# A Performance Prediction Method Utilizing Time-Dependent Subsystem Transfers between Family Systems
However, in practical applications, datasets often exhibit certain correlations, which pose challenges for comprehensive modeling using the aforementioned research methods and result in biased prediction outcomes. To address this issue, [PERSON] et al. employed high-dimensional space mapping for Gaussian mixture clustering to enhance data resolution accuracy when dealing with datasets characterized by significant feature differences, strong nonlinearity, and large volumes of data [29]. Experimental results demonstrate that, compared to the K-means algorithm [30] and GMN algorithm [31], high-dimensional space clustering algorithms can effectively resolve reduced clustering accuracy caused by multi-class data overlap in the original low-dimensional space while simultaneously improving clustering accuracy and reducing false positive rates. For newly constructed or recently implemented complex systems lacking sufficient fault probability and cumulative experience, the aforementioned methods face challenges in providing effective solutions. To address this issue, [PERSON] et al. proposed the establishment of a continuous-time Markov model for equipment and employed the uniform acceleration technique to solve reliability parameters, thereby achieving a reliable prediction for large-scale traction power supply equipment. This approach successfully overcomes the limitations of traditional matrix geometric methods when dealing with problems involving large quantities, enabling efficient and accurate reliability prediction for similar large-scale traction power supply equipment [32]. [PERSON] et al., on the other hand, utilized the spectral SESCD [33] analysis method to extract feature vectors from test data and combined it with the continuous hidden Markov model (CHMM) [34] classification method to achieve the precise prediction of rolling bearing faults. Their work presents a novel approach towards rolling bearing life diagnosis [35]. However, these studies lack feature recognition and the clustering of data within the system and they necessitate a substantial amount of high-quality sample data to support model construction and prediction. Consequently, in the absence of reference samples, it becomes unfeasible to accomplish model building and prediction, thereby impacting the accuracy of predictions. Therefore, this paper proposes a method for predicting hydraulic actuator group system performance, based on time-varying inter-family transitions usingmonitoring data from a specific observation period in FAST. Expanding upon conventional Markov process research, this approach forecasts changes in performance trends by employing family system division and transition matrix calculations [36]. The comparison between predicted results and actual data demonstrates a significant level of concordance for the proposed method, providing a foundation for the health management of hydraulic actuator group systems, as well as for similar systems. The structure of the paper is summarized as follows: In Section 2, the characteristics of complex systems and the applicability of traditional performance prediction methods are discussed. Section 3 introduces the concept of cluster and family subsystems, along with a method for establishing family systems. In Section 4, a transfer matrix between subsystems in the family system is established using Markov processes in the time domain. Section 5 presents the transfer matrix and performance prediction method for cluster systems. To validate the proposed method, an engineering example from the FAST telescope is calculated in Section 6. Finally, the conclusion section, Section 7, summarizes the process of performance prediction for cluster systems based on time-varying inter-family transitions and verifies the accuracy of the predictions. It also suggests that further research can be conducted on inter-family transition prediction methods based on the proposed method in this article, providing support for operating and maintaining complex systems.