# Uncertainty Analysis and Improvement of Propellant Gauging System Applied in Space
## 4 Ground Tests  
### Experiment Setup  
Figure 5 gives the schematic of the experimental setup of the ground test. From Figure 5a,b, one can see the ground test setup. There is a helium gas source of approximately 13-15 MPa, an injection bottle of approximately 1 L, a propellant tank of approximately 70 L, some valves, and pressure and temperature sensors. The volume in the ground test is chosen to be small to reduce the danger as well as reduce the cost, which is approximately 10 times smaller than the theoretical model. LV1 and LV2 are valves used in the high pressure and LV2 and LV4 are valves used in the middle pressure. Temperature sensors T1 and T2 are set in the tube at the injection bottle inlet and outlet and T4 is inside the injection bottle to monitor the injection bottle temperature. Temperature sensors T3 and T5-T13 are installed in the tank inlet tube as well as on the shelf, which is built into the tank to monitor the inner gas temperature. All the test data are analyzed with a PC. When the gas injection test was conducted, the gas injected into the injection bottle and tank is released from LV3 and LV4, which will cause the pressure to be equal to the environment. It should be mentioned that the pressure sensors are selected with ultrahigh precision at 0.04% FS and the temperature sensors are selected with a precision of 0.4% FS, while its response time to the temperature change around is 0.1 s.  
Figure 5: Experimental setup of the ground test ((a) is the schematic, and (b) is the real setup). The initial pressure before infusion in the injection bottle is set at 0.4, 0.5, and 0.6 MPa. Correspondingly, the initial pressure in the tank is set at 0.1 MPa. Figure 6 shows the process of the gas injection method during which the pressure and temperature are recorded. Based on the pressure and temperature and the true value of the tank liquid, the liquid mass gauge uncertainty is calculated. The calculated results fit well with the true value of the liquid mass in the tank, with uncertainty within 0.3% FS after gas injection (t = 0 s in Figure 6c) into the tank for approximately 330 s.  
Figure 6: _Cont._  
From the Monte Carlo simulations, the theoretical uncertainty can be 0.4% FS and the test result on the ground came to 0.4% FS. The test result and the theoretical analysis fit rather well. The reason for the slightly higher accuracy of the ground test than the theoretical result may be that the accuracy of the sensors is larger than the real accuracy sensors can obtain. For example, the pressure sensor with 0.04% FS can likely obtain 0.3% FS or less, which can reduce the final measurement uncertainty. The uncertainty is the ratio of the difference between the calculated volume and the weighed volume to the total tank volume of 70 L.  
Table 2 gives the results of the calculated uncertainties of the gas injection method with different working conditions. From the ground test results, the pressure precision improved to 0.04% FS and the temperature precision improved to 0.4% FS, which can  
Figure 6: Mass gauge process: (**a**) pressure, (**b,c**) temperature, and (**d**) calculated uncertainty. help to improve the mass gauge uncertainties to within 0.4% FS under the injection bottle pressure at 0.37 MPa\(-\)0.62 MPa. From the authors' knowledge, the usual uncertainty of traditional PVT is approximately 2-3% FS. The reported PGS method is approximately 1.6% FS applied in an FY-4 satellite. The newest uncertainty of the RFMG method applied in SHIIVER ranges from 0.5-2% FS [28]. The uncertainty of the TMG method can reach approximately 1% FS according to the ground test [22]. The 0.4% FS uncertainty of the tested adjusted PGS method is relatively high. Compared with the other methods, the adjusted PGS method can reach an ultrahigh precision for a given time. The setup of the adjusted PGS method is relatively simple. The improvement of the uncertainties of the temperature and pressure sensors in the tank can help to reduce the measurement uncertainty a great deal, from 1.6% FS [16; 17] to 0.4% FS.