# A Performance Prediction Method Utilizing Time-Dependent Subsystem Transfers between Family Systems
## 6 Examples of Verification
### FAST Performance Prediction  
The 500 m Aperture Spherical Radio Telescope (FAST) project is a major national scientific foundation project. It is a large spherical coronal radio telescope with an active reflecting surface and an aperture of 500 m. The FAST active reflecting surface system functions as a co-driving parallel mechanism, comprising a main cable network, 2225 sets of driving branches, and 4450 reflecting surface units. Each driving branch consists of nodes, lower cables, and hydraulic actuators [54]. Consequently, the FAST active reflector system exhibits intricate motion coupling relationships. In the event of failure in one or multiple driving branches, it will have adverse implications on the structural strength and reflector accuracy of adjacent areas, thereby affecting the scientific observation capabilities of the telescope [55]. The hydraulic actuator cluster system serves as the driving unit for actively adjusting the surface shape accuracy of FAST's active reflection surfaces, making it a crucial component for normal telescope operation. Moreover, it represents a rare and typical local large-scale electromechanical and hydraulic integrated equipment cluster system in the world. Predicting its lifespan and economically maintaining this equipment cluster system present significant challenges to the engineering and technical community. Figure 2 illustrates the on-site distribution of the FAST hydraulic actuator cluster system. Figure 2: Hydraulic actuator cluster system of FAST. In order to ensure the scientific accuracy of observations, reliable operation, and cost-effective maintenance of the FAST radio telescope, a health monitoring system was implemented at the outset of its design [56]. Table 1 displays the observation data content captured by the actuator. In Table 1, DEVICE ID is the number representing the actuators. CONTROL THEORY is the theoretical control position of the actuators, while CONTROL ACTUAL is the actual position of actuators detected by the position sensor in the health system of FAST. CONTROL TEMPERATURE and CONTROL PRESSURE are the temperature and pressure of hydraulic oil in the tank of the actuators' hydraulic system. According to the structure and observation control of the FAST telescope, each hydraulic actuator operates independently from other hydraulic actuators in both temporal and spatial dimensions. In other words, the failure of one actuator will not impact the normal functioning of the other actuators. Consequently, a parallel reliability logic relationship exists among subsystems within the hydraulic actuator cluster system. The failure of any individual actuator will not directly lead to failures in other actuators or hinder scientific observations; however, it may result in signal loss and affect observation accuracy. The precision of actuator control directly impacts the shape of the target reflection surface in the FAST hydraulic actuator cluster system, thereby significantly influencing scientific observation. Each actuator is assigned a theoretical position based on the observation requirements for achieving the desired reflection surface shape. Simultaneously, a real-time monitoring system continuously tracks and monitors the actual positions of each actuator. Therefore, both the theoretical and actual positions of the actuators are critical parameters for optimizing performance in the actuator cluster system. To facilitate analysis, absolute error is employed as a discriminant parameter to classify family systems prior to conducting life prediction. The calculation formula for absolute error is as follows:  
\[\Delta d=|d_{\text{a}}-d_{\text{t}}| \tag{15}\]  
Here, \(\Delta d\) is the absolute error, \(d_{\text{a}}\) represents the actual position, and \(d_{\text{t}}\) is the theoretical position.