameter systems ([PERSON] et al., 2020; [PERSON] et al., 2020). In addition, the degradation of ship mechanical systems includes at least three phenomena: global degradation, local self-healing, and other noise. Due to the coupling of multiple signals of SHI, it is unrealistic to directly select the prediction method to realize the prediction. Therefore, in order to improve the prediction accuracy, it is necessary to decompose the SHI to separate the degradation trend from fluctuations. Empirical mode decomposition (EMD) and variational mode decomposition (VMD) are often used in decomposition algorithms ([PERSON] et al., 2019; [PERSON] et al., 2020). The VMD could specify the number of decompositions according to the understanding of the physical process to reduce the complexity of the prediction. After signal decomposition, different prediction methods could be chosen according to different signals with the goal of realizing hybrid prediction.