A method and system for predicting particle breakage strength considering pore parameters

Abstract

The application provides a particle crushing strength prediction method and system considering pore parameters, relates to the technical field of geotechnical particle material mechanics, and aims at the problem that the prior art depends on a single parameter, lacks analysis and correlation analysis of the role of the single parameter, the model is single, and prediction accuracy and generalization ability are low.The method uses 3D printing to obtain particles with different particle sizes and pores, obtains the internal microstructure of the particles through micro-CT scanning, extracts pore characteristic parameters, considers multi-dimensional pore parameter characteristics, performs a uniaxial compression crushing experiment, quantifies the relationship between the multi-dimensional pore characteristic parameters and the particle crushing strength, calculates the actual particle crushing strength, establishes a PSO-SVR particle crushing strength prediction model, corrects the crushing strength predicted by the model according to the actual particle crushing strength and based on a calibration factor introduced based on a Weibull model.The application solves the problems in the prior art and improves the prediction accuracy and generalization ability of the model.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of geotechnical granular material mechanics research, and particularly relates to a granular crushing strength prediction method and system considering pore parameters. BACKGROUND

[0002] The statements in this section merely provide background information related to the application and do not necessarily constitute prior art.

[0003] 3D printed granular materials have important application value in the field of engineering materials and additive manufacturing, and their mechanical properties and crushing behavior directly affect resource utilization efficiency and material performance design. The mechanical properties and crushing behavior of granular materials are mainly affected by two types of factors: macroscopic parameters such as particle size and shape; and microscopic characteristics such as pore structure and internal cracks. Among them, the pore as a key controllable factor can be precisely controlled through 3D printing technology, providing an important means for performance optimization in engineering applications.

[0004] Existing research shows that the influence of pores on the mechanical properties and crushing behavior of particles mainly reflects in the following aspects: porosity, existing technologies establish a quantitative relationship between the porosity of porous basalt and engineering properties through image analysis technology; pore size, research shows that the compressive strength of porous ceramics decreases linearly with the increase of pore size under a fixed porosity; pore shape, CT scanning confirms that the pore geometry has a significant impact on material strength; pore distribution, by studying multiple pore geometries, it is found that the spatial arrangement of pores directly affects the crack initiation and propagation behavior.

[0005] At present, the existing research methods mainly include: experimental test methods, such as mechanical property testing, micro-CT observation, etc.; numerical simulation methods, simulation analysis of porous microstructure; theoretical analysis methods, by establishing a compression failure parameter analytical model to predict the crushing strength.

[0006] However, these existing methods still have certain deficiencies: usually rely on a single parameter, lack of systematic analysis of the coupling effect of multiple pore parameters; the empirical formula method used has limited scope of application and cannot adapt to the prediction of different materials; existing technologies lack correlation analysis of pore characteristics and crushing strength, the model is single, and the model prediction accuracy is low and the generalization ability is poor. SUMMARY

[0007] In order to overcome the above-mentioned deficiencies of the prior art, the present application provides a particle breakage strength prediction method and system considering pore parameters. By considering pore parameters, the relationship between porosity, pore number, pore distribution and breakage strength is analyzed and quantified through experiments, a PSO-SVR particle breakage strength prediction model is established, and the problems existing in the prior art are solved through the Weibull model and the calibration factor correction model, thereby improving the prediction accuracy and generalization ability of the model.

[0008] In order to achieve the above-mentioned purpose, one or more embodiments of the present application provide the following technical solutions:

[0009] The present application discloses a particle breakage strength prediction method considering pore parameters, comprising:

[0010] Modeling and preparing porous particles;

[0011] Obtaining the internal microstructure of the porous particles by micro-CT and extracting pore characteristic parameters by image processing;

[0012] Standardizing the pore characteristic parameters to obtain standardized data;

[0013] Performing uniaxial compression breakage experiments based on the standardized data and calculating the actual breakage strength of each particle;

[0014] Grouping the porous particles and fitting each group of particles using the Weibull model to obtain the modulus and characteristic strength of the Weibull model;

[0015] Inputting the standardized data into a support vector regression prediction model for training and optimizing the support vector regression model using a particle swarm algorithm to obtain an optimized particle breakage strength prediction model;

[0016] Using the optimized particle breakage strength prediction model to predict the standardized data to obtain the predicted breakage strength of each group of particles;

[0017] Inputting the predicted breakage strength of each group of particles into the Weibull model to obtain the predicted value characteristic strength;

[0018] Calculating the calibration factor according to the characteristic strength and the predicted value characteristic strength of the Weibull model;

[0019] According to the calibration factor, the final particle breakage strength prediction value is calculated.

[0020] As a further technical solution, modeling and preparing porous particles means parameterizing modeling of porous particles using three-dimensional design software and 3D printing of porous particles.

[0021] As a further technical solution, a three-dimensional design software is used for parameterized modeling of the porous particles, and the specific process is as follows:

[0022] A benchmark solid sphere model is established, wherein the particle size gradient is set to 9-15 mm;

[0023] At each particle size gradient, the porosity is set to 5%, 10%, 15%, 20%, 25%, and 30%, respectively;

[0024] Randomly distributed holes are created inside the sphere, wherein the number of pores is 10-30, the pore size is 0.5-2 mm, the pore distribution is represented by a fractal dimension, and the fractal dimension is in the range of 2-3.

[0025] As a further technical solution, image processing is used to extract pore characteristic parameters, and the specific process is as follows:

[0026] The internal microstructure of each particle is combined and reconstructed to obtain a single particle three-dimensional digital body image;

[0027] The single particle three-dimensional digital body image is denoised, smoothed, and the contrast between the pores and the matrix is enhanced;

[0028] The particle size is extracted from the single particle three-dimensional digital body image by software;

[0029] Three types of labels, pores, matrix, and background, are created, and the pores are segmented;

[0030] The segmented pores are converted into a binary image, and the porosity, pore number, and pore size are extracted;

[0031] Based on the binary image, the fractal dimension of each particle is calculated.

[0032] As a further technical solution, a uniaxial compression crushing experiment is conducted based on the standardized data, and the actual crushing strength of each particle is calculated, and the specific process is as follows:

[0033] During the uniaxial compression crushing experiment, the particles are scanned using micro-CT to obtain images of pore deformation, crack initiation, and through-cracking during compression, and the force-displacement curve of each particle is recorded simultaneously, and the compression characteristics are analyzed to obtain the particle crushing load;

[0034] According to the particle crushing load, the actual crushing strength of each particle is calculated.

[0035] As a further technical solution, Weibull model is used to fit each group of particles to obtain the modulus and characteristic strength of the Weibull model, and the specific process is as follows:

[0036] Based on the uniaxial compression crushing experiment, the cumulative survival probability of the particles in the uniaxial compression experiment is calculated;

[0037] Based on the survival probability and the actual crushing strength of each particle in the uniaxial compression experiment, the Weibull model was used for linear fitting to obtain the modulus and characteristic strength of the Weibull model.

[0038] As a further technical solution, the standardized data is input into the support vector regression prediction model for training. The specific process is as follows:

[0039] Choose a radial basis kernel function and construct a support vector objective function;

[0040] Based on the support vector objective function, the optimal decision function for predicting particle breakage intensity of the support vector regression prediction model is calculated.

[0041] Based on the analysis of uniaxial compression crushing experiments, penalty coefficients and radial basis kernel function kernel width parameters are set and substituted into the optimal decision function for predicting particle crushing strength.

[0042] The standardized data is input into the support vector regression model to obtain the initial predicted values.

[0043] As a further technical solution, the radial basis function is formulated as follows:

[0044] ;

[0045] in, There are two samples. and Similarity measure between them; It is a positive number, representing the kernel width parameter of the radial basis function. Indicates sample and The Euclidean distance between them.

[0046] As a further technical solution, the support vector regression model is optimized using the particle swarm optimization algorithm. The specific process is as follows:

[0047] Set initialization parameters, including the number of iterations, population position, particle position, and velocity;

[0048] Set a fitness function and calculate the initial fitness value, initial individual value, and initial population extreme value for each particle;

[0049] Update the particle's position and velocity, and update the individual and group extreme values. Determine if the global optimal position or maximum number of iterations is satisfied. If so, obtain the penalty coefficient and the optimal value of the radial basis function kernel width parameter of the support vector regression prediction model.

[0050] The second aspect discloses a particle breakage strength prediction system that considers pore parameters, including:

[0051] The data acquisition module is used for modeling and preparing porous particles;

[0052] Microscopic features of porous particles were obtained by micro-CT, and pore feature parameters were extracted by image processing.

[0053] The data preprocessing module is used to standardize the pore characteristic parameters to obtain standardized data;

[0054] The mechanical testing module is used to perform uniaxial compression crushing experiments based on standardized data and calculate the actual crushing strength of each particle.

[0055] The porous particles were grouped, and the Weibull model was used to fit each group of particles to obtain the modulus and feature strength of the Weibull model.

[0056] The model building and optimization module is used to input standardized data into the support vector regression prediction model for training, and to optimize the support vector regression model through the particle swarm algorithm to obtain the optimized particle crushing intensity prediction model.

[0057] The model prediction module is used to predict the standardized data using the optimized particle crushing strength prediction model to obtain the predicted values ​​of particle crushing strength for each group.

[0058] The predicted particle crushing strength values ​​of each group are input into the Weibull model to obtain the predicted characteristic strength.

[0059] The calibration factor is calculated based on the feature strength of the Weibull model and the feature strength of the predicted value.

[0060] Based on the calibration factor, the final predicted value of particle crushing strength is calculated.

[0061] The above one or more technical solutions have the following beneficial effects:

[0062] In this embodiment, porous particles are designed and 3D printed using 3D design software. Microscopic CT is used to obtain the internal microscopic features of the porous particles. Image processing is employed to extract particle size, porosity, number of pores, pore size, and pore distribution. By comprehensively considering multidimensional feature parameters such as particle size, porosity, number of pores, pore size, and pore distribution (fractal dimension), the coupling effect between these parameters is analyzed. This overcomes the limitations of traditional methods that rely on only a single parameter (such as porosity) and significantly improves the accuracy of crushing strength prediction.

[0063] In this embodiment, a micro-CT in-situ loading experiment (uniaxial compression fracture experiment) was conducted to observe the pore deformation, crack initiation, and propagation process in real time. The correlation between pore characteristics (such as critical porosity and dominant pore size) and failure modes was quantitatively analyzed, providing reliable physical mechanism support for the model. Simultaneously, the actual fracture strength of each particle was calculated experimentally. Subsequently, the characteristic strength with a modulus and a particle survival probability of 37% was obtained through Weibull model fitting, providing a data basis for subsequent prediction value correction.

[0064] In this embodiment, a particle breakage strength prediction model (PSO-SVR) is constructed. A support vector regression prediction model (SVR) is employed, combined with a particle swarm optimization (PSO) algorithm, to automatically search for optimal model parameters (penalty factor C, kernel width γ). Compared to traditional grid search methods, this improves computational efficiency while avoiding subjective bias from manual parameter tuning, thus enhancing the model's generalization ability and prediction accuracy. Simultaneously, a calibration factor is introduced based on the Weibull model to correct the predicted breakage strength, effectively reducing prediction bias caused by material batch differences or experimental errors, making the prediction results closer to actual engineering data.

[0065] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0066] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0067] Figure 1 This is a schematic diagram of a particle crushing strength prediction method considering pore parameters according to Embodiment 1 of the present invention.

[0068] Figure 2 The image shown is a CT scan image from Embodiment 1 of the present invention.

[0069] Figure 3 This is a schematic diagram of the force-displacement curve of the uniaxial compression crushing experiment in Embodiment 1 of the present invention;

[0070] Figure 4 This is a schematic diagram of the internal pore distribution of a single particle during the uniaxial compression crushing experiment of Embodiment 1 of the present invention.

[0071] Figure (a) shows the overall pore distribution; Figure (b) shows the pore distribution in half of the region; Figure (c) shows the pore distribution in a quarter of the region; and Figure (d) shows a crack diagram.

[0072] Figure 5This is a schematic diagram showing the relationship between particle crushing strength and porosity during the uniaxial compression crushing experiment of Embodiment 1 of the present invention.

[0073] Figure 6 This is a schematic diagram showing the relationship between particle crushing strength and pore quantity and pore volume during the uniaxial compression crushing experiment of Embodiment 1 of the present invention.

[0074] Figure (a) shows the relationship between particle crushing strength and pore number during the uniaxial compression crushing experiment; Figure (b) shows the relationship between particle crushing strength and pore volume during the uniaxial compression crushing experiment.

[0075] Figure 7 This is a schematic diagram showing the relationship between particle crushing strength and pore size during the uniaxial compression crushing experiment of Embodiment 1 of the present invention.

[0076] Figure 8 This is a schematic diagram showing the relationship between the number of pores involved in crack opening and the crack length and opening angle after particle destruction during the uniaxial compression crushing experiment of Embodiment 1 of the present invention.

[0077] Figure (a) shows the relationship between the number of pores participating in crack opening and the opening angle after particle destruction during the uniaxial compression crushing experiment; Figure (b) shows the relationship between the number of pores participating in crack opening and the crack length after particle destruction during the uniaxial compression crushing experiment. Detailed Implementation

[0078] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0079] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0080] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0081] Example 1

[0082] This embodiment discloses a method for predicting particle breakage strength considering pore parameters.

[0083] To more clearly illustrate this embodiment, a process for predicting particle breakage strength considering pore parameters can be specifically described as follows:

[0084] This embodiment provides a method for predicting particle breakage strength considering porosity parameters, including:

[0085] S1. Modeling and preparing porous particles;

[0086] S2. Obtain the internal microscopic features of porous particles through micro-CT, and extract pore feature parameters using image processing;

[0087] S3. Standardize the pore characteristic parameters to obtain standardized data;

[0088] S4. Based on the standardized data, conduct a uniaxial compression crushing experiment and calculate the actual crushing strength of each particle.

[0089] S5. Group the porous particles and fit each group of particles using the Weibull model to obtain the modulus and feature strength of the Weibull model.

[0090] S6. Input the standardized data into the support vector regression prediction model for training, and optimize the support vector regression model through the particle swarm algorithm to obtain the optimized particle crushing intensity prediction model.

[0091] S7. Use the optimized particle crushing strength prediction model to predict the standardized data and obtain the predicted values ​​of particle crushing strength for each group.

[0092] S8. Input the predicted values ​​of particle crushing strength of each group into the Weibull model to obtain the predicted value characteristic strength;

[0093] The calibration factor is calculated based on the feature strength of the Weibull model and the feature strength of the predicted value.

[0094] Based on the calibration factor, the final predicted value of particle crushing strength is calculated.

[0095] like Figure 1 As shown, in step S1, porous particles are modeled and prepared.

[0096] In this embodiment, modeling and preparing porous particles refers to using 3D design software to parametrically model the porous particles and then 3D printing them.

[0097] (1) Parametric modeling of porous particles was performed using 3D design software.

[0098] The specific process is as follows:

[0099] 1) Establish a reference solid sphere model, where the particle size gradient is set to 9-15 mm.

[0100] 2) For each particle size gradient, the porosity is set to 5%, 10%, 15%, 20%, 25%, and 30%, respectively.

[0101] 3) Create randomly distributed holes inside the sphere, with 10-30 holes of 0.5-2 mm in diameter. Use fractal dimension to represent the hole distribution, with the fractal dimension ranging from 2 to 3.

[0102] Specifically, solid spheres of different sizes were drawn using Solidworks 2022, and randomly distributed pores were created inside them to establish a batch of particles with a diameter of 9-15 mm; porosity of 5%, 10%, 15%, 20%, 25%, and 30%; pore number distribution of 10-30; and pore size of 0.5 mm-2 mm. The particle size refers to the equivalent diameter of the particle. Porosity is the percentage of the total volume of pores within a particle to the total volume of the particle. The number of pores is the total number of identifiable pores inside the particle. The aperture size is taken as the average aperture. Pore ​​distribution refers to the spatial arrangement of pores within a particle, which can be expressed using fractal dimension. This means that, in other words, fractal dimension is used. Indicates pore distribution. The larger the size, the more complex the pore distribution. The range is controlled within the 2-3 range.

[0103] Box counting is used to calculate the fractal dimension. This involves statistically analyzing the number of grid cells of different sizes occupied by the graphic element, and calculating the ratio of the number of grid cells to their respective proportions. Finally, linear regression is performed to obtain the slope, ultimately yielding the fractal dimension. The formula is:

[0104] (1)

[0105] in, For box dimensions, The minimum number of boxes required to cover the target.

[0106] The fractal dimension plugin in ImageJ can be used to calculate the fractal dimension of each particle. The fractal dimension should be kept within the range of 2-3.

[0107] To study the effects of different parameters, the particle size was fixed while the porosity was varied: for each selected particle size value ( (e.g., 9mm, 10mm, 11mm...), create a set of models whose porosity covers six target values: 5%, 10%, 15%, 20%, 25%, and 30%, respectively. Under each combination, the number of pores and pore size are randomly generated within a specified range.

[0108] The number of pores and the size of pores are variables for achieving porosity. Under the premise of satisfying a specific combination of the above, the target porosity is achieved by adjusting the random combination of the above.

[0109] (2) 3D printing porous particles.

[0110] In this embodiment, a resin 3D printer BL-3D-100P2 with a dimensional accuracy of 0.02mm was selected. DLP (Digital Light Processing) curing technology was used, and dental model resin (DModel-06Y) was chosen as the printing material based on its properties. After importing the model into the slicing software, the layer thickness was set, supports were manually added, and the DLP projector projected the spherical slice pattern layer by layer. The resin was then cured using ultraviolet light. After printing, the particles were cleaned, and the supports were removed.

[0111] Through the above steps, 3D printing technology enables precise and controllable parametric design across multiple dimensions, including particle size, porosity, pore number, pore size, and fractal dimension, producing single particles with specific internal pores. Its advantages include the ability to systematically study the influence of porous parameters, high design freedom, and support for personalized customization. By introducing box counting and the ImageJ plugin to calculate fractal dimension, standardized indicators are provided, enabling precise control over the complexity of pore distribution. This provides a new method for the quantitative description of particle microstructure, ensuring that pore arrangement conforms to the characteristics of natural porous materials and improving realism.

[0112] like Figure 1 As shown, in step S2, the internal microscopic features of porous particles are obtained by micro-CT, and the pore feature parameters are extracted by image processing.

[0113] (1) Obtain the internal microscopic features of porous particles by micro-CT.

[0114] The nanoVoxel-2792 high-resolution integrated scanning analysis system manufactured by Tianjin Sanying Precision Co., Ltd. was used to scan each particle and obtain its internal microstructure. The particles were placed in a transparent container, which was then positioned in the center of the stage. The scanning voltage was set to 130kV and the current to 100μA. Each particle was then scanned. Figure 2 As shown.

[0115] (2) Image processing is used to extract pore feature parameters.

[0116] The specific process is as follows:

[0117] 1) Combine and reconstruct the internal microstructure of each particle to obtain a three-dimensional digital image of a single particle.

[0118] 2) Noise reduction and smoothing are performed on the single-particle 3D digital volume image, and the contrast between pores and matrix is ​​enhanced.

[0119] The reconstructed 3D digital volume image was imported into Dragonfly software for noise reduction and smoothing. Then, ImageJ was used to enhance the image contrast, increasing the contrast between the pores and the matrix, making the pore boundaries more clearly visible.

[0120] 3) Extract particle size from single-particle 3D digital volume images using software.

[0121] The reconstructed 3D digital volume image is imported into the dragonfly software, where the particle size can be extracted.

[0122] 4) Create three types of labels: pores, matrix, and background, and segment the pores;

[0123] Next, using the Trainable Weka Segmentation plugin in ImageJ, three types of labels are created: pores, matrix, and background. Regions are manually marked on representative slices, and multiple machine learning operations are performed to obtain the pores inside a single particle.

[0124] 5) Convert the segmented pores into a binary image and extract the porosity, number of pores and pore size.

[0125] The segmented pores are post-processed and converted into a binary image. Porosity, number of pores, and pore size can then be extracted using plugins in ImageJ.

[0126] After performing machine learning segmentation on multiple slices, a training set for 3D printed particles can be obtained. This training set can then be used for pore segmentation of other particles, allowing for faster extraction of the porosity, number of pores, and pore size of individual particles.

[0127] 6) Calculate the fractal dimension of each particle based on the binary image.

[0128] To quantify the relationship between pore distribution and particle failure, fractal dimension was selected. This indicates the complexity of the pore distribution. The larger the value, the more complex the pore distribution. Based on the binary pore image segmented by the above machine learning, the fractal dimension of each particle can be calculated using the Fractal Dimension plugin in ImageJ.

[0129] Following the above steps, micro-CT can non-destructively obtain the three-dimensional spatial distribution of pores within particles without slicing or damaging the sample. It allows direct observation of whether the printed structure matches the design model, identifying structural deviations during printing (such as support residue, pore collapse, and lack of fusion) or material defects (such as cracks and impurities), ensuring structural fidelity. Machine learning-based tools are used for pore identification and segmentation, achieving relatively accurate segmentation. A high-quality training set can be applied to batch process all other particles, ensuring consistent processing standards across all samples, resulting in highly reproducible results, and enabling faster extraction of segments from other particles. Introducing fractal dimension to quantify the complexity and irregularity of pore spatial distribution condenses the complexity of the pore system into a single numerical value, linking microstructural characteristics (how pores are distributed) with macroscopic mechanical properties (how particles are destroyed), which is of great value for materials design, performance prediction, and failure analysis.

[0130] like Figure 1 As shown, in step S3, the pore characteristic parameters are standardized to obtain standardized data.

[0131] Since the units of particle size and various pore parameters are different, the particle size, porosity, number of pores, pore size, and pore distribution (fractal dimension) are standardized to eliminate the influence of dimensions.

[0132] First, obtain a five-column matrix. ,in These represent column vectors containing particle size, porosity, number of pores, pore size, and pore distribution (fractal dimension), respectively.

[0133] (2)

[0134] The standardization formula is: Subtract the mean of all elements in the column from each element in the column, and then divide by the corresponding standard deviation.

[0135] (3)

[0136] in, For matrix The number of elements in each column Representative matrix The various elements in , Corresponding matrices rows and columns, Representative matrix The Middle Calculate the average of all elements in the column. This yields the standardized matrix. The formula is:

[0137] (4).

[0138] like Figure 1 As shown, in step S4, a uniaxial compression crushing experiment is conducted based on the standardized data to calculate the actual crushing strength of each particle.

[0139] The specific process is as follows:

[0140] (1) During the uniaxial compression crushing experiment, micro-CT scans of particles were used to obtain images of the entire process of pore deformation, crack initiation and penetration during particle compression. The force-displacement curves of each particle were recorded simultaneously, and the compression characteristics were analyzed to obtain the particle crushing load.

[0141] In-situ loading experiments were conducted on particles using micro-CT. The particles were placed inside a loading cylinder and connected to a loading device. The loading rate was 2 mm / min. During the loading process, the particles were scanned at intervals using micro-CT to obtain the entire process of pore deformation, crack initiation, and penetration during particle compression.

[0142] From the moment the pressure head begins to contact the particles, the computer synchronously records the force-displacement curve until the sound of the particles breaking is heard and the force-displacement curve shows a significant drop, indicating that the particles have cracked. At this point, the press stops working, the particles are removed, and the force-displacement curves of each particle are obtained to analyze the compression characteristics at each stage.

[0143] During compression, as pressure increases, the particles exhibit contact stability, elasticity, hardening, and failure stages. In the initial loading stage, the indenter begins to contact the particles and gradually compresses them. During this period, displacement continuously increases while the load is applied slowly, and the overall surface tends towards a horizontal plane; this is called the contact stability stage. After the indenter and particles are tightly compressed, the particle enters the elastic stage, as... Figure 3 As shown, the force-displacement curve exhibits a linear change, with a very clear elastic stage. When the particle reaches its elastic limit, it enters the hardening stage, and the load continuously accumulates. The slope of the force-displacement curve first increases and then decreases until it reaches its peak. After the particle reaches its peak, the curve shows a significant drop, indicating significant particle failure. This point is considered the first failure point of the particle, i.e., the instantaneous load at which the particle fails is... .

[0144] (2) Calculate the actual crushing strength of each particle based on the particle crushing load.

[0145] Based on the formula proposed by Jaeger, the measured crushing strength of each particle was calculated. The formula is as follows:

[0146] (5)

[0147] in, The actual crushing strength of a single particle. This represents the load corresponding to the actual crushing strength, i.e., the load value at the instant the particles crush. The particle size is denoted as .

[0148] Analyzing the relationship between particle breakage strength and particle size under the same porosity parameters, it was found that the breakage strength decreases with increasing particle size, exhibiting a size effect. Fitting the experimental values, the formula for calculating the actual breakage strength of each particle in this experiment was obtained as follows:

[0149] (6)

[0150] in, The actual crushing strength of a single particle. It refers to particle size. It is the size effect modulus. It is the size effect coefficient.

[0151] (3) Analyze the changes in the internal pores of the particles based on CT scan images;

[0152] Based on the change process, CT scan images of particles before and after compression were compared to analyze the relationship between pore distribution and crack development location, particle failure, and characteristic parameters and particle breakage strength.

[0153] Relationship between pore distribution, crack propagation location, and particle failure: Macroscopic particle failure depends on the propagation of internal cracks, which is related to the internal pore structure. A single particle contains multiple pores. Using Dragonfly to extract the internal pores of the particle, a schematic diagram of the internal pore distribution is obtained, as shown below. Figure 4 As shown. Among them, Figure 4 (a) shows a front view of a single particle in the loading direction (the entire pore distribution), with the front view divided into two parts along the loading direction. Figure 4 (b) is a schematic diagram of the pore distribution in region 1 / 2. As can be seen from the image, region 1 / 2 has fewer and more dispersed pores, while region 2 / 3 contains larger pores, which are more numerous and concentrated in their distribution. Further dividing the region into 1 / 4 sections, we arrive at four more sections. Figure 4 (c) is a schematic diagram of the pore distribution in the 1 / 4 region, showing the number and density of particles. Further analysis reveals that cracks originate and propagate in the region with the highest concentration of pores, ultimately leading to particle damage. Figure 4 (d) shows a schematic diagram of the crack.

[0154] Relationship between porosity and particle breaking strength: When the porosity is around 0.15%, tending towards solidity, the particles have fewer internal pores, are relatively dense, and have high breaking strength. As porosity increases, the number of internal pores increases, and cracks propagate and merge within multiple pores, accelerating particle breakage. As a result, the breaking strength decreases with increasing porosity. Figure 5 As shown.

[0155] The relationship between pore number, volume, and particle crushing strength: The more pores actually involved in crack initiation, the lower the crushing strength. When the number of pores is large, more crack propagation points are easily formed, increasing the probability of cracks forming from pores. Figure 6 As shown in (a), pore volume reflects the pore size. Large-diameter pores are prone to cracking during compression, thus reducing fracture strength. Figure 6 As shown in (b).

[0156] like Figure 7 As shown, the relationship between pore size and particle crushing strength is as follows: for the same particle type, the larger the pore size, the wider the stress concentration area, and the easier it is for cracks to initiate and propagate in this area.

[0157] The changes in internal porosity of particles were analyzed using images obtained from micro-CT scans during particle compression. The relationship between the number of pores involved in crack initiation and the crack length and opening angle can be analyzed from the CT scan images. Figure 8 As shown.

[0158] Specifically, after particle breakage, the number of pores through which the cracks propagated can be extracted using Dragonfly. The crack angles and the number of pores involved in crack propagation are statistically analyzed. Figure 8 (a) It can be seen that when the number of pores involved in crack propagation is large, the opening angle increases slowly with the increase of the number of pores. However, when the number of pores exceeds a certain amount, the crack path undergoes more deflection and convergence, leading to a greater degree of local opening, which is macroscopically manifested as a significant increase in the opening angle, generally reaching over 10°. Comparing particles of different sizes, it was found that the opening angle growth trend of 9mm and 11mm particles is relatively consistent, while the growth rate of 10mm particles is significantly more gradual, possibly because the internal pore spacing of 10mm particles is larger or the orientation is more uniform. Figure 8 (b) It was found that as the number of pores involved in crack initiation increased, the presence of pores hindered crack development during crack propagation, resulting in a decreasing crack length. In particular, when the number of pores was large, the effective crack propagation length decreased significantly, possibly to only about 1 / 3 of the particle size.

[0159] When analyzing the relationship between porosity, pore number, pore size, fractal dimension, and crushing strength, it was found that the crushing strength of particles is simultaneously affected by multiple porosity parameters, with each parameter having a different proportion of influence on the strength. Linear regression analysis was performed on the data to obtain the proportion of influence of each porosity parameter on the crushing strength. Weighted proportions and standardized coefficients were used to quantify the impact of different porosity parameters on the crushing strength of particles.

[0160] Following the above steps, simultaneous micro-CT scanning during uniaxial compression experiments captured dynamic images of the entire process of deformation, crack initiation, and penetration within the pores of the particles in real time, while simultaneously recording force-displacement curves. This enabled dynamic, visualized, and non-destructive research on the failure mechanism, providing the most direct evidence for understanding the essence of failure. Uniaxial compression failure experiments were conducted on porous particles, and the relationship between porosity, pore quantity, pore size, pore distribution, and particle breakage strength and failure mode was systematically analyzed. This revealed the quantitative influence mechanism of pore parameters on strength and established a causal relationship between pore distribution and failure mode. Particle breakage strength is simultaneously affected by multiple pore parameters (porosity, quantity, pore size, and fractal dimension), with each parameter having a different influence ratio. Linear regression analysis was used to quantify these influences (weighting ratios and standardization coefficients), successfully decomposing the complexity of the porous system into multiple quantifiable dimensions, thereby enabling more accurate interpretation and prediction of particle breakage strength.

[0161] like Figure 1 As shown, in step S5, the porous particles are grouped, and the Weibull model is used to fit each group of particles to obtain the modulus and feature intensity of the Weibull model.

[0162] (1) Group the porous particles.

[0163] To predict the breakage of more 3D-printed porous single particles, particles of the same size but different microstructures in the experimental group were classified and grouped. Based on porosity, the particles were divided into three groups: Group A (porosity 0-10%), Group B (porosity 10-20%), and Group C (porosity 20-30%). Each porosity group was further subdivided: 0.5-1 mm pore size (sub1), 1.0-1.5 mm pore size (sub2), and 1.5-2.0 mm pore size (sub3). Each pore size group was further subdivided based on fractal dimension and number of pores: fractal dimension 2.0-2.5, number of pores 10-20 (type1), fractal dimension 2.5-3.0, number of pores 20-30 (type2). The particle naming format for each group was A-sub1-type1.

[0164] Particles with similar microstructures were grouped into one class, and all groups were divided into a training group (80%) and a test group (20%).

[0165] (2) The Weibull model was used to fit each group of particles to obtain the modulus and feature strength of the Weibull model.

[0166] Numerous physical experiments and numerical simulations have verified that the crushing strength of particles follows a Weibull distribution with a diameter of [missing information]. The survival probability of the particles under uniaxial compression conditions is ,definition:

[0167] (7)

[0168] in, Indicates particle size as The feature intensity has a particle survival probability of 37%. Represents the Weibull modulus. This represents the actual crushing strength of a single particle.

[0169] 1) Based on the uniaxial compression crushing experiment, the cumulative survival probability of particles in the uniaxial compression experiment was calculated.

[0170] Cumulative survival probability of particles It is usually expressed as:

[0171] (8)

[0172] in, This represents the sequence number assigned to a single particle after it has been sorted in ascending order by particle crushing strength. This represents the total number of particles in the experiment.

[0173] After sorting the particle crushing strength in ascending order, the cumulative survival probability of the group of particles can be calculated according to formula (8). .

[0174] 2) Based on the survival probability and the actual crushing strength of each particle in the uniaxial compression experiment, the Weibull model was used for linear fitting to obtain the modulus and characteristic strength of the Weibull model.

[0175] When all particles have the same size, that is Formula (7) can be expressed as follows: and A linear relationship exists:

[0176] (9)

[0177] in, The feature intensity represents a particle survival probability of 37%. Represents the Weibull modulus. Indicates the actual crushing strength of the particles. This represents the cumulative survival probability of the particles.

[0178] Known and ,draw and By plotting the dotted line graph and performing linear fitting on the data, the modulus of the Weibull model can be obtained. With characteristic strength .

[0179] Following the steps outlined above, a four-level hierarchical grouping strategy is proposed. Even with the same particle size and porosity, differences in the size, number, and spatial distribution of internal pores can lead to significant variations in mechanical properties. This method ensures that particles within each final group have highly similar microstructures, resulting in more accurate and reliable fitting results. This grouping allows for a systematic study of how microstructure affects Weibull parameters. Actual crushing strengths obtained from experiments are then substituted into the Weibull model to obtain the modulus and characteristic strength, providing a basis for subsequent calibration of the PSO-SVR model predictions.

[0180] like Figure 1 As shown, in step S6, the standardized data is input into the support vector regression prediction model for training, and the support vector regression model is optimized by the particle swarm optimization algorithm to obtain the optimized particle crushing intensity prediction model.

[0181] S6-1. Input the standardized training group data into the support vector regression prediction model for training.

[0182] (1) Select the radial basis kernel function and construct the support vector objective function.

[0183] Particle size, porosity, pore number, pore size, and pore distribution were used as input variables. Output variables To obtain particle breakage strength for SVR model .

[0184] 1) Select the radial basis kernel function.

[0185] In this embodiment, a radial basis function kernel is used, and the kernel function formula is as follows:

[0186] (10)

[0187] in, There are two samples. and Similarity measure between them; It is a positive number, representing the kernel width parameter of the radial basis function. Indicates sample and The Euclidean distance between samples. The kernel function essentially calculates the similarity between samples.

[0188] For small samples, the radial basis function (RBF) kernel exhibits superior performance and requires fewer parameters compared to other kernel functions. Experimental analysis reveals a significant nonlinear relationship between particle breakage strength and various pore parameters, demonstrating that the RBF kernel can handle complex nonlinear physical problems.

[0189] 2) Construct the support vector objective function.

[0190] For the training set , Given the total number of samples, we are looking for a hyperplane. The hyperplane, serving as the optimal decision function for predicting particle breakage intensity, is expressed as follows:

[0191] (11)

[0192] in, It is the normal force of the hyperplane. It is the translation distance of the hyperplane. This represents the input variables (including particle size and pore parameters).

[0193] The objective function and constraints are as follows:

[0194] (12)

[0195]

[0196] in, This represents the output variable, namely, particle crushing strength. Indicates the penalty coefficient. Indicates the error term. This represents the insensitive loss parameter.

[0197] (2) Based on the objective function of the support vector, the optimal decision function for predicting particle breakage intensity of the support vector regression prediction model is obtained.

[0198] Equation (12) is transformed using the Lagrange equation to obtain its dual form:

[0199] (13)

[0200]

[0201] in, and For Lagrange multipliers, This is the kernel function.

[0202] By solving the above nonlinear programming problem, the coefficients of the optimal decision function are obtained. Thus, the optimal decision function for predicting the crushing strength of SVR particles is obtained:

[0203] (14).

[0204] (2) Based on the analysis of uniaxial compression crushing experiments, the penalty coefficient and radial basis kernel function kernel width parameters are set and substituted into the optimal decision function for predicting particle crushing strength; the standardized data are input into the support vector regression model to obtain the initial prediction value.

[0205] In this embodiment, a penalty coefficient is set. and radial basis kernel function kernel width parameter The value of is determined based on experimental analysis, which shows an exponential relationship between particle size and crushing strength. Particle crushing strength decreases with increasing porosity and pore number, while the relationship between pore size and pore distribution exhibits non-linearity. Based on these conclusions, the overall relationship between particle crushing strength and pore parameters is clear, but local uncertainties exist. Therefore, a penalty coefficient is set. The range is To balance the accuracy and robustness of the model. Radial basis function kernel width parameter. The search range is set based on the nonlinear complexity of the relationship. To capture the nonlinear effects caused by pore parameters, its range is set to [value missing]. Within this range, a penalty coefficient and kernel width parameter are randomly generated and substituted into formula (14) to obtain the initial predicted values ​​of the support vector regression prediction model. The specific process is as follows:

[0206] Penalty coefficient and radial basis kernel function kernel width parameter Substituting into formula (14), the support vector regression (SVR) prediction model is trained using the training set data in the training group to obtain the initial prediction value of the support vector regression prediction model.

[0207] Call the SVR library and execute .fit(x, y), where x is the standardized feature matrix of the training set (each row represents a sample). y is the target value (predicted fracture strength value) of the training set, which includes all standardized pore parameters.

[0208] Following the steps outlined above, the search range for hyperparameters is set based on the explicit physical conclusions drawn from the preceding uniaxial compression experiments. This injects domain knowledge into the starting point of the machine learning process, transforming the optimization process from a blind "black box operation" into a directed and physically grounded intelligent search, significantly improving optimization efficiency and model interpretability. Five standardized microstructural parameters (particle size, porosity, number of pores, pore size, and fractal dimension) are used as input features, and a radial basis function (RBF) kernel is selected. This process transforms the complex nonlinear relationships between the original pore parameters into a linearly separable problem in a high-dimensional space, achieving high-precision fitting of complex nonlinear relationships and joint modeling of high-dimensional pore parameters. The model results are reproducible.

[0209] S6-2. The support vector regression model is optimized using the particle swarm optimization algorithm to obtain the optimized particle breakage intensity prediction model.

[0210] The particle swarm optimization algorithm is used to optimize the support vector regression (SVR) prediction model, in which particles are defined by two attributes: velocity and position.

[0211] (1) Set initialization parameters, including the number of iterations, population position, particle position and velocity.

[0212] (2) Set the fitness function and calculate the initial fitness value, initial individual value and initial population extreme value of each particle.

[0213] The fitness function reflects the prediction accuracy of the model. Negative mean squared error (-MSE) is used as the evaluation metric; a smaller MSE indicates a better model, and taking the negative sign translates to a larger fitness value, which is better. The trained SVR model is used to predict data from the test group. The fitness is calculated based on the deviation between the predicted and actual values, yielding the initial fitness value and initial individual value for each particle. and the initial group extreme value The formula for negative mean square error is as follows:

[0214] (15)

[0215] in, It is the sample size. These are measured values. This is a predicted value.

[0216] (3) Update the position and velocity of the particles, and update the individual extreme value and the group extreme value. Determine whether the global optimal position or the maximum number of iterations is satisfied. If so, obtain the penalty coefficient and the optimal value of the radial basis kernel function kernel width parameter of the support vector regression prediction model.

[0217] In this context, individual extreme value and population extreme value represent the optimal solution found by a single particle during the search process and the optimal solution found by the entire population, respectively. Individual extreme value refers to the optimal solution found by a single particle through iteration during the search process, i.e., the particle's own historical best position. Population extreme value refers to the globally optimal solution found by all particles in the population. Population extreme value is the optimal solution among all individual extreme values, while individual extreme value is the optimal solution for a single particle in its local search.

[0218] The formulas for updating the particle's position and velocity are:

[0219] (16)

[0220]

[0221] in, Indicates the particle in the first... Speed ​​at the next iteration , It is a learning factor. , These represent the individual optimal position and the group optimal position of the particle, respectively. It is the first particle Next iteration position.

[0222] Determine whether the global optimal position or the maximum number of iterations is met. If so, output the optimal values ​​of the penalty factor and kernel width parameters in the support vector regression (SVR) prediction model.

[0223] The maximum number of iterations was set to 500, and the PSO-SVR model was implemented in Python. The PSO model was used to obtain the penalty factor in the output support vector (SVR) regression prediction model. and kernel function kernel width parameter After finding the optimal value, particle size, porosity, number of pores, pore size, and pore distribution are used as input variables. The initial particle crushing strength For output variables Substitute the values ​​into the SVR model for prediction.

[0224] After the above steps, the SVR model optimized by PSO shows a significant improvement in prediction accuracy and generalization ability. The PSO search here is based on a parameter range defined by physical mechanisms. It utilizes domain knowledge to narrow the search scope and improve efficiency, and then uses data-driven optimization to find the optimal solution within this range. It is a combination of theory and data, and the optimized model parameters have clear physical meaning.

[0225] like Figure 1As shown, in step S7, the optimized particle crushing strength prediction model is used to predict the standardized data to obtain the predicted values ​​of particle crushing strength for each group.

[0226] Based on the optimized SVR model, the predicted particle breakage intensity values ​​for each training group were obtained. .

[0227] like Figure 1 Figure 1 As shown, in step S8, the predicted values ​​of particle crushing intensity of each group are input into the Weibull model to obtain the predicted value feature intensity; based on the feature intensity of the Weibull model and the predicted value feature intensity, the calibration factor is calculated; based on the calibration factor, the final predicted value of particle crushing intensity is calculated.

[0228] (1) Input the predicted values ​​of particle crushing strength of each group into the Weibull model to obtain the predicted characteristic strength.

[0229] Substituting the predicted fragmentation strength values ​​of each group into the Weibull model yields a characteristic strength with a predicted particle survival probability of 37%. .

[0230] (2) Calculate the calibration factor based on the feature strength of the Weibull model and the feature strength of the predicted value.

[0231] Actual crushing strength Substituting into the Weibull model yields: , The feature intensity represents a 37% actual particle survival probability. The feature intensity is used to predict a particle survival probability of 37%. Based on... and Calculate calibration factor The formula is:

[0232] (17)

[0233] (3) The final predicted value of particle crushing strength is calculated based on the calibration factor.

[0234] The model's final predicted value of particle crushing strength The calculation formula is:

[0235] (18)

[0236] in, These are the predicted values ​​of particle crushing strength for each group obtained from the optimized particle crushing strength prediction model.

[0237] Following the above steps, a comparison is made between model predictions and actual values ​​at the statistical distribution characteristic value level. A dynamic calibration factor k, adjustable under different conditions, is introduced specifically to correct systematic biases in the model predictions. Predictions calibrated using physical experimental probability distributions are closer to engineering realities. The calibration process focuses on the characteristic strength with a survival probability of 37%, which is both a key parameter of the Weibull distribution and a commonly used representative indicator of material strength, possessing clear physical meaning and more scientifically reflecting the dispersion of particle strength. The final output value not only includes the complex nonlinear relationships learned by the SVR model from the data but also inherits the strength dispersion characteristics of actual materials represented by the Weibull statistical model. This calibration step significantly increases the reliability and safety of the prediction results in practical engineering applications.

[0238] S9. Based on the standardized data, perform prediction training and testing according to steps S6 to S8, and use root mean square error to evaluate the prediction accuracy.

[0239] (1) Use the training group (80%) data divided above for prediction training and the test group (20%) data for prediction.

[0240] (2) The root mean square error is used to evaluate the prediction accuracy.

[0241] A Weibull plot of the predicted fracture strength after calibration was drawn and compared with the experimentally obtained Weibull plot to determine the similarity between the two lines. The RMSE (Real Mean Squared Error) was used for quantitative evaluation; a smaller RMSE value indicates a smaller error. The RMSE expression is:

[0242] (19)

[0243] in, This is the actual value. It is a predicted value. It refers to the number of samples.

[0244] In this embodiment, particles of different sizes and pore sizes are obtained using 3D printing. Considering the multidimensional parameter characteristics of pores, the internal microstructure of the particles is obtained through microscopic CT scanning, pore characteristic parameters are extracted, and uniaxial compression crushing experiments are conducted. CT images of the particles before, during, and after compression are compared to analyze the changes in pore size during compression and the relationship between pore distribution and crack development and failure modes. The relationship between porosity, pore number, pore distribution, and crushing strength is analyzed by controlling variables. Based on statistical analysis methods, the relationship between porosity, pore number, pore size, pore distribution, and particle crushing strength is quantified. A PSO-SVR particle crushing strength prediction model is established, and a calibration factor is introduced based on the Weibull model to correct the predicted crushing strength. The combination of mechanical experiments and model prediction is used to achieve particle crushing strength prediction, improving prediction accuracy and generalization ability.

[0245] Example 2

[0246] This embodiment discloses a particle breakage strength prediction system that considers pore parameters, including:

[0247] The data acquisition module is used for modeling and preparing porous particles;

[0248] Microscopic features of porous particles were obtained by micro-CT, and pore feature parameters were extracted by image processing.

[0249] The data preprocessing module is used to standardize the pore characteristic parameters to obtain standardized data;

[0250] The mechanical testing module is used to perform uniaxial compression crushing experiments based on standardized data and calculate the actual crushing strength of each particle.

[0251] The porous particles were grouped, and the Weibull model was used to fit each group of particles to obtain the modulus and feature strength of the Weibull model.

[0252] The model building and optimization module is used to input standardized data into the support vector regression prediction model for training, and to optimize the support vector regression model through the particle swarm algorithm to obtain the optimized particle crushing intensity prediction model.

[0253] The model prediction module is used to predict the standardized data using the optimized particle crushing strength prediction model to obtain the predicted values ​​of particle crushing strength for each group.

[0254] The predicted particle crushing strength values ​​of each group are input into the Weibull model to obtain the predicted characteristic strength.

[0255] The calibration factor is calculated based on the feature strength of the Weibull model and the feature strength of the predicted value.

[0256] Based on the calibration factor, the final predicted value of particle crushing strength is calculated.

[0257] The method steps in Example 1 are implemented based on a particle breakage strength prediction system that takes into account pore parameters.

[0258] Example 3

[0259] The purpose of this embodiment is to provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the above-described method.

[0260] Example 4

[0261] The purpose of this embodiment is to provide a computer-readable storage medium.

[0262] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, performs the steps of the above method.

[0263] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0264] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for predicting particle breakage strength considering pore parameters, characterized in that, include: Modeling and preparing porous particles; Microscopic features of porous particles were obtained by micro-CT, and pore feature parameters were extracted by image processing. The pore characteristic parameters are standardized to obtain standardized data; Based on the standardized data, a uniaxial compression crushing experiment was conducted to calculate the actual crushing strength of each particle. The porous particles were grouped, and the Weibull model was used to fit each group of particles to obtain the modulus and feature strength of the Weibull model. process For: diameter is The survival probability of the particles under uniaxial compression conditions is ,definition: ； in, Indicates particle size as The feature intensity has a particle survival probability of 37%. Represents the Weibull modulus. This represents the actual crushing strength of a single particle. The standardized data is input into the support vector regression prediction model for training, and the support vector regression model is optimized by the particle swarm algorithm to obtain the optimized particle crushing intensity prediction model. The optimized particle crushing strength prediction model was used to predict the standardized data and obtain the predicted values ​​of particle crushing strength for each group. The predicted particle crushing strength values ​​of each group are input into the Weibull model to obtain the predicted characteristic strength. The calibration factor is calculated based on the feature strength of the Weibull model and the feature strength of the predicted value. Based on the calibration factor, the final predicted value of particle crushing strength is calculated.

2. The method for predicting particle breakage strength considering pore parameters as described in claim 1, characterized in that, Modeling and fabricating porous particles refers to using 3D design software to parametrically model porous particles and then 3D printing them.

3. The method for predicting particle breakage strength considering pore parameters as described in claim 2, characterized in that, The process of parametrically modeling porous particles using 3D design software is as follows: Establish a benchmark solid sphere model, where the particle size gradient is set to 9-15 mm; For each particle size gradient, the porosity was set to 5%, 10%, 15%, 20%, 25%, and 30%, respectively. Create randomly distributed pores inside the sphere, with 10-30 pores and a diameter of 0.5-2 mm. Use fractal dimension to represent the pore distribution, with the fractal dimension ranging from 2 to 3.

4. The method for predicting particle breakage strength considering pore parameters as described in claim 1, characterized in that, The pore feature parameters are extracted using image processing. The specific process is as follows: The internal microstructure of each particle is combined and reconstructed to obtain a three-dimensional digital image of a single particle. The single-particle 3D digital volume image is denoised and smoothed, and the contrast between the pores and the matrix is ​​enhanced. Particle size is extracted from a single-particle 3D digital volume image using software. Create three categories of labels: pores, matrix, and background, and segment the pores; The segmented pores are converted into a binary image, and the porosity, number of pores, and pore size are extracted. The fractal dimension of each particle is calculated based on the binary image.

5. The method for predicting particle crushing strength considering pore parameters as described in claim 1, characterized in that, Based on the standardized data, a uniaxial compression crushing experiment was conducted to calculate the actual crushing strength of each particle. The specific process is as follows: During the uniaxial compression crushing experiment, micro-CT scans of the particles were used to obtain images of the entire process of pore deformation, crack initiation and penetration during particle compression. The force-displacement curves of each particle were recorded simultaneously, and the compression characteristics were analyzed to obtain the particle crushing load. Calculate the actual crushing strength of each particle based on the particle crushing load.

6. The method for predicting particle breakage strength considering pore parameters as described in claim 1, characterized in that, The Weibull model was used to fit each group of particles to obtain the modulus and feature intensity of the Weibull model. The specific process is as follows: Based on the uniaxial compression crushing experiment, the cumulative survival probability of particles in the uniaxial compression experiment was calculated. Based on the survival probability and the actual crushing strength of each particle in the uniaxial compression experiment, the Weibull model was used for linear fitting to obtain the modulus and characteristic strength of the Weibull model.

7. The method for predicting particle crushing strength considering pore parameters as described in claim 1, characterized in that, The standardized data is then input into the support vector regression prediction model for training. The specific process is as follows: Choose a radial basis kernel function and construct a support vector objective function; Based on the support vector objective function, the optimal decision function for predicting particle breakage intensity of the support vector regression prediction model is calculated. Based on the analysis of uniaxial compression crushing experiments, penalty coefficients and radial basis kernel function kernel width parameters are set and substituted into the optimal decision function for predicting particle crushing strength. The standardized data is input into the support vector regression model to obtain the initial predicted values.

8. The method for predicting particle breakage strength considering porosity parameters as described in claim 1, characterized in that, The radial basis function kernel function is formulated as follows: ； in, There are two samples. and Similarity measure between them; It is a positive number, representing the kernel width parameter of the radial basis function. Indicates sample and The Euclidean distance between them.

9. The method for predicting particle crushing strength considering pore parameters as described in claim 1, characterized in that, The support vector regression model is optimized using the particle swarm optimization algorithm. The specific process is as follows: Set initialization parameters, including the number of iterations, population position, particle position, and velocity; Set a fitness function and calculate the initial fitness value, initial individual value, and initial population extreme value for each particle; Update the particle's position and velocity, and update the individual and group extreme values. Determine if the global optimal position or maximum number of iterations is satisfied. If so, obtain the penalty coefficient and the optimal value of the radial basis function kernel width parameter of the support vector regression prediction model.

10. A particle crushing strength prediction system considering pore parameters, characterized in that, Implementing a particle breakage strength prediction method considering pore parameters as described in any one of claims 1-9, comprising: The data acquisition module is used for modeling and preparing porous particles; Microscopic features of porous particles were obtained by micro-CT, and pore feature parameters were extracted by image processing. The data preprocessing module is used to standardize the pore characteristic parameters to obtain standardized data; The mechanical testing module is used to perform uniaxial compression crushing experiments based on standardized data and calculate the actual crushing strength of each particle. The porous particles were grouped, and the Weibull model was used to fit each group of particles to obtain the modulus and feature strength of the Weibull model. The model building and optimization module is used to input standardized data into the support vector regression prediction model for training, and to optimize the support vector regression model through the particle swarm algorithm to obtain the optimized particle crushing intensity prediction model. The model prediction module is used to predict the standardized data using the optimized particle crushing strength prediction model to obtain the predicted values ​​of particle crushing strength for each group. The predicted particle crushing strength values ​​of each group are input into the Weibull model to obtain the predicted characteristic strength. The calibration factor is calculated based on the feature strength of the Weibull model and the feature strength of the predicted value. Based on the calibration factor, the final predicted value of particle crushing strength is calculated.

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