# Optimizing Retention Bunkers in Copper Mines with Numerical Methods and Gradient Descent
## 1 Introduction
They enable modeling of the particle flow, predicting stresses on elements interacting with particles, determining the degree of energy dispersion, and describing the segregation process [21]. The latter process, especially, is extensively analyzed due to various material flow variants in chutes [22; 23]. In this research work [24], it was shown that the conveyor element and chute are more susceptible to wear with larger particle sizes, and the wear of the receiving belt is accelerated with a decrease in its speed. Previous research results show that the wear, stress, and accumulated contact energy of the transfer point chute are closely related to the belt speed, the angle of the chute's inclination, and the type of granular materials [25]. In other studies [26], it has been proven that the angle of inclination and the height of the transfer point in the transfer chute directly affect the speed and trajectory of the falling material, which in turn has a significant impact on the wear of both the chute and the conveyor belt. The geometry and type of deflector, as well as the number of shelves in the chute, determine the direction of material flow and its speed, which directly affects wear patterns and material transfer efficiency. Additionally, the physical properties of the transported material, such as the shape and size of particles, influence local changes in flow and material speed, which also significantly affects the wear of the chute and conveyor belt. Appropriate manipulation of parameter ranges in numerical modeling also allows minimizing fluctuations in power consumption of devices and ensuring adequate system throughput [27]. A detailed qualitative and quantitative analysis of operational issues with the receiving bin is presented in the paper [5]. The most frequent type of damage was abrasive wear of the top layer of steel elements in contact with the flowing material. Elements such as the vertical seals, the lining of the bin drawer, and the lining of the front wall of the receiving bin were most susceptible to abrasive wear. Different algorithms are used to optimize the operating parameters of transfer points. In the work [28], the authors utilized the E-SVR Surrogate Model for results obtained through numerical simulation in the EDEM environment. The sole aim of the research was to minimize the maximum forces during the impact of falling material on the belt. In another study [29], the authors used raw results of numerical simulations to optimize the design parameters of a scraper conveyor, based mainly on the obtained correlations. It is also possible to forecast wear and the impact of external factors on wear using regression methods, as was performed in a study [30] where the Plackett-Burman method was utilized. It is also common practice to rely on appropriate wear models [31], where results from numerical simulations or evolutionary models based on purely theoretical assumptions are used. The main issue with most conducted research is that the analysis is performed within a very narrow range of variability in design or operational parameters, and methods based on optimization through simple correlation analysis do not always provide clear results. Considering all the presented research results, a clear conclusion can be formulated that for the design of transfer points, including those related to retention bunker receiving bins, the main factors influencing an accelerated degradation process are the force of the material pressing on the structural elements and the velocity of ore particle flow. The results of these studies unequivocally suggest that both changes in design and operational parameters may reduce wear in conveyor transfer point chutes and similar steel structures. Therefore, these assumptions can be implemented for the optimization of dosing devices. The main goal of this article is to limit the impact of ore mass on the device's structure and reduce the material flow speed to improve wear parameters while ensuring optimal performance of the receiving bin.