Random generation method of star and non-star lunar soil particle morphology based on limited scanning

Abstract

The application discloses a kind of star and non-star lunar soil particle morphology random generation method based on limited scanning, it is related to lunar soil particle morphology simulation technical field.The method provided by the present application obtains the three-dimensional scanning data of lunar soil particle first;Then process lunar soil scanning data, close the internal pore of lunar soil particle, obtain the outer surface point cloud of lunar soil particle;Again, through surface parameterization and spherical harmonic expansion under Cartesian coordinate system, the reconstruction of star / non-star lunar soil particle is realized;Again, based on the spherical harmonic function spectrum of lunar soil particle spherical harmonic coefficient matrix, new spherical harmonic coefficient matrix is randomly generated;Finally, based on the spherical harmonic coefficient matrix randomly generated, lunar soil particle is reconstructed.The present application realizes the three-dimensional reconstruction and random generation of star and non-star lunar soil particle under the condition of limited scanning data, can be applied to lunar soil morphology fine numerical modeling and lunar soil particle 3D printing, provides an effective way for breaking through the restriction of lunar soil research to lunar sample scarcity.

Description

Technical Field

[0001] This invention relates to the field of lunar soil particle morphology simulation technology, and particularly to a method for randomly generating lunar soil particle morphology. Background Technology

[0002] Lunar regolith, as a loose weathered layer covering the lunar surface, is directly affected by human activities related to lunar exploration and construction. Whether it's the stability of probe landings, the mobility of lunar rovers, or the in-situ construction of future lunar bases, all are closely related to the physical and mechanical properties of lunar regolith.

[0003] Given the extremely high cost of Earth-Moon transportation, in-situ 3D printing using lunar regolith is one of the main technological means for constructing lunar facilities. Accurate understanding of lunar regolith properties is a crucial prerequisite for ensuring the safety of lunar surface activities and achieving efficient utilization of lunar regolith. However, real lunar regolith samples are extremely scarce, making it difficult to support large-scale engineering application research.

[0004] Numerical simulation based on the discrete element method has become a key tool for in-depth exploration of the complex mechanical behavior of lunar regolith under sample-constrained conditions. The reliability of the simulation results largely depends on the accurate characterization of lunar regolith particle morphology. However, existing simulation studies often oversimplify the description of particle morphology, failing to fully reflect the true complex morphology of lunar regolith particles, leading to uncertainties in the simulation results and consequently affecting the accuracy of engineering designs.

[0005] Developing high-precision methods for reconstructing and randomly generating the 3D morphology of lunar soil particles is a core technological requirement for improving numerical simulation prediction capabilities and supporting in-situ 3D printing engineering practices using lunar soil. Current methods for particle reconstruction and random generation based on spherical harmonics focus on spherical harmonic expansion in spherical coordinates. This method has been relatively maturely applied to processing conventional Earth soil particles (such as star-shaped particles, which are mostly nearly circular or simply convex), but it has limitations in reconstructing non-star-shaped particles.

[0006] Lunar regolith particles, due to their unique formation environment, exhibit extremely high morphological complexity and significant non-convexity, such as irregular depressions and complex pore structures. This non-convexity leads to strong mechanical interlocking between particles, directly affecting the macroscopic shear strength, compressibility, and stacking and molding behavior of lunar regolith during 3D printing. On the other hand, existing random generation methods based on spherical harmonics typically require statistical analysis of a large number of original particles to obtain the probability distribution of the particle's spherical harmonic function spectrum, and then using mathematical methods to generate a new set of spherical harmonic function spectra to randomly generate morphologically similar particles. However, lunar regolith samples are extremely rare, making it difficult to obtain statistically significant distribution samples.

[0007] Therefore, how to achieve three-dimensional spherical harmonic random generation in Cartesian coordinates using a simple method under the condition of small sample original particles is the key bottleneck for realizing rapid and precise random generation of non-star-shaped lunar soil particles, and it is also a technical problem that urgently needs to be solved. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a method for randomly generating the morphology of star-shaped and non-star-shaped lunar regolith particles based on finite scanning. First, lunar regolith particles are scanned and the scanned images are processed to obtain a set of coordinates for points on the outer surface of the particles. Second, based on surface parameterization and spherical harmonic expansion in Cartesian coordinates, the three-dimensional morphology of the lunar regolith particles is accurately reconstructed. Then, a new spherical harmonic coefficient matrix is ​​randomly generated based on the original spherical harmonic function spectrum calculated from the spherical harmonic coefficient matrix. Finally, the lunar regolith particles are reconstructed using the newly generated spherical harmonic matrix, thus achieving the random generation of lunar regolith particles. This invention is specifically implemented through the following techniques.

[0009] This invention provides a method for randomly generating the morphology of star-shaped and non-star-shaped lunar soil particles based on finite scanning, comprising the following steps:

[0010] Obtain three-dimensional scan images of the original lunar soil particles and classify the original lunar soil particles;

[0011] The three-dimensional scan image data of each original lunar soil particle is processed to close the internal pores of the original lunar soil particle, thereby obtaining the point cloud of the outer surface of the original lunar soil particle.

[0012] Obtain the spatial coordinate information set of the point cloud on the outer surface of the original lunar soil particles in the spherical coordinate system; based on the spatial coordinate information set, perform spherical harmonic expansion of the spatial coordinates of the points on the outer surface of the original lunar soil particles in the Cartesian coordinate system to obtain the initial spherical harmonic coefficient matrix of each original lunar soil particle.

[0013] The initial spherical harmonic function spectrum is calculated using the initial spherical harmonic coefficient matrix, and a new spherical harmonic coefficient matrix is ​​randomly generated using the initial spherical harmonic function spectrum;

[0014] Using the new spherical harmonic coefficient matrix, random lunar soil particles similar to the original lunar soil particles are reconstructed and generated.

[0015] Furthermore, Raman spectroscopy and CT scanning were used to classify the original lunar soil particles.

[0016] Furthermore, the original lunar regolith particles were preliminarily classified into multi-mineral, single-mineral, and glass particles using Raman spectroscopy.

[0017] Each original lunar regolith grain was subjected to a CT scan, and the multi-mineralized original lunar regolith grains were classified into basalt grains, breccia grains, and cement grains.

[0018] Before performing a CT scan, lunar soil particles can be adhered to an epoxy resin plate with gaps between them to prepare a lunar soil particle scanning sample. Each lunar soil particle's CT three-dimensional scan image consists of at least 8,000 voxels.

[0019] Furthermore, the method for processing the three-dimensional scan image data of each of the original lunar soil particles includes single-particle segmentation, median filtering, grayscale threshold segmentation, impurity removal, gap closure and filling, and generation of the outer surface of the original lunar soil particles.

[0020] Furthermore, the method for generating the outer surface of the original lunar soil particles is as follows:

[0021] The step artifacts caused by voxels in the three-dimensional scan image data of the original lunar soil particles are removed by the moving cube algorithm to generate a smooth outer surface of the original lunar soil particles.

[0022] The outer surface of the original lunar soil particles is characterized by a triangular mesh with a certain number of grids to obtain a three-dimensional point coordinate information set of the point cloud on the outer surface of the original lunar soil particles.

[0023] Furthermore, the method for obtaining the spatial coordinate information set of the point cloud of the outer surface of the original lunar soil particles in spherical coordinates is as follows:

[0024] Using the surface parameterization method, a continuous bijection from the Cartesian coordinate system to the unit sphere is performed on the outer surface point cloud of the original lunar soil particles to obtain the spatial coordinate information set in the spherical coordinate system, as shown in Equation I;

[0025] Formula I;

[0026] Where S is the set of spatial coordinate information in spherical coordinates, and θ k and φ k These are the co-latitude angle and azimuth angle of the k-th point cloud of the original lunar soil particles in the spherical coordinate system, respectively.

[0027] Furthermore, the surface parameterization method involves establishing a continuous bijective mapping from the Cartesian coordinate system to a unit sphere for the point cloud of the original lunar regolith particle's outer surface. Specifically, for any point on the lunar regolith particle's surface, its Cartesian coordinates (x, y, z) are uniquely mapped to spherical coordinates (θ, φ) on the unit sphere, and the corresponding radial distance r(θ, φ) is recorded. This completely characterizes the irregular particle surface as a set of spatial coordinate information in the spherical coordinate system.

[0028] Furthermore, based on the spatial coordinate information set, the method for obtaining the initial spherical harmonic coefficient matrix of each original lunar regolith particle by performing a spherical harmonic expansion of the spatial coordinates of the outer surface points in the Cartesian coordinate system is as follows:

[0029] Based on the spatial coordinate information set, the spherical harmonic order is set to 25, and the spatial coordinates of the outer surface points of the original lunar soil particles are expanded in Cartesian coordinates, as shown in Equation II.

[0030] Formula II;

[0031] Where n and m are the spherical harmonic order and degree, respectively, n = 0, 1, ..., 25; θ is the colatitude angle, defined in [0, π]; φ is the azimuth angle, defined in [0, 2π]; C n,l m Y represents the spherical harmonic coefficients of order n and order m in the l direction, where l represents the x, y, or z direction; n m Let m be the spherical harmonic basis functions of order n;

[0032] The initial spherical harmonic coefficient matrix of each original lunar soil particle is obtained by fitting and solving using the least squares method, as shown in Formulas III and IV.

[0033] Formula III;

[0034] Formula IV.

[0035] Furthermore, the method for calculating the initial spherical harmonic function spectrum using the initial spherical harmonic coefficient matrix is ​​as follows:

[0036] Substitute the initial spherical harmonic coefficient matrix into Equation V to calculate the initial spherical harmonic function spectra in the x, y, and z directions;

[0037] Formula V;

[0038] In the formula, L n,l Let be the nth-order initial spherical harmonic function spectrum of lunar soil particles in the x, y, or z directions. , , are the second-order Euclidean norms of the spherical harmonic coefficient vectors; n=0,1,…,25.

[0039] Furthermore, based on the initial spherical harmonic function spectrum, the method for randomly generating a new spherical harmonic coefficient matrix is ​​as follows:

[0040] Based on the principle of conjugate symmetry of the spherical harmonic coefficient matrix and the principle of making the new spherical harmonic function spectrum the same as the initial spherical harmonic function spectrum of the original lunar soil particles, an arbitrary number of new spherical harmonic coefficient matrices and corresponding new spherical harmonic function spectra are repeatedly and randomly generated according to formulas VI and VII.

[0041] Formula VI;

[0042] Formula VII;

[0043] Among them, a n,l m and b n,l m Let a be a random number between 0 and 1 that follows a uniform distribution. 1,x 0 b 1,x 1 a 1,y 0 a 1,y 1 a 1,z 1 b 1,z 0 All values ​​are 0 to ensure the direction of the main axis of the random particles.

[0044] Optionally, a n,l m and b n,l m Random generation is achieved using methods such as Mason twisting.

[0045] The method for reconstructing and generating random lunar regolith particles similar to the original lunar regolith particles using the new spherical harmonic coefficient matrix is ​​as follows:

[0046] Using the new spherical harmonic coefficients in the new spherical harmonic coefficient matrix as weights, and combining them with the spatial coordinates of the outer surface points of lunar soil particles, the spherical harmonic expansion formula in the Cartesian coordinate system is used to obtain the coordinate set of surface points of random lunar soil particles, thereby reconstructing and generating random lunar soil particles.

[0047] Furthermore, the method for reconstructing and generating random lunar soil particles similar to the original lunar soil particles using the new spherical harmonic coefficient matrix is ​​as follows: using the new spherical harmonic coefficients in the new spherical harmonic coefficient matrix as weights, and combining the spatial coordinates of the outer surface points of the lunar soil particles with the spherical harmonic expansion formula in the Cartesian coordinate system, the coordinate set of the surface points of the random lunar soil particles is obtained, thereby reconstructing and generating random lunar soil particles.

[0048] Furthermore, the method provided by the present invention also includes: verifying the similarity between the random lunar soil particles and the original lunar soil particles.

[0049] Furthermore, by calculating the multi-scale morphological parameters of random lunar soil particles, the morphological similarity of randomly generated particles can be quantitatively verified.

[0050] Optionally, the specific verification method is as follows:

[0051] Calculate the particle's slenderness ratio, sphericity, convexity, and roundness.

[0052] The slenderness ratio is calculated from the lengths of the three principal axes of the particles (P1>P2>P3), and is the average of the flatness ratio (P3 / P2) and the elongation ratio (P2 / P1).

[0053] Sphericity is the ratio of the surface area of ​​a sphere of equal volume to that of a particle to the actual surface area of ​​the particle.

[0054] Convexity is the ratio of a particle's volume to its smallest convex hull volume.

[0055] Roundness is based on the curvature-weighted average of the local edges of the particles, reflecting the sharpness of the edges.

[0056] The above indicators systematically describe particle morphology from three scales: overall shape, local angularity, and surface texture.

[0057] Compared with existing technologies, the advantages of this invention are as follows: First, the method of this invention acquires three-dimensional images of different types of lunar regolith particles (including star-shaped and non-star-shaped particles) through high-resolution CT scanning, and obtains point clouds of the particle's outer surface through image processing. Based on this, accurate reconstruction of the three-dimensional morphology of the lunar regolith particles is achieved through surface parameterization and spherical harmonic expansion in Cartesian coordinates. Furthermore, this invention calculates the spherical harmonic function spectrum based on the spherical harmonic coefficient matrix and reconstructs the particles using randomly generated spherical harmonic coefficient matrices, achieving efficient generation of a large number of lunar regolith particle models with morphological characteristics similar to the original particles. Attached Figure Description

[0058] Figure 1 The diagram below illustrates the steps of the method for reconstructing and randomly generating three-dimensional morphology of lunar soil particles according to the present invention.

[0059] Figure 2 For example: High-resolution CT scan results of lunar soil particles.

[0060] Figure 3 The image shows scanned images of different types of lunar soil particles and the processing steps.

[0061] Figure 4 For example: A schematic diagram comparing the three-dimensional reconstructed morphology of lunar soil particles with different spherical harmonic orders.

[0062] Figure 5 Image: A schematic diagram showing the morphological comparison between the reconstructed lunar soil particles and the original lunar soil particle image.

[0063] Figure 6 For example: A schematic diagram comparing the morphology of randomly generated lunar soil particles with that of reconstructed lunar soil particle images.

[0064] Figure 7 The image shows a comparison of the multi-scale morphological parameter distributions of randomly generated particles and reconstructed particles.

[0065] Figure 8The comparison results are as follows: spherical harmonic reconstruction in spherical coordinates and spherical harmonic reconstruction in Cartesian coordinates. Detailed Implementation

[0066] The technical solution of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] Example 1

[0068] The method for randomly generating the morphology of star-shaped and non-star-shaped lunar soil particles based on finite scanning provided in this embodiment is as follows: Figure 1 As shown, the specific steps are as follows.

[0069] Step 1: Obtain 3D scan images and corresponding data of the original lunar soil particles, and classify the original lunar soil particles.

[0070] This embodiment uses Raman spectroscopy and CT scanning to determine the type of original lunar regolith particles. The specific steps are as follows:

[0071] (1) Based on Raman spectroscopy analysis, the particles were initially classified. Multi-mineral particles showed superposition of multi-phase characteristic peaks, single-mineral particles showed only a single mineral characteristic peak group, while glass particles showed a broad diffuse envelope peak. Therefore, the original lunar soil particles were initially classified into multi-mineral, single-mineral and glass particles.

[0072] Since the morphology of lunar soil particles varies depending on the type, this embodiment, by pre-labeling the particle type, allows for the direct retrieval of the corresponding particle sample according to actual needs in the actual application after random generation.

[0073] (2) Adhere the original lunar soil particles to an epoxy resin plate, leaving a gap between adjacent original lunar soil particles, and prepare a scanning sample of original lunar soil particles.

[0074] (3) A high-resolution CT scan was then performed, with each scanned particle consisting of at least 8,000 voxels. Based on the three-dimensional CT scan images, the multi-mineralized original lunar regolith particles could be further classified into basalt particles, breccia particles, and cement particles. For example... Figure 2 As shown, the basalt grains are relatively uniform inside and often appear bright white to grayish-white; the breccia grains show angular breccia boundaries, fissures and fragments of different gray levels inside, and the grain edges are mostly irregular with obvious edges; the cement grains contain a large number of porous and fissure structures.

[0075] In this step, at least one of each type of particle mentioned above should be obtained.

[0076] Step 2: Process the 3D scan image data of each original lunar soil particle to close the internal pores of the original lunar soil particle and obtain the point cloud of the outer surface of the original lunar soil particle.

[0077] like Figure 3 As shown, the processing of lunar soil 3D scanning data includes five parts: single-particle segmentation, median filtering, grayscale thresholding segmentation, pore closure and filling, and particle outer surface generation. The specific method for this step is as follows:

[0078] 1. Single-particle segmentation

[0079] Individual raw lunar soil particles were segmented and extracted to obtain CT scan data of each particle for subsequent processing.

[0080] 2. Median Filtering

[0081] Median filtering was applied to the scanned images of each original lunar soil grain to remove noise.

[0082] 3. Gray-scale threshold segmentation

[0083] The watershed algorithm is used for grayscale thresholding to distinguish the solid part of the original lunar soil particles from other parts, resulting in a binarized image.

[0084] The specific method of the watershed algorithm is as follows:

[0085] (1) The preprocessed grayscale image is regarded as a topographic map, with grayscale values ​​corresponding to altitude and the internal area of ​​the particles corresponding to low-lying areas.

[0086] (2) Then, an initial marker point is set in the core area of ​​the particle, and the water level is simulated to rise gradually from the marker point. The area that the water overflows is the particle area.

[0087] (3) When the water surfaces of adjacent particles are about to meet, the algorithm builds a watershed boundary at the meeting point to prevent the regions from merging.

[0088] (4) Finally, based on the watershed boundary, each particle is distinguished from the background. The particle area is marked as white and the background is marked as black to obtain a binarized image.

[0089] 4. Remove impurities

[0090] Based on the number of voxels, isolated small regions with a total number of voxels less than 8000 are identified as impurities and removed.

[0091] Based on this, the internal structure of the retained effective particles was analyzed. The voxel markers of each particle were traversed one by one, and the voxels of cavities marked as background inside the particles were counted. Any closed cavity completely surrounded by solid particles and not connected to the external background was identified as an internal pore. At the same time, slender background regions that extend linearly inside the particles, connecting the particle surface and the interior or penetrating both sides of the particles, were identified as internal fissures.

[0092] By removing impurities, the pores and fissures inside each original lunar soil particle were identified.

[0093] 5. Closing pores and filling

[0094] The pores and fissures inside each original lunar soil particle were closed and filled to avoid the internal pore structure from affecting the subsequent spherical harmonic reconstruction.

[0095] 6. The outer surface of the generated primitive lunar soil particles

[0096] (1) The step artifacts caused by voxels are removed by moving cube algorithm to generate a smooth original lunar soil particle outer surface.

[0097] The specific method of the moving cube algorithm is as follows:

[0098] ① Divide the binary voxel data of the particle into several adjacent small cubic voxel units. The 8 vertices of each voxel unit are marked as 0 or 1 depending on whether they are inside or outside the particle. Thus, each unit has a total of 256 vertex marking combinations.

[0099] ② For each voxel element, a predefined triangular patch configuration table is looked up based on its vertex calibration combination. Triangular patches that intersect with the particle surface are generated within the voxel element through interpolation. The vertex positions are accurately calculated using linear interpolation to approximate the actual surface positions.

[0100] ③ After traversing all voxel units, all triangular patches are stitched together into a continuous triangular mesh surface. This mesh surface is smooth and continuous, eliminating the blocky staircase effect of the original voxel data, and finally outputting a high-precision granular 3D surface model for subsequent geometric parameter calculation. Among them, the isosurface threshold is set to 0.5 (normalized density value), which is located in the middle position between the solid (1) and the background (0) to ensure that the isosurface accurately passes through the voxel boundary.

[0101] (2) The outer surface of the original lunar regolith particles is represented by a triangular mesh with 5000 grids, and the three-dimensional point coordinate information set V=(x) of the point cloud of the outer surface of the original lunar regolith particles is finally obtained. k ,y k ,z k ), where k is the point cloud number.

[0102] Step 3: Perform surface parameterization on the point cloud of the outer surface of the original lunar regolith particles to obtain a set of spatial coordinate information in spherical coordinates. Based on the set of spatial coordinate information, perform spherical harmonic expansion of the spatial coordinates of the outer surface points of the original lunar regolith particles in Cartesian coordinates to obtain the initial spherical harmonic coefficient matrix of each original lunar regolith particle, so as to realize the subsequent accurate reconstruction of the original lunar regolith particles.

[0103] 1. Based on the surface parameterization method, the point cloud of the outer surface of the original lunar soil particles is continuously bijected from the Cartesian coordinate system to the unit sphere, and the spatial coordinate information set S in the spherical coordinate system is obtained, as shown in Equation I.

[0104] Formula I;

[0105] Where S is the set of spatial coordinate information in spherical coordinates, and θ k and φ k These are the co-latitude angle and azimuth angle of the k-th point cloud of the original lunar soil particles in the spherical coordinate system.

[0106] The surface parameterization method specifically involves establishing a continuous bijective mapping from the Cartesian coordinate system to a unit sphere for the point cloud of the original lunar regolith grain's outer surface. That is, for any point on the lunar regolith grain's surface, its Cartesian coordinates (x, y, z) are uniquely mapped to spherical coordinates (θ, φ) on the unit sphere, and the corresponding radial distance r(θ, φ) is recorded. This completely represents the irregular grain surface as a set of spatial coordinate information in the spherical coordinate system. For example... Figure 4 As shown in the second image from the left.

[0107] 2. Based on the theory of spherical harmonic functions (i.e., the higher the spherical harmonic order, the more accurate the particle morphology reconstruction), such as Figure 4 As shown in the figure, when n=1, 5, 10, 20 and 25, as the spherical harmonic order n increases, the shape of the reconstructed particles becomes closer and closer to the original particles.

[0108] Therefore, in this step, the spatial coordinates of the outer surface points of the original lunar soil particles are expanded in Cartesian coordinates with n=25 (i.e., the spherical harmonic order is 25), as shown in Equation II.

[0109] Formula II;

[0110] Where n and m are the spherical harmonic order and degree, respectively, n = 0, 1, ..., 25; θ is the colatitude angle, defined in [0, π]; φ is the azimuth angle, defined in [0, 2π]; C n,l m Y represents the spherical harmonic coefficients of order n and order m in the l direction, where l represents the x, y, or z direction; n m Let be the spherical harmonic basis functions of order n and degree m.

[0111] 3. Using the least squares method, the initial spherical harmonic coefficient matrix of each original lunar regolith grain is obtained by fitting and solving. As shown in Formulas III and IV; thus achieving a fine three-dimensional reconstruction of the original lunar soil particles, such as Figure 5 As shown.

[0112] Formula III;

[0113] Formula IV;

[0114] The specific method of "finding the solution using the least squares method" is as follows: Solving the spherical harmonic coefficient matrix is ​​essentially solving an overdetermined system of equations. Since there is no exact solution that strictly satisfies all equations, we instead seek an "optimal" approximate solution that minimizes the overall bias produced when this solution is substituted into all equations. By constructing the sum of squared residuals of all equations as the objective function, and taking the derivative of the objective function and setting the derivative to zero, we can derive a normal system of equations. This system of equations is normal and usually solvable. Solving this normal system of equations yields the spherical harmonic coefficient matrix that minimizes the sum of squared residuals.

[0115] Step 4: Using the initial spherical harmonic coefficient matrix Calculate the spherical harmonic spectrum L n Using the spherical harmonic function spectrum L n Randomly generate a new spherical harmonic coefficient matrix .

[0116] This step is based on the initial spherical harmonic coefficient matrix. Calculate the spectrum of spherical harmonic functions L n Furthermore, while ensuring the spherical harmonic function spectrum remains unchanged, the spherical harmonic coefficients are randomly perturbed to satisfy conjugacy, thereby generating a new spherical harmonic coefficient matrix. The specific steps are as follows.

[0117] 1. The initial spherical harmonic coefficient matrix shown in Equation III Substitute into the following formula V to calculate the initial spherical harmonic spectrum L in the x, y, and z directions. n ;

[0118] Formula V;

[0119] In the formula, L n,l The spectrum of the nth spherical harmonic function of the original lunar soil particles in the l direction (i.e., the x, y, or z direction) is given. , , are the second-order Euclidean norms of the spherical harmonic coefficient vectors; n=0,1,…,25.

[0120] 2. Based on the initial spherical harmonic function spectrum of a single original lunar regolith grain, an infinite number of new spherical harmonic coefficient matrices can be randomly generated. .

[0121] The random generation formulas for the new spherical harmonic coefficient matrix are shown in equations VI and VII below; repeating this process yields any number of new spherical harmonic coefficient matrices. and the corresponding new spherical harmonic function spectrum .

[0122] Formula VI;

[0123] Formula VII;

[0124] In the formula, a n,l m and b n,l m Let a be a random number between 0 and 1 that follows a uniform distribution. 1,x 0 b 1,x 1 a 1,y 0 a 1,y 1 a 1,z 1 b 1,z 0 All are 0 to ensure the principal axis direction of random particles. n,l m and b n,l m Random generation is achieved using methods such as Mason twisting.

[0125] In this embodiment, the Mersenne rotation algorithm is specifically based on the Mersenne prime number 2. 19937 -1 sets the state space period, and updates the state register group through bitwise operations (including cyclic shift, XOR and nonlinear combination) to output the high-bit integer value; then, through floating-point normalization, the integer range is mapped to the standard uniform interval [0,1).

[0126] During the random generation of the new spherical harmonic coefficient matrix, the new spherical harmonic coefficient matrix Two principles must also be met:

[0127] (1) It satisfies the basic requirement of a spherical harmonic coefficient matrix, namely, conjugate symmetry. For an element of order l in the matrix, the coefficient corresponding to the negative degree "-m" is equal to the complex conjugate of the coefficient of the positive degree "m" multiplied by the phase factor (−1). m .

[0128] (2) The new spherical harmonic function spectrum is the same as the initial spherical harmonic function spectrum of the original lunar soil particles. During the random generation process, the spherical harmonic spectrum values ​​(morphological weights) of each order (l) of the original particles are not changed, so that no matter how the coefficients of each order (m) are adjusted, the morphological characteristics of the generated particles are highly consistent with the original samples.

[0129] Step 5: Utilize the randomly generated new spherical harmonic coefficient matrix The reconstructed random lunar soil particles are similar to the original lunar soil particles.

[0130] Based on the generated new spherical harmonic coefficient matrix Combining this with Equation II above, the optimized new spherical harmonic coefficients are assigned as weights to the corresponding spherical harmonic basis functions to obtain the surface point coordinate set of random lunar regolith particles. Finally, random lunar regolith particles are reconstructed and generated. These random lunar regolith particles possess morphological characteristics similar to the original particles, such as... Figure 6 As shown.

[0131] By calculating the multi-scale morphological parameters of random lunar soil particles, the morphological similarity of randomly generated particles can be quantitatively verified. Specifically, the aspect ratio, sphericity, convexity, and roundness of the particles are calculated.

[0132] The slenderness ratio is calculated from the lengths of the three principal axes of the particles (P1>P2>P3), and is the average of the flatness ratio (P3 / P2) and the elongation ratio (P2 / P1).

[0133] Sphericity is the ratio of the surface area of ​​a sphere of equal volume to that of a particle to the actual surface area of ​​the particle.

[0134] Convexity is the ratio of a particle's volume to its smallest convex hull volume.

[0135] Roundness is based on the curvature-weighted average of the local edges of the particles, reflecting the sharpness of the edges.

[0136] The above indicators systematically describe particle morphology from three scales: overall shape, local angularity, and surface texture.

[0137] Figure 7 As shown. From Figure 7 As can be seen, the method of this embodiment can randomly generate particles that are similar in the distribution of morphological parameters such as aspect ratio, sphericity, convexity, and roundness to the original lunar soil particles.

[0138] Comparative examples: Controlled trials using other methods

[0139] 1. Reconstruction of non-star-shaped particles based on spherical harmonic expansion in spherical coordinates

[0140] In particle morphology reconstruction studies, while the spherical harmonic expansion method in spherical coordinates has a natural advantage in representing star-shaped particles (i.e., each ray originating from the origin intersects the particle surface at only one point), it is not suitable for reconstructing non-star-shaped particles. The fundamental reason lies in the single-valuedness constraint inherent in the geometric definition of spherical coordinates: in spherical coordinates, the particle surface is represented as a single-valued function of the radial distance r(θ,ϕ) with respect to the two polar angles. However, for non-star-shaped particles, such as grooved, ring-shaped, or bifurcated structures, rays in the same spatial direction (θ,ϕ) intersect the particle surface at multiple points, leading to multi-valued radial distances. Therefore, a single r(θ,ϕ) cannot fully describe the particle boundary.

[0141] Therefore, spherical harmonic expansion in spherical coordinates is inherently limited by star-shaped topology and cannot be directly used as an effective method for reconstructing non-star-shaped particles. Figure 8 The comparison between spherical harmonic reconstruction in spherical coordinates and spherical harmonic reconstruction in Cartesian coordinates clearly shows that spherical harmonic reconstruction in Cartesian coordinates has better adaptability to non-star-shaped particles.

[0142] 2. A random generation method based on establishing the joint probability density function of the spherical harmonic function spectrum

[0143] The limitation of this method in terms of sample quantity requirements is that a reliable estimation of the joint probability density function requires a large number of real particle samples. However, given the special nature and rarity of lunar soil samples, the sample quantity is insufficient to construct a smooth and non-sparse joint probability density distribution in the high-dimensional spectral space, thus limiting the applicability of this method.

[0144] The above detailed embodiments describe the implementation of the present invention; however, the present invention is not limited to the specific details described in the above embodiments. Within the scope of the claims and technical concept of the present invention, various simple modifications and changes can be made to the technical solution of the present invention, and these simple modifications all fall within the protection scope of the present invention.

Claims

1. A method for randomly generating the morphology of star-shaped and non-star-shaped lunar soil particles based on finite scanning, characterized in that, Includes the following steps: Obtain three-dimensional scan images of the original lunar soil particles and classify the original lunar soil particles; The three-dimensional scan image data of each original lunar soil particle is processed to close the internal pores of the original lunar soil particle, thereby obtaining the point cloud of the outer surface of the original lunar soil particle. Obtain the spatial coordinate information set of the point cloud of the outer surface of the original lunar soil particles in a spherical coordinate system; Based on the spatial coordinate information set, the spatial coordinates of the outer surface points of the original lunar soil particles are expanded in Cartesian coordinates to obtain the initial spherical harmonic coefficient matrix of each original lunar soil particle. The initial spherical harmonic function spectrum is calculated using the initial spherical harmonic coefficient matrix, and a new spherical harmonic coefficient matrix is ​​randomly generated using the initial spherical harmonic function spectrum; Using the new spherical harmonic coefficient matrix, random lunar soil particles similar to the original lunar soil particles are reconstructed and generated.

2. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, The original lunar soil particles were classified using Raman spectroscopy and CT scanning.

3. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, The method for processing the three-dimensional scan image data of each of the original lunar soil particles includes: single particle segmentation, median filtering, grayscale threshold segmentation, impurity removal, gap closure and filling, and generation of the outer surface of the original lunar soil particles.

4. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, The method for generating the outer surface of the original lunar soil particles is as follows: The step artifacts caused by voxels in the three-dimensional scan image data of the original lunar soil particles are removed by the moving cube algorithm to generate a smooth outer surface of the original lunar soil particles. The outer surface of the original lunar soil particles is characterized by a triangular mesh with a certain number of grids to obtain a three-dimensional point coordinate information set of the point cloud on the outer surface of the original lunar soil particles.

5. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, The method for obtaining the spatial coordinate information set of the point cloud of the outer surface of the original lunar soil particles in spherical coordinates is as follows: Using the surface parameterization method, a continuous bijection from the Cartesian coordinate system to the unit sphere is performed on the outer surface point cloud of the original lunar soil particles to obtain the spatial coordinate information set in the spherical coordinate system, as shown in Equation I; Formula I; Where S is the set of spatial coordinate information in spherical coordinates, and θ k and φ k These are the co-latitude angle and azimuth angle of the k-th point cloud of the original lunar soil particles in the spherical coordinate system, respectively.

6. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, Based on the aforementioned spatial coordinate information set, the method for obtaining the initial spherical harmonic coefficient matrix of each original lunar regolith particle by performing a spherical harmonic expansion of the spatial coordinates of the outer surface points in the Cartesian coordinate system is as follows: Based on the spatial coordinate information set, the spherical harmonic order is set to 25, and the spatial coordinates of the outer surface points of the original lunar soil particles are expanded in Cartesian coordinates, as shown in Equation II. Formula II; Where n and m are the spherical harmonic order and degree, respectively, n = 0, 1, ..., 25; θ is the colatitude angle, defined in [0, π]; φ is the azimuth angle, defined in [0, 2π]; C n,l m Y represents the spherical harmonic coefficients of order n and order m in the l direction, where l represents the x, y, or z direction; n m Let m be the spherical harmonic basis functions of order n; The initial spherical harmonic coefficient matrix of each original lunar soil particle is obtained by fitting and solving using the least squares method, as shown in Formulas III and IV. Formula III; Formula IV.

7. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, The method for calculating the initial spherical harmonic function spectrum using the initial spherical harmonic coefficient matrix is ​​as follows: Substitute the initial spherical harmonic coefficient matrix into Equation V to calculate the initial spherical harmonic function spectra in the x, y, and z directions; Formula V; In the formula, L n,l Let be the nth-order initial spherical harmonic function spectrum of lunar soil particles in the x, y, or z directions. , , are the second-order Euclidean norms of the spherical harmonic coefficient vectors; n=0,1,…,25.

8. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, The method for randomly generating a new spherical harmonic coefficient matrix based on the initial spherical harmonic function spectrum is as follows: Based on the principle of conjugate symmetry of the spherical harmonic coefficient matrix and the principle of making the new spherical harmonic function spectrum the same as the initial spherical harmonic function spectrum of the original lunar soil particles, an arbitrary number of new spherical harmonic coefficient matrices and corresponding new spherical harmonic function spectra are repeatedly and randomly generated according to formulas VI and VII. Formula VI; Formula VII; Among them, a n,l m and b n,l m Let a be a random number between 0 and 1 that follows a uniform distribution. 1,x 0 b 1,x 1 a 1,y 0 a 1,y 1 a 1,z 1 b 1,z 0 All values ​​are 0 to ensure the direction of the main axis of the random particles.

9. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, The method for reconstructing and generating random lunar regolith particles similar to the original lunar regolith particles using the new spherical harmonic coefficient matrix is ​​as follows: Using the new spherical harmonic coefficients in the new spherical harmonic coefficient matrix as weights, and combining them with the spatial coordinates of the outer surface points of lunar soil particles, the spherical harmonic expansion formula in the Cartesian coordinate system is used to obtain the coordinate set of surface points of random lunar soil particles, thereby reconstructing and generating random lunar soil particles.

10. The method for randomly generating star-shaped and non-star-shaped lunar soil particle morphology based on finite scanning according to claim 1, characterized in that, It also includes verifying the similarity between the random lunar soil particles and the original lunar soil particles.

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