## 1 Introduction  
The Altitude Test Facility (ATF) compressor system is an important piece of equipment for high-altitude environment simulation tests [1, 2]. The system is composed of a centrifugal compressor, pipe network, and valve. The compressor system can transport, compress, and heat up the gas to meet the needs of different altitude conditions. As the main rotating machinery in the ATF system, the compressor system consumes a huge proportion of electric energy [3, 4]. In the context of energy conservation and the implementation of a dual-carbon policy, higher requirements are put forward for ATF compressor systems. Therefore, it makes sense to develop a more energy-efficient ATF compressor system with higher performance and enhanced security. Based on the above requirements, scientific problems such as the structural optimization design of ATF compressor systems, risk avoidance, and intelligent improvement in the process flow are addressed based on research on the thermodynamic, control, and stability characteristics of ATF compressor systems. However, the nonlinear thermodynamic system of the ATF compressor, characterized by a high degree of coupling, a complex structure, and many parameters, presents challenges when studying its characteristics [5]. The utilization of digital twin technology is widely acknowledged as a dependable approach to address the investigation of intricate systems [6]. Efficient execution can be achieved in prediction, simulation, monitoring, inspection, and design studies. In digital twin technology, a key core technology is the multi-scale, efficient, and accurate modeling method. Therefore, the research focus of this paper is to obtain a high-precision, dynamic, and accurate surge modeling method for ATF compressor systems under complex conditions. The digital twin creates a virtual model of a physical entity using digital methods, enabling the simulation of its behavior in the real environment through data analysis. It further enhances the capabilities of the physical entity by facilitating interactive feedback between virtual and real domains, a fusion analysis of data, the iterative optimization of decisions, and other techniques [7]. The concept of the digital twin was first proposed by Professor [PERSON] [8] in the Product Lifecycle Management course at the University of Michigan and is defined as a three-dimensional model, including physical products, virtual products, and the connection between them. In a review, [PERSON] et al. [9] expounded on the developmental prospects, technical challenges, and application modes of digital twin technology. They further expanded upon [PERSON] three-dimensional concept of digital twins to encompass five dimensions: physical entity, virtual model, twin data, virtual representation, and connection relationships. Digital twin technology has achieved some achievements in the fields of real-time data acquisition theory [10], human-computer interaction [11], structure damage monitoring [12], real-time operational state detection [13], fault location [14], and so on. A methodology design using model-driven engineering (MDE) is proposed by [PERSON] that strives toward being both flexible and generic [15]. The interaction effect between real space and virtual space is verified using a practical industrial example. The research on digital twin modeling technology for compressor systems primarily focuses on optimizing the efficiency of computational fluid dynamics (CFD). [PERSON] et al. [16] conducted a high-performance parallel simulation study on the flow mechanism generated by the rotational stall of a multi-stage axial compressor in real gas turbines. Digital twin technology has been widely adopted in recent years; however, there is a dearth of research on the modeling method for predicting the dynamic characteristics of compressor complex systems. The ATF compressor system is a complex thermodynamic system.