# Fault Coupling Analysis and Reliability Assessment of Actuation System Based on Bond Graph Model
## 6 Conclusions  
In this paper, we construct a dissimilar redundancy actuation system consisting of HA/EHA by using a bond graph model, aiming at the complex structure of the actuation system, multiple energy coupling shifts and transitions, and the challenge of efficiently building a degradation model for it. The fault coupling phenomena caused by the degeneration of the actuated system's components and the energy dissipation during the degeneration are presented. The fault coupling mechanism is analyzed and the three most common forms of degradation, namely, wear, fatigue, and aging, are described. The component degradation and fault coupling mechanisms of the actuation system are combined  
Figure 17: Reliability of actuation system under different injection faults.  
with the bond graph model of the actuation system using an encoding method to construct a fault coupled degradation model of the actuation system with explicit mechanism support. Through fault mechanism analysis, different types of faults are injected and the impact of fault propagation in the system on the system output is analyzed to complete the system's fault coupling analysis. The fault coupling model and three degenerate parameter distributions are used to evaluate the reliability of the actuation system.  
This paper proposes a new mechanism model of dissimilar redundancy actuation systems for MEA and incorporates the effect of dissipated energy accumulation on the degradation of the system. By injecting three different types of faults (wear, fatigue, and aging), the impact of the different faults on the actuation system's degradation is compared. The nonlinearity of fault coupling is increased by the injection of multiple faults at the same time. It is confirmed that the degeneracy of the system components is exacerbated by the fault coupling due to the accumulation of dissipated energy. Moreover, the dissipated energy will have a different effect on it due to the different distribution locations. Within the range of parameters analyzed in this paper, the fatigue faults occurring in the hydraulic rod and motor of the rudder surface have the greatest impact on the actuation system, and should be paid more attention to in practical work. In contrast to conventional approaches, this model is able to observe the degradation process of each component in the entire actuation system to analyze the cause of the system faults, and has the advantage of intuitive results and strong interpretation. The bond graph model makes the injection of different types of faults more convenient and addresses the problem that the degradation process of the system is difficult to describe due to various physical degradation mechanisms. Moreover, the mechanism model can be combined with the parameter uncertainty distribution to calculate the reliability of the system, which provides a theoretical basis for the reliability improvement of the actuation system of MEA, and further guarantees the operational safety of MEA.  
Conceptualization, Z.Z., X.L. and X.C.; methodology, Z.Z.; software, X.L.; validation, X.C. and X.L.; investigation, X.Z.; writing--original draft preparation, X.L.; writing--review and editing, Z.Z. and X.C.; supervision, Z.Z. and X.C. All authors have read and agreed to the published version of the manuscript.  
This study was co-supported by the National Key Research and Development Program of China (2022 YFF1101103) the R&D Program of Beijing Municipal Education Commission (No. KM202210011001), and the Research Foundation for Youth Scholars of Beijing Technology and Business University (QNJJ2021-35).  
The authors declare no conflict of interest.