## 1 Introduction
### Literature Review  
Early research on ship system reliability analysis primarily relied on the binary state concept, where the system was either in normal operation or in a failure state [3]. Common methods, such as Fault Tree Analysis (FTA) and reliability block diagram (RBD), were used to assess the reliability of ship systems, providing valuable insights for system design and fault detection [4]. Since equipment often operates under various states, such as degraded or failure states, the binary state model cannot accurately represent the evolution of equipment reliability [5]. As a result, some scholars have adopted methods like Markov models and Generalized Generating Functions (GGFs) to assess the reliability of multi-state ship systems [6]. However, these methods have their limitations. For instance, the Markov method faces the issue of state explosion when analyzing multi-state systems with numerous components [7]. To address these issues, Bayesian networks (BNs) have been applied to the reliability analysis of lubrication systems. [PERSON] et al. [8] used Bayesian network modeling to identify weak links and propose improvements, but their inference relied on preset data, lacking real-time capabilities. [PERSON] et al. [9] combined Fault Tree Analysis (FTA) and BN to analyze the ship lubrication system, identifying key components and recommending backup monitoring, but their analysis was limited to the design phase. It could not achieve real-time inference. With the increasing complexity of industrial equipment, static Bayesian analysis methods struggle to meet the demands of real-time health monitoring. As an extension of Bayesian networks, Dynamic Bayesian Networks (DBNs) can process time-series data and capture dynamic changes in systems. DBNs not only inherit the advantages of Bayesian networks in handling uncertainty but also reduce the number of conditional probability table parameters compared to Markov models, addressing some of the state explosion issues and making them suitable for complex reliability evaluation systems [10]. Additionally, the root nodes in DBNs can be divided into multi-state nodes, which effectively describe the fault evolution of multi-state equipment and analyze the impact of different maintenance strategies on system reliability. Currently, DBN-based reliability analysis methods are widely applied in complex systems, such as train control systems and underwater drilling trees, showing promising evaluation results [11]. [PERSON] et al. [12] proposed a method for converting dynamic reliability block diagrams (DRBDs) into DBNs, demonstrating their efficient analysis capabilities for large-scale critical systems. [PERSON] et al. [13] developed a DBN-based intelligent factory health assessment model, showing excellent performance in equipment health-level prediction. In recent years, multidimensional data analysis techniques have demonstrated significant advantages in information fusion, fault pattern recognition, and condition assessment within the field of complex system fault diagnosis. [PERSON] et al. [14] proposed a multi-channel tensor fusion method, highlighting the strong coupling characteristics among multi-channel sensors--such as temperature, pressure, and oil quality analysis--in marine lubricating oil systems. Tensor-based modeling can more effectively capture high order features of system operating states, providing a feasible basis for fault identification in subsequent reliability evaluations by enabling the use of high dimensional classifiers such as tensor machines. [PERSON] et al. [15] developed an expert system for power transformer fault diagnosis based on multidimensional data fusion and factor analysis. This system achieves data fusion at the decision level and employs factor analysis to calculate fusion weights, thereby improving diagnostic accuracy. The approach was validated on a 110 kVtransformer. [PERSON] et al.