# Fault Coupling Analysis and Reliability Assessment of Actuation System Based on Bond Graph Model
## 4 Fault Coupling Analysis and Reliability Assessment  
The model construction and the analysis of the fault coupling mechanism have been presented in previous sections, and the fault coupling model for the actuated system with explicit mechanism support has been formulated. In this section, the established model will be used for fault analysis and reliability assessment of the actuation system. The bond graph model in fault analysis has the advantage that it makes it simple to change the parameters of any component in the model and observe the impact of this change on the overall system, as well as the output of each component. Therefore, different types of faults will be injected by varying the correlation coefficients of the three degeneracies (wear, fatigue, and aging), and the actuator output to the rudder surface is then compared for fault coupling analysis. The fault coupling model is used to evaluate the reliability of the actuation system. When the output of the HA to the control surface is insufficient, the HA is considered to have failed to perform its job properly. At this point, the backup actuator EHA continues to work and the energy output of the HA is switched off. The output is deemed insufficient when the actuator's displacement velocity to the hydraulic rod's output is less than 0.03 m/s. Figure 6 shows the simulation results for the output of each component of the left baffle actuation system with normal parameters. The rod displacement velocity of the left baffle, the output of the HA pump source, the EHA motor, and the EHA pump are chosen separately. Simulation results following the injection wear failure are shown in Figure 7. The specific wear rate in the Archard formula is improved with respect to injection wear failure. According to previous studies on the range of specific wear rate of steel alloy materials [27], \(K/H=0.0001\) is viewed as severe wear, and the value of the specific wear rate \(K/H\) used in normal operation is 0.000013. The wear rate that is used in case of injection failure is 0.00006. Most of the wear is in the hydraulic rod and motor. The output of the HA pump source under the fault is higher than under normal conditions when the actuator is switched on because the main frictional failure occurs in the hydraulic rod. It can also be seen that the peak displacement velocity of the hydraulic rod is 0.045 m/s after the start of the EHA. The peak value is 0.05 m/s under normal conditions since the fault occurs in the hydraulic rod of the control surface, and the two rods affect the output of the EHA to the control surface during HA operation. Moreover, the injection of wear faults accelerates the degradation of the EHA motor and reduces the pump output, leading to local fault coupling. At the same time, the injection of wear faults produces more dissipative energy and leads to a global fault coupling of the system. Figure 8 shows the injection fatigue fault where the Paris formula constants \(C\) and \(M\) correspond to steel alloy materials. As the stress strength \(\Delta K\) approaches the fracture toughness \(K_{IC}\), rapid uncontrolled crack growth occurs. The fracture toughness \(K_{IC}\) of the steel alloy material is 100 [28], while the stress intensity factor \(\Delta K\) is set to 30 during normal operation and 50 during injection failure. Figure 6: Simulation results of single control surface in normal operation. Figure 7: Simulation results of single control surface in case of injection wear failure. Fatigue occurs primarily in areas with wear, namely, the rod and the motor. Compared to the simulation results under normal conditions, this is comparable to the injection of wear fault, but the fatigue fault makes the actuation system's degradation more obvious. When HA fails, the degradation of the HA pump is very small, indicating that fatigue injection leads to rapid rod degradation and, ultimately, HA failure.