# Deep Learning-Based Estimation of Muckpile Fragmentation Using Simulated 3D Point Cloud Data
## 4 Simulation-Based Learning Data Generation  
### Creation of Muckpile CG Model  
The generation of the muckpile CG model was carried out using simulation. As shown in Figure 7, a large number of muckpile CG models were generated by automatically repeating these procedures:  
(a)  
In step (a), the particle size distribution of the muckpile CG model to be generated was set as shown in Figure 9. Here, the particle size distribution was changed randomly within the range of [2.36, 4.76, 9.5, 19, 26.5, 37.5, 53, 75] (mm) from 0 mm to 80 mm in 8 stages, allowing the generation of muckpile with various particle size distributions. Figure 8: Example of Particle-size Distribution. Figure 9: Particle Size Distribution of CG Muckpile. Next, in step (b), a rock CG model was randomly selected from 18 different shaped rock CG models, and in step (c), the rocks were scaled according to the 8-stage particle size distribution set in step (a) ranging from 0 mm to 80 mm, [2.36, 4.76, 9.5, 19, 26.5, 37.5, 53, 75] (mm). In order to generate a more faithful muckpile CG model, actual rock CG models obtained by 3D scanning were used for the rocks, and mesh division was performed on the rocks by vertices, edges, and faces to accurately perform scaling of rock sizes and collision detection during free fall. Figure 10 shows a rock CG model with mesh division, which is divided into multiple polygons. The particle size of the rock CG model was determined by the length when a Bounding-Box was applied. The Bounding-Box used the values calculated by Oriented Bounding-Box as the particle size, as shown in Figure 11. First, the 3D covariance matrix was calculated from the mesh vertex coordinates of the rock CG model, and the eigenvalues were calculated. When the eigenvectors are sorted in descending order of eigenvalues as \(e_{1}\), \(e_{2}\), and \(e_{3}\), they become the first, second, and third principal components, respectively, and form an orthonormal basis. The Bounding-Box is set with these axes. The length is determined by calculating the difference between the vertex with the maximum value and the vertex with the minimum value for each axis. Considering the situation in which a rock passes through the sieve mesh in measurements using a sieve, the size of the second axis was used as the particle size of the rock 3D CG model. After that, by repeating steps (b) and (c), a large number of rock groups were generated, and in step (d), the rocks were placed in mid-air in the simulation, and in step (e), the rocks were freely dropped to form the muckpile CG model. The process of rock CG models accumulating and forming the muckpile CG model is shown in Figure 12. Figure 12a shows the rock CG models being generated in mid-air. The green-framed board shown here is a board that repels when a rock CG model collides with it, and four slanted boards and a cylindrical board were placed to accumulate the rock CG models around the center. In Figure 12b, the falling rock CG models are shown forming the muckpile CG model while colliding with the board. In this way, the formation of the muckpile CG model as shown in Figure 12c was performed. Figure 11: OBB: Oriented Bounding-Box. Figure 10: Segmentation by Mesh. In addition, when dropping the rock CG models, the physical calculations based on the parameters shown in Table 1 were applied. Dynamic Friction is the friction coefficient for moving objects, and Static Friction represents the friction coefficient used for stationary objects. Both of these friction coefficients were set to 0.9 in order to make all the rock CG models used in this experiment accumulate. These two friction coefficients are used with values ranging from 0 to 1. In the case of 0, the object does not stop, like on ice, and in the case of 1, the object does not move unless a strong force or gravity is applied to it. Bounciness indicates how much elasticity is on the surface, and in this experiment, the purpose was to accumulate, so it was set to 0.1.