## 3 Experimental Validation of the ATF Compressor System
### Experimental Verification of Dynamic Conditions  
The real-time simulation and experimental verification of two dynamic conditions of the compressor ATF system are carried out. Figures 9 and 10 depict the physical valve actuation during the transition from gas supply preparation to active gas supply conditions in the operational system. At the beginning of the two conversion conditions, the inlet valve is less than 5% open, the exhaust valve 2# is fully opened, and the air supply valve 3# and the anti-surge valve 4# are fully closed. In the air supply preparation phase, the air supply valve 3# will be opened, the exhaust valve 2# will be closed, and the compressor gas will be transported to the downstream equipment rather than discharged to the atmosphere. After the completion of the gas supply transformation, the inlet valve is gradually opened so that the system enters the stage of high-power and high-pressure gas supply for testing, and the downstream pressure of the compressor rises to the gas supply condition. After supplying air for some time, open the exhaust valve 2# to a small opening of about 8%, and reduce the air supply valve 3# to a small opening of about 90%. The system enters the stable gas supply condition discussed in Section 3.1. Figures 9 and 10 compare the physical and virtual space real-time simulation interaction of the BPNN-MDSG digital twin model with two similar dynamic conditions. Figures 11 and 12 show the comparison between the actual and real-time simulation values of compressor flow rate, inlet pressure, and outlet pressure in the above two dynamic working conditions. The two dynamic conditions have similar results; the virtual space real-time simulation of pressure and flow is consistent with the actual value measured by the sensor, and the overall error is small. For dynamic working condition 1, as shown in Figure 9, the overall error of flow rate is 4.38%, the overall error of compressor inlet pressure is 2.35%, and the overall error of outlet pressure is 1.66%. For the dynamic working condition 2 described in Figure 10, the overall error of the flow rate is 4.57%, the overall error of the compressor inlet pressure is 2.74%, and the overall error of the outlet pressure is 1.22%. In general, under dynamic conditions, the flow error and pressure error of BPNN-MDSG compressor digital twin real-time simulation are less than 5% and 3%, respectively. Figure 11: Simulation and actual results of the BPNN-MDSG model in dynamic condition 1: (**a**) The result of the mass flow comparison. (**b**) The result of the pressure comparison. Figure 10: Valve operation data in dynamic condition 2. Under the same working condition, we found that, in the 40-60 s of working condition 1, the actual and simulated value of the compressor outlet pressure continued to rise close to 350 kPa and began to drop to about 300 kPa in the 60 s. In condition 2, after the system enters the gas supply condition, the compressor outlet pressure enters the steady state after 300 kPa. The reasons for the different maximum value and variation in compressor outlet pressure in the same dynamic working condition are discussed. This difference is mainly influenced by the pressure boundaries read by downstream devices in the actual physical system. The equipment boundary pressure in the middle and lower reaches of condition 1 is greater than that in condition 2. More specifically, the downstream equipment for the gas supply line can be viewed as a high-pressure gas source storage tank, the outlet of which is provided with a throttle valve to control the gas source pressure. In condition 1, the initial opening of the control valve is small, resulting in excessive pressure in the air source storage tank, which affects the upstream compressor pressure. In the first 60 seconds, the throttle valve of the downstream air source opens the valve and releases part of the gas to reduce the pressure, thus reducing the outlet pressure of the upstream compressor by 300 kPa.