A Method for Random Generation and Refined Modeling of Tidal Flat Sand Particles Based on Generative Adversarial Neural Networks

Abstract

This invention discloses a method for random generation and refined modeling of tidal flat sand particles based on generative adversarial neural networks (GANs). The steps are as follows: Sand samples are scanned layer by layer using micro-CT to obtain slice images of different layers. A particle contour extraction method based on semantic segmentation is used to segment the slice datasets of different layers of sand particles. A GAN algorithm is then used to construct a discriminator D and a generator G, repeatedly adversarially, until Nash equilibrium is reached, generating slice images of sand particles at different layers. These generated slice images are then reconstructed and stacked to obtain discrete point cloud coordinates of the particle surface morphology. Finally, a method is used to model the surface points (x, y, z) of the particles. N By performing 3D reconstruction using a spherical harmonic function, a 3D reconstruction model of randomly generated tidal flat sand particles is obtained. This invention employs generative adversarial neural networks from deep learning for the random generation and refined modeling of tidal flat sand particles, solving the problem of random sand particle generation and demonstrating both accuracy and advanced technology.

Description

Technical Field

[0001] This invention belongs to the technical field of random generation and refined modeling methods for tidal flat sand particles, specifically involving a random generation and refined modeling method for tidal flat sand particles based on generative adversarial neural networks. Background Technology

[0002] Sand of various shapes and sizes exists widely in nature, including quartz sand, calcareous sand, river sand, and tidal flat sand. Currently, there is considerable research on methods for analyzing the microstructure of sand particles in quartz sand, calcareous sand, and river sand, but less research on methods for randomly generating tidal flat sand particles. In studies of random particle generation methods, Fourier series expansion is generally used for two-dimensional particles, while spherical harmonic function expansion is used for three-dimensional particles. However, the random generation of particles in both dimensions has significant limitations and is computationally complex, making it difficult to achieve the goal of randomly simulating real-world particles.

[0003] Tidal flat sand foundations contain a large amount of tidal flat sand, resulting in low bearing capacity. To investigate the relevant mechanical properties of tidal flat sand, in addition to macroscopic experiments, it is necessary to analyze the microscopic morphology of tidal flat sand particles. Random particle generation methods should be employed, and numerical simulations of tidal flat sand with different particle shapes should be conducted to fully understand the macro-microscopic interaction mechanism and thus gain a deeper understanding of its relevant properties. However, conventional methods, such as two-dimensional random generation based on Fourier series expansion and three-dimensional random generation based on spherical harmonic function expansion, have significant limitations in realistically generating a large number of particles. Therefore, it is necessary to adopt a random generation and refined modeling method for tidal flat sand particles based on generative adversarial neural networks (GANs), using artificial intelligence deep learning algorithms to achieve realistic simulation and generate a large number of naturally occurring tidal flat sand particles. Summary of the Invention

[0004] Technical problem to be solved: In view of the above-mentioned technical problems, the present invention provides a method for random generation and refined modeling of tidal flat sand particles based on generative adversarial neural networks, which can effectively solve the shortcomings of the above-mentioned three-dimensional random generation method, such as the large limitation of generating a large number of real particles and the complexity of calculation.

[0005] Technical solution: A method for random generation and refined modeling of tidal flat sand particles based on generative adversarial neural networks, including the following steps:

[0006] S1. Select tidal flat sand particles and place them in a container so that each tidal flat sand particle is separated by a plastic sheet.

[0007] S2. Micro-CT layer-by-layer scanning of tidal flat sand particles was used to obtain slice images of different layers of each tidal flat sand particle. The slice dataset of different layers of each tidal flat sand particle was segmented by a particle contour extraction method based on semantic segmentation.

[0008] S3. Using a generative adversarial neural network algorithm, a discriminator D and a generator G are constructed. The dataset of slices representing different layers of tidal flat sand particles is used as the training dataset and input into the generator G. The discriminator D, combined with a comprehensive weighted evaluation index related to the real dataset, judges the reasonableness of the sand particle slice images generated by the generator G. If unreasonable, the image is not output and is fed back to the generator G for retraining and optimization until the tidal flat sand particle slice images generated by the generator G successfully pass the discrimination of the discriminator D, and the generator G satisfies... Minimum, discriminator D satisfies To maximize the Nash equilibrium and satisfy the following objective function:

[0009]

[0010] Output it.

[0011] In the formula, z1 represents the noise variable. Let p represent a given distribution. data Represents the true distribution of the sample. This indicates that a neural network, by taking a noise variable z1 as input, can map... D (x) This represents a neural network, where the input data is real data or... The output data is a real number between 0 and 1; D(G) (z1) ) indicates input G (z1) The subsequent neural network, Represents the expected value of real data. Indicates the expected data to be generated. The generator G represents the loss function. Let D represent the loss function of the discriminator, and V(D,G) represent the objective function. This represents the optimization process of the objective function;

[0012] S4. Reconstruct and stack the slice images of different layers of tidal flat sand particles generated by the generative adversarial neural network algorithm to obtain discrete point cloud coordinates of particle surface morphology information. Then, use the Nth order spherical harmonic function for particle surface points (x, y, z) for three-dimensional reconstruction to obtain a randomly generated three-dimensional reconstruction model of tidal flat sand particles.

[0013] Preferably, the standard for selecting tidal flat sand particles in step S1 is that the impurity content is less than 10%.

[0014] Preferably, the particle contour extraction method based on semantic segmentation in step S2 is a lightweight U-net network. The lightweight U-net network randomly deactivates the slice images of different layers of tidal flat sand particles and inputs them into four downsampling blocks for convolutional layer encoding and pooling operations for compression. The slice images are compressed to the bottom feature layer, and the upsampling blocks decode and output images of the same size as the slice images. Finally, the slice images are output using binarization processing.

[0015] Furthermore, in the creation of the lightweight U-net network dataset, the sliding window method was used to crop slice images of different layers of tidal flat sand particles.

[0016] Preferably, the evaluation indicators in step S3 include overall shape, edge angle or ellipticity, and roughness.

[0017] Preferably, the specific process of step S4 is as follows:

[0018] S41. Spherical Parameterization: Point cloud data coordinate transformation, creating a one-to-one mapping from a 3D closed surface to a unit sphere, corresponding each point on the surface of tidal flat sand particles to the polar coordinates of the unit sphere. X = (x, y, z) can be represented as:

[0019]

[0020]

[0021]

[0022]

[0023] In the formula, x, y, and z are the coordinate values ​​of a one-to-one mapping from a three-dimensional closed surface to a unit sphere in the Cartesian coordinate system, and θ is the polar angle of each discrete point on the particle surface. Let r be the azimuth angle of each discrete point on the particle surface, and r be the polar radius of each discrete point on the particle surface.

[0024] S42. Expand the 0th order spherical harmonic function of the point (x, y, z) on the particle surface to determine the coordinates of the particle center, and move the origin of the coordinate system to the coordinates of the particle center.

[0025] S43. Solve for the direction of the particle's principal axis and rotate the particle so that its long, medium, and short principal axes are aligned with the x, y, and z axes of the global coordinate system, respectively.

[0026] S44. Three-dimensional reconstruction is performed using the Nth-order spherical harmonic function of the particle surface point (x, y, z). As the total order N of the spherical harmonic function increases, the reconstructed particle morphology becomes increasingly similar to the real particle.

[0027]

[0028]

[0029]

[0030] In the formula, These are the spherical harmonic coefficients corresponding to the x, y, and z coordinates, respectively. Let m be a spherical harmonic function of order n and degree m. For the accompanying Legendre polynomial, where,

[0031]

[0032]

[0033] The magnitude of the coefficients of order n is:

[0034]

[0035]

[0036]

[0037] In the formula, a xn for The magnitude of the coefficient at the x-coordinate corresponding to the order of the spherical harmonic coefficients, a yn for The magnitude of the coefficient at the spherical harmonic coefficient order corresponding to the y-coordinate, a zn for The magnitude of the coefficients at the spherical harmonic order corresponding to the z-coordinate.

[0038] Beneficial effects: 1) This invention uses generative adversarial neural networks in deep learning to randomly generate and refine the modeling of tidal flat sand particles, successfully solving the problem of random sand particle generation, and has a certain degree of accuracy and advancement;

[0039] 2) This invention uses artificial intelligence deep learning algorithms to randomly generate tidal flat sand particles, achieving the purpose of realistically simulating and generating a large number of natural tidal flat sand particles;

[0040] 3) This invention achieves the convenience and randomness of random generation of tidal flat sand particles. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0042] Figure 2 This is a schematic diagram of the process of generating random tidal flat sand particle slice images based on generative adversarial neural networks according to the present invention;

[0043] Figure 3 This invention is based on the real particle feature map of tidal flat sand extracted by generative adversarial neural network;

[0044] Figure 4 These are CT slice images (a) of tidal flat sand particles and slice images (b) randomly generated based on generative adversarial neural networks in embodiments of the present invention. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments:

[0046] Example 1

[0047] like Figure 1 As shown, the method for random generation and refined modeling of tidal flat sand particles based on generative adversarial neural networks includes the following steps:

[0048] S1. Select tidal flat sand particles with impurity content of less than 10% and minimal interference with micro-CT scanning, and place them in a plastic tube with an inner diameter and height of 10 mm. This ensures that each tidal flat sand particle is separated by a plastic sheet, facilitating subsequent image segmentation.

[0049] S2. Microscopic CT layer-by-layer scanning of tidal flat sand particles was used to obtain slice images of different layers of each tidal flat sand particle. The slice dataset of different layers of each sand particle was segmented by a particle contour extraction method based on semantic segmentation. The particle contour extraction method based on semantic segmentation is a lightweight U-net network. The lightweight U-net network randomly deactivates the slice images of different layers of each tidal flat sand particle and inputs them into 4 downsampling blocks for convolutional layer encoding and pooling operations for compression. The slice images are compressed to the bottom feature layer. The upsampling blocks decode and output images of the same size as the slice images. Finally, the slice images are output using binarization. In the creation of the lightweight U-net network dataset, the sliding window method is used to crop the slice images of different layers of each tidal flat sand particle to ensure that the input and output image sizes are consistent with the input layer size.

[0050] S3, such as Figure 2 As shown, a generative adversarial neural network (GAN) algorithm is used to construct a discriminator D and a generator G. The dataset of slices representing different layers of tidal flat sand particles is used as the training dataset and input into the generator G. The discriminator D, combined with a comprehensive weighted evaluation index related to the real dataset, judges the reasonableness of the sand particle slice images generated by the generator G. If unreasonable, it is not output and is fed back to the generator G for retraining and optimization until the tidal flat sand particle slice images generated by the generator G successfully pass the discrimination of the discriminator D, and the generator G satisfies... Minimum, discriminator D satisfies To maximize the Nash equilibrium and satisfy the following objective function:

[0051]

[0052] Output it.

[0053] In the formula, z1 represents the noise variable. Let p represent a given distribution. data Represents the true distribution of the sample. This indicates that a neural network, by taking a noise variable z1 as input, can map... D (x) This represents a neural network, where the input data is real data or... The output data consists of real numbers between 0 and 1; Indicates input The subsequent neural network, Represents the expected value of real data. Indicates the expected data to be generated. The generator G represents the loss function. Let D represent the loss function of the discriminator, and V(D,G) represent the objective function. The objective function is optimized by keeping the generator G constant, adjusting the discriminator D to distinguish between real and fake data, maximizing V(D,G), and keeping the discriminator D constant, adjusting the generator G to make fake data judged as real, minimizing V(D,G), and continuously generating adversarial responses to reach the optimal state.

[0054] S4. Reconstruct and stack the slice images of different layers of tidal flat sand particles generated by the generative adversarial neural network algorithm to obtain discrete point cloud coordinates of particle surface morphology information. Then, use the Nth order spherical harmonic function for the particle surface points (x, y, z) for three-dimensional reconstruction to obtain a randomly generated three-dimensional reconstruction model of tidal flat sand particles. The specific process is as follows:

[0055] S41. Spherical Parameterization: Point cloud data coordinate transformation, creating a one-to-one mapping from a 3D closed surface to a unit sphere, corresponding each point on the surface of tidal flat sand particles to the polar coordinates of the unit sphere. X = (x, y, z) can be represented as:

[0056]

[0057]

[0058]

[0059]

[0060] In the formula, x, y, and z are the coordinate values ​​of a one-to-one mapping from a three-dimensional closed surface to a unit sphere in the Cartesian coordinate system, and θ is the polar angle of each discrete point on the particle surface. Let r be the azimuth angle of each discrete point on the particle surface, and r be the polar radius of each discrete point on the particle surface.

[0061] S42. Expand the 0th order spherical harmonic function of the point (x, y, z) on the particle surface to determine the coordinates of the particle center, and move the origin of the coordinate system to the coordinates of the particle center.

[0062] S43. Solve for the direction of the particle's principal axis and rotate the particle so that its long, medium, and short principal axes are aligned with the x, y, and z axes of the global coordinate system, respectively.

[0063] S44. Three-dimensional reconstruction is performed using the Nth-order spherical harmonic function of the particle surface point (x, y, z). As the total order N of the spherical harmonic function increases, the reconstructed particle morphology becomes increasingly similar to the real particle.

[0064]

[0065]

[0066]

[0067] In the formula, These are the spherical harmonic coefficients corresponding to the x, y, and z coordinates, respectively. Let m be a spherical harmonic function of order n and degree m. For the accompanying Legendre polynomial, where,

[0068]

[0069]

[0070] The magnitude of the coefficients of order n is:

[0071]

[0072]

[0073]

[0074] In the formula, a xn for The magnitude of the coefficient at the x-coordinate corresponding to the order of the spherical harmonic coefficients, a yn for The magnitude of the coefficient at the spherical harmonic coefficient order corresponding to the y-coordinate, a zn for The magnitude of the coefficients at the spherical harmonic coefficient order corresponding to the z-coordinate.

[0075] Figure 4 (a) in the image is a CT slice image of tidal flat sand particles. The slice image randomly generated by the generative adversarial neural network obtained by the method of this invention is shown below. Figure 4As shown in (b), the results show that the present invention successfully solves the problem of random generation of sand particles, and has a certain degree of accuracy and advancement; it uses artificial intelligence deep learning algorithm to randomly generate tidal flat sand particles, achieving the purpose of realistic simulation and generating a large number of natural tidal flat sand particles; and it realizes the convenience and randomness of random generation of tidal flat sand particles.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for random generation and refined modeling of beach sand grains based on generative adversarial neural networks, characterized in that, The method comprises the following steps: S1, selecting the beach sand particles and placing them in a container, so that each beach sand particle is separated by a plastic sheet; S2, using micro-CT to scan the beach sand particles layer by layer to obtain slice images of different layers of each beach sand particle, and using a particle contour extraction method based on semantic segmentation to segment the slice data set of each beach sand particle in different layers; S3, adopt the generative adversarial neural network algorithm, construct the discriminator D and the generator G, input the slice data set segmented from each beach sand particle different layer as the training data set into the generator G, the discriminator D combines the comprehensive weighted evaluation index related to the real data set, discriminates the rationality of the sand particle slice image generated by the generator G, and does not output and feedback to the generator G for retraining optimization if it is not reasonable, until the sand particle slice image generated by the generator G successfully passes the discrimination of the discriminator D, the generator G meets minimum, the discriminator D meets maximum, reaches Nash equilibrium, and meets the following objective function: outputting, wherein z1 denotes a noise variable, denotes a given distribution, p data denotes a true distribution of a sample, denotes a neural network that can map out D (x) denotes a neural network that inputs data that is either real data or output data is a real number from 0 to 1; denotes input a neural network after denotes a real data expectation, denotes a generated data expectation, denotes a generator G loss function, denotes a discriminator D loss function, V(D, G) denotes an objective function; denotes an optimization process of the objective function; S4, reconstructing and stacking the slice images of different layers of beach sand particles generated by the generative adversarial neural network algorithm to obtain particle surface morphology information discrete point cloud coordinates, and using an N-order spherical harmonic function for particle surface points (x, y, z) for three-dimensional reconstruction to obtain a randomly generated three-dimensional reconstruction model of the beach sand particle.

2. The generative adversarial neural network based random generation and refinement modeling method of intertidal sand particles according to claim 1, characterized in that: The standard for selecting beach sand particles in step S1 is that the impurity content is less than 10%.

3. The generative adversarial neural network based random generation and refinement modeling method of beach sand particles according to claim 1, characterized in that: In step S2, the particle contour extraction method based on semantic segmentation is a lightweight U-net network, which is a lightweight U-net network that randomly inactivates each slice image of different layers of beach sand particles and inputs 4 downsampling blocks for convolution layer encoding and pooling operation compression. The slice image is compressed to the bottom feature layer, and the up-sampling block decodes and outputs an image with the same size as the slice image. Finally, a binary processing output slice image is output.

4. The generative adversarial neural network based random generation and refinement modeling method of intertidal sand particles according to claim 3, characterized in that: In the data set creation of the lightweight U-net network, a sliding window method is used to crop each slice image of different layers of beach sand particles.

5. The generative adversarial neural network based random generation and refinement modeling method of beach sand particles according to claim 1, characterized in that: The evaluation indexes in step S3 include overall shape, corner degree or ellipticity, and roughness.

6. The generative adversarial neural network based random generation and refinement modeling method of beach sand particles according to claim 1, characterized in that, The specific process of step S4 is: S41, spherical parameterization: point cloud data coordinate conversion, creating a one-to-one mapping from a three-dimensional closed surface to a unit sphere, and one-to-one correspondence between each point on the surface of the beach sand particle and the polar coordinates of the unit sphere, X=(x, y, z) can be represented as: In the formula, x, y, z are coordinate values of a one-to-one mapping of a three-dimensional closed surface to a unit sphere in a Cartesian coordinate system, θ is a polar angle of each discrete point on the surface of the particle, is an azimuth angle of each discrete point on the surface of the particle, and r is a polar radius of each discrete point on the surface of the particle. S42, expand the 0-order spherical harmonic function of the particle surface point (x, y, z), determine the particle center coordinates, and move the origin of the coordinate system to the particle center coordinates; S43, solve the particle principal axis direction, and rotate the particle so that the long, medium and short principal axes of the particle are aligned with the x, y and z axes of the global coordinate system, respectively; S44, three-dimensional reconstruction of the N-order spherical harmonic function of the particle surface point (x, y, z), as the total order N of the spherical harmonic function increases, the reconstructed particle shape is more and more similar to the real particle, wherein are the x, y, z coordinate corresponding spherical harmonics coefficients, respectively; is a spherical harmonic of order n, degree m, is the associated Legendre polynomial, wherein, The order n coefficient amplitude is: where a xn is the coefficient amplitude in the x coordinate corresponding to the order of the spherical harmonic coefficient, a yn is the coefficient amplitude in the y coordinate corresponding to the order of the spherical harmonic coefficient, a zn is the coefficient amplitude in the z coordinate corresponding to the order of the spherical harmonic coefficient.

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