## 3 Results and Discussion
### Center-of-Gravity Coordinates Calculation  
The center-of-gravity coordinates of sample 1# calculated by the program and marked are shown in Figure 14a. The center of gravity G and center of form C of the material did not coincide. Two holes were drilled at positions A and B in the figure for rope suspension. The center of gravity measured and determined by the rope suspension method is shown in Figure 14b, the measurement static data are shown in Table 9. Comparing the distances from the center of gravity to hole A and hole B by calculation with those by the actual rope suspension method, the error was about 3.5%. As shown in the above experimental results, the DE-XRT shading of low-energy as an important discriminant parameter can reduce the influence of fan-shaped effect, cross-talk noise and X-ray source noise on identification to a certain extent, and can judge overexposure and underexposure. The mean shading of low-energy of the material can be used to judge and select the overall overexposed materials and underexposed \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Material** & \(\mathbf{\beta_{1}}\) & \(\mathbf{\beta_{2}}\) & \(\mathbf{\beta_{3}}\) & \(\mathbf{\beta_{4}}\) & \(\mathbf{\beta_{5}}\) & \(\mathbf{\beta_{6}}\) & **RMSE** \\ \hline Mg & 0.808 & \(-9.353\) & 0.230 & 0.011 & 62.377 & \(1.057\times 10^{-4}\) & 0.731 \\ Al & 0.441 & \(-2.443\) & 0.015 & \(8.812\times 10^{-3}\) & 36.290 & \(-5.329\times 10^{-5}\) & 0.279 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Thickness calibration surface coefficients. Figure 14: (**a**) Calculation mark of center of gravity and center of form; (**b**) Measuring the center-of-gravity with rope Scheme 9. Center-of-gravity calculation and measurement. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample No.** & **Mass of Calculation (g)** & **Mass of Measurement (g)** & **Error (\%)** \\ \hline
1\# & 171.12 & 163.81 & 4.46 \\
2\# & 152.54 & 145.68 & 4.71 \\
5\# & NA & 52.57 & NA \\
6\# & NA & 48.74 & NA \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Mass calculation. materials, both of which are difficult to identify under certain conditions. The selected effective points within the material range according to the shading threshold, combined with comparison of the R_value mean distance with the R_value calibration surface of \(S_{L}\)-\(x\)-\(R\), can identify the material, reduce the fan-shaped effect caused by the DE-XRT point X-ray source and improve the identification accuracy. The overall laboratory sample identification accuracy by count basis was 85%, and the identification accuracy of heavy and light metals reached 100%, which was good enough for the DE-XRT without other sensor fusion. The material mass and the center-of-gravity coordinates could be calculated combining the material identification with the integral calculation method of the \(S_{L}\)-\(x\)-\(t\) thickness calibration surface, which is beneficial for the separation of identified materials and control of falling point distance by the gas-ejection method with variable gas pressure and/or action time. Therefore, it is possible to realize the automatic sorting of many kinds of bulk materials by DE-XRT at one time, and sorting quality and efficiency will be improved. Taking non-ferrous metal sorting throughput as an example, it is estimated at 50 ton/h with our method and it would increase accordingly when belt line width and line speed are both increased. The method in this paper could make identification more accurate and refined, compared with security inspections limited to qualitative classification for explosives and non-explosives (see References [23; 24; 25]). It is simpler and easier to apply than the SQP algorithm in Reference [20], and does not need equipment parameters, such as accurate detection probability, accumulation factor, photon number, etc., which are usually difficult to obtain. It is featured by an identification accuracy equivalent to that of Delft University of Technology [5], but does not need to be equipped with sensors such as EMS.