# Optimizing Retention Bunkers in Copper Mines with Numerical Methods and Gradient Descent
## 5 Discussion  
The observed discrepancy between the simulated and measured values, specifically the broader range of variation in simulated values (from 500 kN down to 275 kN) compared  
Figure 14: Parameters of the optimized bin operation: (**a**) load on the bin drawer, (**b**) retention bunker filling, (**c**) bin capacity, and (**d**) average particle velocity on the bin drawer. Figure 13: Ore flow in the optimized receiving bin in the EDEM environment. to the relatively constant measured range (from 425 kN to 500 kN), can be attributed to several factors inherent in the DEM simulation. These may include model simplifications, assumptions regarding material properties, and the method used to represent the complex interactions and behaviors of copper ore particles within the bin. The constancy of measured values over a larger timescale and under conditions of significant decrease in the filling of the retention bunker suggests that the real-world system may exhibit buffering or compensatory mechanisms that are not fully captured or accurately represented in the simulation model. This could be due to the dynamic nature of ore flow and the feeder's response to varying load conditions, which may not be fully accounted for in the simulation parameters. To address this discrepancy and better match the measured values, we are considering several adjustments to the simulation parameters. These include refining the material properties of the copper ore (such as particle size distribution, shape, friction, and cohesion), improving the representation of the feeder and retention bunker geometry, and incorporating more dynamic feedback mechanisms that mimic the real-world system's response to changing conditions. Assuming that the simulation error is the same for all experiments, it is indeed possible to directly compare the results for the purpose of optimization, which has been accomplished in this article. The analysis of data from various response surfaces allowed us to draw significant conclusions about the factors influencing the operation of the receiving bin. It was found that the two independent factors having the greatest impact on the force exerted on the bin's drawer \(F\) are the length of the drawer \(L\) and the surface area of the bin's outlet opening \(S\). Another important aspect is the velocity of particles \(v\) on the surface of the drawer, which is primarily determined by the frequency of the drawer's movement \(f\). This works in conjunction with the surface area of the bin's outlet opening \(S\) to collectively influence the capacity \(Q\) of the receiving bin. Among other independent factors, it was observed that the angle of inclination of the drawer \(\beta\) has some effect on the force exerted \(F\), but its significance is not statistically important at the established level of confidence. Among all the factors analyzed, offset of the retention bunker axis \(d\) showed the least influence on the studied responses. In Table 6, the primary and optimized values of the independent factors, as well as the responses obtained for them, are compiled. The results obtained from the optimization algorithm are promising. To minimize the pressure force \(F\) on the drawer surface, it proved optimal to significantly reduce its length \(L\) and to maximize the offset of the receiving bin relative to the retention bunker's axis \(d\). The achieved reduction in force \(F\) results from shortening the length of the receiving bin drawer \(L\), which allowed for a reduction in its mass. Consequently, less material accumulates on the drawer, and the pressure exerted by the column of material is decreased, due to the concurrent shortening of the bin's feed chute from the retention bunker side. As a result, a smaller amount of material rests on the rear part of the drawer. The offset of the receiving bin relative to the retention bunker's axis \(d\) likely had a beneficial effect on altering the interactions between ore grains.