A method and system for statistical characterization and random reconstruction of multiphase multiscale microstructures

Abstract

The application discloses a kind of multiphase multiscale microstructure statistical characterization and random reconstruction method and system, belong to the field of microstructure statistical characterization, microstructure random reconstruction, finite element mesh division, statistical characterization method uses point correlation diagram to carry out multiphase multiscale microstructure statistical characterization, point correlation diagram includes vertex and edge, it is assumed that each phase is formed by several spherical seeds, phase relationship is represented by the relative position relationship between spherical seeds, vertex is with the radius distribution and total volume fraction of seed to represent all seeds of a phase, edge is with the form of point correlation function to indicate the relative position relationship between seed.The method of the application is universal to microstructure with any number of phases, any phase relationship, any scale, can represent composite tomography image as point correlation diagram, can randomly reconstruct point correlation diagram into voxel grid, can divide microstructure voxel grid into finite element tetrahedral grid.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of microstructure statistical characterization, microstructure random reconstruction, finite element mesh partitioning, and more particularly relates to a multi-phase multi-scale microstructure statistical characterization and random reconstruction method and system. BACKGROUND

[0002] The mechanical properties and electrochemical properties of composite materials are closely related to their multi-phase multi-scale microstructure. Statistical characterization of multi-phase multi-scale microstructure uses statistical parameters to describe the microstructure, which helps to understand and analyze the performance of composite materials. Random reconstruction generates virtual microstructure based on statistical characterization parameters, and virtual microstructure can be used for performance prediction and design of composite materials. Mesh partitioning method converts virtual material model into unstructured mesh that can be used for finite element simulation, laying a foundation for physical and chemical performance prediction and microstructure design of virtual microstructure. Multi-phase multi-scale microstructure is the difficulty of statistical characterization, random reconstruction and mesh partitioning of composite materials, and is also the key to the special performance of composite materials.

[0003] Current multi-phase multi-scale microstructure statistical characterization, random reconstruction and mesh partitioning methods are limited to single-phase or two-phase microstructure, and cannot be directly migrated to multi-phase multi-scale composite material microstructure with more than three phases. For example, patent CN111289542A uses second phase particle size statistics to characterize the second phase in the material, patent CN108765554A uses microstructure dictionary to characterize two-phase porous medium and perform random reconstruction, and patent CN115984511A provides a parallel hexahedral volume average conformal mesh partitioning method for single-phase objects.

[0004] Therefore, it is a technical problem in the field to provide a microstructure statistical characterization, random reconstruction and mesh partitioning method suitable for any number of phases, any interphase relationship and any scale. SUMMARY

[0005] In view of the above defects or improvement needs of the prior art, the present application provides a multi-phase multi-scale microstructure statistical characterization and random reconstruction method and system, which aims to provide a microstructure statistical characterization, random reconstruction and mesh partitioning method suitable for any number of phases, any interphase relationship and any scale, thereby solving the technical problem that the current multi-phase multi-scale microstructure statistical characterization, random reconstruction and mesh partitioning method is limited to single-phase or two-phase microstructure and cannot be directly migrated to multi-phase multi-scale composite material microstructure with more than three phases.

[0006] To achieve the above-mentioned purpose, according to one aspect of the present application, the following technical solution is provided:

[0007] A method for statistically characterizing a multi-phase and multi-scale microstructure, the method comprising: generating a point correlation graph for statistically characterizing the multi-phase and multi-scale microstructure, the point correlation graph comprising vertices and edges, wherein each phase is represented by a plurality of spherical seeds, a relationship between phases is represented by relative positions between the spherical seeds, each vertex represents all seeds of one phase, and each edge represents a relative position between seeds.

[0008] Preferably, the method comprises the following steps:

[0009] (1) Predefining a seed set for each phase in the three-dimensional tomographic image, the seed set comprising a sufficient number of seeds capable of filling the region of the phase in the three-dimensional tomographic image;

[0010] (2) Filling the region of the corresponding phase in the three-dimensional tomographic image with the seeds in the pre-defined seed set in descending order of radius, allowing a set amount of overlap between the seeds during the filling, and ensuring that the seeds of each phase do not exceed the region of the phase in the three-dimensional tomographic image, determining the coordinates of all seeds of the phase after the filling, and abandoning the filling of seeds that have insufficient space in the pre-defined seed set; and filling the regions of all phases in the three-dimensional tomographic image in this way;

[0011] (3) For a phase, statistically characterizing the radius distribution of the seeds filled into the region of the phase in the three-dimensional tomographic image and the total volume fraction of the seeds, using the total volume fraction of the seeds as the volume fraction of the phase, and completing the establishment of a single vertex of the point correlation graph; and completing the establishment of all vertices of the point correlation graph in this way;

[0012] (4) For a phase, statistically characterizing the distances between the seeds of the phase and the seeds of other phases or another phase, calculating the point correlation function, and completing the establishment of a single edge from the phase to itself or another phase; and completing the establishment of all edges of the point correlation graph in this way.

[0013] Preferably, step (1) is specifically: determining the radius interval of the seeds of a phase according to the maximum and minimum sizes of the phase in the three-dimensional tomographic image, generating a sufficient number of seeds for each radius sub-interval divided from the radius interval by a set step length as the seed set of the phase, i.e., the pre-defined seed set;

[0014] In step (2), the set amount of overlap is 0-0.4 of the radius of the larger seed in the overlapping seeds of two phases.

[0015] In step (3), the method for statistically characterizing the radius distribution of the seeds is: statistically characterizing the radius of the seeds filled into the region of the phase in the three-dimensional tomographic image, fitting the statistical data of the radius of the seeds using a prior model of the radius distribution, and obtaining the radius distribution of the seeds.

[0016] In step (4), the point correlation function is the probability density function of the distance between seeds. The point correlation function is obtained by fitting the statistical data of the distance between seeds using the prior model of the probability density function.

[0017] Preferably, in the above method, by recombining the vertices and edges of the existing point correlation graph, and / or setting the seed radius distribution and phase volume fraction corresponding to the vertices of the point correlation graph, and / or setting the point correlation function corresponding to the edges of the point correlation graph, a statistical representation of a new microstructure with different phase numbers, different phase scales, phase volume fractions and / or phase relationships is constructed.

[0018] According to another aspect of the present invention, the following technical solution is also provided:

[0019] A method for stochastic reconstruction of multiphase, multiscale microstructures includes the following steps:

[0020] (S1) Sample the seeds of the vertices of the point correlation graph multiple times until the total volume of the sampled seeds reaches the set phase volume, and complete the reconstruction of a single vertex of the point correlation graph; complete the reconstruction of all vertices in this way.

[0021] The point correlation graph is used to statistically characterize multiphase and multiscale microstructures. It includes vertices and edges. Each phase is composed of several spherical seeds, and the relationship between phases is characterized by the relative positional relationship between the spherical seeds. The vertices represent all seeds of a phase by the radius distribution of the seeds and the total integral number. The edges represent the relative positional relationship between the seeds in the form of point correlation functions.

[0022] (S2) Divide all seeds into multiple batches according to their radius;

[0023] (S3) The coordinates of all seeds are taken as random points within the material domain space;

[0024] (S4) From large radius batch to small radius batch, iteratively sample the points-related graph edges that the seeds in each radius batch participate in to redetermine the coordinates of the seeds and complete the reconstruction of the points-related graph edges.

[0025] (S5) Calculate the Lagurre-Voronoi diagram for all seeds to obtain the polygon space occupied by each seed, discretize all the polygons to obtain a voxel mesh, and assign attributes to the voxel mesh, including the phase to which the voxel mesh belongs.

[0026] Preferably, in step (S4), the method for re-determining the coordinates through seed iteration sampling within each radius batch is as follows:

[0027] (S41) For any one seed in the current radius batch, under the condition that the last completed reconstruction batch and the seed coordinates of other seeds in the current radius batch are known, the probability of the seed appearing at each position in the material space is calculated by a point correlation function to obtain a probability density function of the seed position in the material space; the probability density function is sampled to obtain the position of the seed as the coordinate of the current seed and update it, completing one iteration;

[0028] (S42) Repeat step (S41) until the set convergence or stopping condition is met.

[0029] Further preferably, after obtaining the probability density function, the probability density function is sampled multiple times to obtain multiple positions of the seed as the coordinates of a small batch seed in the current radius batch and update it, completing one iteration, and the small batch seed is 1% to 20% of all seeds in the same phase in the current radius batch.

[0030] The reciprocal square of the proportion of small batch seeds to the total number of seeds in the same phase in the current radius batch is used as the upper limit of the number of iterations, and the iteration is stopped when the upper limit of the number of iterations is reached.

[0031] Preferably, in step (S2), the square of the seed radius is used as the weight of the radius seed, the frequency of the radius is multiplied by the weight corresponding to the radius to obtain the ordinate, and the radius is used as the abscissa to obtain a statistical histogram of different radius seeds; the MultiOTSU algorithm is used on the statistical histogram to divide the seed radius batch, and all seeds are divided into multiple batches with similar space volumes.

[0032] Further preferably, the MultiOTSU algorithm is recursively called on the sub-interval of the statistical histogram to divide the radius batch, and 6 or more radius batches are obtained.

[0033] According to another aspect of the present application, the following technical solutions are also provided:

[0034] A finite element tetrahedral mesh division method of a multi-phase multi-scale microstructure voxel grid, which is used for the voxel grid obtained by the multi-phase multi-scale microstructure random reconstruction method, and comprises the following steps:

[0035] (T1) Using morphological operations to remove structures in the voxel grid that do not conform to the actual microstructure or do not constitute a closed region, to complete the preprocessing optimization of the voxel grid;

[0036] (T2) Extracting the surface mesh of each phase region in the voxel grid, removing the repeated vertices between the surface meshes, and combining to obtain a multi-phase surface mesh including the phase surface and the phase interface;

[0037] (T3) calculating a residual image of each phase in the voxel grid and summing up to obtain a multi-phase residual image; determining a weight of each voxel in the voxel grid according to the residual in the multi-phase residual image and assigning the voxel grid to obtain a weight voxel grid; and obtaining a weight of each vertex of the multi-phase surface grid through linear interpolation of the weight voxel grid;

[0038] (T4) coarsening and optimizing the multi-phase surface grid into a triangular surface grid and controlling the density of vertex distribution in the vicinity of each vertex during the optimization process by the weight of the vertex to obtain an optimized multi-phase triangular surface grid;

[0039] (T5) performing tetrahedral mesh partitioning on the multi-phase triangular surface grid to obtain a multi-phase multi-scale microstructure finite element tetrahedral mesh.

[0040] Preferably, in step (T1), a morphological opening operation with a depth of 2-3 is performed on each phase of the voxel grid to remove holes and thin layers with a thickness of a single voxel; and a rolling ball algorithm is used to smooth the region occupied by each phase in the voxel grid, wherein the rolling ball radius is 0.4-0.8 times the minimum seed radius of each phase, and convex and concave structures with a local curvature radius less than the rolling ball radius are smoothed;

[0041] In step (T2), a marching cubes algorithm or a dual contouring algorithm is used to extract the surface grid of each phase region in the voxel grid;

[0042] In step (T3), the residual image is obtained by subtracting the image smoothed by a Gaussian filter with a kernel size of 3x3x3 or 5x5x5 or the mean value from the original image; and the weight voxel grid is obtained by squaring the multi-phase residual image to the power of 2-3 and then smoothing the image by a Gaussian filter with a kernel size of 3x3x3 or 5x5x5;

[0043] In step (T4), a Centroidal Voronoi algorithm is used to coarsen and optimize the multi-phase surface grid into a triangular surface grid, and the density of vertex distribution is controlled by the area of the triangle during the optimization process, and the number of vertices is reduced to 1 / 10-1 / 20 of the original multi-phase surface grid during the optimization process;

[0044] In step (T5), a tetgen software is used to perform tetrahedral mesh partitioning on the multi-phase triangular surface grid; and in the tetgen software, the minimum line angle of the tetrahedron is set to 15-20 degrees, and the maximum radius ratio of the tetrahedron edge to the circumscribed circle is set to 1.5-2.

[0045] According to another aspect of the present application, the following technical solutions are also provided:

[0046] A multi-phase multi-scale microstructure statistical characterization system, the system uses a point correlation graph to statistically characterize a multi-phase multi-scale microstructure, the point correlation graph includes vertices and edges, each phase is composed of a plurality of spherical seeds, and the relationship between phases is represented by the relative position relationship between the spherical seeds, the vertices represent all seeds of a phase in terms of the radius distribution and the total volume fraction of the seeds, and the edges represent the relative position relationship between the seeds of each phase in the form of a point correlation function.

[0047] Preferably, the multi-phase multi-scale microstructure statistical characterization system described above comprises:

[0048] A phase seed set predefinition module is configured to predefine a seed set for each phase in a three-dimensional tomographic image, and the seed set contains sufficient seeds to fill the phase region in the three-dimensional tomographic image.

[0049] A seed fitting module is configured to fill the region of the corresponding phase in the three-dimensional tomographic image with the seeds in the pre-defined seed set in descending order of radius, allowing a certain amount of overlap between the seeds during filling, and ensuring that the seeds of each phase do not exceed the region of the phase in the three-dimensional tomographic image, and determining the coordinates of all seeds of the phase after filling is completed, and the seeds that cannot be filled into the pre-defined seed set are abandoned; in this way, the regions of all phases in the three-dimensional tomographic image are filled.

[0050] A vertex establishment module is configured to, for a phase, statistically characterize the radius distribution and total volume fraction of the seeds filled into the region of the phase in the three-dimensional tomographic image, and complete the establishment of a single vertex of the point correlation graph by using the total volume fraction of the seeds as the volume fraction of the phase; in this way, the establishment of all vertices in the point correlation graph is completed.

[0051] An edge establishment module is configured to, for a phase, statistically characterize the distance between the seeds of the phase and other seeds in the phase or the seeds of another phase, calculate a point correlation function, and complete the establishment of a single edge from the phase to itself or another phase; in this way, the establishment of all edges in the point correlation graph is completed.

[0052] According to another aspect of the present application, the following technical solutions are also provided:

[0053] A multi-phase multi-scale microstructure random reconstruction system comprises:

[0054] A vertex random reconstruction module is configured to sample the seeds of a vertex of the point correlation graph multiple times until the total volume of the sampled seeds reaches a set phase volume, and complete the reconstruction of a single vertex of the point correlation graph; in this way, the reconstruction of all vertices is completed.

[0055] The point correlation graph comprises vertices and edges, each phase is composed of a plurality of spherical seeds, the relative position relationship between the spherical seeds represents the phase-to-phase relationship, the vertices represent all the seeds of a phase in terms of the radius distribution and the total volume fraction of the seeds, and the edges represent the relative position relationship between the seeds of each phase in the form of a point correlation function.

[0056] The radius batch division module is configured to divide all the seeds of the point correlation graph into a plurality of batches according to the radius from large to small.

[0057] The seed coordinate initialization module is configured to take the coordinates of all the seeds as random points in the material domain space.

[0058] The edge iterative sampling and random reconstruction module is configured to sequentially determine the coordinates of the seeds by iteratively sampling the edges of the point correlation graph in which the seeds participate, from the large-radius batch to the small-radius batch, to complete the reconstruction of the edges of the point correlation graph.

[0059] The voxel meshing module is configured to calculate the polygon space occupied by the seeds, discretize all the polygons to obtain a voxel grid, and assign an attribute to the voxel grid, the attribute comprising a phase to which the voxel grid belongs.

[0060] According to another aspect of the present application, the following technical solutions are also provided:

[0061] A finite element tetrahedral mesh division system of a multi-phase and multi-scale microstructure voxel grid, characterized in that the voxel grid obtained by the multi-phase and multi-scale microstructure random reconstruction method comprises the following modules:

[0062] The preprocessing module is configured to remove the structures in the voxel grid that do not conform to the actual microstructure or do not constitute a closed region by using morphological operations, and complete the preprocessing optimization of the voxel grid.

[0063] The multi-phase surface mesh extraction module is configured to extract the surface mesh of each phase region in the voxel grid, remove the repeated vertices between the surface meshes, and combine to obtain a multi-phase surface mesh comprising phase surfaces and phase interfaces.

[0064] The voxel grid residual error weight calculation module is configured to calculate the residual error images of each phase in the voxel grid and sum them to obtain a multi-phase residual error image, determine the weight of each voxel in the voxel grid according to the residual error in the multi-phase residual error image, and assign the weight to the voxel grid to obtain a weight voxel grid, and obtain the weight of each vertex of the multi-phase surface mesh by linear interpolation on the weight voxel grid.

[0065] A residual weight guided surface mesh optimization module is configured to coarsen and optimize a multi-phase surface mesh into a triangular surface mesh, and control the density of vertex distribution in the vicinity of each vertex during the optimization process by the weight of the vertex, to obtain an optimized multi-phase triangular surface mesh.

[0066] A tetrahedral mesh partitioning module is configured to perform tetrahedral mesh partitioning on the multi-phase triangular surface mesh, to obtain a multi-phase multi-scale microstructure finite element tetrahedral mesh.

[0067] Overall, compared with the prior art, the above technical solutions conceived by the present application can achieve the following beneficial effects:

[0068] 1. The multi-phase multi-scale microstructure statistical characterization method provided by the present application uses seeds with a radius obeying a set distribution to describe phases, and allows the seeds within the same phase to overlap, which can characterize phases with multiple scale characteristics and irregular shapes within the microstructure. Large-radius seeds represent large-scale characteristics within a phase, and small-radius seeds represent small-scale characteristics within a phase. Overlapping seeds can form regions with arbitrary shapes, representing phases with irregular shapes such as ellipsoidal and coral shapes.

[0069] 2. The multi-phase multi-scale microstructure statistical characterization method provided by the present application introduces a point correlation function between spherical seeds to describe the relationship between phases, which can more accurately characterize multi-phase microstructures. Existing methods treat different phases as independent components without considering the spatial relationship between different phases within the microstructure; or indirectly describe the relationship between phases based on the geometric characteristics of the microstructure, without distinguishing different inter-phase relationships between multiple phases constituting the microstructure.

[0070] 3. The multi-phase multi-scale microstructure statistical characterization method provided by the present application uses a point correlation graph to describe the phases and inter-phase relationships within the microstructure, which can characterize microstructures with any number of phases. Existing methods can only statistically characterize the microstructure of specific materials with specific phases using parameters. In the present method, the addition of vertices to the point correlation graph can characterize microstructures with any number of phases, and the addition of edges to the point correlation graph can represent the spatial position relationship between any two phases.

[0071] 4. The multi-phase multi-scale microstructure statistical characterization method provided by the present application can automatically and quantitatively establish statistical characterization for tomographic microstructures through the process of filling tomographic images with seeds and fitting the seed radius distribution and seed distance distribution. Compared with the method of manually identifying second phase particles in patent CN111289542A, the present method saves labor and is more efficient.

[0072] 5、The multi-phase multi-scale microstructure statistical characterization method provided by the application can use the information provided by the tomographic image of the microstructure of one material to establish a statistical characterization of the microstructure of another material. By setting / combining the vertices / edges of the point correlation graph extracted from the scanning image, a characterization of the microstructure of a different material (or a new material) can be formed based on the point correlation graph characterization of the existing material microstructure. However, the existing method can only form different characterizations of the microstructure of the same material with a specific phase by modifying the characteristic parameters.

[0073] 6、The multi-phase multi-scale microstructure random reconstruction method provided by the application is more efficient in completing random reconstruction of the microstructure based on a sampling method. The existing reconstruction method based on an optimization / matching method needs to repeatedly calculate the characterization parameters of the reconstructed microstructure and gradually adjust the microstructure until it meets the target characterization. For example, the patent CN108765554A needs to repeatedly traverse the structure dictionary to find the structure that matches the current reconstructed local position array element. However, the method does not need to repeatedly calculate the microstructure characterization, but directly uses the radius probability density function and point correlation function information provided in the microstructure characterization to perform reconstruction, which is more efficient.

[0074] 7、The multi-phase multi-scale microstructure random reconstruction method provided by the application can efficiently reconstruct microstructures with a large number of seeds and obtain a high-resolution microstructure voxel grid. In the random reconstruction process, the coordinates of the seeds in the small batch are updated at the same time, so the algorithm time complexity is independent of the number of seeds and the resolution of the material voxel grid, and is only related to the set small batch size. Compared with the existing method of reconstructing the microstructure one seed / voxel unit at a time, the method is not limited by the number of seeds and the accuracy of the voxel grid in the reconstructed microstructure in terms of calculation time.

[0075] 8、The multi-phase multi-scale microstructure random reconstruction method provided by the application can divide all seeds into multiple radius batches with similar volume fractions according to the radius, and more accurately complete the reconstruction of the multi-scale microstructure. Compared with the method of uniformly spacing multiple radius batches in the seed radius interval, the radius division method provided in the patent can avoid the simultaneous reconstruction of large-scale seeds that occupy most of the material space, reduce the mutual influence between large-scale seeds during reconstruction, and is beneficial to improve the accuracy of the sampling reconstruction method.

[0076] 9. The finite element tetrahedral mesh partitioning method of the multi-phase multi-scale microstructure voxel grid provided by the application can process multi-phase interfaces and adaptively partition multi-scale structures, and has the characteristics of no distortion, high cell quality, and small number of mesh cells. In the method, the residual of the multi-phase voxel grid is used as an index of the amount of local structure detail information, and a weight for controlling vertex density is provided for the triangular surface mesh optimization process. The mesh partitioning method can ensure that the information at the small microstructure is not lost in the mesh partitioning process, while reducing the mesh density at the large-scale microstructure, reducing the number of mesh cells, and reducing the calculation amount of finite element simulation on the mesh partitioned by the method.

[0077] 10. The finite element tetrahedral mesh partitioning method of the multi-phase multi-scale microstructure voxel grid provided by the application can partition a mesh with uniform vertex density transition between multi-scales, and can remove defects such as holes, sharp protrusions and depressions of the microstructure voxel grid, avoiding errors caused by non-uniform and defective structures in the mesh in finite element simulation. The Gaussian filtering process of the residual image smooths the weight voxel grid used in the surface mesh optimization, and the Rolling ball algorithm removes protrusions and depressions with a local radius of curvature smaller than the relative seed radius. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 is a flow chart of the multi-phase multi-scale microstructure statistical characterization method in the preferred embodiment of the application;

[0079] Figure 2 is a flow chart of the multi-phase multi-scale microstructure random reconstruction method in the preferred embodiment of the application;

[0080] Figure 3 is a flow chart of the sampling iterative random reconstruction algorithm of the point correlation graph edge in the preferred embodiment of the application;

[0081] Figure 4 is a flow chart of the finite element tetrahedral mesh partitioning method of the multi-phase multi-scale microstructure voxel grid in the preferred embodiment of the application. DETAILED DESCRIPTION

[0082] In order to make the purpose, technical scheme and advantages of the application clearer, the application will be further described in detail below with reference to the drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the application and do not limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0083] This invention provides a method for statistical characterization and random reconstruction of multiphase, multiscale microstructures, and a finite element tetrahedral mesh generation method adapted to voxel mesh models of multiphase, multiscale microstructures. The method of this invention is universally applicable to microstructures with any number of phases, arbitrary phase relationships, and arbitrary scales. It can characterize tomographic images of multiphase, multiscale microstructures into point correlation maps, randomly reconstruct point correlation maps into voxel-represented multiphase, multiscale microstructures, and divide the voxel microstructure mesh into finite element tetrahedral meshes. The multiphase, multiscale microstructure described in this invention is preferably a lithium-ion battery electrode microstructure.

[0084] This invention provides a statistical characterization method for multiphase and multiscale microstructures. The method uses point correlation graphs to perform statistical characterization of multiphase and multiscale microstructures. The point correlation graph includes vertices and edges. Each phase is composed of several spherical seeds, and the relationship between phases is characterized by the relative positional relationship between the spherical seeds. The vertices represent all seeds of a phase by the radius distribution of the seeds and the total integral. The edges represent the relative positional relationship between the seeds of each phase in the form of point correlation functions.

[0085] like Figure 1 As shown in the embodiments of the present invention, the statistical characterization method for multiphase, multiscale microstructures based on point correlation maps includes:

[0086] Three-dimensional tomographic images are acquired in advance, and the number of phases in the images, the size of each phase, the area occupied by each phase, and the volume fraction of each phase are known.

[0087] Phase seed set predefinition steps: Assume each phase consists of spherical seeds with different radii. The vertices of the point correlation graph represent all seeds of a phase by the radius distribution of the seeds and the total integral. When predefining the seed set, for each vertex, determine the maximum and minimum radii of the phase's seeds based on the phase's maximum and minimum dimensions, and generate a sufficient number of seeds for each radius within the range of maximum and minimum radii as the phase seed set corresponding to that vertex. Predefine all seed sets using the same method.

[0088] Seed fitting steps for 3D tomographic images: For a given phase, using seeds from the corresponding vertices in descending order of radius, fill the region of that phase within the 3D tomographic image with these seeds. Some overlap between seeds is allowed during filling, ensuring that each seed does not exceed the region of that phase within the tomographic image. After filling, the coordinates of all seeds are determined, and seeds without sufficient space are discarded. The same method is used to fill the regions of all phases in the 3D tomographic image with seeds.

[0089] The step of establishing the vertex of the point correlation graph: assuming that the radius of each phase seed conforms to a certain distribution, the sum of the volumes of the phase seeds is close to the volume occupied by the phase in the material domain. The radius of the seed filled into the scanning image of a phase is counted, and the radius distribution is fitted using the prior model of the radius distribution to obtain the phase seed radius distribution; the total volume of a certain phase seed is counted as the volume fraction of the phase. The establishment of a single vertex of the point correlation graph is completed (i.e., the phase seed radius distribution and the volume fraction of the phase represented by the total volume of the phase seed are obtained). The establishment of all vertices in the point correlation graph is completed in the same way.

[0090] The step of establishing the edge of the point correlation graph: assuming that there is a certain joint distribution between the seeds of the phase (the probability density function of the seed distance is the point correlation function, which defines the probability of the occurrence of each distance value between the seeds), and the edge of the point correlation graph represents the relative position relationship between different seeds in the form of the point correlation function. For a phase, the distance between the seed of the phase and other seeds (or the seed of another phase) in the phase is counted, and the point correlation function probability density function prior model is used to fit the statistical data of the relative position to obtain the point correlation function between a certain seed and all other seeds in the phase where the seed is located, and the establishment of a single edge from the phase to itself (or another phase) is completed; in this way, the establishment of all edges in the point correlation graph is completed. The above operation is performed on the relative position correlation between all interested phase seeds to complete the establishment of all edges in the point correlation graph, which describes the position relationship between the phases in the microstructure. In order to reduce the difficulty of subsequent random reconstruction of the virtual microstructure, all edges between the phases can not be established here.

[0091] As a preferred embodiment, the establishment step of the vertex of the point correlation graph is completed by manually setting the seed radius distribution corresponding to the vertex of the point correlation graph and the volume fraction of the phase, without the need to calculate all vertex data from the seed fitting of the scanning image. The material microstructure with different scale phases and phase volume fractions can be actively designed.

[0092] As a preferred embodiment, the point correlation function corresponding to the edge of the point correlation graph is manually set, without the need to calculate all point correlation functions from the seed fitting of the scanning image, allowing the microstructure with different inter-phase relationships to be actively designed.

[0093] As a preferred embodiment, the vertex and edge of the point correlation graph can be combined to constitute a virtual microstructure statistical representation with different numbers of phases, different phase volume fractions and inter-phase relationships.

[0094] The cost of actually scanning the microstructure is high, and the present application can use the vertices and edges of the point correlation graph extracted from the existing scanning data to generate a new virtual microstructure by recombination and parameter adjustment. Since the vertices and edges of the point correlation graph conform to the morphological characteristics of the material microstructure, the recombined virtual microstructure still conforms to the morphological characteristics of the material microstructure, and can be used for finite element simulation to predict the performance of the material (such as a battery electrode), and the cost of sample manufacturing and scanning imaging is avoided.

[0095] As a preferred embodiment, the position of a seed of a certain phase that can be filled in the current scanning image is determined by distance transformation, i.e., the position where the nearest distance to the phase region boundary and other seed surfaces is greater than the seed radius.

[0096] As a preferred embodiment, when the seed fits the tomographic image, the overlap between the two seeds is 0-0.4 of the larger seed radius.

[0097] As a preferred embodiment, the relative position between a certain seed and other seeds is described using the nearest distance between the certain seed and the other seeds, and the position of a seed of a certain phase is assumed to be determined by an independent joint distribution of the point correlation function of the seed a and the seeds of other phases.

[0098] The point correlation graph is established for the three-dimensional tomographic image by the above-mentioned microstructure statistical characterization method, and the point correlation graph can be used to describe and analyze the geometric morphology of the microstructure. Next, the point correlation graph is converted into a voxel grid by a random reconstruction method, and then the voxel grid is divided into a finite element tetrahedral grid, which can be used for finite element simulation to analyze the special performance such as electrochemistry of the material.

[0099] As shown in Figure 2 The present application also provides a multi-phase and multi-scale microstructure random reconstruction method based on a point correlation graph, which comprises the following steps:

[0100] The point correlation graph vertex random reconstruction step: the seed radius distribution defined for the point correlation graph vertex is sampled multiple times until the total volume of the seed reaches the set phase volume, and the reconstruction of a single vertex is completed. The above sampling operation is performed on all corresponding vertices to obtain a seed set of each phase.

[0101] The radius batch division step: all seeds are divided into multiple batches according to the radius from large to small. The seeds of the large-radius batch are reconstructed first, and the seeds of the small-radius batch are reconstructed later. It is assumed that the position of each batch of seeds is determined by the point correlation function between the previous (larger radius) seed batch and the current batch of seeds, and subsequent reconstruction is performed.

[0102] The seed position of larger radius reconstructed first affects the seed position of smaller radius reconstructed later, which is determined by the seed position of larger radius reconstructed first, i.e. the seed whose coordinates are fixed after reconstruction.

[0103] Seed space coordinate initialization step: the coordinates of all seeds are random points in the material domain space.

[0104] Iterative sampling random reconstruction step of point correlation graph edge: for each seed in the current radius batch, the probability density function of the seed in the material space is obtained by calculating the probability of each position in the material space appearing the seed through the point correlation function under the condition of knowing the seed positions of the previous batch seeds and other seeds in the current radius batch. The position sampled from the probability density function is taken as the coordinate of the current seed. The above operation is repeatedly performed for all seeds in the current radius batch until the convergence criterion or stopping condition is reached. The same operation is performed for the seeds in each radius batch in the order from the large radius batch to the small radius batch until the coordinates of all seeds are determined according to the point correlation function defined by the point correlation graph edge.

[0105] Seed representation microstructure voxelization step: the Lagurre-Voronoi diagram (weighted Voronoi diagram) is calculated for all phase seeds to obtain the polygon space occupied by each seed, and the voxel grid is discretized by all polygons, wherein the polygon regions corresponding to different phase seeds are assigned different attributes (i.e. the voxel grid is assigned the phase to which it belongs), and the seed-represented microstructure is converted into a voxel grid. The voxel grid is a grid structure composed of voxel grid units.

[0106] As a preferred embodiment, the ratio of the total volume of vertex seeds to the seed volume corresponding to the mean of the seed radius distribution is taken as the number of seed radius samples, and on the basis of the sampling number, the number of seeds required to approach the desired volume fraction (i.e. the total volume of vertex seeds) is further determined.

[0107] As a preferred embodiment, the distance transform and point correlation function of the distance from the phase seed whose coordinates are to be updated to the surface or center of other known coordinate seeds are used to determine the probability of each position in space appearing a certain phase seed, to obtain the probability density function of the coordinates of the phase seed.

[0108] Further preferably, as shown in Figure 3 the coordinates of multiple seeds of the same phase (a small batch) are determined by sampling the calculated probability density function multiple times to speed up the iteration process and reduce the time complexity of the algorithm. The number of small batch seeds is 1% to 20% of the total number of seeds of the phase in the current radius batch. According to the sampling iteration progress, the number of small batch seeds can be gradually reduced to ensure the convergence of the iteration.

[0109] As a preferred embodiment, the 2-3 power of the seed radius is taken as the weight of each radius seed, and the frequency of the radius multiplied by the weight corresponding to the radius is taken as the vertical coordinate, and the radius is taken as the horizontal coordinate to obtain a statistical histogram of seeds of different radii; the statistical histogram of seeds of different radii is subjected to batch division of seed radii using the MultiOTSU algorithm, and all seeds are divided into multiple batches with similar spatial volumes.

[0110] Further preferably, the MultiOTSU algorithm is recursively called on the statistical histogram sub-interval to divide the radius batch, to process the case of 6 or more radius batches.

[0111] As a preferred embodiment, the convergence criterion is that the mean square error of the probability density change of the inter-seed point correlation function after multiple iterations is less than 1%.

[0112] Further preferably, the reciprocal of the square of the proportion of small batches of seeds in the total number of seeds in the current radius batch is taken as the upper limit of the number of iterations, and the number of iterations greater than or equal to the upper limit is taken as the stopping condition of the iteration algorithm.

[0113] As a preferred embodiment, the watershed algorithm is used in the voxel gridding step to obtain the polygonal space occupied by each seed and discretized into a voxel grid, approximating the Lagurre-Voronoi diagram division.

[0114] As shown in Figure 4 The present application also provides a finite element tetrahedral mesh division method based on a multi-phase multi-scale microstructure voxel grid model, which comprises:

[0115] The voxel grid preprocessing step: morphological operations are used to remove structures in the voxel grid that do not conform to reality or do not constitute a closed region, to complete the preprocessing optimization of the voxel grid. Structures that do not constitute a closed region include single voxel thickness holes and thin layers. Structures that do not conform to reality include sharp protrusions and depressions, as well as unrealistic overhanging structures, such as active particles suspended in electrode materials that are not realistic.

[0116] The multi-phase surface grid extraction step: an isosurface extraction algorithm (i.e., the marching cubes algorithm) is used to extract the surface grid of each phase region in the voxel grid. Repetitive vertices between the surface grids are removed, and a multi-phase surface grid including phase surfaces and phase interfaces is obtained by merging.

[0117] The step of calculating the residual weight of the voxel grid: the residual images of each phase in the voxel grid are calculated and summed to obtain a multi-phase residual image. The weight of each voxel in the voxel grid is determined according to the residual in the multi-phase residual image, and the weight voxel grid is obtained by assigning weights to the voxel grid. The weight of each vertex of the multi-phase surface grid is obtained by linear interpolation of the weight voxel grid.

[0118] The step of residual weight guided surface grid optimization: on the basis of the weight of each vertex of the multi-phase surface grid set in the above step, the multi-phase surface grid is coarsened and optimized into a triangular surface grid, and the density of the vertex distribution in the vicinity of each vertex is controlled by the weight during the optimization process, to obtain an optimized multi-phase triangular surface grid.

[0119] The step of tetrahedral mesh division: the multi-phase triangular surface grid obtained in the above step is subjected to tetrahedral mesh division using the tetgen software to obtain a multi-phase multi-scale composite material microstructure finite element tetrahedral mesh.

[0120] Further preferably, the dual contouring algorithm (three-dimensional isosurface extraction algorithm) is used to extract the isosurfaces of different phases that retain local geometric features to obtain the surface grid.

[0121] As a preferred embodiment, morphological opening operation processing with a depth of 2-3 is performed on each phase of the voxel grid to remove single voxel thickness holes and thin layers.

[0122] As a preferred embodiment, the Centroidal Voronoi algorithm is used to coarsen and optimize the multi-phase surface grid, wherein the vertex weight is the local surface area with different weights, and the density of the vertex distribution is controlled by controlling the area of the triangle.

[0123] Further preferably, the rolling ball algorithm (rolling ball method) is used to smooth the phase-occupied regions in the voxel grid, wherein the minimum seed radius of each phase is 0.4-0.8 as the rolling ball radius, and obvious protrusions and recessed structures are removed.

[0124] As a preferred embodiment, the residual image is obtained by subtracting the original image from the image smoothed by a Gaussian filter with a kernel size of 3x3x3 or 5x5x5 or the mean value.

[0125] As a preferred embodiment, the 2-3th power of the multi-phase residual image is smoothed by a Gaussian filter with a kernel size of 3x3x3 or 5x5x5 to obtain the weight voxel grid.

[0126] As a preferred embodiment, the number of vertices in the Centroidal Voronoi algorithm is reduced to 1 / 10-1 / 20 of the original multi-phase surface grid.

[0127] As a preferred embodiment, the minimum line angle of the tetrahedron in the tetgen software is set to 15-20 degrees, and the maximum radius ratio of the tetrahedron side and the circumscribed circle is 1.5-2. The properties of the tetrahedral grid unit are specified by the seed center coordinates and the seed phase properties in the tetgen software

[0128] The embodiment of the present application also provides a multi-phase multi-scale microstructure statistical characterization system, which uses a point correlation graph to statistically characterize a multi-phase multi-scale microstructure, the point correlation graph comprising vertices and edges, each phase being composed of a plurality of spherical seeds, the relationship between phases being represented by the relative position relationship between the spherical seeds, the vertices representing all seeds of a phase in terms of the radius distribution and the total volume fraction of the seeds, and the edges representing the relative position relationship between the seeds of each phase in the form of a point correlation function.

[0129] The multi-phase multi-scale microstructure statistical characterization system comprises:

[0130] A phase seed set predefinition module is configured to predefine a phase seed set for each phase in a three-dimensional tomographic image, the phase seed set predefinition module containing a sufficient number of seeds capable of filling the phase region in the three-dimensional tomographic image.

[0131] A seed fitting module is configured to fill the region of the corresponding phase in the three-dimensional tomographic image with the seeds in the pre-defined phase seed set from large to small in terms of radius, the seeds being allowed to have a certain amount of overlap during the filling, and the seeds of each phase being ensured not to exceed the region of the phase in the three-dimensional tomographic image, the coordinates of all seeds of the phase being determined after the filling, and the seeds that cannot be filled into the three-dimensional tomographic image due to insufficient space being abandoned; and all the regions of the phases in the three-dimensional tomographic image are filled in this way.

[0132] A vertex establishment module is configured to, for a phase, statistically determine the radius distribution and the total volume fraction of the seeds filled into the region of the phase in the three-dimensional tomographic image, and to complete the establishment of a single vertex of the point correlation graph by taking the total volume fraction of the seeds as the volume fraction of the phase; and all the vertices of the point correlation graph are established in this way.

[0133] An edge establishment module is configured to, for a phase, statistically determine the distance between the seeds of the phase and other seeds in the phase or the seeds of another phase, to calculate a point correlation function, and to complete the establishment of a single edge from the phase to itself or another phase; and all the edges of the point correlation graph are established in this way.

[0134] The embodiment of the present application also provides a multi-phase multi-scale microstructure random reconstruction system, comprising:

[0135] a vertex random reconstruction module, configured to sample seeds of a point-related graph vertex multiple times until a total volume of the sampled seeds reaches a set phase volume, to complete reconstruction of a single vertex of the point-related graph; and in this way, reconstruction of all vertices is completed;

[0136] wherein the point-related graph comprises vertices and edges, each phase is composed of a plurality of spherical seeds, and a relationship between phases is represented by a relative position relationship between the spherical seeds, the vertices represent all seeds of a phase in terms of a radius distribution and a total volume fraction of the seeds, and the edges represent the relative position relationship between the seeds of the phases in the form of a point-related function;

[0137] a radius batch division module, configured to divide all seeds of the point-related graph into a plurality of batches according to radii from large to small;

[0138] a seed coordinate initialization module, configured to take coordinates of all seeds as random points in a material domain space;

[0139] an edge iterative sampling random reconstruction module, configured to sequentially perform iterative sampling of edges of a point-related graph in which seeds participate, to re-determine coordinates of the seeds, from a large-radius batch to a small-radius batch, to complete reconstruction of the edges of the point-related graph;

[0140] a voxel meshing module, configured to calculate a polygon space occupied by the seeds, to discretize all the polygons to obtain a voxel grid, and to assign an attribute to the voxel grid, the attribute comprising a phase to which the voxel grid belongs.

[0141] The embodiment of the present application further provides a finite element tetrahedral mesh division system of a multi-phase multi-scale microstructure voxel grid, comprising:

[0142] a preprocessing module, configured to remove structures that do not conform to actual microstructures or do not constitute a closed region in the voxel grid by using morphological operations, to complete preprocessing optimization of the voxel grid;

[0143] a multi-phase surface mesh extraction module, configured to extract a surface mesh of each phase region in the voxel grid, to remove repeated vertices between the surface meshes, and to combine to obtain a multi-phase surface mesh comprising phase surfaces and phase interfaces;

[0144] a voxel grid residual weight calculation module, configured to calculate residual images of each phase in the voxel grid and sum the residual images to obtain a multi-phase residual image, to determine a weight of each voxel in the voxel grid according to residuals in the multi-phase residual image, and to assign the weight to the voxel grid to obtain a weight voxel grid, and to obtain a weight of each vertex of the multi-phase surface mesh by linear interpolation on the weight voxel grid;

[0145] a residual weight guided surface mesh optimization module for coarsening and optimizing the multi-phase surface mesh into a triangular surface mesh, and controlling the density of the vertex distribution in the region near each vertex with the weight of the vertex during the optimization process to obtain an optimized multi-phase triangular surface mesh;

[0146] a tetrahedral mesh partitioning module for performing tetrahedral mesh partitioning on the multi-phase triangular surface mesh to obtain a multi-phase multi-scale microstructure finite element tetrahedral mesh.

[0147] The multi-phase multi-scale microstructure statistical characterization method, the random reconstruction method and the finite element tetrahedral mesh partitioning method of the voxel mesh provided by the present application are further described in detail below in combination with embodiments.

[0148] Embodiment 1

[0149] Ternary nickel-cobalt-manganese (NMC) is commonly used to manufacture the positive electrode of a battery, and the microstructure thereof helps to understand and predict the performance of the battery in the charge-discharge cycle. In this embodiment, a LiNi 1 / 3Mn 1 / 3 Co 1 / 3 O2(NMC) electrode image is selected for SRXTM imaging, with a resolution of 370x370x370 nm per voxel 3 , and the size of the material domain is 100x100x100 voxels, which contains both the pore and active material phases.

[0150] First, the regions occupied by the two phases are distinguished from the tomographic image, the volume fraction of the active particles is set to 42%, and the gray threshold of the CT image is obtained by binary search. The part higher than the threshold is regarded as the active particle, and vice versa. The volume fractions of the active particle and the pore at this threshold are 42% and 58%, respectively.

[0151] Next, the point correlation graph is statistically characterized from the segmented three-dimensional tomographic image.

[0152] According to the tomographic image, the diameter of the spherical active material particle is about 1-2 μm, so the seed radius of the active particle phase of the point correlation graph is set to 1-2 μm, and a sufficient initial seed set with a radius of 1-2 μm and a step length of 370 nm is generated.

[0153] The scanning image is filled with a maximum seed radius of 0.4 according to the seed radius from large to small, until the seeds in the set cannot be filled into their respective phase regions in the scanning image, and an approximate representation of the scanning image is obtained.

[0154] The radius distribution of active particles and pore phase seeds, the volume fraction of active particles and pore phase seeds, and the distance distribution probability density function (two-point correlation function) between active particle seeds are extracted from the microstructure represented by the above seeds. It is assumed that the radius of the active particles and the pore phase seeds obeys a uniform distribution, and the distance between the active particles is normalized by the statistical data. By fitting the two radius statistics and the distance statistics between the active particles, the vertices and edges of the point correlation graph are established.

[0155] The point correlation function is multiplied by the distance and then normalized, which increases the tendency of dispersion between seeds, and a more dispersed virtual microstructure representation is obtained from the point correlation graph.

[0156] The virtual microstructure is then randomly reconstructed from the point correlation graph by a sampling iteration method.

[0157] First, the seed radius corresponding to the vertex of the point correlation graph is sampled until the total volume fraction of the seeds reaches a set value. A seed set with a radius of the active particle phase and the pore phase obeying a set distribution is obtained, and the reconstruction of the point correlation graph vertex is completed. The cube of the seed radius is set as the weight, and the MultiOTSU algorithm is used to divide the seeds into four different sets according to the radius from large to small. A radius batch set with similar seed radius is obtained.

[0158] The coordinates of all seeds are initialized as random points inside the material domain. For each seed batch, 10% of the active particle seeds are randomly selected as a small batch. The probability of the active particle small batch seeds appearing at each point in the material domain space is calculated according to the defined point correlation function between the remaining active particle seeds in the batch and the previously determined position of the active particle seeds and the small batch of active particle seeds. This process is calculated by distance transformation and the probability density function in the point correlation function. By sampling the probability density function, the coordinates of this active particle small batch seed are updated. The updated coordinates satisfy the point correlation function under the premise that the coordinates of other seeds are known, ensuring that there is no large overlap between the seeds and that the seeds have a tendency to disperse. For the pore phase particle seeds, fill the remaining space outside the active particles in the same way to ensure that the area where the active particle seeds are located is not covered. For each radius batch of active particles and pore phase, repeat the above operation until the iteration is completed for 100 times. And every 10 iterations, reduce the proportion of small batch seeds by 0.5%.

[0159] After the coordinates of the seeds are determined by iterative sampling, the watershed algorithm is used to label each voxel in the space to its seed, and then the attributes of each voxel in the space are labeled according to the phase to which the seed belongs, and the microstructure voxel grid is obtained.

[0160] The microstructure voxel grid obtained is then divided using a multi-phase and multi-scale finite element tetrahedral meshing method.

[0161] The small pore defects in the structure are removed by morphological opening operation with depth 2, and the optimized voxel grid containing two phases is obtained. The isosurface of active particles and pore phase is extracted using marching cubes algorithm, and the isosurface grid of the two phases is merged into two-phase surface grid by removing duplicate vertices.

[0162] For the optimized voxel grid, the mean smoothed image with kernel size of 3x3x3 and the residual of the original image of the two phases are calculated. The square of the residual is taken as the weight of each point in the voxel grid, and the weight at the vertex coordinate of the surface grid is obtained by interpolation.

[0163] The vertex weight is taken as the vertex weight of the centroid Voronoi algorithm, and the two-phase surface grid is optimized to reduce the number of vertices to 1 / 16 of the original two-phase surface grid vertex number, and the optimized two-phase surface grid is obtained.

[0164] In tetgen, the surface grid is tetrahedralized with the parameters of tetrahedron minimum line angle 20 degrees, edge and maximum radius of circumscribed circle ratio 1.5, and the finite element grid containing active particles and pore two phases is obtained.

[0165] Example 2

[0166] Graphite is a common negative electrode material, and its microstructure affects the lithium ion insertion and lithium dendrite growth. In this embodiment, Li x C6 negative electrode, with a resolution of 200x200x200nm per voxel 3 , and the size of the material domain is 100x100x100 voxels. It contains graphite active particles with high gray value, carbon gum phase with low imaging gray value and smaller size, and pore phase with almost no X-ray absorption.

[0167] First, the area occupied by the pore phase is distinguished from the tomographic image, and the volume fraction of active particles and carbon gum is set to 52%, and the volume fraction of pores is set to 48%. The threshold for dividing pores and solids is obtained by binary search, and the domain segmentation of the scanned image is completed.

[0168] Next, the point correlation graph is established from the segmented three-dimensional tomographic image to statistically represent it.

[0169] According to the size of the particles and carbon gum in the image, the seed radius of the active particles is set to 1-2μm, the seed radius of the carbon gum phase is set to 0.2-0.4μm, and the seed radius of the pore phase is set to 0.2-2μm. The seed set of the point correlation graph is initialized, and a sufficient number of seeds are generated for each radius with a step size of 200nm.

[0170] The seeds in the scanning image are filled with a seed radius of 0.4 of the maximum overlap between seeds in descending order of seed radius until the seeds in the set cannot be filled into their respective phase regions in the scanning image, obtaining a seed approximation of the scanning image. The larger scale features of the solid phase region in the scanning image are occupied by active particle seeds, the smaller scale features of the solid phase region are occupied by carbon gel phase seeds, and the pore phase region is occupied by pore phase seeds of different sizes.

[0171] The radius distribution of the active particles, carbon gel phase, pore phase seeds, the volume fraction of the active particles, carbon gel phase, pore phase seeds, the distance distribution probability density function between active particle seeds (two-point correlation function), the two-point correlation function between carbon gel phase seeds, and the two-point correlation function of the distance from the surface of the active particle seeds to the carbon gel phase seeds are extracted from the microstructure represented by the above-mentioned seed fitting. Assuming that the radii of the active particles, carbon gel phase, and pore seeds all obey a uniform distribution, the distance between active particle seeds, the distance between carbon gel phase seeds, and the distance from the surface of the active particle seeds to the carbon gel phase seeds are all normalized as statistical data smoothing results to obtain the distribution probability density function. By fitting the statistical data of the radii of the three phase seeds and the distance statistical data between active particles, carbon gel phase, and carbon and active particle seeds, the vertices and edges of the point correlation graph are established.

[0172] The virtual microstructure is then randomly reconstructed from the point correlation graph by a sampling iteration method.

[0173] First, the seed radii corresponding to the vertices of the point correlation graph are sampled until the total volume fraction of the seeds reaches a set value, obtaining the seed set of the active particle phase, carbon gel phase, and pore phase, and completing the reconstruction of the vertices of the point correlation graph. Using the MultiOTSU algorithm, the seeds are first divided into 2 sub-sets according to the radius from large to small, and then each of the 2 sub-sets is divided into 3 sub-sets, obtaining 6 seed radius batch sets with similar radii.

[0174] The coordinates of all seeds are initialized as random points inside the material domain. The initial proportion of the small batch is set to 10% of the number of seeds of the same phase in the current radius batch. In each radius batch, for the active particle phase seeds with larger radii, their small batch seed coordinates are updated in the same way as in Example 1. For the carbon gel phase seeds with radii smaller than the active particles, in addition to considering the spatial probability density determined by the point correlation function within the carbon gel phase, the spatial probability density determined by the point correlation function defined by the active particles relative to the carbon gel phase seeds also needs to be calculated. These two probabilities jointly determine the probability density of the small batch carbon gel phase seed taking a certain coordinate in space in an independent multiplication manner. The pore phase fills the remaining space under the premise of ensuring that it does not overlap with the active particles and carbon gel phase and that the internal overlap is less than 0.4 of the radius. The above operation is repeated for the seeds of the three phases in each radius batch until the iteration is completed for 100 times. And every 10 iterations, the proportion of the small batch seeds is reduced by 0.5%.

[0175] After the seeds coordinates are determined by iterative sampling, watershed algorithm is used to label each voxel in the space with the seed it belongs to, and then the attributes of each voxel in the space are labeled according to the seed it belongs to, to obtain the microstructure voxel grid.

[0176] The microstructure voxel grid is divided using the same method as in Example 1 to obtain Li x C6 electrode three-phase multiscale finite element microstructure.

[0177] Those skilled in the art will easily understand that the above description is only a preferred embodiment of the present application and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method of statistical characterization of a multiphase multiscale microstructure, characterized in that, The point correlation graph is used for statistical characterization of a multi-phase multi-scale microstructure, the point correlation graph comprises vertices and edges, each phase is composed of a plurality of spherical seeds, and a relative position relationship between the spherical seeds is used to represent a relationship between phases, each vertex represents all seeds of one phase in terms of a radius distribution and a total volume fraction of the seeds, and each edge represents a relative position relationship between seeds of each phase in the form of a point correlation function; The method comprises the following steps: (1) Predefining a seed set for each phase in a three-dimensional tomographic image, the seed set comprising sufficient seeds capable of filling a phase region in the three-dimensional tomographic image; (2) Filling the seed set in the three-dimensional tomographic image according to a radius from large to small, allowing a set amount of overlap between the seeds, and ensuring that the seeds of each phase do not exceed the phase region in the three-dimensional tomographic image, and determining the coordinates of all seeds of the phase after filling, and abandoning the filling of seeds that have no enough space in the seed set; in this way, the phase regions in the three-dimensional tomographic image are filled; (3) For one phase, the radius distribution and total volume fraction of the seeds filled into the phase region in the three-dimensional tomographic image are counted, and the total volume fraction of the seeds is used as the volume fraction of the phase, and the establishment of a single vertex of the point correlation graph is completed; in this way, the establishment of all vertices in the point correlation graph is completed; (4) For one phase, the distances between the seeds of the phase and the seeds of other phases or another phase are counted, and a point correlation function is calculated, and the establishment of a single edge from the phase to itself or another phase is completed; in this way, the establishment of all edges in the point correlation graph is completed.

2. A method of statistical characterization of a multiphase multiscale microstructure according to claim 1, wherein, Step (1) is specifically: determining a radius interval of the seeds of the phase according to the maximum and minimum sizes of the phase in the three-dimensional tomographic image, generating sufficient seeds in each radius sub-interval divided by a set step length in the radius interval as the seed set of the phase, that is, the pre-defined seed set; In step (2), the set amount of overlap is 0-0.4 of the larger seed radius of the overlapping seeds of two phases; In step (3), the method for counting the radius distribution is: counting the radius of the seed filled into the phase region in the three-dimensional tomographic image, fitting the seed radius statistical data using a prior model of the radius distribution, and obtaining the radius distribution of the seed; In step (4), the point correlation function is a probability density function of the distance between the seeds.

3. A method of statistical characterization of a multiphase multiscale microstructure according to claim 1, wherein, By recombining the vertices and edges of the existing point correlation graph, and / or setting the radius distribution of the seed corresponding to the vertex of the point correlation graph and the volume fraction of the phase, and / or setting the point correlation function corresponding to the edge of the point correlation graph, a statistical characterization of a new microstructure with different phase numbers, different phase scales, phase volume fractions and / or phase relationships is formed.

4. A method of polyphasic multiscale microstructure stochastic reconstruction, characterized in that, The multi-phase multi-scale microstructure is characterized by any one of claims 1-3, and the method comprises the following steps: (S1) repeatedly sampling the seeds of the vertices of the point correlation graph until the total volume of the sampled seeds reaches a set phase volume, and the reconstruction of a single vertex of the point correlation graph is completed; in this way, the reconstruction of all vertices is completed; The point correlation graph comprises vertices and edges, each phase is composed of a plurality of spherical seeds, the relationship between phases is represented by the relative position relationship between the spherical seeds, the vertices represent all seeds of a phase in terms of the radius distribution and the total volume fraction of the seeds, and the edges represent the relative position relationship between the seeds of each phase in the form of a point correlation function; (S2) dividing all seeds of the point correlation graph into a plurality of batches according to the radius size; (S3) taking the coordinates of all seeds as random points in the material domain space; (S4) sequentially determining the coordinates of the seeds in each radius batch by iteratively sampling the edges of the point correlation graph in which the seeds participate, to complete the reconstruction of the edges of the point correlation graph, from the large-radius batch to the small-radius batch; (S5) calculating the polygons occupied by all seeds, discretizing all polygons to obtain a voxel grid, and assigning an attribute to the voxel grid, wherein the attribute comprises a phase to which the voxel grid belongs.

5. A method of poly-phase multi-scale microstructure stochastic reconstruction according to claim 4, wherein, In step (S4), the method for iteratively sampling and determining the coordinates of the seeds in each radius batch is as follows: (S41) for any seed in the current radius batch, under the condition that the seed coordinates of the other seeds in the last completed reconstruction radius batch and the current radius batch are known, the probability of each position in the material space appearing the seed is calculated through the point correlation function, to obtain a probability density function of the position of the seed in the material space; the position sampled from the probability density function is taken as the coordinate of the current seed and is updated, to complete one iteration; (S42) repeating step (S41) until a set convergence or stop condition is met.

6. A method of poly-phase multi-scale microstructure stochastic reconstruction according to claim 5, wherein, After obtaining the probability density function, the probability density function is sampled multiple times, and the multiple positions sampled from the probability density function are taken as the coordinates of the seeds in a small batch in the current radius batch and are updated, to complete one iteration, and the small batch seeds are 1% to 20% of all seeds of one phase in the current radius batch. The reciprocal square of the proportion of the small batch seeds in the total number of seeds of the same phase in the current radius batch is taken as the upper limit of the number of iterations, and the iteration is stopped when the upper limit of the number of iterations is reached.

7. A method of multi-phase multi-scale microstructure stochastic reconstruction as defined in claim 4, wherein, In step (S2), the square of the radius of the seed is taken as the weight of the radius seed, the frequency of the radius is multiplied by the weight corresponding to the radius to obtain the vertical coordinate, and the radius is taken as the horizontal coordinate, to obtain a statistical histogram of seeds of different radii. The statistical histogram is divided into a plurality of batches by using the MultiOTSU algorithm, and all seeds are divided into batches with similar spatial volume.

8. A finite element tetrahedral meshing method of a multi-phase multi-scale microstructure voxel grid, characterized in that, The voxel grid obtained by the method of any one of claims 4-7 is subjected to the following steps: (T1) removing structures that do not conform to the actual microstructure or do not constitute a closed region in the voxel grid by using morphological operations, to complete the preprocessing optimization of the voxel grid; (T2) extracting the surface mesh of each phase region in the voxel grid, removing repeated vertices between the surface meshes, and merging to obtain a multi-phase surface mesh comprising phase surfaces and phase interfaces; (T3) calculating the residual image of each phase in the voxel grid and summing to obtain a multi-phase residual image; determining the weight of each voxel in the voxel grid according to the residual in the multi-phase residual image, and assigning the weight to the voxel grid, to obtain a weight voxel grid; The weight of each vertex of the multi-phase surface grid is obtained by linear interpolation of the weight voxel grid; (T4) coarsening and optimizing the multi-phase surface grid into a triangular surface grid, and controlling the density of the vertex distribution in the vicinity of each vertex by the weight of the vertex during the optimization process, to obtain an optimized multi-phase triangular surface grid; (T5) tetrahedral mesh partitioning of the multi-phase triangular surface grid to obtain a multi-phase multi-scale microstructure finite element tetrahedral mesh.

9. The multi-phase multi-scale microstructure voxel grid finite element tetrahedral mesh partitioning method of claim 8, wherein, in step (T1), a morphological opening operation with a depth of 2-3 is performed on each phase of the voxel grid to remove holes and thin layers with a thickness of a single voxel; and a rolling ball algorithm is used to smooth the region occupied by each phase in the voxel grid, wherein the rolling ball radius is 0.4-0.8 times the minimum seed radius of each phase, and convex and concave structures with a local curvature radius less than the rolling ball radius are smoothed; in step (T2), a marching cubes algorithm or a dual contouring algorithm is used to extract the surface grid of each phase region in the voxel grid; in step (T3), the residual image is obtained by subtracting the image smoothed by a Gaussian filter with a kernel size of 3x3x3 or 5x5x5 or the average image from the original image; the 2-3 power of the multi-phase residual image is smoothed by a Gaussian filter with a kernel size of 3x3x3 or 5x5x5 to obtain the weight voxel grid; in step (T4), the Centroidal Voronoi algorithm is used to coarsen and optimize the multi-phase surface grid into a triangular surface grid, and the density of the vertex distribution is controlled by the area of the triangle during the optimization process, and the number of vertices is reduced to 1 / 10-1 / 20 of the original multi-phase surface grid; in step (T5), the tetgen software is used to perform tetrahedral mesh partitioning on the multi-phase triangular surface grid; in the tetgen software, the minimum line angle of the tetrahedron is set to 15-20 degrees, and the maximum radius ratio of the tetrahedron edge to the circumscribed circle is 1.5-2.

10. A multi-phase, multi-scale microstructure statistical characterization system, comprising: The system uses a point correlation graph for statistical characterization of a multi-phase multi-scale microstructure, the point correlation graph including vertices and edges, each phase being composed of a plurality of spherical seeds, and the relative position relationship between the spherical seeds representing the relationship between phases, the vertices representing all seeds of a phase in terms of the radius distribution and the total volume fraction of the seeds, and the edges representing the relative position relationship between the seeds of each phase in the form of a point correlation function; The system comprises: a phase seed set predefinition module configured to predefine a seed set for each phase in a three-dimensional tomographic image, the seed set including sufficient seeds capable of filling the phase region in the three-dimensional tomographic image; and a seed fitting module, configured to fill the regions of the corresponding phase in the three-dimensional tomography image with the seeds in the predefined seed set in descending order of radius, allowing a certain amount of overlap between the seeds during the filling, and ensuring that the seeds of each phase do not exceed the region of the phase in the three-dimensional tomography image, and determining the coordinates of all the seeds of the phase after the filling is completed, and discarding the seeds in the predefined seed set that have no enough space for filling; in this way, the regions of all the phases in the three-dimensional tomography image are filled; a vertex establishing module, configured to, for a phase, count the radius distribution of the seeds filled into the region of the phase in the three-dimensional tomography image and the total volume fraction of the seeds, and use the total volume fraction of the seeds as the volume fraction of the phase to complete the establishment of a single vertex of the point correlation graph; in this way, the establishment of all the vertices in the point correlation graph is completed; an edge establishing module, configured to, for a phase, count the distances between the seeds of the phase and the seeds of other phases or other seeds in the phase, calculate the point correlation function, and complete the establishment of a single edge from the phase to itself or another phase; in this way, the establishment of all the edges in the point correlation graph is completed.

11. A poly-phase multiscale microstructure stochastic reconstruction system using the method of any one of claims 4-7, characterized in that, comprises: a vertex random reconstruction module, configured to sample the seeds of a vertex of the point correlation graph multiple times until the total volume of the sampled seeds reaches a set phase volume, and complete the reconstruction of a single vertex of the point correlation graph; in this way, the reconstruction of all the vertices is completed; wherein the point correlation graph comprises vertices and edges, each phase is composed of a plurality of spherical seeds, and the relationship between the phases is represented by the relative position relationship between the spherical seeds, the vertex represents all the seeds of a phase in the form of radius distribution and total volume fraction, and the edge represents the relative position relationship between the seeds of each phase in the form of the point correlation function; a radius batch division module, configured to divide all the seeds of the point correlation graph into a plurality of batches in descending order of radius; a seed coordinate initialization module, configured to take the coordinates of all the seeds as random points in the material space; an edge iterative sampling random reconstruction module, configured to, from a large-radius batch to a small-radius batch, sequentially sample the seeds in each radius batch to re-determine the coordinates of the seeds according to the point correlation graph edges in which the seeds participate, and complete the reconstruction of the edges of the point correlation graph; a voxel gridding module, configured to calculate the polygon space occupied by the seeds, discretize all the polygons to obtain a voxel grid, and assign an attribute to the voxel grid, the attribute comprising a phase to which the voxel grid belongs.

12. A finite element tetrahedral meshing system of a multi-phase multi-scale microstructure voxel grid, characterized in that, for the voxel grid obtained by the method of any one of claims 4-7, the following modules are called: a preprocessing module, configured to remove structures in the voxel grid that do not conform to the actual microstructure or do not constitute a closed region by using morphological operations, and complete the preprocessing optimization of the voxel grid; a multi-phase surface grid extraction module, configured to extract the surface grid of each phase region in the voxel grid, remove the repeated vertices between the surface grids, and combine to obtain a multi-phase surface grid comprising phase surfaces and phase interfaces; a voxel grid residual weight calculation module, configured to calculate a residual image of each phase in the voxel grid and sum the residual images to obtain a multi-phase residual image; determine the weight of each voxel in the voxel grid according to the residual in the multi-phase residual image, and assign the voxel grid to obtain a weight voxel grid; and obtain the weight of each vertex of the multi-phase surface grid by linear interpolation on the weight voxel grid; a residual weight guided surface grid optimization module, configured to coarsen and optimize the multi-phase surface grid into a triangular surface grid, and control the density of the vertex distribution in the vicinity of each vertex in the optimization process according to the weight of the vertex, to obtain an optimized multi-phase triangular surface grid; a tetrahedral mesh division module, configured to perform tetrahedral mesh division on the multi-phase triangular surface grid to obtain a multi-phase multi-scale microstructure finite element tetrahedral mesh.

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