## 4 Simulation of Shovel Force
### Material Calibration
#### 4.1.2 Parameter Calibration Based on BP NNLA  
(1) Factor analysis  
During the material stacking section, several factors influence the state of the material stacking. These factors mainly include Poisson's ratio (A), material density (B), shear modulus (C), restitution coefficient (D), static friction coefficient (E), and dynamic friction coefficient (F). Before calibration, it is necessary to analyze the sensitivities and interactions of these factors [24]. The factors' range of fluctuation is between 0.5 and 1.5 times the baseline. Factors that have a significant impact on the stacking angle are referred to as major influencing factors. The main influencing factors are selected for analysis. In Figure 6, the factor chart shows that factors E and F have significant impacts on the stacking angle. Although factor D has a smaller impact, it has a wide practical range of fluctuation. Therefore, the factors D, E, and F are chosen as the calibration factors. Figure 4: Static calibration experiment: (**a**) particle size measurement in ore samples; (**b**) repose angle measurement in ore samples. Figure 5: Dynamic calibration experiment: (**a**) GPS layout; (**b**) shoveling process. (2) Calibration of physical parameters  
Calibration is primarily divided into physical parameter calibration, density calibration, and repose-angle calibration. Physical parameter calibration requires the use of EDEM software. By means of EDEM software, density and repose angle are calibrated. For density calibration, the particle density is adjusted to the measured density [25]. Repose-angle calibration, restitution coefficient, static friction coefficient, and dynamic friction coefficient are selected as the calibration factors. The three-factor and four-level full factorial experimental design table is established, comprising a total of 64 experiments. The parameters with the smallest difference from the actual repose angle are chosen as the calibration parameters, as shown in Figure 7.  
Figure 6: Factor diagram: (**a**) primary effect diagram of repose angle; (**b**) interaction diagram of repose angle. The calibration of physical parameters includes density calibration and repose-angle calibration. The density calibration process is illustrated in Figure 7a, which indicates that the actual repose density is first obtained through experiments. Subsequently, the particle density in EDEM is adjusted to match the measured density after settling [26]. The simulation process for repose-angle calibration is depicted in Figure 7b. Using the recovery coefficient, static friction coefficient, and dynamic friction coefficient as calibration factors, the three-factor, four-level, full factorial experimental design table is established, comprising 64 sets of experiments. The parameter set with the smallest deviation from the actual repose angle is chosen for the calibrated parameters. The final particle parameters are presented in Figure 8. In the EDEM simulation process, the particle shape used is depicted in Figure 7c. When using the triple sphere, the particle more closely resembles a real ore. The annotations in Figure 7c indicate the maximum values and midpoint values in each direction within the space occupied by the particle. Figure 7: Physical parameter calibration model: (**a**) density calibration; (**b**) repose-angle calibration; (**c**) definition of material particles. (3) Mechanical Parameter Calibration  
By adjusting the parameters of the bucket and the material interaction pile, the mechanical parameters are calibrated. The parameters that conform to the rules of hydraulic cylinder force are selected as the input layer nodes of the BP NNLA model [27]. Material parameters obtained from the calibration are imported to establish the material pile model. The three-factor and three-level full factorial calibration experimental design table is established. A combined simulation model is created. Measured cylinder-displacement curves and vehicle-speed variation curves are imported into the model.