A method and system for generating soil and rock particle models with multi-level shape parameter control

Abstract

This invention relates to the field of digital modeling technology for geotechnical engineering materials, specifically to a method and system for generating geotechnical particle models with multi-level shape parameter control. The invention includes the following steps: setting multi-level shape parameters according to the target particle shape; generating an initial surface height matrix based on fractal parameters through Fourier transform; constraining the elongation index of the particles based on the initial surface height matrix and smoothing the matrix boundaries to obtain individual particles; performing a mutation operation based on a Gaussian kernel function on the population formed by the individual particles generation by generation, mapping the mutated particles from a spherical coordinate grid to an icosahedral grid, using the difference between their shape parameters and the target value as the fitness value of a genetic algorithm, and filtering out low-fitness particles generation by generation to achieve iterative optimization of the particle shape, finally outputting the target particle file. This invention can generate particles with a wide variety of shapes and highly matches the morphology and texture of real particles.

Description

Technical Field

[0001] This invention relates to the field of digital modeling technology for geotechnical engineering materials, specifically to a method and system for generating geotechnical particle models with multi-level shape parameter control. Background Technology

[0002] Natural sand particles exhibit diverse morphologies, and their geometry, as a key attribute, significantly controls the macroscopic mechanical behavior of particle assemblies, thereby directly affecting the assessment and design safety of engineering problems such as the bearing capacity of sandy soil foundations and slope stability. Therefore, accurately quantifying and characterizing the particle shape effect is fundamental to improving the accuracy of soil mechanical response prediction and the reliability of engineering design. The prerequisite for achieving this quantification is the establishment of a high-fidelity three-dimensional geometric model of the particles.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on particle generation technology, but significant limitations remain. For instance, image generation methods based on CT scans are limited by spatial resolution, making it difficult to achieve full-domain reconstruction of three-dimensional morphology and precise capture of specific cross-sections. While traditional generation methods based on geometry, such as spherical harmonic functions, can parameterize and control shape, they lack characterization of the surface texture mechanism of real sand particles, making it difficult to reconstruct their complex morphologies. Therefore, it is necessary to propose a multi-level particle shape control generation method to address the difficulties in multi-level parameter control and large errors in existing particle generation technologies, as well as the significant differences from real particles due to insufficient surface texture characterization, thereby achieving high-fidelity reconstruction of complex particle morphologies. Summary of the Invention

[0004] To address the shortcomings of existing methods and the needs of practical applications, and in order to solve the aforementioned problems, this invention provides a method for generating soil and rock particle models with multi-level shape parameter control, comprising the following steps:

[0005] Multi-level shape parameters are set according to the target particle shape, including elongation index, edge angle, and roughness. Based on fractal parameters, an initial surface height matrix is ​​generated through Fourier transform. Based on the initial surface height matrix, the elongation index of the particles is constrained and the matrix boundary is smoothed to obtain individual particles. The population formed by the individual particles is subjected to mutation operation based on Gaussian kernel function generation by generation. The mutated particles are mapped from spherical coordinate grid to icosahedral grid. The difference between their shape parameters and the target value is used as the fitness value of the genetic algorithm to filter out particles with low fitness, thereby achieving iterative optimization of particle shape and finally outputting the target particle file.

[0006] Optionally, the elongation index satisfies:

[0007]

[0008] in, Elongation index Let the longest side of the smallest enclosing cuboid of the particle be the boundary. The longest side of the cuboid that the particle contains; the edge angle satisfies:

[0009]

[0010] in, For edge angle, The total number of discrete points. It is the reconstructed particle surface in spherical coordinates. The polar radius of a discrete point The polar radius of the equivalent ellipsoid. Let i be the polar angle of the discrete point i. Let be the azimuth angle of discrete point i;

[0011] The roughness satisfies:

[0012]

[0013] in, For the reference surface particle volume, The surface area of ​​the reference plane. Let be the area of ​​the i-th triangular mesh on the reference plane. To reconstruct the local deviation between the particle surface and the reference particle surface.

[0014] Optionally, the fractal parameters include:

[0015] The fractal parameters of the basic roughness texture component satisfy: , , , ;

[0016] The fractal parameters of the low-frequency topographic relief component satisfy: , , , ;

[0017] The fractal parameters of the high-frequency small-scale bulge component satisfy: , , , ;

[0018] The fractal parameters of the mid-frequency terrain enhancement component satisfy: , , , ;

[0019] For surface roughness variance, for index, The distance between the inflection points of spatial distribution. This is the cutoff wave vector.

[0020] Optionally, generating the initial surface height matrix based on fractal parameters via Fourier transform includes the following steps:

[0021] Based on fractal parameters, the height matrix of the corresponding components is generated through Fourier transform;

[0022] A rough surface height matrix is ​​generated by combining the height matrices of all components. The rough surface height matrix is ​​then post-processed using a median filtering algorithm to generate an initial surface height matrix with complex micro-texture features.

[0023] Optionally, generating the height matrix of the corresponding components based on fractal parameters through Fourier transform includes the following steps:

[0024] Based on the Hurst exponent and the cutoff wave vector, calculate the power spectral density corresponding to each discrete wave vector component and generate the power spectral density matrix.

[0025] The power spectral density matrix is ​​subjected to amplitude spectrum transformation to obtain the amplitude spectrum matrix;

[0026] The amplitude spectrum matrix and the phase matrix are combined into a frequency domain matrix to reconstruct the complete frequency domain signal, and the height matrix of the corresponding component is generated by Fourier transform.

[0027] Optionally, the elongation index of the particles is constrained based on the initial surface height matrix, satisfying:

[0028]

[0029] in, This represents the surface height matrix after constraining the elongation exponent. and These represent the polar angle and azimuth angle in a spherical coordinate system, respectively. The target elongation index, Represents the maximum value of the matrix. Represents the initial surface height matrix. This is the height offset constant.

[0030] Optionally, the matrix boundaries are smoothed to satisfy:

[0031] The generated altitude matrix in longitude The boundary must be continuous to ensure a seamless connection of meridians when mapped to spherical coordinates;

[0032] In polar regions, a point at any longitude must be related to its longitude. The points on the surface should maintain continuity to avoid abrupt changes at the polar edges.

[0033] Optionally, the mutation operation based on a Gaussian kernel function is performed on the population formed by the individual particles, satisfying:

[0034] If the Gaussian kernel matrix extends beyond the matrix boundary in the y-coordinate direction, the excess portion is completely discarded.

[0035] If the Gaussian kernel matrix extends beyond the matrix boundary in the x-coordinate direction, it will be cyclically mapped to the other side of the boundary.

[0036] For each valid mutation site, the mutated gene value is:

[0037]

[0038] in, This represents the gene value after mutation. The height matrix represents the height matrix in the figure. Gene values, For the selected effective mutation sites, For random variation weights, It is the value at the corresponding position in the Gaussian kernel matrix.

[0039] Optionally, the difference between its shape parameters and the target value is used as the fitness value of the genetic algorithm, satisfying:

[0040]

[0041] in, Indicates the fitness value. These represent the elongation index, edge angle, and roughness of the target soil particle model, respectively. , , These are the elongation index, edge angle, and roughness calculated for the current particle, respectively. These are the weight values ​​for each shape parameter.

[0042] This invention achieves precise multi-scale control of particle shape from macro to micro. By defining and independently controlling three core shape parameters—elongation index, edge angle, and roughness—which correspond to the overall outline, edge features, and surface texture of the particle, respectively, it can systematically generate particle morphologies covering different geometric properties, overcoming the limitations of single or subjective shape descriptions in traditional methods.

[0043] Secondly, this invention significantly improves the physical realism and generation efficiency of virtual particle models. It utilizes Fourier transform based on fractal theory to synthesize rough surfaces with complex statistical characteristics, efficiently reproducing the microscopic texture of naturally weathered or broken particles. Combined with a genetic algorithm and an adaptive mutation optimization framework, it can automatically and efficiently iteratively generate particle models whose shape parameters strictly conform to the target values, achieving a good balance between fidelity and computational cost.

[0044] Finally, this invention provides a key foundation for refined numerical analysis in geotechnical engineering. The generated particle model can be directly used for numerical simulations such as discrete element method to construct high-quality virtual specimens. This enables a more reliable study of the microscopic mechanism influence of particle shape on macroscopic behaviors such as stacking structure, mechanical response (e.g., strength, deformation), and fluid seepage. This helps to deepen the understanding of constitutive relations of geotechnical materials and provides more accurate theoretical tools for engineering design and risk prediction.

[0045] Secondly, to efficiently execute the multi-level shape parameter controlled soil and rock particle model generation method provided by this invention, this invention also provides a multi-level shape parameter controlled soil and rock particle model generation system, including a processor, an input device, an output device, and a memory. The processor, input device, output device, and memory are interconnected. The memory stores a computer program containing program instructions. The processor is configured to call the program instructions to execute the multi-level shape parameter controlled soil and rock particle model generation method as described in the first aspect of this invention. The multi-level shape parameter controlled soil and rock particle model generation system of this invention has a compact structure and stable performance, and can stably execute the multi-level shape parameter controlled soil and rock particle model generation method provided by this invention, further improving the overall applicability and practical application capability of this invention. Attached Figure Description

[0046] Figure 1 A flowchart illustrating a method for generating a soil particle model with multi-level shape parameter control, provided in an embodiment of the present invention;

[0047] Figure 2 This is a schematic diagram of multi-layer shape control parameters for target particles provided in an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of a height matrix and spherical coordinate mapping provided in an embodiment of the present invention;

[0049] Figure 4 This is a schematic diagram of a height matrix component generation process provided in an embodiment of the present invention;

[0050] Figure 5 This is a schematic diagram of the height matrix topography of each component provided in an embodiment of the present invention;

[0051] Figure 6 This is a schematic diagram illustrating the boundary continuity processing of height matrix mapping spherical coordinates provided in an embodiment of the present invention;

[0052] Figure 7 A pseudo-color schematic diagram of Gaussian kernel variation on a height matrix provided in an embodiment of the present invention;

[0053] Figure 8 This is a schematic diagram of mapping a spherical coordinate mesh to an icosahedral mesh, provided in an embodiment of the present invention.

[0054] Figure 9 This is a schematic diagram illustrating the shape iteration of generated particles according to an embodiment of the present invention;

[0055] Figure 10 The particle morphology distribution diagram with different shape parameters is provided for the embodiments of the present invention.

[0056] Figure 11 This is a framework diagram of a multi-level shape parameter controlled soil particle model generation system provided in an embodiment of the present invention. Detailed Implementation

[0057] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0058] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0059] Please see Figure 1 To address the aforementioned problems, this invention provides a method for generating soil and rock particle models with multi-level shape parameter control, such as... Figure 1 As shown, in one embodiment, the method includes the following steps:

[0060] S1. Set multi-level shape parameters according to the target particle shape, including elongation index, edge angle and roughness.

[0061] In this embodiment, based on a multi-level particle morphology quantitative evaluation framework, particle shape is characterized from three different levels: the first level is the overall outline, the second level is the sharpness or roundness of the particle, and the third level is the undulation of the particle surface, also known as surface texture. Figure 2 As shown, To define the shortest side of the smallest containment cuboid for the particle, we set shape control parameters for the target particle at these three levels and analyzed the multi-level shape parameters.

[0062] Specifically, the elongation index satisfies:

[0063]

[0064] in, Elongation index Let the longest side of the smallest enclosing cuboid of the particle be the boundary. The longest side of the smallest enclosing cuboid of the particle;

[0065] The point cloud on the particle surface is triangularly meshed and then converted to spherical coordinates. The polar radius of each discrete point is obtained. polar angle and azimuth Expand the polar radius of each discrete point using a spherical harmonic function, i.e.:

[0066]

[0067] in, Indicates the order is Number of times spherical harmonic basis functions, Let be the total order of the spherical harmonics. These are the coefficients of the spherical harmonic function.

[0068] The reference ellipsoid surface is obtained through principal component analysis, and the particle surface is reconstructed using a spherical harmonic function with a total order of N=8 to eliminate the influence of surface roughness. The reconstructed particle surface is then obtained. The edge angle is calculated using the difference in polar radii between the reference ellipsoid and the reconstructed particle surface. This edge angle satisfies the following conditions:

[0069]

[0070] in, For edge angle, The total number of discrete points. It is the reconstructed particle surface in spherical coordinates. The polar radius of a discrete point The polar radius of the equivalent ellipsoid. Let i be the polar angle of the discrete point i. Let be the azimuth angle of discrete point i.

[0071] The particle surface is reconstructed using a spherical harmonic function with a total order of N=8 to eliminate the influence of surface roughness and obtain a reference particle surface. Subsequently, the particle surface is reconstructed using a spherical harmonic function with a total order of N=15 to preserve surface roughness details and obtain a reconstructed particle surface. The roughness is calculated based on the local deviation between the reference particle surface and the reconstructed particle surface, and the roughness satisfies:

[0072]

[0073] in, For the reference surface particle volume, The surface area of ​​the reference plane. Let be the area of ​​the i-th triangular face mesh on the reference plane. To reconstruct the local deviation between the particle surface and the reference particle surface.

[0074] S2. Based on fractal parameters, the initial surface height matrix is ​​generated through Fourier transform.

[0075] In this embodiment, multiple particle surface terrains are generated based on Fourier transform and fractal parameter control. The height matrices of different component terrains are superimposed and surface smoothing is performed to obtain the initial particle surface height matrix.

[0076] like Figure 3 As shown, the height matrix of the target rough surface From spherical coordinate functions Generate, where, The polar radius is defined in spherical coordinates and set according to the grid resolution, with the x-axis spacing of each pixel block being [value missing]. The length in the y direction is The element values ​​of the height matrix are determined by... A joint decision, in which, For surface roughness variance, for index, The distance between the inflection points of spatial distribution. To cut off the wave vector, The resolution is the azimuth and polar angle of the spherical coordinate grid.

[0077] In this embodiment, the fractal parameters include:

[0078] The fractal parameters of the basic roughness texture component satisfy: , , , ;

[0079] The fractal parameters of the low-frequency topographic relief component satisfy: , , , ;

[0080] The fractal parameters of the high-frequency small-scale bulge component satisfy: , , , ;

[0081] The fractal parameters of the mid-frequency terrain enhancement component satisfy: , , , .

[0082] Furthermore, the step of generating an initial surface height matrix with complex micro-texture features based on the fractal parameters and through Fourier transform includes the following steps:

[0083] S21. Based on the fractal parameters, generate the height matrix of the corresponding components through Fourier transform;

[0084] The step of generating the height matrix of the corresponding components based on the fractal parameters through Fourier transform includes the following steps:

[0085] like Figure 4 As shown, firstly, based on the Hurst exponent and the cutoff wave vector, the power spectral density corresponding to each discrete wave vector component is calculated, and a power spectral density matrix is ​​generated.

[0086] Introducing the concepts of wave vectors in the x and y directions, the wave vectors in the x and y directions... , They are respectively:

[0087]

[0088] Thus, a two-dimensional wave vector matrix is ​​constructed. ,satisfy:

[0089]

[0090] in, It is the element value of the height matrix Z at grid point (i,j), i.e., the polar radius. , Let i and j be the corresponding spatial coordinates, and i and j be the indices in the x and y directions, respectively. In this embodiment, all elements of a two-dimensional matrix are represented using the notation "(row index, column index)," where the "row index" corresponds to the y-direction or polar direction, and the "column index" corresponds to the x-direction or azimuth direction.

[0091] The two-dimensional wave vector matrix constructed above is the basic coordinate framework for frequency domain analysis. It serves as a bridge connecting spatial domain height information and frequency domain statistical characteristics, ensuring that the generated rough surface possesses preset fractal and statistical features.

[0092] Furthermore, according to the Hurst index and cutoff wave vector ( ), calculate the power spectral density corresponding to each discrete wave vector component. Generate power spectral density matrix This matrix quantitatively characterizes the distribution characteristics of surface undulation signal energy at different spatial frequencies, satisfying:

[0093]

[0094] in, The radial distance in spherical coordinates is the cutoff wave vector. Used to control high-frequency attenuation.

[0095] In this embodiment, to ensure that the final generated surface height distribution meets the preset fractal dimension and roughness statistical characteristics, the power spectral density can also be subjected to amplitude scaling transformation based on the preset surface roughness variance:

[0096] First, calculate the root mean square of the unscaled surface. ,satisfy: , Indicates the wave vector (q) x [i],q y The power spectral density value at [j]);

[0097] Second, calculate the scaling factor, which satisfies: ;

[0098] Third, calculate the PSD matrix after standardization root mean square. ,satisfy:

[0099] Next, the power spectral density matrix is ​​subjected to amplitude spectrum transformation to obtain the amplitude spectrum matrix.

[0100] To ensure that the surface height matrix generated by the inverse Fourier transform is a purely real-valued function (i.e., its imaginary part is strictly zero) and conforms to the real-valued characteristics of the physical surface morphology, a random phase matrix that satisfies specific mathematical constraints needs to be generated. The constraints are as follows:

[0101] 1. The range of element values ​​is This ensures the physical rationality of the phase value and avoids distortion in the conversion from the frequency domain to the spatial domain due to phase jumps or exceeding the reasonable range.

[0102] 2. The phase matrix must satisfy conjugate symmetry, that is:

[0103] Furthermore, regarding the power spectral density matrix Amplitude spectrum transformation is performed to obtain the amplitude spectrum matrix. And conjugate symmetry processing is performed to ensure the realness of the output of the subsequent inverse Fourier transform, and the amplitude spectrum conversion satisfies:

[0104] .

[0105] Finally, the amplitude spectrum matrix and the phase matrix are combined into a frequency domain matrix to reconstruct the complete frequency domain signal, and the height matrix of the corresponding component is generated by Fourier transform.

[0106] The amplitude spectrum matrix and the phase matrix are combined into a frequency domain matrix. Reconstruct the complete frequency domain signal to satisfy:

[0107]

[0108] Furthermore, the frequency domain matrix Performing an inverse Fourier transform converts the complex representation in the frequency domain back to the real height distribution in the time domain, ultimately obtaining the height matrix of the corresponding components. ,satisfy: ,in, Operators that extract the real part return the real part when applied to complex numbers. The two-dimensional inverse Fourier transform operator is used to transform a frequency domain function back to a time domain function. The overall shape of the height matrix for different components is as follows: Figure 5 As shown.

[0109] S22. Generate a rough surface height matrix by combining the height matrices of all components. Post-process the rough surface height matrix using a median filtering algorithm to generate an initial surface height matrix with complex micro-texture features.

[0110] After generating each individual surface component, the height matrices of each component are linearly superimposed to obtain... Furthermore, quantile thresholds are used to dynamically limit extreme values ​​on the height matrix, smoothing out regions below the 35th quantile (pits) and regions above the 90th quantile (peaks) to obtain the limited matrix. ,satisfy:

[0111]

[0112] in, Representation matrix The 35th percentile value in ascending order of element values. Representation matrix The 90th percentile value in ascending order of element values.

[0113] Based on this, a median filtering algorithm is used to post-process the generated rough surface height matrix to remove noise and small random fluctuations while retaining larger features. The specific implementation process is as follows:

[0114] For each position in the matrix A two-dimensional neighborhood window W is defined centered on it, and this window covers the row direction of the first... Arriving at the Row, covering the first row in the column direction Listed to number The two-dimensional neighborhood range of the column is defined. All elements within the neighborhood W are sorted in ascending order of value, and the value at the median position after sorting is taken as the output value of that point. If the neighborhood range exceeds the matrix boundary, pixels outside the boundary are not included in the median value calculation. Finally, an initial surface height matrix with complex micro-texture features is obtained. .

[0115] S3. Based on the initial surface height matrix, constrain the elongation index of the particles and smooth the matrix boundaries to obtain individual particles.

[0116] To improve optimization efficiency and shorten iteration calculation time, the elongation index of the initial particles is constrained within a reasonable range preset by the target elongation index, thereby reducing the shape difference between the initial particles and the target particles.

[0117] In spherical coordinates, the initial particle surface height function satisfies:

[0118]

[0119] in, This represents the surface height matrix after constraining the elongation exponent. and These represent the polar angle and azimuth angle in a spherical coordinate system, respectively. The target elongation index, Represents the maximum value of the matrix. Represents the initial surface height matrix. This is the height offset constant.

[0120] Furthermore, to ensure the boundary continuity of the rough surface height matrix when mapped to spherical coordinates, such as Figure 6 As shown, the height matrix Two conditions need to be met:

[0121] The generated altitude matrix in longitude The boundary must be continuous to ensure a seamless connection of meridians when mapped to spherical coordinates;

[0122] In polar regions, a point at any longitude must be related to its longitude. The points on the surface should maintain continuity to avoid abrupt changes at the polar edges.

[0123] Specifically, a boundary smoothing method based on cosine weighted interpolation is adopted, and the specific implementation steps are as follows:

[0124] height matrix The first k1 rows of the upper boundary are divided into left and right sub-matrices according to their columns. , :

[0125]

[0126] Construct the longitude weight vector w j :

[0127] .

[0128] Where, on the equatorial side w1=0, on the pole side w1=0. .

[0129] Calculate the mean of the upper and lower boundary rows of the matrix. and The boundary values ​​and the mean are mixed according to weights to calculate the smoothed height of the upper boundary. :

[0130]

[0131] The same interpolation method as the upper boundary is used when processing the lower boundary.

[0132] Similar to the processing of the upper and lower boundaries, extract the matrix. k2 column region on both the left and right boundaries , :

[0133]

[0134]

[0135] Construct the dimension weight vector v i :

[0136]

[0137] Where the internal side v1=0, and the boundary side... .

[0138] The calculated heights of the left and right boundaries after smoothing are obtained. , :

[0139]

[0140]

[0141] The processed heights are then filled back into the corresponding areas of the original height matrix. When filling the heights at the upper and lower boundaries, the new heights for the longitude intervals (0, π) or (π, 2π) must be included. Mirror symmetry is performed to ensure that a point at any longitude remains continuous with a point at longitude +π, thus avoiding abrupt changes at the polar edges.

[0142] Through the above processing, the initial particle surface height matrix with geometric adaptation and smooth boundary transition is finally obtained. While maintaining the surface microstructure characteristics, it strictly satisfies the continuity and periodicity conditions of spherical coordinate mapping. For ease of use in the subsequent genetic algorithm, it is defined as follows: Each particle's surface height matrix is ​​considered as an individual particle in the population.

[0143] S4. Perform a mutation operation based on Gaussian kernel function on the population formed by the individual particles generation by generation, map the mutated particles from the spherical coordinate grid to the icosahedral grid, use the difference between its shape parameter and the target value as the fitness value of the genetic algorithm, filter out particles with low fitness, realize the iterative optimization of particle shape, and finally output the target particle file.

[0144] Specifically, the population is subjected to mutation operations based on Gaussian kernel functions. In each operation, the following Gaussian kernel mutation steps are performed on all particles of the current generation:

[0145] The physical mechanism of local deformation on the surface of real particles is simulated using a Gaussian kernel function, and its performance on the height matrix is ​​as follows: Figure 7 As shown.

[0146] Given a 2×2 covariance matrix And calculate the determinant of the covariance matrix. and inverse matrix .

[0147] In one Generate a Gaussian kernel matrix on the grid. Pick Any integer in the range.

[0148] For each grid point Its Gaussian kernel coefficient Calculated using the following formula:

[0149]

[0150] in, for The covariance matrix, From the center position of the Gaussian distribution To the target location The position offset vector. Specifically, It can be expanded as follows:

[0151]

[0152] Applying to the entire Gaussian kernel mesh, generating a discrete Gaussian kernel matrix. :

[0153]

[0154] In the height matrix any position As the center of the Gaussian kernel perturbation, this position must guarantee the entire Gaussian kernel. It can be completely covered in the matrix superior.

[0155] Furthermore, if the Gaussian kernel matrix exceeds the boundary, special handling will be applied to different dimensions:

[0156] If the Gaussian kernel matrix is ​​in the y-coordinate direction (latitude exceeding +90° or -90°, i.e.) If the coordinates are below 0° or above 180° and exceed the matrix boundary, the excess portion is completely discarded.

[0157] If the Gaussian kernel matrix is ​​in the x-coordinate direction (longitude exceeding +180° or -180°, i.e.) If the coordinates are below 0 or above 360° and exceed the matrix boundary, they will be cyclically mapped to the other side of the boundary.

[0158] For each valid mutation location, its height value (gene value) is increased by a perturbation factor, which is the product of the Gaussian kernel coefficient and a randomly generated mutation strength:

[0159]

[0160] in, This represents the gene value after mutation. The height matrix represents the height matrix in the figure. Gene values, For the selected effective mutation sites, For random variation weights, It is the value at the corresponding position in the Gaussian kernel matrix.

[0161] Based on this, the mutated particles are mapped from a spherical coordinate grid to an icosahedral grid, and the difference between their shape parameters and the target value is used as the fitness value of the genetic algorithm.

[0162] Specifically, based on the golden ratio Initialize the coordinates of 12 vertices in space, as follows:

[0163] By constructing 20 initial triangular faces through vertex index relationships, a basic framework of a regular icosahedron is formed.

[0164] For each vertex Perform normalization and project onto a unit sphere, as follows:

[0165]

[0166] in, The normalized vertex

[0167] Based on recursion level parameters (Value range 0-5, default value 4), each recursive call will split all triangular faces into 4 sub-triangles:

[0168] For example, when triangle ABC is split, calculate the midpoint of each side (e.g., the midpoint of AB). Midpoint of BC Midpoint of AC And generate new triangles. , , , .

[0169] According to recursion level The number of vertices is shown in Table 1.

[0170] Table 1. Vertex Count Table

[0171] Recursion level 0 1 2 3 4 5 Number of vertices 12 42 162 642 2562 10242

[0172] Finally, duplicate vertices are eliminated by spatial location matching to ensure that the mesh is a closed manifold surface (without cracks or overlaps) and to ensure mesh topology consistency.

[0173] Furthermore, the rough surface height matrix is ​​mapped to all vertices of the icosahedron. Through resampling, the original regular latitude and longitude grid is mapped to the spherical grid unfolded from the icosahedron, ensuring a more uniform icosahedral grid in polar regions, avoiding the singularity problem of the original latitude and longitude grid at the poles, and ensuring the accuracy of subsequent area / volume calculations. The specific operations are as follows:

[0174] height matrix Extending along the longitude and latitude directions, it forms three cycles. To eliminate boundary jumps, the radial heights of all vertices on the icosahedron are then obtained using two-dimensional interpolation based on the vertices of the rough surface height matrix and mapped to the icosahedral mesh. ,like Figure 8 The images shown are the results of mapping spherical coordinate meshes to icosahedral meshes at different recursion levels.

[0175] Calculate the difference of shape parameters at three different levels based on the mapped surface vertices. First, map the icosahedral mesh spherical coordinate system to the Cartesian coordinate system:

[0176]

[0177]

[0178]

[0179] Then, the shape parameters of each layer are calculated, and the following formula is used to calculate... This value is used as Fitness in genetic algorithms:

[0180]

[0181] in, Indicates the fitness value. These represent the elongation index, edge angle, and roughness of the target soil particle model, respectively. , , These are the elongation index, edge angle, and roughness calculated for the current particle, respectively. These are the weight values ​​for each shape parameter.

[0182] Furthermore, within the framework of the genetic algorithm, random perturbations based on the Gaussian kernel function are applied to individual particles generation by generation to filter out particles with low fitness, thereby achieving iterative optimization of particle shape and finally outputting a three-dimensional particle geometric model that satisfies the preset shape parameters. This includes the following steps:

[0183] An elite selection strategy is employed to identify and record the fitness value after each generation of mutation. The lowest individual particles, such as Figure 9 As shown, based on this individual particle, mutation operations are continued to obtain the next generation of particles, and this process is repeated iteratively to optimize the particle shape. When the iterative convergence condition is met ( Less than the preset threshold Or the number of iterations reaches the preset maximum value. Output the final rough surface height matrix. .Will After surface resampling and icosahedral reconstruction, irregular particles that meet the preset shape parameters are obtained. Figure 10 This is a schematic diagram of the three-dimensional morphological distribution under different shape parameter controls.

[0184] Please see Figure 11 In this embodiment, to efficiently execute the multi-level shape parameter controlled soil and rock particle model generation method provided by the present invention, the present invention also provides a multi-level shape parameter controlled soil and rock particle model generation system, including: an input device, an output device, a processor, and a memory. The input device, output device, processor, and memory are interconnected. The memory contains program instructions for the steps of the multi-level shape parameter controlled soil and rock particle model generation method. The multi-level shape parameter controlled soil and rock particle model generation system of the present invention has a compact structure and stable performance, and can stably execute the multi-level shape parameter controlled soil and rock particle model generation method of the present invention, further improving the overall applicability and practical application capability of the present invention.

[0185] In this embodiment, the processor may be a central processing unit, but it can also be other general-purpose processors, digital signal processors, application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (OPGs), other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor. Input devices can be used to acquire data. Output devices can be used to output the results obtained by storing program instructions contained in a computer program in the memory provided by this invention. The memory may include read-only memory and random access memory (RAM), and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory (RAM).

[0186] In one possible implementation, the memory may include a stored program area and a stored data area. The stored program area may store the operating system and applications required for at least one function; the stored data area may store data created during use. Furthermore, the memory may include read-only memory and random access memory, and provides instructions and data to the processor. The memory stores the operating system and operating instructions, executable modules, or data structures, or subsets thereof, or extended sets thereof. The operating instructions may include various operation instructions for implementing various operations. The operating system may include various system programs for implementing various basic tasks and handling hardware-based tasks.

[0187] The embodiment also provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for generating a soil particle model with multi-level shape parameter control.

[0188] The storage medium can include various media that can store program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0189] In summary, this invention provides a key foundation for refined numerical analysis in geotechnical engineering. The generated particle model can be directly used for numerical simulations such as discrete element method to construct high-quality virtual samples. This enables a more reliable study of the microscopic mechanism influence of particle shape on macroscopic behaviors such as stacked structures, mechanical responses (e.g., strength and deformation), and fluid seepage. This helps to deepen the understanding of constitutive relations of geotechnical materials and provides more accurate theoretical tools for engineering design and risk prediction.

[0190] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the present invention.

Claims

1. A method for generating a multi-level shape parameter controlled soil particle model, characterized in that, The method comprises the following steps: The multi-level shape parameters are set according to the target particle shape, and the multi-level shape parameters comprise an elongation index, an edge angle and roughness; An initial surface height matrix is generated through Fourier transform based on the fractal parameters; The elongation index of the particle is constrained and the matrix boundary is smoothed based on the initial surface height matrix, so as to obtain a particle individual; A population formed by the particle individual is subjected to a mutation operation based on a Gaussian kernel function, the mutated particle is mapped from a spherical coordinate grid to an icosahedral grid, the difference between the shape parameters of the particle and the target value is taken as the fitness value of the genetic algorithm, the particles with low fitness are screened, the iterative optimization of the particle shape is realized, and finally a target particle file is output; The fractal parameters comprise: The fractal parameters of the base rough texture component satisfy: , , , ; The fractal parameters of the low-frequency terrain fluctuation component satisfy: , , , ; The fractal parameters of the high-frequency small-size bump component satisfy: , , , ; The fractal parameters of the intermediate frequency terrain enhancement component satisfy: , , , ; for surface roughness variance, for exponent, for spatial distribution break point spacing, for cutoff wave vector; The elongation index of the particle is constrained based on the initial surface height matrix, and the constraint satisfies: wherein, denotes the surface height matrix after constraining the elongation index, and denote the polar and azimuthal angles of the spherical coordinate system, respectively, is the target elongation index, denotes the maximum value of the matrix, denotes the initial surface height matrix, is the height offset constant; The population formed by the particle individual is subjected to the mutation operation based on the Gaussian kernel function, and the mutation operation satisfies: If the Gaussian kernel matrix exceeds the matrix boundary in the y coordinate direction, the exceeding part is completely discarded; If the Gaussian kernel matrix exceeds the matrix boundary in the x coordinate direction, the exceeding part is cyclically mapped to the other side of the boundary; For each effective mutation position, the gene value after mutation is: wherein, denotes the gene value after mutation, denotes the height matrix at the gene value of is the selected effective mutation position, is the random mutation weight, is the value of the corresponding position in the Gaussian kernel matrix.

2. The method of claim 1, wherein the method further comprises: The elongation index satisfies: wherein is the elongation index, is the longest side of the smallest containing cuboid of the particle, is the longest side of the smallest containing cuboid of the particle. The edge angle satisfies: wherein, is an angle, is a total number of discrete points, is a polar radius of the reconstructed surface of the particle in spherical coordinates at the discrete point, is a polar radius of the equivalent ellipsoid, is a polar angle of the discrete point i , is an azimuthal angle of the discrete point i . The roughness satisfies: wherein, is the volume of the reference surface particle, is the surface area of the reference surface particle, is the area of the reference surface particle's nth triangular mesh, i is the area of the reference surface particle's nth triangular mesh, is the local deviation of the reconstructed particle surface from the reference particle surface.

3. The method of claim 1, wherein the method further comprises: The initial surface height matrix is generated through Fourier transform based on the fractal parameters, and the method comprises the following steps: The height matrix of the corresponding component is generated through Fourier transform based on the fractal parameters; The height matrix of the corresponding component is generated through Fourier transform based on the fractal parameters; 4. The method of claim 3, wherein the method further comprises: The height matrix of the corresponding component is generated through Fourier transform based on the fractal parameters. The height matrix of the corresponding component is generated through Fourier transform based on the fractal parameters, and the method comprises the following steps: The power spectral density corresponding to each discrete wave vector component is calculated according to the Hurst index and the cutoff wave vector, so as to generate a power spectral density matrix; The amplitude spectrum matrix is obtained through amplitude spectrum conversion of the power spectral density matrix; 5. The method of claim 1, wherein the method further comprises: The amplitude spectrum matrix and the phase matrix are combined into a frequency domain matrix to reconstruct a complete frequency domain signal, and the height matrix of the corresponding component is generated through Fourier transform. The generated height matrix at the longitude ° boundary must satisfy continuity, ensuring seamless joining of the meridians when mapped to the spherical coordinates; In polar regions, a point at any longitude must be continuous with a point at its longitude plus or minus 180 degrees, avoiding a discontinuity at the polar edge.

6. The method of claim 1, wherein the multi-level shape parameter control is applied to the rock and soil particle model. The matrix boundary is smoothed, and the smoothing satisfies: wherein, denotes a fitness value, are elongation index, angularity and roughness of the target rock-soil particle model respectively, , , are elongation index, angularity and roughness calculated by the current particle respectively, are weight values of each shape parameter respectively.

7. A multi-level shape parameter controlled geotechnical particle model generation system, characterized by, The difference between the shape parameters of the particle and the target value is taken as the fitness value of the genetic algorithm, and the fitness value satisfies: The multi-level shape parameter controlled rock-soil particle model generation system comprises an input device, an output device, a processor and a memory, the input device, the output device, the processor and the memory are connected to each other, the memory comprises program instructions, and the program instructions are used to execute the multi-level shape parameter controlled rock-soil particle model generation method in any one of claims 1-6.

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