# Fault Coupling Analysis and Reliability Assessment of Actuation System Based on Bond Graph Model
## 4 Fault Coupling Analysis and Reliability Assessment
After switching to EHA, the rod speed did not reach 0.05 m/s in normal operation, but rather dropped to 0.04 m/s, indicating that fatigue caused the rod to degrade. Even if the actuator is switched, the rod acting on the control surface is shared, so the normal output cannot be obtained after the switch. Moreover, fatigue failure causes more energy dissipation, which results in fault coupling. The velocity of the rod can only reach 0.04 m/s when the EHA is at work. Figure 9 shows the result of injection aging failure. In the injection of an aging fault, the parameter \(A_{0}\) of the Arrhenius equation is changed. As more leakage results from the injection of aging faults, it can be seen that the degradation of the HA pump source and EHA hydraulic pump is more obvious than it would be under normal operation conditions, because aging faults lead to an increase in dissipated energy, forming the system's global fault coupling, and the motor degradation rate is faster than the normal result. The above three types of degradation, namely, wear, fatigue, and aging, are injected into the faults separately, and the output of each component in the single control surface is compared and analyzed with the results of normal operation. The output displacement velocities of the seven rods in the overall actuation system will then be observed, and the effect of different fault injections on the actuation system will be compared. This will result in a fault coupling analysis of the actuation system. Figure 10 shows the simulation results for the seven control surface outputs when the actuation system parameters are normal, corresponding to the seven rod speeds, namely, right aileron, right spoiler, left spoiler, left aileron, rudder, right elevator, and left elevator  
Figure 8: Simulation results of single control surface under injection fatigue failure. As can be seen from the results, the first failure of the rudder HA in Figure 9 leads to the switching of the EHA. This is mainly because the rudder is in the center and suffers the most from dissipated energy, so the degradation is most severe. It can be seen that under the influence of field energy composed of dissipated energy, the rudder surface and actuator close to the center of the actuation system will be affected more, and the accumulated energy dissipation in its space will be more, which will eventually lead to the occurrence of fault coupling and make its degradation more serious. In contrast, the fault phenomenon will appear in advance. Figure 10: Seven control surface rod displacement speed operation results under normal operation. Figure 9: Simulation results of single control surface under injection aging failure. As different types of faults are injected, the actuator operation is affected in various degrees. Figures 11-13 correspond to the actuation system output to the seven control surfaces during the injection of wear, fatigue, and aging faults, respectively. The injection of these faults results in the failure time of HA being advanced by 24.8%, 52.5%, and 12.5% in the actuation system, respectively. The occurrence of fatigue faults has the greatest impact on the actuator's operation, resulting in its failure. Figures 14 and 15 correspond to the results of the injection of three kinds of faults at the same time. Three axes represent key coefficients of three kinds of faults, respectively: specific wear rate \(K/H\), stress factor intensity \(\Delta K\), and pre-exponential factor \(A_{0}\) of the Arrhenius equation. Use color variations to indicate failure times under different conditions. The selection range of the three degradation parameters of wear, fatigue, and aging is consistent with the above mentioned in this section. From the right side of Figure 14, it can be seen that as the fatigue parameter gradually approaches 50 from 30, the color in the figure changes to blue, indicating that the failure time is getting shorter and all blue areas in the figure are concentrated on the right.