Battery material particle distribution optimization method

Abstract

The invention belongs to the technical field of battery material particle distribution optimization, and relates to a battery material particle distribution optimization method, which comprises the following steps: S1, establishing a statistical distribution model of particle sizes; s2, performing particle sampling according to the particle size distribution model; s3, configuring initial positions of the particles; s4, constructing a system energy function based on the overlapping state between particles, and calculating the total energy of the system; s5, adjusting the particle position through an iterative optimization algorithm, and reducing the total energy of the system; s6, determining the minimum porosity of the system by taking whether the particle overlapping proportion exceeds a set threshold value or not as a criterion; and S7, generating and outputting optimized particle distribution data. According to the method, a particle arrangement method combining key particle size parameter modeling, random sampling and energy optimization is adopted, overlapping energy minimization is realized through an optimization algorithm, a porosity iterative convergence strategy based on an overlapping volume threshold is established, low calculation cost is ensured, and verifiable three-dimensional visual arrangement data is output.

Description

Technical Field

[0001] This invention relates to the field of battery material particle distribution optimization technology, and in particular to a method for optimizing battery material particle distribution. Background Technology

[0002] In the field of batteries, the uniformity of particle size distribution and spatial arrangement of core particulate materials such as positive electrode, negative electrode and electrolyte directly determine the battery's energy density, conductivity and cycle stability. If the particle size is agglomerated or the arrangement is uneven, it can easily lead to an imbalance in the electrode pore structure, such as large pores wasting volume, small pores being insufficiently wetted by electrolyte, or discontinuous conductive / ion conduction networks, which restricts battery performance. However, traditional control methods have obvious limitations. Methods based on empirical formulas have a narrow range of application and become ineffective when materials are changed or processes are adjusted. Offline measurement methods have time lag and cannot capture the dynamic arrangement of particles in real time, which not only wastes materials but also makes it difficult to achieve fine control, becoming a key bottleneck for improving battery performance. Summary of the Invention

[0003] To address the aforementioned problems, this invention discloses a method for optimizing the particle distribution of battery materials. The technical solution of this invention is implemented as follows: This invention discloses a method for optimizing the particle distribution of battery materials, the method comprising the following steps: S1, Establish a statistical distribution model of particle size; S2, Particle sampling is performed based on the particle size distribution model; S3, configures the initial position of the particles; S4, construct the system energy function based on the inter-particle overlap state, and calculate the total system energy; S5 uses an iterative optimization algorithm to adjust particle positions and reduce the total system energy; S6. The minimum porosity of the system is determined based on whether the particle overlap ratio exceeds a set threshold. S7 generates and outputs the optimized particle distribution data.

[0004] Preferably, the particle size distribution model in S1 is established by one of the following methods: (1) Particle size distribution data were obtained based on tests; (2) Obtain the statistical distribution model through the key particle size parameters D10, D50 and D90.

[0005] Preferably, when obtaining particle size distribution data using the test, the method is selected from one of the following: laser particle size analyzer, dynamic light scattering instrument, single-particle optical sensing technology, scanning mobility particle size analyzer, sedimentation method, Coulter particle size analyzer, and optical microscope image recognition. When using the key particle size parameters to build a model, a log-normal distribution is used for fitting, and a conversion relationship between the volume distribution function and the number distribution function is established.

[0006] Preferably, step S2 specifically includes the following steps: S2.1, Input predefined parameters including spatial side length Target porosity Mass percentage of each material particle and the density of each material particle ; S2.2, Calculate the target total filling volume Normalize the total mass M of the system to the nearest unit, and calculate the mass of each type of material particle k. and the volume of solid occupied Summing gives the sum of the volumes of all material particles. ; S2.3, using the scaling factor Scaling the target total filling volume to the actual filling volume of each material particle k ; S2.4, for each type of material particle k, sample the material particles according to their particle size distribution function, sampling one material particle at a time and accumulating the volume until the total volume is reached. 。

[0007] Preferably, step S4 specifically includes the following steps: S4.1, let the geometric center positions of the i-th particle and the j-th particle be respectively... and Their corresponding diameters are respectively and ; S4.2, Calculate the overlap depth of the two particles. : , hour, >0 indicates that overlap actually occurred; if there is no overlap, then... =0, in, Denotes the Euclidean norm; S4.3, Calculate the total system energy E:

[0008] Preferably, step S5 includes the following steps: S5.1 Initial parameter settings: including total energy function, material particle position coordinate vector, and material particle position initialization; S5.2, Optimizer parameter configuration: including optimization algorithm, historical steps, convergence tolerance, and maximum number of iterations.

[0009] Preferably, in step S5.2, the optimization algorithm is selected from one of L-BFGS, Adam optimizer, BFGS algorithm and conjugate gradient algorithm.

[0010] Preferably, in step S6, the minimum porosity is obtained through the following steps: S6.1, at the target porosity The following steps are taken: Optimization algorithms are applied to adjust the particle positions, the sum of the overlapping volumes between particles in space is calculated, and the ratio of this sum to the total volume of space is calculated to obtain the system's overlap ratio. S6.2, Determine the feasibility of the target porosity based on the overlap ratio and update the target porosity range: If the overlap ratio is less than or equal to the set threshold, then the current target porosity is... It is feasible to adjust and narrow the range of the porosity target value for the next iteration; If the overlap ratio is greater than the set threshold, then the current target porosity is determined. Not feasible; S6.3 When the overlap ratio is detected to be greater than the set threshold, the iteration stops. At this time, the porosity target value that meets the overlap ratio threshold condition in the previous iteration represents the minimum porosity of the system within the acceptable overlap range.

[0011] Preferably, the overlapping volume The calculation is based on the geometric derivation of the overlapping regions of spheres, as follows:

[0012] Where d represents the distance between the centroids of the two material particles. , These represent the radii of the corresponding material particles.

[0013] Preferably, the output particle distribution data in S7 includes at least one of the following: generating a particle size distribution probability density function and a cumulative distribution function, drawing a particle size histogram, generating a 3D particle arrangement visualization, and outputting the final optimized particle data file.

[0014] The advantages of this invention are as follows: The proposed method for optimizing the particle distribution of battery materials, by combining key particle size parameter modeling, random sampling, and energy optimization strategies, minimizes the overlapping energy of particle arrangement and establishes an iterative convergence mechanism for porosity based on an overlap threshold. This method offers advantages such as low computational cost and the ability to output visualized data. It has broad application prospects in the field of new energy batteries, effectively optimizing the distribution and pore structure of battery material particles, thereby improving product performance, enhancing mechanical properties, improving functional performance, and increasing manufacturing efficiency. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only one embodiment of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is an image showing the optimized three-dimensional spatial sphere arrangement of particle A from Example 1. Figure 2 This is a particle size distribution diagram of the NCM cathode powder obtained by laser particle size analyzer in Example 2; Figure 3 This is a particle size distribution diagram of the optimized NCM cathode powder from Example 2; Figure 4 This is a three-dimensional spatial spherical arrangement image of the optimized NCM cathode powder from Example 2. Detailed Implementation

[0017] The technical solutions of the present invention will now be clearly and completely described with reference to the embodiments and accompanying drawings. 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.

[0018] Traditional particle size distribution design methods mainly rely on empirical formulas or experimental measurements, which makes it difficult to accurately control particle arrangement and porosity, resulting in low optimization efficiency.

[0019] To address the aforementioned issues, this application proposes a method for optimizing the particle distribution of battery materials. It combines key particle size parameter modeling, random sampling, and energy optimization in particle arrangement. The optimization algorithm minimizes overlapping energy and establishes an iterative convergence strategy for porosity based on an overlap volume threshold, ensuring low computational cost and outputting verifiable 3D visualized arrangement data. This overcomes the problems of difficulty in precisely controlling particle arrangement and porosity, and low optimization efficiency in existing technologies. Given a particle size distribution, this method iteratively reduces the target porosity. If the overlap ratio at a certain target porosity does not exceed a set overlap ratio threshold, the porosity is further reduced until the overlap ratio exceeds the threshold. If the current target porosity is deemed infeasible, it means the spatial density has reached its limit, and further compression without severe overlap is impossible. At this point, the iteration ends, and the previous target porosity is selected.

[0020] This invention discloses a method for optimizing the particle distribution of battery materials, comprising the following steps: S1, Establish a statistical distribution model of particle size; S2, Particle sampling is performed based on the particle size distribution model; S3, configures the initial position of the particles; S4, construct the system energy function based on the inter-particle overlap state, and calculate the total system energy; S5 uses an iterative optimization algorithm to adjust particle positions and reduce the total system energy; S6. The minimum porosity of the system is determined based on whether the particle overlap ratio exceeds a set threshold. S7 generates and outputs the optimized particle distribution data.

[0021] The technical method proposed in this application is applicable to various materials with particulate morphology within the battery system. The scope of application includes, but is not limited to, the following categories, and the following list is only for illustrative purposes and is not intended to limit the scope of protection of this application: electrode-related particulate materials, functional auxiliary particulate materials, particulate coating materials for membrane performance modification, and electrolyte system-related particulate materials.

[0022] All materials that have particulate morphology characteristics within a battery system and can be processed or have their performance controlled by the technical methods of this application are within the scope of application of this application and are not limited to the aforementioned specific categories.

[0023] This application does not impose any special restrictions on the method of modeling particle size distribution. Any method that can reasonably model the particle size distribution of a particle system without departing from the inventive concept of this application is applicable to this application. The examples are merely illustrative and not intended to limit the scope of protection.

[0024] For example, particle size distribution modeling can be performed using direct testing methods such as laser particle size analyzers, dynamic light scattering instruments, single-particle optical sensing technology, scanning mobility particle size analyzers, sedimentation methods, Coulter particle size analyzers, and optical microscopes with image recognition; particle size distribution functions can also be calculated using key particle size parameters (D10, D50, D90).

[0025] Accordingly, this application does not impose any special restrictions on the optimization algorithm used in the energy minimization process. Any algorithm suitable for nonlinear optimization problems can be adopted, including but not limited to L-BFGS, Adam optimizer, BFGS algorithm, Conjugate Gradient, etc. Other optimization algorithms known in the art can also be selected according to the size, complexity and computational efficiency requirements of the specific problem.

[0026] In this embodiment of the invention, step S1 specifically includes: The particle size distribution function is calculated using key particle size parameters (D10, D50, D90). For example: Assume that the particle size D and its volume fraction follow a log-normal distribution, i.e.: ; in: It is the logarithmic mean. It is the logarithmic standard deviation.

[0027] The particle size distribution calculation process is as follows: a) Calculate the logarithmic mean (i.e., the logarithmic median): ; b) Calculate the logarithmic standard deviation: ; in, It is the 90th percentile of the standard normal distribution.

[0028] c) Calculate the particle volume distribution function: According to the log-normal distribution formula, the particle diameter is D Volume distribution function of particles for: ; d) Calculate the particle number distribution function: The volume of each particle is: ; Then at a certain particle size D At this point, the quantity distribution function should satisfy: ; Calculate the unnormalized quantity distribution:

[0029] Calculate the normalization factor Z using numerical integration: ; After normalization, the quantity distribution function can be obtained. : ; In this embodiment of the invention, step S2 specifically includes: S2.1, Input known parameters: Space side length : The side length of the cube in the target simulation space.

[0030] Target porosity ϕ: the volume fraction of pores in space.

[0031] Mass proportion of each material The sum of the masses of all materials equals 1, that is... .

[0032] Density of each material .

[0033] S2.2, Calculate the target total filling volume: According to the side length By considering the porosity ϕ, the actual volume of solid particles required to fill the required area can be obtained. ; The material volume is allocated according to its mass percentage. For each material k, its occupied solid volume is... It can be determined by its mass percentage The following can be calculated based on density: Assume the total mass of the system is (unit normalized); The mass of each material is: The corresponding volume is: ; The total volume of all materials is: ; S2.3, Calculate the actual filling volume for each type of particle: Use the scaling factor Scaling this total to the actual volume: ; The actual filling volume of each type of particle is: ; S2.4, Sample the particle size set so that the total volume meets the requirement: For each type of material particle k, material particles are sampled according to their particle size distribution function. One material particle is sampled at a time, and the volumes are accumulated to ensure that the total volume satisfies: ; In this embodiment of the invention, step S3 specifically includes: Particles are randomly placed within a two-dimensional or three-dimensional material space. For each particle, the initial position coordinates of its geometric center are generated independently in each dimension, with the generation range being from its radius to the side length of the container minus its radius. That is, the coordinate components of the i-th particle are within [r...]. i , -r i Random sampling is performed within the range to ensure that the particles are located inside the cubic container without initial overlap with the boundary.

[0034] Material space definition: Based on the particle size of the material, define a sufficiently large material space and fill the material particles into this space.

[0035] In this embodiment of the invention, step S4 specifically includes: In the particle arrangement simulation method involved in this invention, the concept of particle overlap depth is introduced to model and evaluate the degree of mutual penetration between particles in the system. Assume that the geometric center positions of the i-th particle and the j-th particle are respectively... and Their corresponding diameters are and The contact criterion for the two particles is: ; When the Euclidean distance between two particles is less than the sum of their radii, it indicates that they have geometrically overlapped. In this case, the depth of overlap is defined. for: ; in: Denotes the Euclidean norm; >0 indicates that an overlap actually occurred; If they do not overlap, then =0.

[0036] To achieve structural stability and physical rationality of the particle system, an energy function based on overlap minimization and boundary penalty is defined. In this function, the geometric overlap between any two particles is considered an "energy" contribution, the magnitude of which is related to the overlap depth between the particles. Proportional: ; In this embodiment of the invention, step S5 specifically includes: To minimize the energy of the particle system, an optimization algorithm is used to iteratively solve for the particle positions. The objective is to minimize the total energy of the system, making the particle arrangement more rational and reducing excessive overlap between particles.

[0037] Initial parameter settings: Optimization objective function: In this invention, the objective function is the total energy function, which includes the repulsion energy between particles and the penalty term between particles and the boundary, and is used to measure the stability of the current particle system state.

[0038] Optimization variable: Particle position coordinate vector (i.e., the center coordinates of each particle in three-dimensional space).

[0039] Initial values: Particle positions are initialized to a non-overlapping random distribution, ensuring that each particle is within the boundary range and maintains a minimum distance from other particles.

[0040] Optimizer parameter configuration: Algorithm type: The method employs algorithms such as L-BFGS, Adam optimizer, BFGS algorithm, and Conjugate Gradient. This method retains a limited amount of historical gradient information in each iteration to approximate the inverse of the Hessian matrix, thereby obtaining an efficient descent direction.

[0041] Historical steps: set to a finite number (e.g., 100) to construct an approximate Hessian matrix.

[0042] Convergence tolerance: Usually set to a small value (e.g.) This ensures that the optimization process terminates when an approximate optimal solution is reached.

[0043] Maximum number of iterations: Set to a large value (e.g., 2000) to ensure that the optimizer has a sufficient chance to converge.

[0044] In this embodiment of the invention, step S6 specifically includes: The initial porosity is set based on the particle characteristics, generally greater than the minimum porosity of a single-size particle. An iterative strategy is used to gradually narrow down the range of the target porosity value. In each iteration, a target porosity value is first set. Based on the current particle arrangement, the particles are adjusted using an energy minimization optimization algorithm, with the optimization objective being to minimize the total system energy. Then, the total overlap volume between all particles in the space is calculated. The ratio of this total overlap volume to the total space volume is calculated to obtain the overlap ratio. If the overlap ratio exceeds a set threshold (usually set to 1%), the current target porosity is deemed infeasible, meaning that the spatial density has reached its limit and further compression cannot be achieved without causing severe overlap, thus ending the iteration.

[0045] Overlapping volume The calculation is based on the geometric derivation of the overlapping regions of spheres, specifically employing the method of subtracting the area of ​​the overlapping region from the superposition of the volumes of the spherical caps to ensure the accuracy and numerical stability of the calculation results. Its mathematical expression is as follows: ; Where d represents the distance between the centers of mass of the two particles. , These are the radii of the corresponding particles.

[0046] For example, if the target porosity is 26%, the overlap ratio does not exceed the set threshold. If the porosity is then reduced to, say, 25%, the overlap ratio exceeds the threshold, and the porosity is considered to be no longer suitable for reduction; that is, 26% is the minimum value.

[0047] In this embodiment of the invention, step S7 specifically includes: Generate the particle size distribution probability density function (PDF) and the cumulative distribution function (CDF); Draw a particle size histogram and analyze the final particle size distribution; Generate a 3D visualization of particle arrangement; Output the final optimized particle data file for use in subsequent projects.

[0048] The technical solution of the present invention will be described in more detail below through embodiments.

[0049] Example 1: A method for optimizing the particle distribution of battery materials, where the particle size is a single size, and the L-BFGS algorithm is selected when minimizing energy.

[0050] (1) Objectives and system settings: Target material: Particle A (ideal rigid sphere); Particle size: Single size, diameter D = 1μm; Container: Cube, side length = 50μm; Optimization objective: To determine the minimum porosity of the system using an energy minimization method (the theoretical maximum packing limit is known to be 26%).

[0051] (2) The specific implementation process shall be carried out in accordance with steps S1 to S7 of the present invention: S1. Establish a particle size distribution model: Since the particles are of a single size, the quantity distribution is directly determined as follows: all particles have a diameter of D=1 μm and a radius of r=0.5 μm.

[0052] S2, Particle Sampling and Volume Assignment, Input Parameter: Spatial Side Length = 50 μm, the target porosity attempt sequence is ϕ∈ [0.30, 0.24], the search step size is 0.01; the material is a single component with a mass ratio of 1, the density ρ is set to 1 g / cm³ (unit normalization, which does not affect the volume calculation), and the overlap ratio threshold is 1%.

[0053] Calculate the total volume of the container. =125000 .

[0054] When ϕ=0.3, the total volume of particle A is .

[0055] Single particle volume The number of particles is .

[0056] S3, Configure the initial position of the particles: Independently and randomly sample the center coordinates of all particles in each dimension within the interval [0.5, 49.5] μm to ensure that the initial positions of all particles are located inside the container and do not overlap.

[0057] Following steps S4 to S6, the L-BFGS algorithm is selected as the optimizer, with the historical steps set to 100 and the convergence tolerance set to 1e. -5 The maximum number of iterations is 2000, and the particle positions are iteratively optimized to minimize the total system energy E.

[0058] Determining the minimum porosity: Starting with ϕ = 0.30, the target porosity value was iteratively reduced. After each optimization, the overall overlap volume ratio of the system was calculated. When the porosity was 26%, the overlap ratio was less than 1%; when further trying ϕ = 0.25, the overlap ratio exceeded 1%. Based on this, the minimum porosity of the system was determined to be 26%.

[0059] S7, Output Results: Outputs the final optimized particle position data and generates results as shown below. Figure 1 The three-dimensional spatial arrangement of spheres is shown in the visualization image. (3) Implementation effect: In this embodiment, the minimum porosity result consistent with the theoretical expectation (26%) was successfully obtained through optimization method, which verifies the effectiveness and accuracy of the method of the present invention in processing single particle size system.

[0060] Example 2: A method for optimizing the particle distribution of battery materials, which uses a laser particle size analyzer to test the particle size distribution and selects the L-BFGS algorithm when minimizing energy.

[0061] (1) Objectives and system settings: Target material: Nickel-cobalt-manganese (NCM) cathode powder (considered as a single material component, without distinguishing between two phases / coating); Particle size distribution: obtained by laser particle size analyzer, the volumetric particle size distribution is as follows. Figure 2 As shown; Container: Cube, side length = 50μm; Optimization objective: Based on the measured particle size distribution, determine the minimum porosity of the NCM particle system using this optimization method.

[0062] (2) The specific implementation process shall be carried out in accordance with steps S1 to S7 of the present invention: S1, Establish a particle size distribution model: The volume distribution measured by the laser particle size analyzer is as follows: Figure 2 As shown.

[0063] S2, Particle Sampling and Volume Distribution, Input Parameter: Spatial Side Length = 50 μm, the target porosity attempt sequence is ϕ ∈ [0.32, 0.24], the search step size is 0.01; the material is a single component with a mass percentage of 1 and an overlap threshold of 1%.

[0064] Calculate the total volume of the container. =125000 .

[0065] When ϕ=0.32, the total volume of NCM particles ; Random sampling is performed according to a log-normal distribution. Particle sizes are generated sequentially, and their volumes are accumulated until the total volume of NCM particles reaches a certain value. This allows us to determine the particle set.

[0066] S3, Configure the initial position of the particles: The center coordinates of all sampled particles are independently and randomly sampled in each dimension within the interval [0.5, 49.5] μm to ensure that the initial position of all particles is inside the container.

[0067] Following steps S4 to S6, the L-BFGS algorithm is selected as the optimizer, with the historical steps set to 100 and the convergence tolerance set to 1e. -5 The maximum number of iterations is 2000, and the particle positions are iteratively optimized to minimize the total system energy E.

[0068] Starting with ϕ = 0.32, the target porosity value was iteratively reduced. After each optimization, the overall overlap volume ratio of the system was calculated. When the porosity was 24.5%, the overlap ratio was less than 1%; when further attempts were made to achieve even lower porosities, the overlap ratio exceeded 1%. Based on this, the minimum porosity of this NCM particle system was determined to be 24.5%.

[0069] S7, Output Results: The optimized particle size distribution of the NCM ternary cathode material is as follows: Figure 3 As shown, the three-dimensional spatial arrangement of spheres is as follows: Figure 4 As shown.

[0070] It should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing particle distribution in battery materials, characterized in that, The steps include the following: S1, Establish a statistical distribution model of particle size; S2, Particle sampling is performed based on the particle size distribution model; S3, configure the initial position of the particles; S4, construct the system energy function based on the inter-particle overlap state, and calculate the total system energy; S5 uses an iterative optimization algorithm to adjust particle positions and reduce the total system energy; S6. The minimum porosity of the system is determined based on whether the particle overlap ratio exceeds a set threshold. S7 generates and outputs the optimized particle distribution data.

2. The method according to claim 1, characterized in that, The particle size distribution model in S1 is established through one of the following methods: (1) Particle size distribution data were obtained based on tests; (2) Obtain the statistical distribution model through the key particle size parameters D10, D50 and D90.

3. The method according to claim 2, characterized in that, When obtaining particle size distribution data using the aforementioned test, the method is selected from one of the following: laser particle size analyzer, dynamic light scattering instrument, single-particle optical sensing technology, scanning mobility particle size analyzer, sedimentation method, Coulter particle size analyzer, and optical microscope image recognition. When using the key particle size parameters to build a model, a log-normal distribution is used for fitting, and a conversion relationship between the volume distribution function and the number distribution function is established.

4. The method according to claim 1, characterized in that, S2 specifically includes the following steps: S2.1, Input predefined parameters including spatial side length Target porosity Mass percentage of each material particle and the density of each material particle ; S2.2, Calculate the target total filling volume Normalize the total mass M of the system to the nearest unit, and calculate the mass of each type of material particle k. and the volume of solid occupied Summing gives the sum of the volumes of all material particles. ; S2.3, using scaling factor Scaling the target total filling volume to the actual filling volume of each material particle k ; S2.4, for each type of material particle k, sample the material particles according to their particle size distribution function, sampling one material particle at a time and accumulating the volume until the total volume is reached. 。 5. The method according to claim 1, characterized in that, S4 specifically includes the following steps: S4.1, let the geometric center positions of the i-th particle and the j-th particle be respectively... and Their corresponding diameters are respectively and; S4.2, Calculate the overlap depth of the two particles. : ， hour, >0 indicates that overlap actually occurred; if there is no overlap, then... =0, in, Denotes the Euclidean norm; S4.3, Calculate the total system energy E: 。 6. The method according to claim 1, characterized in that, S5 includes the following steps: S5.1 Initial parameter settings: including total energy function, material particle position coordinate vector, and material particle position initialization; S5.2, Optimizer parameter configuration: including optimization algorithm, historical steps, convergence tolerance, and maximum number of iterations.

7. The method according to claim 6, characterized in that, In S5.2, the optimization algorithm is selected from one of L-BFGS, Adam optimizer, BFGS algorithm and conjugate gradient algorithm.

8. The method according to claim 1, characterized in that, In step S6, the minimum porosity is obtained through the following steps: S6.1, at the target porosity The following steps are taken: Optimization algorithms are applied to adjust the particle positions, the sum of the overlapping volumes between particles in space is calculated, and the ratio of this sum to the total volume of space is calculated to obtain the system's overlap ratio. S6.2, Determine the feasibility of the target porosity based on the overlap ratio and update the target porosity range: If the overlap ratio is less than or equal to the set threshold, then the current target porosity is... It is feasible to adjust and narrow the range of the porosity target value for the next iteration; If the overlap ratio is greater than the set threshold, then the current target porosity is determined. Not feasible; S6.3 When the overlap ratio is detected to be greater than the set threshold, the iteration stops. At this time, the porosity target value that meets the overlap ratio threshold condition in the previous iteration represents the minimum porosity of the system within the acceptable overlap range.

9. The method according to claim 8, characterized in that, The overlapping volume The calculation is based on the geometric derivation of the overlapping regions of spheres, as follows: Where d represents the distance between the centroids of the two material particles. , These represent the radii of the corresponding material particles.

10. The method according to claim 1, characterized in that, The output particle distribution data in S7 includes at least one of the following: generating a particle size distribution probability density function and a cumulative distribution function, drawing a particle size histogram, generating a 3D particle arrangement visualization, and outputting the final optimized particle data file.

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