A method for optimizing the distribution of battery material particles

Abstract

The application 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 size; S2, sampling particles according to the particle size distribution model; S3, configuring the initial position of the particles; S4, constructing a system energy function based on the overlapping state between the particles, and calculating the total energy of the system; S5, adjusting the particle position through an iterative optimization algorithm to reduce the total energy of the system; S6, taking whether the particle overlapping ratio exceeds a set threshold as a criterion to determine the minimum porosity of the system; and S7, generating and outputting the optimized particle distribution data. The application combines the particle arrangement method of modeling, random sampling and energy optimization of key particle size parameters, realizes the minimization of overlapping energy through an optimization algorithm, establishes a porosity iterative convergence strategy based on the overlapping volume threshold, and guarantees low calculation cost and output of verifiable three-dimensional visual arrangement data.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of battery material particle distribution optimization, in particular to a battery material particle distribution optimization method. BACKGROUND

[0002] In the field of batteries, the uniformity of particle size distribution and the spatial arrangement of core particle materials such as positive electrodes, negative electrodes, and electrolytes directly determine the energy density, conductivity, and cycle stability of the battery: if the particle size is aggregated or arranged unevenly, it is easy to lead to an imbalance in the pore structure of the electrode, such as wasted volume in large pores, insufficient electrolyte immersion in small pores, or discontinuous conductive / ionic conduction network, which restricts the performance of the battery.

[0003] However, traditional control methods have obvious limitations. Methods based on empirical formulas have a narrow application range and are invalid when materials are changed or processes are adjusted. Offline measurement methods have time lags and cannot capture the dynamic arrangement of particles in real time, resulting in material waste and making it difficult to achieve fine control, which is a key bottleneck for improving battery performance. SUMMARY

[0004] To solve the above problems, a battery material particle distribution optimization method is disclosed in the present application. The technical solution of the present application is as follows:

[0005] The present application discloses a battery material particle distribution optimization method, which comprises the following steps:

[0006] S1, establishing a statistical distribution model of particle size;

[0007] S2, sampling particles according to the particle size distribution model;

[0008] S3, configuring the initial position of the particles;

[0009] S4, constructing a system energy function based on the overlapping state between particles and calculating the total energy of the system;

[0010] S5, adjusting the particle position through an iterative optimization algorithm to reduce the total energy of the system;

[0011] S6, determining the minimum porosity of the system by taking whether the particle overlap ratio exceeds a set threshold as a criterion;

[0012] S7, generating and outputting the optimized particle distribution data.

[0013] Preferably, the particle size distribution model in S1 is established by one of the following methods:

[0014] (1) obtaining particle size distribution data based on testing;

[0015] (2) Obtain statistical distribution model by key particle size parameters D10, D50, D90.

[0016] Preferably, when obtaining particle size distribution data by the test, the method is selected from one of laser particle size analyzer, dynamic light scattering instrument, single particle optical sensing technology, scanning mobility particle sizer, sedimentation method, coulter particle size analyzer, optical microscope image recognition;

[0017] When establishing the model by the key particle size parameters, the lognormal distribution is used for fitting, and the conversion relationship between the volume distribution function and the number distribution function is established.

[0018] Preferably, the S2 specifically comprises the following steps:

[0019] S2.1, input the predetermined parameters including the space side length , target porosity , mass proportion of each material particle , and density of each material particle ;

[0020] S2.2, calculate the target total filling volume , normalize the system total mass M, calculate the mass and the occupied solid volume of each material particle k, and sum to obtain the sum of the volumes of all material particles ;

[0021] S2.3, scale the target total filling volume to the actual filling volume of each material particle k by the scaling factor ; ;

[0022] S2.4, for each material particle k, sample the material particles according to the particle size distribution function thereof, sample one material particle at a time and accumulate the volume until the total volume 。

[0023] Preferably, the S4 specifically comprises the following steps:

[0024] S4.1, set the geometric center positions of the i th particle and the j th particle as and , and the corresponding diameters as and ;

[0025] S4.2, calculate the overlap depth of the two particles :

[0026] ,

[0027] time, >0 means that the overlap actually occurs; if no overlap, then =0,

[0028] where, denotes the Euclidean norm;

[0029] S4.3, calculate the total system energy E:

[0030]

[0031] Preferably, the S5 comprises the following steps:

[0032] S5.1, initial parameter setting: including total energy function, position coordinate vector of material particles, material particle position initialization;

[0033] S5.2, optimizer parameter configuration: including optimization algorithm, history step number, convergence tolerance, maximum iteration number.

[0034] Preferably, in the S5.2, the optimization algorithm is selected from one of L-BFGS, Adam optimizer, BFGS algorithm and conjugate gradient algorithm.

[0035] Preferably, in the S6, the minimum porosity is obtained by the following steps:

[0036] S6.1, at the target porosity , the optimization algorithm is applied to adjust the particle position, the sum of the overlapping volume between particles in the space is calculated, and the ratio of the sum to the total volume of the space is calculated to obtain the overlap ratio of the system;

[0037] S6.2, determine the feasibility of the target porosity according to the overlap ratio and update the target porosity range:

[0038] If the overlap ratio is ≤ a set threshold, the current target porosity is feasible, adjust and narrow the attempt range of the porosity target value in the next iteration;

[0039] If the overlap ratio is > a set threshold, it is determined that the current target porosity is not feasible;

[0040] S6.3, when the overlap ratio > a set threshold is detected, stop iteration, at this time, the porosity target value in the last iteration that satisfies the overlap ratio threshold condition represents the minimum porosity of the system within the acceptable overlap range.

[0041] Preferably, the calculation of the overlapping volume is based on the geometric derivation of the sphere overlap region, specifically as follows:

[0042]

[0043] wherein d represents the distance between the centers of the two material particles, 、 are the radii of the corresponding material particles, respectively.

[0044] Preferably, the output particle distribution data in S7 includes at least one of generating a particle size distribution probability density function and a cumulative distribution function, drawing a particle size histogram, generating a 3D particle arrangement visualization image, and outputting a final optimized particle data file.

[0045] The advantages of the present application are as follows:

[0046] The battery material particle distribution optimization method proposed in the present application realizes the minimization of the overlap energy of particle arrangement by combining key particle size parameter modeling, random sampling, and energy optimization strategy, and establishes a porosity iterative convergence mechanism based on the overlap threshold, which has the advantages of low calculation cost and output of visual data. This method has wide application prospects in the field of new energy batteries, and can effectively optimize the distribution and pore structure of battery material particles, thereby improving product performance, enhancing mechanical properties, improving functional performance, and improving manufacturing efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0047] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only one embodiment of the present application, and those skilled in the art can obtain other drawings according to these drawings without creative labor.

[0048] Figure 1 Figure 4 is a three-dimensional spherical arrangement image of the optimized particle A of Example 1.

[0049] Figure 2 Figure 5 is a laser particle size analyzer test particle size distribution graph of the NCM positive electrode powder of Example 2.

[0050] Figure 3 Figure 6 is a particle size distribution graph of the optimized NCM positive electrode powder of Example 2.

[0051] Figure 4 Figure 7 is a three-dimensional spherical arrangement image of the optimized NCM positive electrode powder of Example 2. DETAILED DESCRIPTION

[0052] The technical solutions of the present application will be described clearly and completely below in combination with the embodiments of the present application and the drawings. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application.

[0053] The conventional particle size distribution design method mainly relies on empirical formula or experimental measurement, and it is difficult to accurately control the particle arrangement and porosity, and the optimization efficiency is low.

[0054] In view of the above problems, the present application provides a battery material particle distribution optimization method, which combines key particle size parameter modeling, random sampling and energy optimization particle arrangement method, realizes the minimization of overlapping energy through an optimization algorithm, and establishes a porosity iterative convergence strategy based on the overlapping volume threshold, which ensures low calculation cost and outputs verifiable three-dimensional visual arrangement data. Overcome the problems in the prior art, such as difficult to accurately control the particle arrangement and porosity, low optimization efficiency, etc. The method gradually reduces the target porosity by iteration under the given particle size distribution of the material particles. When the overlap ratio under a certain target porosity does not exceed the set overlap ratio threshold, the porosity is further reduced until the overlap ratio exceeds the threshold, then it is determined that the current target porosity is not feasible, which means that the space density has reached the limit and cannot be further compressed without causing serious overlap. At this time, the iteration is ended, and the last target porosity is selected.

[0055] The present application discloses a battery material particle distribution optimization method, comprising the following steps:

[0056] S1, a statistical distribution model of particle size is established;

[0057] S2, particle sampling is performed according to the particle size distribution model;

[0058] S3, the initial position of the particle is configured;

[0059] S4, a system energy function is constructed based on the overlapping state between particles, and the total energy of the system is calculated;

[0060] S5, the particle position is adjusted by an iterative optimization algorithm to reduce the total energy of the system;

[0061] S6, the minimum porosity of the system is determined by taking whether the particle overlap ratio exceeds the set threshold as the criterion;

[0062] S7, the optimized particle distribution data is generated and output.

[0063] The technical method proposed in the present application is applicable to various materials in the battery system with a particle morphology, and the application scope specifically includes but is not limited to the following categories, and the following enumeration is only exemplary and is not a limitation on the protection scope of the present application: electrode-related particle materials, functional auxiliary particle materials, particle coating materials for improving the performance of separators, and electrolyte system-related particle materials.

[0064] Any material with a particle morphology characteristic in the battery system and capable of being processed or performance-regulated by the technical method of the present application belongs to the application scope of the present application and is not limited by the aforementioned specific categories.

[0065] The modeling method of the particle size distribution of the present application is not particularly limited, and any method capable of reasonably modeling the particle size distribution of the particle system is applicable to the present application without violating the inventive concept of the present application, and the examples are only exemplary and are not a limitation on the protection scope.

[0066] For example, the particle size distribution modeling can use direct testing methods such as laser particle size analyzers, dynamic light scattering instruments, single-particle optical sensing technology, scanning mobility particle sizers, sedimentation methods, Coulter particle size analyzers, and optical microscopes + image recognition, etc. The particle size distribution function can also be calculated by key particle size parameters (D10, D50, D90).

[0067] Correspondingly, in the energy minimization process, the optimization algorithm used in the present application is also not particularly limited. Any algorithm applicable to nonlinear optimization problems can be used, including but not limited to L-BFGS, Adam optimizer, BFGS algorithm, Conjugate Gradient (Conjugate Gradient Method), 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.

[0068] Step S1 in the embodiment of the present application is specifically:

[0069] The particle size distribution function is calculated by key particle size parameters (D10, D50, D90) For example:

[0070] Assuming that the particle size D and its volume ratio follow a lognormal distribution, i.e.:

[0071] ;

[0072] Wherein: is the log mean, is the log standard deviation.

[0073] The particle size distribution calculation process is as follows:

[0074] a) Calculate the logarithmic mean (i.e., the logarithmic median):

[0075] ;

[0076] b) Calculate the logarithmic standard deviation:

[0077] ;

[0078] in, It is the 90th percentile of the standard normal distribution.

[0079] c) Calculate the particle volume distribution function:

[0080] According to the log-normal distribution formula, the particle diameter is D Volume distribution function of time particles for:

[0081] ;

[0082] d) Calculate the particle number distribution function:

[0083] The volume of each particle is:

[0084] ;

[0085] Then at a certain particle size D At this point, the quantity distribution function should satisfy:

[0086] ;

[0087] Calculate the unnormalized quantity distribution:

[0088]

[0089] Calculate the normalization factor Z using numerical integration:

[0090] ;

[0091] After normalization, the quantity distribution function can be obtained. :

[0092] ;

[0093] In this embodiment of the invention, step S2 specifically includes:

[0094] S2.1, Input known parameters:

[0095] Space side length : The side length of the cube in the target simulation space.

[0096] Target porosity ϕ: the volume fraction of pores in space.

[0097] Mass fraction of each material : sum of all materials mass is 1 .

[0098] Density of each material .

[0099] S2.2, Calculate target total filling volume:

[0100] According to the side length and porosity ϕ, the solid particle volume actually needed to fill can be obtained:

[0101] ;

[0102] Assign material volume according to mass fraction, for each material k, its solid volume can be calculated by its mass fraction and density:

[0103] Assume the total mass of the system is (unit normalized);

[0104] The mass of each material is;

[0105] The corresponding volume is:

[0106] ;

[0107] The total volume of all materials is:

[0108] ;

[0109] S2.3, Calculate the actual filling volume of each type of particle:

[0110] Use the scaling factor to scale the total volume to the actual volume:

[0111] ;

[0112] The actual filling volume of each type of particle is:

[0113] ;

[0114] S2.4, Sample the particle size set so that its volume sum meets the requirements:

[0115] For each material particle k, according to its particle size distribution function, sample the material particles, sample one material particle at a time and accumulate the volume, so that the total volume meets:

[0116] ;

[0117] The step S3 in the embodiment of the present application is specifically:

[0118] The particles are randomly placed in a two-dimensional or three-dimensional material space. For each particle, the initial position coordinates of the geometric center are independently generated in each dimension, and the generated range is from the radius to the side length of the container minus the radius, that is, the coordinate component of the i-th particle is randomly sampled in the range of [r i , -r i ] to ensure that the particles as a whole are located inside the cubic container without initial overlap with the boundary.

[0119] Material space definition: according to the particle size of the material, a material space large enough to fill the material particles is defined.

[0120] The step S4 in the embodiment of the present application is specifically:

[0121] In the particle arrangement simulation method involved in the present application, in order to model and evaluate the degree of mutual penetration between particles in the system, the concept of particle overlap depth is introduced. Assuming that the geometric center positions of the i-th particle and the j-th particle are and , and the corresponding diameters are and respectively , then the contact criterion of the two particles is:

[0122] ;

[0123] When the Euclidean distance between the two particles is less than the sum of their radii, it means that the two particles have geometric overlap. At this time, the overlap depth of the two particles is defined as :

[0124] ;

[0125] Wherein:

[0126] represents the Euclidean norm;

[0127] >0 means that actual overlap occurs;

[0128] If there is no overlap, =0.

[0129] To realize the 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 of any two particles is regarded as an "energy" contribution, and its size is proportional to the overlap depth between the particles:

[0130] ;

[0131] The step S5 in the embodiment of the present application is specifically:

[0132] To achieve the energy minimization of the particle system, an optimization algorithm is used to iteratively solve the particle positions. The goal is to minimize the total energy of the system, making the particle arrangement tend to a reasonable state, and reducing the excessive overlap between particles.

[0133] Initial parameter setting:

[0134] Optimization objective function: In the present application, the objective function is the total energy function, which includes the repulsive energy term between particles and the penalty term between particles and the boundary, to measure the stability of the current particle system state.

[0135] Optimization variable: The position coordinate vector of the particle (i.e. the center coordinate of each particle in three-dimensional space).

[0136] Initial value: The particle position is initialized as a random distribution without overlap, ensuring that each particle is within the boundary range and maintains a minimum distance from other particles.

[0137] Optimizer parameter configuration:

[0138] Algorithm type: L-BFGS, Adam optimizer, BFGS algorithm, Conjugate Gradient (Conjugate Gradient Method) and other algorithms are used. This method retains a limited number of historical gradient information in each iteration, which is used to approximate the inverse of the Hessian matrix, thereby obtaining an efficient descent direction.

[0139] History step: Set to a limited number (such as 100), used to construct the approximate Hessian matrix.

[0140] Convergence tolerance: Usually set to a small value (such as ), to ensure that the optimization process is terminated when the approximate optimal solution is reached.

[0141] Maximum number of iterations: Set to a larger value (such as 2000), to ensure that the optimizer has sufficient opportunity to converge.

[0142] The step S6 in the embodiment of the present application is specifically:

[0143] The initial porosity is set according to the particle condition, and is generally greater than the minimum porosity of the single-size particle. An iterative strategy is adopted to gradually narrow the attempt range of the porosity target value. In each iteration process, a porosity target value is first set, and the particles are adjusted through the energy minimization optimization algorithm according to the current particle arrangement condition, and the optimization target is to minimize the total energy of the system. Then, the total overlap volume between all particles in the space is calculated. The total overlap volume is compared with the total volume of the space to obtain the overlap ratio. If the overlap ratio exceeds the set threshold (usually set to 1%), it is determined that the current target porosity is not feasible, which means that the space density has reached the limit and cannot be further compressed without causing serious overlap, and the iteration is ended.

[0144] Overlap volume The calculation is based on the geometric derivation of the sphere overlap region, and specifically adopts the method of adding the spherical cap volume and subtracting the overlap region area to ensure the accuracy and numerical stability of the calculation result. The mathematical expression is as follows:

[0145] ;

[0146] Wherein, d represents the distance between the centers of the two particles, 、 are the radii of the corresponding particles.

[0147] For example: the target porosity is 26%, and the overlap ratio does not exceed the set threshold. Then, the porosity is reduced to 25%, and it is found that the overlap ratio exceeds the threshold, and it is considered that the porosity cannot be further reduced, that is, 26% is the minimum value.

[0148] The step S7 in the embodiment of the application is specifically:

[0149] Generating a particle size distribution probability density function (PDF) and a cumulative distribution function (CDF);

[0150] Drawing a particle size histogram to analyze the final particle size distribution;

[0151] Generating a 3D particle arrangement visualization diagram;

[0152] Outputting a final optimized particle data file for subsequent engineering use.

[0153] The technical solutions of the application will be described in more detail through embodiments.

[0154] Embodiment 1: A battery material particle distribution optimization method, the particle size of the particle is single size, and the L-BFGS algorithm is selected when the energy is minimized.

[0155] (1) Target and system settings:

[0156] Target material: Particle A (ideal rigid sphere);

[0157] Particle size: single size, diameter D = 1 μm;

[0158] Container: cube, side length = 50 μm;

[0159] Optimization goal: find the minimum porosity of this system by energy minimization method (theoretical maximum packing limit is known to be 26%).

[0160] (2) The implementation process is performed according to steps S1 to S7 of the application:

[0161] S1, a particle size distribution model is established: since the particles are of a single size, the number distribution is directly determined as all particles having a diameter D = 1 μm and a radius r = 0.5 μm.

[0162] S2, particle sampling and volume allocation, input parameters: spatial side length = 50 μm, target porosity attempt sequence is ϕ∈ [0.30, 0.24], search step size 0.01; the material is a single component, the mass ratio is 1, the density ρ is set to 1 g / cm³ (unit normalization, which does not affect volume calculation), and the overlap ratio threshold is 1%.

[0163] The total volume of the container is calculated as =125000 .

[0164] When ϕ=0.3, the total volume of particle A is .

[0165] The volume of a single particle is , and the number of particles is .

[0166] S3, configure the initial position of the particles: the center coordinates of all particles in each dimension are independently randomly sampled within the interval [0.5, 49.5] μm, ensuring that all particle initial positions are located inside the container and have no overlap.

[0167] According to the steps of S4 to S6, the L-BFGS algorithm is selected as the optimizer, the history step size is set to 100, the convergence tolerance is set to 1e -5 , the maximum number of iterations is set to 2000, and the particle positions are iteratively optimized to minimize the total energy E of the system.

[0168] Determination of the minimum porosity: starting from ϕ = 0.30, iteratively optimize the porosity target value in sequence. After each optimization, calculate the overall overlap volume ratio of the system. When the porosity is 26%, the overlap ratio is less than 1%; when further attempts ϕ = 0.25, the overlap ratio exceeds 1%. Accordingly, it is determined that the minimum porosity of the system is 26%.

[0169] S7, output result: output the final optimized particle position data, and generate a three-dimensional space sphere arrangement visualization image as shown in Figure 1 . (3) Implementation effect: through the optimization method, the minimum porosity result consistent with the theoretical expectation (26%) is successfully obtained, which verifies the effectiveness and accuracy of the method in processing single particle size system.

[0170] Example 2: A battery material particle distribution optimization method, the particle size distribution is tested by a laser particle size analyzer, and the L-BFGS algorithm is selected when the energy is minimized.

[0171] (1) Target and system setting:

[0172] Target material: nickel-cobalt-manganese (NCM) positive electrode powder (regarded as a single material component, not distinguished as two-phase / coated);

[0173] Particle size distribution: obtained by laser particle size analyzer, the volume-based particle size distribution is as shown in Figure 2 .

[0174] Container: cube, side length = 50 μm;

[0175] Optimization target: according to the measured particle size distribution, the minimum porosity of the NCM particle system is obtained by the optimization method.

[0176] (2) The specific implementation process is performed according to the steps S1 to S7 described in the application:

[0177] S1, establish a particle size distribution model: the volume distribution measured by the laser particle size analyzer is as shown in Figure 2 .

[0178] S2, particle sampling and volume distribution, input parameters: space side length = 50 μm, target porosity attempt sequence is ϕ ∈ [0.32, 0.24], search step 0.01; the material is a single component, the mass ratio is 1, and the overlap ratio threshold is 1%.

[0179] The total volume of the container is calculated as =125000 .

[0180] When ϕ = 0.32, the total volume of NCM particles ;

[0181] According to the lognormal distribution, the particle size is generated in turn and the volume is accumulated until the total volume of NCM particles reaches , so as to determine the particle set.

[0182] S3, configure the initial position of the particle:

[0183] The center coordinates of all the particles generated by sampling are independently randomly sampled in the interval [0.5, 49.5] μm in each dimension, so as to ensure that all the initial positions of the particles are located inside the container.

[0184] According to the steps of S4 to S6, the L-BFGS algorithm is selected as the optimizer, the history step number is set to 100, the convergence tolerance is set to 1e -5 , and the maximum iteration number is set to 2000, and the particle position is iteratively optimized to minimize the total energy E of the system.

[0185] Starting from ϕ = 0.32, the porosity target value is sequentially reduced for iterative optimization. After each optimization, the overall overlap volume ratio of the system is calculated. When the porosity is 24.5%, the overlap ratio is less than 1%; when further trying a lower porosity, the overlap ratio exceeds 1%. Accordingly, it is determined that the minimum porosity of the NCM particle system is 24.5%.

[0186] S7, output the result: the particle size distribution of the optimized NCM ternary positive electrode material is shown in Figure 3 , and the three-dimensional space sphere arrangement image is shown in Figure 4 .

[0187] It should be noted that the above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method of optimizing a distribution of battery material particles, the method comprising: determining a target distribution of battery material particles; and adjusting a distribution of battery material particles to the target distribution. The method comprises the following steps: S1, establishing a statistical distribution model of particle size; S2, sampling particles according to the particle size distribution model; S3, configuring the initial position of the particles; S4, constructing a system energy function based on the overlapping state between the particles and calculating the total energy of the system; S5, adjusting the position of the particles through an iterative optimization algorithm to reduce the total energy of the system; S6, determining the minimum porosity of the system by taking whether the overlapping ratio of the particles exceeds a set threshold as a criterion; S7, generating and outputting the optimized particle distribution data.

2. The method of claim 1, wherein, The particle size distribution model in S1 is established by one of the following methods: (1) obtaining particle size distribution data based on testing; (2) obtaining a statistical distribution model through key particle size parameters D10, D50 and D90.

3. The method of claim 2, wherein when the particle size distribution data is obtained through testing, the method is selected from one of a laser particle size analyzer, a dynamic light scattering instrument, a single-particle optical sensing technology, a scanning mobility particle sizer, a sedimentation method, a Coulter particle size analyzer and optical microscope image recognition; and when the model is established through the key particle size parameters, a lognormal distribution is used for fitting, and a conversion relationship between a volume distribution function and a number distribution function is established. The S2 specifically comprises the following steps: The S4 specifically comprises the following steps:

4. The method of claim 1, wherein, S4.3, calculating the total energy E of the system: S2.1, inputting predetermined parameters including spatial side length , target porosity , mass proportion of each material particle , and density of each material particle ; S2.2, calculate the target total fill volume , calculate the mass of each material particle k, normalized by the system total mass M , and the solid volume fraction , summing to get the total volume of all material particles ; S2.3, scaling the target total fill volume to the actual fill volume of each material particle k scaling the target total fill volume to the actual fill volume of each material particle k ; S2.

4. For each material particle k, sample material particles according to its particle size distribution function, one material particle at a time and accumulate volume, until the total volume 。 5. The method of claim 1, wherein, The S5 comprises the following steps: S4.1, set the geometric center positions of the i-th particle and the j-th particle as and , respectively, which correspond to diameters of and d j , respectively; S4.2, calculating the depth of overlap of the two particles : ， time, > 0 means that the overlap actually occurred; if there was no overlap, = 0, wherein denotes the Euclidean norm; S5.1, initial parameter setting: including the total energy function, the position coordinate vector of the material particles and the initialization of the position of the material particles; 。 6. The method of claim 1, wherein, S5.2, optimizer parameter configuration: including the optimization algorithm, the historical step number, the convergence tolerance and the maximum iteration number. In S5.2, the optimization algorithm is selected from one of an L-BFGS, an Adam optimizer, a BFGS algorithm and a conjugate gradient algorithm. In S6, the minimum porosity is obtained through the following steps:

7. The method of claim 6, wherein, S6.2, judging the feasibility of the target porosity according to the overlapping ratio and updating the target porosity range:

8. The method of claim 1, wherein, S6.3, when it is detected that the overlapping ratio is greater than the set threshold, the iteration is stopped, and the target porosity value that meets the overlapping ratio threshold condition in the last iteration represents the minimum porosity of the system within the acceptable overlapping range. S6.1, at the target porosity Next, the optimization algorithm is applied to adjust the particle positions, the sum of the overlapping volumes between particles in the space is calculated, and the ratio of the total volume of the space is calculated to obtain the overlapping ratio of the system. In S7, the output particle distribution data includes at least one of generating a particle size distribution probability density function and a cumulative distribution function, drawing a particle size histogram, generating a 3D particle arrangement visualization diagram and outputting a final optimized particle data file. If the overlap ratio is < a set threshold, then the current target porosity is feasible, adjust and narrow the range of the porosity target value for the next iteration; If the overlap ratio > set threshold, then determine the current target porosity Not feasible; ​ 9. The method of claim 8, wherein, The overlapping volume The calculation is based on a geometric derivation of the sphere intersection region, as follows: where d denotes the distance between the centers of the two material particles, , are the radii of the corresponding material particles, respectively.

10. The method of claim 1, wherein, ​

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