# Fault Coupling Analysis and Reliability Assessment of Actuation System Based on Bond Graph Model
## 1 Introduction  
In recent years, the more electrical aircraft (MEA) actuation system has rapidly grown to support the development of ecological civilization and promote a low-carbon and environmentally friendly lifestyle. The power-by-wire (PBW) technology flight control system has gradually replaced the conventional hydraulic system due to easy leakage, low efficiency, and complex pipeline, among other reasons. Modern MEA gradually unifies the secondary energy into electrical energy, effectively improving the fuel economy, reliability, and maintenance of the aircraft [1; 2]. For instance, the most common universal aircraft Gulfstream 650 uses a hydraulic actuator (HA)/electro-hydrostatic actuator (EHA) in dissimilar redundancy actuation systems. The actuation system of the large aircraft Airbus A380 features a 2E/2H redundancy design to improve aircraft reliability and reduce fuel consumption [3]. Scholars have given considerable attention to the study of MEA actuation systems in recent years due to the wide range of applications of multi-electric technologies in the aviation industry. Various studies have been carried out to improve the reliability of actuation systems by optimizing their design and control. In the study from [PERSON] et al. [4], a hydraulic energy recovery EHA system has been proposed, which can effectively reduce motor heating and minimize failure rate. [PERSON] et al. [5] designed a high-speed permanent magnet synchronous motor used in EHA to optimize the driving motor of EHA, enhance its heat dissipation performance, and reduce loss. [PERSON] et al. [6] designed an active load-sensitive EHA and achieved high dynamic performance through proportional integral derivative (PID) control while reducing motor heating and improving actuation system reliability. An aircraft actuation system is a very complex electromechanical system that includes electrical, mechanical, and hydraulic energy, as well as other energy transfers and transformations. Operationally, wear, aging, fatigue, and other degradations can cause an actuationsystem failure, affecting the safe operation of the aircraft. Therefore, to ensure its safety in addition to improving its reliability in design and optimization, fault analysis, reliability evaluation, and other studies must be carried out. Fault analysis and reliability assessment of actuation systems require the construction of a corresponding model. With the rapid development of artificial intelligence, data-driven research methods for complex electromechanical systems have been rapidly developed. Operational data of the system components are normally collected through sensors. Using deep learning and other methods to determine the relationships between input and output data, system operation prediction, as well as fault diagnosis and analysis can be achieved. Deep learning is used in some studies to investigate the degradation failure of EHA [7; 8]. [PERSON] et al. [9] proposed a fault tree method for hydraulic systems failure analysis in case of incomplete data. [PERSON] et al. [10] used particle swarm optimization to optimize the fusion convolutional neural network for fault diagnosis of EHA. [PERSON] et al. [11] analyzed the degradation mechanism of EHA, developed a physics-based long short-term memory (LSTM) degradation model, and predicted the degradation of EHA. However, while this data-driven approach can identify the operational rules of complex systems through data without any prior knowledge, it requires a large amount of complete operational data as support and the data collection cost is typically high. When data collection is difficult, it can be a choice to establish a physical mechanism model to describe the degradation process of the system. [PERSON] et al. [12] proposed a reliability assessment method using the physics of failure (POF) model for key power electronic components. [PERSON] et al.