## 4 Simulation Conditions and Procedures  
### Measurement of the Bulk Material Distribution  
The traditional dynamic model of belt conveyor assumes that the bulk materials are uniformly distributed, without considering the influence of the non-uniform distribution of bulk materials. The non-uniform bulk material distribution model is obtained by integrating the instantaneous bulk material flow cross section, and the accuracy is higher than that of the traditional uniform distribution model.  
Experimental measurements have been used to verify the correctness and accuracy of the measurement system of the non-uniform bulk material distribution (Figure 8). The materials for the measurement is iron ore powder (bulk density \(\rho\), 2980 kg/m\({}^{3}\)) which provided by Wuhan Iron & Steel (group) Corp. To measure the distribution of the iron ore powder on the moving belt, constant speeds of 0.5 m/s, 1.0 m/s, and 1.5 m/s were selected as suitable values, which were controlled by using the frequency converter in the control cabinet. A spherical cap was used to calibrate the spatial coordinates captured by the measurement system. After that, the perpendicular distance and horizontal width of the adjustable bracket were set 583 mm and 820 mm respectively. The resolution of the laser scanner was set 10 mm/\(\pm\)35 mm over a typical range of 30 m. Next, experiments were performed as the iron ore powder was poured on the belt artificially in three flow rates of 2.971 kg/s (1 L/s), 8.911 kg/s (3 L/s), and 14.853 kg/s (5 L/s) from the guild chute. Standard volumes of 1 L, 3 L, 5 L were used to verify the volumes measured by the measurement system. The triangular area accumulation method [48] was used to calculate the cross-sectional area of iron ore powder. Then, the measured data of instantaneous iron ore powder distribution with a flow rate of 8.911 kg/s (3L/s) at a stable speed of 1.0 m/s are shown in Figure 9.  
The original data curve in Figure 9 shows that the transient iron ore powder distribution fluctuates violently. Due to the high resolution of the laser scanner, the non-uniform bulk material distribution model can better reflect the real state of bulk material transportation. However, the violently fluctuation of original data may affect the measurement of real logistics morphology. Therefore, a mean filter is adopted to smooth the original data. Through experimentation, the average of every 30 frames is smoother than every 15 frames. For verification, 9 sets of measurements had been designed to obtain non-uniform iron ore powder distribution. Every 8 measurement values from 10 measurements corresponding to the same level standard flow rate of iron ore power were recorded after removing the maximum and minimum values. Table 2 shows the repeated measurements corresponding to standard volumes at three speeds of the belt and their repeatability. The average error between the laser measurement and the artificial measurement is within 3%. The repeatability and correlation (_RPT_) are more than 98%. In addition, the variation coefficient (CV) of the measurement value at different speeds is less than 2%, which means that the belt speed has a small influence on the measurement results. In the subsequent dynamic simulation test, the non-uniform bulk material distributions on  
Figure 8: Experimental measurements of the non-uniform iron ore powder distribution. (**a**) Iron ore powder in standard volume was poured on the belt artificially. (**b**) The fitting of iron powder cross-section in real-time.  
Figure 9: The measured data of instantaneous non-uniform iron ore powder distribution with a flow rate of 8.911 kg/s (3L/s) at a stable speed of 1.0 m/s.  
belt, which are used for establishing the discrete model of the belt conveyor system, can be obtained from this measurement system.