A rapid stacking method for the ball element DDA model of ballast specimens and the stacked model

Abstract

The present invention relates to a rapid stacking method for a ball element DDA model of a ballast specimen. When the method of the present invention first conducts a stacking simulation on newly input ballast particles, the ballast particles located in the lower layer are temporarily deleted, and only one layer of ballast particles on the surface that may come into contact with the newly input ballast particles is used for contact judgment; thereafter, the random iteration method is used to narrow down the range and find the landing points of the ballast particles. In the method of the present invention, by simplifying the existing particles, the time required for particle contact judgment is reduced, and the efficiency of contact judgment is improved; the bisection method is used to calculate the particle potential energy, providing a basis for the reasonable position of the particles in the specimen; the random iteration is used to gradually narrow down the range, and the position of the ballast particles is repeatedly fine-tuned, so that the position of the ballast particles can reach the specified accuracy. Combining the various steps of the present invention, the method of the present invention has a relatively fast speed during the stacking of the ballast particle model, and the stacking efficiency is greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of railway numerical simulation, and particularly relates to a rapid stacking method for a ball element DDA model of a ballast sample and the stacked model. Background Art

[0002] The discontinuous deformation analysis method (DDA) is a numerical analysis method for discontinuous bodies based on the principle of minimum potential energy. [1 , compared with other numerical analysis methods for discontinuous bodies such as the discrete element method, a key difference is that its solution adopts an implicit calculation method, that is, the unknown variables are not obtained through direct explicit calculation, but by solving the overall equilibrium equation. The DDA simulation of particle shape mainly uses blocks as calculation units. However, calculating the contact between different blocks is very complex, and it is difficult to form a stable and efficient contact algorithm. Huang [2] further simplifies the block calculation unit in DDA into a ball unit and develops a three-dimensional ball unit DDA software. The contact type of the ball unit DDA is simpler, so the calculation efficiency is higher.

[0003] In the actual application process of ballast, the ballast is located among other ballasts to form a ballast accumulation body and is subject to the mutual forces transmitted by adjacent ballasts. If numerical simulation is used to study the crushing of ballast in the accumulation body, it is necessary to restore the true shape of the accumulation body during the modeling process. Currently, there are mainly the following two modeling methods for the particle accumulation body with a true shape [3,4] : (1) The falling stacking method (rainfall method), in which particles are arranged in a larger space and allowed to move downward and accumulate together; (2) The servo plate loading method, in which several movable servo plates are used to compress a larger range of particles together. As Figure 1 shown.

[0004] In previous numerical experiments, although the servo plate loading method is simpler to operate, it cannot present the natural stacking state of the sample. Therefore, the gravity falling method is often used for the natural stacking of the ballast accumulation body. This method requires reasonable arrangement of the initial positions of the particles before falling. Usually, the space is divided using a bounding box or a bounding sphere, and then the shaped particles are replaced into the positions where the bounding box is located, and then mechanical calculations are performed until the particles accumulate in the container. The reason why many scholars adopt this method is that on the one hand, natural falling and stacking conforms to the actual situation of ballast stacking, and on the other hand, for irregular particles, it is relatively difficult to reasonably arrange the spatial positions of these particles, while allowing them to spontaneously stack and arrange under their own weight is relatively intuitive and convenient. However, this method also has its problems, that is, it consumes a large amount of calculation time. During the stacking calculation, all irregular ballast particles participate in the calculation and consume the same amount of computing resources as the loading calculation. When the loading process is not complex, the stacking calculation instead occupies a larger part of the calculation time.

[0005] The present invention develops a rapid stacking method for the spherical element DDA model of ballast specimens, which can improve the stacking efficiency and concentrate more computing resources on the loading calculation.

[0006] [1] SHI, GEN-HUA. Discontinuous Deformation Analysis: A New Numerical Model for the Statics and Dynamics of Deformable Block Structures[J]. Engineering Computations, 1992, 9(2): 157-168.

[0007] [2] YuYong J, GangHai H, ZhiYe Z, Fei Z, Long W, et al. An improved three-dimensional spherical DDA model for simulating rock failure[J], Science China - technological Sciences, 2015, 58(9): 1533-1541.

[0008] [3] Lu Lijin. Fine-grained modeling and discrete element analysis of railway ballast particle breakage[D]. Nanjing: Southeast University, 2021.

[0009] [4] Lin Sihan. Research on the morphological characteristics of ballast and its application in discrete element models[D]. Kunming: Kunming University of Science and Technology, 2019. Summary of the Invention

[0010] To solve the above problems, the present invention provides a rapid stacking method for the spherical element DDA model of ballast specimens, including the following steps:

[0011] Step (1) Simplify existing particles

[0012] When performing stacking simulation on newly input ballast particles, temporarily delete the ballast particles located in the lower layer, and only use one layer of ballast particles on the surface that may come into contact with the newly input ballast particles for contact judgment;

[0013] Step (2) Use the random iteration method to narrow down the range and find the landing points of the ballast particles.

[0014] On the basis of the above solution, the Monte Carlo method is used when simplifying existing particles in step (1).

[0015] Based on the above solution, the specific steps for simplifying existing particles using the Monte Carlo method are as follows:

[0016] The projection area can be indirectly calculated using the Monte Carlo method. Take 100 random points on the sphere. The random number generator random() function can obtain uniform random numbers in the range [0, 1]. The formula for the random points is:

[0017] θ = random() × 2π

[0018]

[0019] x = r × cosθ + x1

[0020] y = r × sinθ + y1

[0021] Where: x1, y1 are the coordinates of the center of the sphere; R is the radius of the sphere.

[0022] Traverse all spherical units. If the point (x, y) is within the projection range of other spheres and the z coordinate of this sphere is larger, then this point is blocked; randomly generate 100 random points within the spherical unit. If most points are blocked, then this sphere should be simplified; after all spherical units are simplified, only the spherical unit particles in the top layer above the ballast accumulation body are retained for contact judgment during the accumulation simulation.

[0023] Based on the above solution, most points being blocked means that more than 80% of the random points are blocked. Traverse all spherical units to determine if more than 80% of the points are blocked. If so, then this spherical unit is simplified.

[0024] Based on the above solution, the specific process of step (2) is as follows:

[0025] (2-1) When iterating, the initial values need to be determined first. Use the random() function to randomly select 1000 groups of α, β, x, y; where the ranges of α and β are (0, 2π); x and y are within the container range; calculate the result of z using the bisection method, and take the group of α, β, x, y corresponding to the smallest z as the initial value of the iteration, denoted as α0, β0, x0, y0. This smallest z value is defined as the current optimal z value, denoted as z0;

[0026] (2-2) Based on the initial values obtained in step (2-1), randomly fine-tune to obtain optimized spatial position parameters α, β, x, y;

[0027] The random fine-tuning ranges of α and β are The random fine-tuning range of x and y is (-0.005, 0.005);

[0028] (2-3) Based on the optimized spatial position parameters α, β, x, y obtained in step (2-2), use the bisection method to calculate the z value corresponding to the fine-tuned α, β, x, y, and compare this z value with the initial z value:

[0029] When this z value is greater than or equal to the initial z value, return to step (2-2) and continue to randomly fine-tune based on α0, β0, x0, y0 to obtain the optimized spatial position parameters α, β, x, y;

[0030] When this z value is less than the initial z value, the current optimal z value completes one iteration. At this time, this z value replaces the original optimal z value (i.e., z0), and at the same time, the initial position parameters (α0, β0, x0, y0) are iterated to the corresponding α, β, x, y that generate this minimum z value;

[0031] (2-4) Based on the new α0, β0, x0, y0 obtained in step (2-3), multiply range α and range β by 0.95 on the basis of the previous iteration to obtain range α1 and range β1 , multiply range x and range y by 0.8 on the basis of the previous iteration to obtain range x1 and range y1 , and randomly fine-tune within the reduced ranges to obtain new optimized spatial position parameters α, β, x, y;

[0032] (2-5) Based on the new optimized spatial position parameters α, β, x, y obtained in step (2-4), use the bisection method to calculate the z value corresponding to the fine-tuned α, β, x, y, and compare this z value with the optimal z value iterated in step (2-3);

[0033] When this z value is greater than or equal to the optimal z value iterated in step (2-3), return to step (2-4), and based on the new α0, β0, x0, y0 obtained in step (2-3), randomly fine-tune within the reduced ranges to obtain new optimized spatial position parameters α, β, x, y; [[ID=3-]]

[0034] When this z value is less than the optimal z value iterated in step (2-3), another iteration is completed. At this time, this z value iteratively replaces the optimal z value iterated in step (2-3), and at the same time, the initial position parameters are iterated to the corresponding α, β, x, y that generate this minimum z value;

[0035] After each iteration, continuously loop through steps (2-4)-(2-5) using the corresponding α, β, x, and y values of the new minimum z value; finally, obtain the placement coordinates α, β, x, y, z of the ballast with sufficient accuracy, place the ballast at this coordinate position, and proceed with the placement of the next ballast.

[0036] Based on the above solution, the method for generating random numbers for the optimized spatial position parameters α, β, x, y in step (2-2) is as follows:

[0037] α = α0 + (random() - 0.5) × range α

[0038] β = β0 + (random() - 0.5) × range β

[0039] x = x0 + (random() - 0.5) × range x

[0040] y = y0 + (random() - 0.5) × range y

[0041] where: random() is a random number generator in the range [0, 1]; range α 、range β is range x 、range y is 0.01; α0, β0, x0, y0 are the initial values for iterative calculation.

[0042] Based on the above solution, the method for generating random numbers for the newly optimized spatial position parameters α, β, x, y in step (2-4) is as follows:

[0043] α = α0 + (random() - 0.5) × range α1

[0044] β = β0 + (random() - 0.5) × range β1

[0045] x = x0 + (random() - 0.5) × range x1

[0046] y = y0 + (random() - 0.5) × range y1

[0047] In the formula: range α1 、range β1For range in the formula that generates random numbers of optimized spatial position parameters before iteration α 、range β Multiply the value by 0.95, range x1 、range y1 For range in the formula that generates random numbers of optimized spatial position parameters before iteration x 、range y Multiply the value by 0.8; random() is a random number generator in the range of [0, 1]; α0, β0, x0, y0 are the new initial values obtained in step (2 - 3);

[0048] Based on the above solution, the specific process of the bisection method is as follows:

[0049] First, set the upper boundary z max for the movement of the falling ballast particles, and the lower boundary z min , move the ballast particles to the midpoint position between the upper and lower boundaries, and determine whether it contacts the simplified existing particles;

[0050] If it is determined that there is no contact, update the upper boundary to the midpoint position between the original upper and lower boundaries at this time; then, move the ballast particles to the midpoint position between the new upper and lower boundaries; then re - judge whether it contacts the existing particles;

[0051] If it is determined that there is contact, update the lower boundary to the midpoint position between the original upper and lower boundaries at this time, then move the ballast particles to the midpoint position between the upper boundary and the new lower boundary, and re - judge whether it contacts the existing particles;

[0052] By repeatedly judging the contact and continuously updating the upper and lower boundaries, when the upper boundary z max - the lower boundary z min is less than the set threshold, output z max , at this time, the upper boundary z max is the minimum z value at which the falling ballast particles do not contact the existing particles. Since the threshold for controlling z max - z min ensures that z max infinitely approaches the z value at which the ballast particles contact the existing particles.

[0053] Based on the above solution, the set threshold is 1.5e - 5.

[0054] In the method of the present invention, by simplifying the existing particles, the time required for particle contact judgment is reduced, and the efficiency of contact judgment is improved; using the dichotomy method to calculate the particle potential energy provides a basis for determining the reasonable position of the particles in the specimen; using random iteration to gradually narrow the range and repeatedly fine-tuning the position of the ballast particles enables the position of the ballast particles to reach the specified accuracy. Combining the various steps of the present invention, the method of the present invention has a relatively fast speed and a large improvement in stacking efficiency when stacking the ballast particle model. Description of the Drawings

[0055] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0056] Figure 1 Schematic diagram of the ballast stacking body modeling method in the prior art;

[0057] Figure 2 Schematic diagram of the simplification of existing particles in the method of the present application;

[0058] Figure 3 Schematic diagram of the generation of random points within a circle by different methods; among them, a are randomly distributed dots with non-uniform distribution; b are randomly distributed dots with uniform distribution;

[0059] Figure 4 Schematic diagram of the principle of particle simplification in the method of the present application;

[0060] Figure 5 Result diagram of particle simplification in the method of the present application;

[0061] Figure 6 Spatial transformation schematic diagram of the ballast particles in step (2) of the method of the present application;

[0062] Figure 7 Efficiency comparison diagram of ballast stacking using the method of the present invention and the rain drop method in the prior art. Detailed Embodiments

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0064] Embodiment 1

[0065] In order to improve the computing efficiency and concentrate more computing resources on the loading calculation, this application proposes a fast stacking method for ballast specimen models. The specific method is as follows:

[0066] Step (1): Simplify the existing particles

[0067] Since the contact judgment of particles is frequently used in the position calculation of ballast particles, in order to reduce the time required for contact judgment, the existing particles can be simplified. It should be noted that when the ballast is placed, it only contacts the particles in the top layer and does not contact the particles in the lower layer. Therefore, this method temporarily deletes the particles in the lower layer and only retains the particles in the upper layer, reducing the complexity of contact calculation and accelerating the computing efficiency.

[0068] Calculate the placement position of each particle in turn. After the calculation, simplify the existing particles and only use the surface layer for contact judgment. The simplification effect is as Figure 2 shown. The green particles participate in the calculation, and the blue ones do not.

[0069] The simplification judgment criterion is the occlusion relationship between particles, that is, the particles on the outermost surface of the particle accumulation are retained. If simply segmented according to the z-direction coordinates of the particles, the upper surface shape of the ballast accumulation is relatively complex and a large z-coordinate range needs to be retained. In this paper, the method of judging whether to retain according to the projected area on the xoy plane is selected. If a particle is occluded multiple times by the particles above it, its projected area on the xoy plane will decrease. As Figure 2 shown, when the projected area is less than a set threshold, the particle will be temporarily deleted.

[0070] It is relatively difficult to directly calculate the projected area. This application uses the Monte Carlo method to simplify the existing particles.

[0071] Using the Monte Carlo method, the projected area can be indirectly calculated. Take 100 random points on the small ball. The random number generator random() function can obtain uniformly distributed random numbers in the range of [0, 1]. The formula for the random points is:

[0072] θ = random() × 2π

[0073]

[0074] x = r × cosθ + x1

[0075] y = r × sinθ + y1

[0076] In the formula: x1, y1 are the coordinates of the center of the ball; R is the radius of the ball.

[0077] It should be noted that if the radius r is uniformly distributed as r = random() × R, the generated points will be concentrated near the center of the circle rather than uniformly distributed, such as Figure 3 -a. Let the radius be The distribution can generate uniform points within the circle, such as Figure 3 -b.

[0078] Simplified principle as Figure 4 As shown. Traverse all ball units. If the point (x, y) is within the projection range of other balls and the z coordinate of the ball is larger, then this point is occluded. Randomly generate random points within 100 ball units. If most of the points are occluded, then the ball should be simplified. In this invention, after trial calculation, this judgment threshold is set to 80%. Traverse all ball units and determine whether more than 80% of the points are occluded. If so, they should be simplified.

[0079] like Figure 5 As shown in the figure, after the ballast pile is simplified, only a layer of green particles on top of the ballast is retained for contact judgment during accumulation. The other blue particles will not come into contact with the newly added ballast. Therefore, the efficiency of ballast contact judgment is greatly improved by simplifying the existing particles through the Monte Carlo method.

[0080] Step (2) Use random iteration method to narrow down the range and find the landing point of ballast particles

[0081] The position of a particle with a real shape in space can be uniquely determined by five parameters α, β, x, y, and z. α and β are the rotation angles, and x, y, and z are the center of gravity. The center of gravity of the particle is initially located at the origin, so the following can be done: Figure 6 The five ways shown are for spatial transformation. Figure 6 Rotation about the z-axis is not included because rotation about the z-axis can be combined with rotations about the x- and y-axes. To place a particle at the spatial position (α, β, x, y, z), first rotate it by β about the y-axis, then by α about the x-axis, and finally translate the center of gravity to (x, y, z).

[0082] The specific process of narrowing down the scope is as follows:

[0083] (2-1) When iterating, you need to first determine the initial value. Use the random() function to randomly select 1000 groups of α, β, x, and y; the range of α and β is (0, 2π); x and y are within the container range; use the bisection method to calculate the result of z, and take the group of α, β, x, and y corresponding to the smallest z as the initial value of the iteration (denoted as α0, β0, x0, y0). This smallest z value is defined as the current optimal z value (denoted as z0).

[0084] (2-2) Based on the initial values obtained in step (2-1) (i.e., α0, β0, x0, y0), randomly fine-tune to obtain optimized spatial position parameters α, β, x, y;

[0085] The formulas for generating random numbers for the optimized spatial position parameters α, β, x, y are as follows:

[0086] α = α0 + (random() - 0.5) × range α

[0087] β = β0 + (random() - 0.5) × range β

[0088] x = x0 + (random() - 0.5) × range x

[0089] y = y0 + (random() - 0.5) × range y

[0090] Where: random() is a random number generator in the range [0, 1]; range α 、range β is range x 、range y is 0.01; α0, β0, x0, y0 are the initial values for iterative calculation;

[0091] At this time, the random fine-tuning range of α, β is The random fine-tuning range of x, y is (-0.005, 0.005);

[0092] (2-3) Based on the optimized spatial position parameters α, β, x, y obtained in step (2-2), use the bisection method to calculate the z value corresponding to the fine-tuned α, β, x, y, and compare this z value with the initial z value (the optimal z value obtained in step (2-1), i.e., z0):

[0093] When this z value is greater than or equal to the initial z value, return to step (2-2) and continue to randomly fine-tune based on α0, β0, x0, y0 to obtain optimized spatial position parameters α, β, x, y;

[0094] When this z value is less than the initial z value, the current optimal z value completes the first iteration, defined as the initial iteration. At this time, this z value replaces the original optimal z value (i.e., z0), and at the same time, the initial position parameters (α0, β0, x0, y0) are iterated to the α, β, x, y corresponding to the generation of this minimum z value (i.e., the newly generated α, β, x, y replace the original α0, β0, x0, y0);

[0095] (2 - 4) Based on the new α0, β0, x0, y0 obtained in step (2 - 3) (the new α0, β0, x0, y0 after iteration), multiply range α and range β by 0.95 based on the previous iteration to obtain range α1 and range β1 , multiply range x and range y by 0.8 based on the previous iteration to obtain range x1 and range y1 , and randomly fine - tune within the reduced range to obtain the new optimized spatial position parameters α, β, x, y;

[0096] The formula for generating random numbers for the new optimized spatial position parameters α, β, x, y is:

[0097] α = α0+(random() - 0.5)×range α1

[0098] β = β0+(random() - 0.5)×range β1

[0099] x = x0+(random() - 0.5)×range x1

[0100] y = y0+(random() - 0.5)×range y1

[0101] Where: range α1 , range β1 are the range α , range β values in the formula for generating random numbers of the optimized spatial position parameters before iteration multiplied by 0.95, range x1 , range y1 are the range x , range y values in the formula for generating random numbers of the optimized spatial position parameters before iteration multiplied by 0.8; random() is a random number generator in the range [0, 1]; α0, β0, x0, y0 are the new initial values obtained in step (2 - 3) or step (2 - 5);

[0102] (2-5) Based on the newly optimized spatial position parameters α, β, x, y obtained in step (2-4), use the bisection method to calculate the z value corresponding to the fine-tuned α, β, x, y, and compare this z value with the optimal z value iterated in step (2-3) (the smaller z value after iteration);

[0103] When this z value is greater than or equal to the optimal z value iterated in step (2-3), return to step (2-4). At this time, based on the new α0, β0, x0, y0 obtained in step (2-3), randomly fine-tune within the reduced range to obtain the newly optimized spatial position parameters α, β, x, y;

[0104] When this z value is less than the optimal z value iterated in step (2-3), another iteration is completed. At this time, this z value replaces the optimal z value iterated in step (2-3), and at the same time, the initial position parameters (α0, β0, x0, y0) are iterated to the corresponding α, β, x, y that generate this minimum z value (that is, the newly generated α, β, x, y replace the original α0, β0, x0, y0 in step (2-3));

[0105] (2-6) After each iteration is completed, continuously loop steps (2-4)-(2-5) using the new minimum z value and the corresponding α, β, x, y for the next iteration; finally, obtain the placement coordinates α, β, x, y, z of the ballast with sufficient accuracy, place the ballast at this coordinate position, and proceed with the placement of the next ballast.

[0106] It should be further clarified for the above steps that: after each iteration is completed, range α and range β are multiplied by 0.95 based on the previous iteration; range x and range y are multiplied by 0.8 based on the previous iteration. Taking range α as an example, the initial range α is After the initial iteration is completed in step 2-3, the reduced range α in step 2-4 is After the optimal z value is iterated in step 2-5 and then returned to step 2-4 to reduce the range α to Then the optimal z value is iterated in step 2-5 and continues to be returned to step 2-4 to reduce the range α to range β 、range x 、range y and so on.

[0107] The specific steps of the dichotomy method in the above steps are as follows:

[0108] For a ballast particle, if the rain - fall method is used for stacking, the ballast particle falls under the action of gravity. After the fall is completed, the ballast particle is in a spatial position where a gravitational potential energy reaches a minimum value. Therefore, if we want to improve the calculation efficiency of the fall, we can start from this point to obtain the spatial position of the ballast corresponding to the minimum value of the gravitational potential energy. After obtaining the result, directly move the ballast particle to the corresponding spatial position, thereby accelerating the calculation of the rain - fall method. In this way, the calculated result is similar to that of the rain - fall method, but because the mechanical calculation process for each time step is omitted and the ballast is directly placed at the spatial position of the minimum potential energy, the calculation efficiency is greatly improved.

[0109] Among the five parameters (α, β, x, y, z) describing the spatial position of the ballast, z is the parameter that determines the potential energy size. According to the principle of minimum potential energy, when the other four spatial position parameters are determined, z can be uniquely determined. Given the four spatial position parameters of the ballast, the ballast can only move up and down. During the process of moving from top to bottom, the new ballast does not initially contact the simplified existing particles, and then contacts the existing particles after continuing to move downward.

[0110] First, set the upper boundary \(z_{up}\) of the moving ballast particle max and the lower boundary \(z_{down}\) min . Move the ballast particle to the mid - point position between the upper boundary and the lower boundary, and judge whether it contacts the simplified existing particles;

[0111] If the judgment shows no contact, at this time update the upper boundary to the mid - point position between the original upper boundary and the lower boundary; then, move the ballast particle to the mid - point position between the new upper boundary and the lower boundary; then re - judge whether it contacts the existing particles;

[0112] If the judgment shows contact, at this time update the lower boundary to the mid - point position between the original upper boundary and the lower boundary, and then move the ballast particle to the mid - point position between the upper boundary and the new lower boundary, and re - judge whether it contacts the existing particles;

[0113] By repeatedly judging the contact and continuously updating the upper and lower boundaries, when \(z_{up}\) max − \(z_{down}\) min is less than \(1.5e - 5\), output \(z_{up}\) max . At this time, \(z_{up}\) max is the minimum \(z\) value when the falling ballast particle does not contact the existing particles. Since controlling the threshold of \(z_{up}\) max − \(z_{down}\) min ensures that \(z_{up}\) max infinitely approaches the \(z\) value at which the ballast particle contacts the existing particles.

[0114] The method in the embodiment and the rain-falling method in the prior art are respectively used to stack 80 ballast particles, and the results are as Figure 7 shown. Through comparison, it can be found that the method of the present invention greatly improves the efficiency of ballast stacking.

[0115] Using the method of the present invention, after 54 minutes, 80 ballast particles have all been stacked through the rapid stacking method. While for the ballast stacked by the falling stacking method, at 54 minutes, it has only fallen a certain distance in the container, and most of the ballast has not yet touched the bottom of the container.

[0116] Each embodiment in this specification is described in a related manner. For the same and similar parts between the embodiments, reference can be made to each other. Each embodiment focuses on the differences from other embodiments. The above description is only a preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention are included in the protection scope of the present invention.

Claims

1. A rapid stacking method for the ball element DDA model of a ballast specimen, characterized in that, It includes the following steps: Step (1): Simplify the existing particles When performing a stacking simulation on newly added ballast particles, temporarily delete the ballast particles located in the lower layer, and only use one layer of ballast particles on the surface that may come into contact with the newly added ballast particles for contact judgment; Step (2): Use the random iteration method to narrow down the range and find the landing points of the ballast particles; When using the Monte Carlo method to simplify the existing particles in Step (1), the specific steps for using the Monte Carlo method to simplify the existing particles are as follows: The Monte Carlo method can be used to indirectly calculate the projected area. Take 100 random points on the sphere. The random number generator random() function can obtain a uniform random number in the interval [0, 1]. The formula for the random points is: θ = random() × 2π x = r × cosθ + x1 y = r × sinθ + y1 In the formula: x1, y1 are the coordinates of the center of the sphere; R is the radius of the sphere; Traverse all sphere units. If the point (x, y) is within the projected range of other spheres and the z coordinate of this sphere is larger, then this point is blocked. Randomly generate 100 random points within the sphere units. If most of the points are blocked, then this sphere should be simplified. After all sphere units are simplified, only one layer of sphere unit particles above the ballast stacking body is retained for contact judgment during stacking simulation.

2. The rapid stacking method of a ballast specimen ball unit DDA model according to claim 1, characterized in that, Most of the points being blocked means that more than 80% of the random points are blocked. Traverse all sphere units to determine whether more than 80% of the points are blocked. If so, then this sphere unit is simplified.

3. A rapid stacking method for the ball element DDA model of a ballast specimen, according to claim 1, characterized in that The specific process of Step (2) is as follows: (2-1) When iterating, it is necessary to first determine the initial values. Use the random() function to randomly select 1000 groups of α, β, x, y; where the ranges of α and β are (0, 2π); x and y are within the container range. Use the bisection method to calculate the result of z, and take the group of α, β, x, y corresponding to the smallest z as the initial value of the iteration, denoted as α0, β0, x0, y0. This smallest z value is defined as the current optimal z value, denoted as z0; (2-2) Based on the initial values obtained in Step (2-1), randomly fine-tune to obtain optimized spatial position parameters α, β, x, y; The random fine-tuning range of α and β is The random fine-tuning range of x and y is (-0.005, 0.005); (2-3) Based on the optimized spatial position parameters α, β, x, y obtained in Step (2-2), use the bisection method to calculate the z value corresponding to the fine-tuned α, β, x, y, and compare this z value with the initial z value: When this z value is greater than or equal to the initial z value, return to Step (2-2) and continue to randomly fine-tune based on α0, β0, x0, y0 to obtain optimized spatial position parameters α, β, x, y; When this z value is less than the initial z value, the current optimal z value completes one iteration, defined as the initial iteration. At this time, this z value replaces the original optimal z value (i.e., z0), and at the same time, the initial position parameters are iterated to the corresponding α, β, x, y that generate this smallest z value; (2-4) Based on the new α0, β0, x0, y0 obtained in step (2-3), range α and range β are multiplied by 0.95 based on the previous iteration to obtain range α1 and range β1 . Range x and range y are multiplied by 0.8 based on the previous iteration to obtain range x1 and range y1 . Random fine-tuning is performed within the reduced range to obtain new optimized spatial position parameters α, β, x, y; (2-5) Based on the new optimized spatial position parameters α, β, x, y obtained in Step (2-4), use the bisection method to calculate the z value corresponding to the fine-tuned α, β, x, y, and compare this z value with the optimal z value iterated in Step (2-3); When the z value is greater than or equal to the optimal z value iterated in step (2-3), return to step (2-4). Based on the new α0, β0, x0, and y0 obtained in step (2-3), randomly fine-tune within the reduced range to obtain new optimized spatial position parameters α, β, x, and y. When the z value is less than the optimal z value iterated in step (2-3), one iteration is completed. At this time, the z value iteration replaces the optimal z value iterated in step (2-3), and at the same time, the initial position parameters are iterated to the corresponding α, β, x, and y that generate the minimum z value. (2-6) After each iteration is completed, continuously loop steps (2-4)-(2-5) using the corresponding α, β, x, and y of the new minimum z value for the next iteration; finally, obtain the placement coordinates α, β, x, y, z of the ballast with sufficient accuracy, place the ballast at this coordinate position, and place the next ballast. The method for generating random numbers for the optimized spatial position parameters α, β, x, and y in step (2-2) is as follows: α = α0 + (random() - 0.5) × range α β = β0 + (random() - 0.5) × range β x = x0 + (random() - 0.5) × range x y = y0 + (random() - 0.5) × range y where: random() is a random number generator in the range of [0, 1]; range α and range β is range x and range y is 0.01; α0, β0, x0, y0 are the initial values for iterative calculation; The formula for generating random numbers for the new optimized spatial position parameters α, β, x, and y in step (2-4) is as follows: α = α0 + (random() - 0.5) × range α1 β = β0+(random() - 0.5)×range β1 x = x0 + (random() - 0.5) × range x1 y = y0 + (random() - 0.5) × range y1 where: range α1 and range β1 are the range α and range β in the formula for generating random numbers of optimized spatial position parameters before iteration, multiplied by 0.95, range x1 and range y1 are the range x and range y in the formula for generating random numbers of optimized spatial position parameters before iteration, multiplied by 0.8; random() is a random number generator in the range [0, 1].

4. A rapid stacking method for the ball element DDA model of a ballast sample, according to claim 3, characterized in that The specific process of the bisection method is as follows: First, set the upper boundary z of the movement of the falling ballast particles max , the lower boundary z min , move the ballast particles to the midpoint position between the upper and lower boundaries, and determine whether they are in contact with the existing particles after simplification; If it is determined that there is no contact, at this time, update the upper boundary to the midpoint position between the original upper boundary and the lower boundary; then, move the ballast particle to the midpoint position between the new upper boundary and the lower boundary; then re-determine whether it is in contact with the existing particles. If it is determined that there is contact, at this time, update the lower boundary to the midpoint position between the original upper boundary and the lower boundary, move the ballast particle to the midpoint position between the upper boundary and the new lower boundary, and re-determine whether it is in contact with the existing particles. Judge and continuously update the upper and lower boundaries through repeated contact. When the upper boundary z max - the lower boundary z min is less than the set threshold, output z max . At this time, the upper boundary z max is the minimum z value at which the falling ballast particles do not contact the existing particles. Since controlling the z max - z min threshold ensures that z max infinitely approaches the z value at which the ballast particles contact the existing particles.

5. A rapid stacking method for the ball element DDA model of a ballast specimen, according to claim 4, characterized in that The set threshold is 1.5e-5.

6. A DDA model of a ball unit for a ballast sample, characterized in that, It is quickly stacked using the method described in any one of claims 1-5.

Images