# A Performance Prediction Method Utilizing Time-Dependent Subsystem Transfers between Family Systems
## 7 Conclusions  
To tackle the challenges of limited reference samples, initial failures, and complex environmental variables in reliability engineering for newly developed or implemented complex systems, this paper proposes a cluster system performance prediction method based on time-varying inter-family transitions through clustering within the cluster system and utilizing state partitioning and Markov transitions. The proposed approach is validated using monitoring data from the hydraulic actuator of the FAST radio telescope health monitoring system, with the absolute error of the actuator as the key performance parameter. The results demonstrate that the proposed cluster system performance prediction method in this study, based on time-varying inter-family transfer, can accurately forecast the failure transfer of hydraulic actuators with a fitting accuracy of 0.9906. These research findings offer scientific guidance for the operation, maintenance, and health management of the FAST hydraulic actuator cluster system to ensure precise observations using the FAST radio telescope. The method of predicting the performance of cluster systems based on time-varying inter-family transfer can also be applied to numerous hydraulic engineering projects, particularly those involving cluster systems. This method is applicable to the prediction of hydraulic system maintenance, optimization of energy efficiency, monitoring the health condition of the system, optimization of working conditions, and fault diagnosis. Moreover, future investigations can be conducted based on this study to explore multi-dimensional key performance parameters in inter-family transfer, providing support for safe and reliable operation, fault prediction, data processing, and operational maintenance of complex systems. The health monitoring system of the FAST radio telescope serves as a highly representative example, showcasing the integration of mechatronics in a typical group system. The remarkable accuracy achieved in predicting its lifespan demonstrates the applicability of this method for performance prediction in similar mechatronics integrated systems. Therefore, these research methods can be employed for system and application design, encompassing hydraulic system monitoring and prediction platforms, maintenance management systems for hydraulic systems, energy-efficient optimization controllers, health monitoring programs for hydraulic systems, working condition optimization tools, fault diagnosis systems, etc. The integration of these systems and applications will offer comprehensive solutions for hydraulic engineering--from real-time monitoring to performance prediction, maintenance, and optimization--thereby enhancing the reliability of hydraulic systems while reducing maintenance costs and ensuring efficient operation under diverse working conditions. Conceptualization, W.C.; methodology, W.C.; software, R.G. ; validation, J.W. ; formal analysis, J.Z. ; investigation, M.Z. ; resources, W.C.; data curation, Z.L. ; writing--original draft preparation, Z.L. ; writing--review and editing, W.C.; visualization, Z.L. ; supervision, J.Z. ; project administration, R.G. ; funding acquisition, W.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 12173054, 52075469; the Open fund of Shanxi Key Laboratory of Hydraulic Technology, grant number YYJS2022 KF12; the Young Elite Scientists Sponsorship Program by CAST, grant number 2023 QNRC001; and the Open Foundation of Key Laboratory of Space Launching Site Reliability Technology, grant number sys-2021-03-3. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The data present in this study are available on request from the corresponding author. The data are not publicly available due to privacy.