## 3 Experimental Validation of the ATF Compressor System  
To verify the reliability of the BPNN-MDSG model of digital twin technology, an ATF compressor simulation system is developed. The BPNN-MDSG's digital twin model is based on actual physical devices, including compressors, complex pipe networks, valves, as well as pressure, temperature, flow sensors, and computers that transmit and store data. A virtual system for the thermodynamic performance simulation of the ATF compressor system is obtained by using the BPNN-MDSG model. There are digital twin data, such as sensor data, control data, real-time simulation data, and historical data, to realize interaction between actual physical devices and virtual systems. Figure 4: The BPNN prediction and the actual performance curve. Figure 5 shows the details of the compressor unit in the actual ATF system and the thermal parameter transfer of the corresponding virtual digital system. The ATF system is composed of dozens of structurally similar gas supply and gas extraction compression units. The compressor units can operate in series, parallel, or a combination of both simultaneously. Through the coordinated operation of multiple units, the pressures of the main supply pipeline and the main exhaust pipeline are stabilized within the target range, such as 180 kPa for the supply pipeline and 30 kPa for the exhaust pipeline. In addition, the system also includes multiple auxiliary components such as cooling modules, drying modules, and refrigeration systems. When conducting the high-altitude environment simulation test, multiple units are required to work together to ensure that the temperature and pressure inside the high-altitude test chamber reach the target high-altitude environment conditions. The core component of the ATF system is the compressor unit. Therefore, in this paper, a typical single compressor unit is taken as an example to introduce and verify the aforementioned modeling method. The typical ATF compressor unit is shown in Figure 5, consisting of one compressor, four valves, and two sections of pipeline network. The compressor is a centrifugal compressor with a constant speed at 5876 rpm, with a designed flow rate of 80 kg/s and a working pressure ratio of 2.2-3.4. The blue curve in Figure 4 is the pressure ratio performance curve obtained through testing. The valves in the system are butterfly valves. Valve 1# serves as the inlet valve, with its upstream connected to the atmosphere and a diameter of 1.6 m. Valve 2# functions as the waste gas valve, discharging exhaust gases to the atmosphere downstream with a diameter of 1.0 m. Valve 3# operates as the air supply valve, connecting to the downstream air chamber at its outlet with a diameter of 1 m. Valve 4# is designated the anti-surge valve, primarily controlling recirculation flow with a diameter of 0.45 m. Sensors are installed at the compressor inlet and outlet to obtain flow and pressure during operation. Temperature sensors are installed in the pipelines before and after the compressor. Their measurement range is \(-50\)\({}^{\circ}\)C to \(250\)\({}^{\circ}\)C. Typical accuracy was \(\pm 0.1\)\({}^{\circ}\)C within this range. Sensor signals are conditioned and digitized. Data was acquired at a frequency of 0.125 s (8 Hz). This ensured adequate temporal resolution for transient analysis. In the ATF compressor system shown in Figure 5, the inlet and outlet temperatures of the compressor are related to the ambient temperature. As in the experiments of this section, the atmospheric temperature is 15 \({}^{\circ}\)C, and the atmospheric pressure is 95.8 kPa. The range of the imported temperature collected is [9, 18.1]\({}^{\circ}\)C, and the range of the compressor outlet temperature is [151.1, 193]\({}^{\circ}\)C. During the simulation in the digital twin space, the environmental temperature is taken as the input. At the same time, the thermal physical property parameters of the gas in REFPROPM are called in real time.