A method and system for predicting the permeation characteristics of a system of spherical particles based on machine learning

Abstract

This invention discloses a method and system for predicting the permeability of spherical particle systems based on machine learning. The method uses the discrete element method to generate assemblies of spherical particles with different gradations, and performs region segmentation on the particle samples to establish a sample dataset containing particle material gradation information and three-dimensional image structure. Then, the permeability of the particle samples is calculated using the lattice Boltzmann method and the D3Q19 lattice model. The method extracts macroscopic and microscopic structural features of the particle samples; constructs a dataset for training the machine learning model; trains the machine learning model, and finally obtains a model that can accurately and effectively predict permeability based on the multi-scale structural features of the particle material. This invention overcomes the limitation that macroscopic structural parameters cannot accurately describe the complex internal structure of pores. Furthermore, by constructing a machine learning-based permeability prediction model based on the extracted structural parameters, it solves the problems of long testing times and limited testing equipment due to the large range of particle size variations in traditional seepage tests.

Description

Technical Field

[0001] This invention relates to the field of porous media permeation technology, and in particular to a method and system for predicting the permeation characteristics of spherical particle systems based on machine learning. Background Technology

[0002] Permeability, as a crucial parameter characterizing the fluid conduction properties in porous media, is applied in various fields such as water conservancy, geotechnical engineering, agriculture, and oil extraction. For example, in water conservancy projects, the permeability characteristics of rockfill are a key factor in the stable operation of dams and a major focus of dam quality and safety monitoring. Traditional permeability studies are generally conducted in-situ or indoors, such as borehole pumping tests and indoor seepage tests, but these are often limited by testing equipment and facilities, making it difficult to obtain permeability data in a timely manner. Therefore, some studies have proposed empirical formulas for permeability based on structural characteristic parameters of porous media, such as porosity, inhomogeneity coefficient, and curvature coefficient. However, these studies treat porous media as a whole, using only macroscopic parameters to describe the structure, which is rather one-sided and cannot accurately and comprehensively summarize the internal structure of porous media. Therefore, accurate permeability results cannot be obtained based on empirical formulas. Currently, there is an urgent need for a highly timely numerical simulation method that can accurately and rapidly predict the permeability of porous media.

[0003] In recent years, machine learning has developed rapidly and has been widely used to analyze various complex situations. Research on permeability prediction of porous media based on machine learning has also been conducted. However, most existing prediction methods remain at the two-dimensional level and use a limited number of feature parameters, leaving significant room for improvement in prediction performance. For example, the prior art disclosed in CN109191423B presents a method for predicting the permeability of porous media based on machine image intelligent learning. This method selects multiple groups of the same porous media material with different dry densities and determines the true permeability of each group. SEM images of each group of porous media material are obtained using SEM scanning, and the mean gray level, gray level variance, image energy, image entropy, and fractal dimension of each SEM image are calculated. An extreme learning machine neural network model is used to train and learn the five image feature parameters of each SEM image and their corresponding true permeability, determining the relationship between the five image feature parameters and the true permeability. During prediction, the SEM image parameters of the porous media material with unknown permeability are input, and the extreme learning machine neural network model can predict the permeability of the porous media material. While this method can predict permeability, it has certain limitations in simulating porous media using SEM2D graphics, and cannot truly reflect the overall properties of porous media.

[0004] Therefore, it can be seen that the existing methods have technical problems of poor prediction accuracy and timeliness. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a rapid prediction method for the permeability characteristics of spherical particle systems based on machine learning. This method not only reflects the complex pore structure within the spherical particle system through particle packing but also extracts pore structure features at multiple scales, including macroscopic and microscopic, to describe the complex pore structure of the particulate material, enabling accurate and rapid prediction of its permeability. Based on particle gradation information and compaction degree, this invention constructs numerical samples of the particulate material. Subsequently, it uses methods such as the lattice Boltzmann model to perform numerical simulations of permeability characteristics, obtaining the permeability of the particulate material. Simultaneously, based on macroscopic and microscopic scale extraction of sample structural information, and using the pore structure feature parameters of the particulate material as input and the permeability as output, a machine learning model for predicting the permeability characteristics of particulate materials is established and trained. Using this method, the permeability characteristics of particulate materials can be obtained quickly and accurately.

[0006] The technical solution adopted in this invention is as follows:

[0007] The first aspect provides a machine learning-based method for predicting the permeability characteristics of spherical particle systems, including:

[0008] S1: Based on the gradation information and compaction degree of spherical granular materials, aggregates of granular materials with different gradations are generated by the discrete element method and compressed to obtain calculation samples. Then, region segmentation is performed to establish a sample dataset containing gradation information of spherical granular materials, confining pressure and three-dimensional image structure.

[0009] S2: Based on the lattice Boltzmann method and the D3Q19 lattice model, the permeability of the samples in the sample dataset is calculated to obtain the permeability of the spherical particle material.

[0010] S3: Extract structural features from the samples in the sample dataset. The extracted structural features include macroscopic scale parameters and microscopic scale parameters.

[0011] S4: Based on the calculated permeability of the particulate material and the extracted structural features, construct a machine learning model dataset and divide it into a training dataset; construct a machine learning model, train it using the random forest algorithm based on the training dataset, and obtain a trained permeability prediction model.

[0012] S5: Predict the permeability of the spherical particle system using a trained permeability prediction model.

[0013] In one implementation, step S1 includes:

[0014] S1.1: Obtain the gradation information of spherical granular materials based on known engineering data;

[0015] S1.2: Based on the gradation information of spherical granular materials, several granular aggregates with different gradations are generated by the discrete element method. The sample in the granular aggregate is compressed according to the degree of compaction to obtain the calculated sample.

[0016] S1.3: Based on the position information of the spherical particles in the calculation sample, the porous region and the solid region are divided, with the value "0" representing the porous phase and the value "1" representing the solid phase, so that the three-dimensional image structure is transformed into a three-dimensional digital matrix form, and a sample dataset containing the gradation information of the spherical particle material, the confining pressure and the three-dimensional image structure is established. The sample dataset is represented in binary file format.

[0017] In one implementation, step S2 includes:

[0018] S2.1: The permeability of the samples in the sample dataset was calculated using the lattice Boltzmann method. The D3Q19 lattice model was selected, and the model was based on the single-relaxation-time BGK model. Specifically, the water flow direction was set as the x-direction, and the entire flow domain space was discretized into lattice points. The fluid motion process was transformed into the collision and migration process of fluid particles. The collision and migration process of fluid particles was realized through iterative evolution based on the distribution function of fluid particles. The evolution process is shown in the following equation:

[0019]

[0020] In the formula, f n Let be the non-equilibrium distribution function of the particle; x is the particle position; e n The velocity of the particle in the nth direction is t; the discrete time is τ; the relaxation time is f. n,eq Let be the particle equilibrium distribution function;

[0021] S2.2: When the flow simulation reaches a steady state, the velocity distribution of the flow field is calculated using formula (1);

[0022] S2.3: Based on the velocity distribution of the calculated flow field, the spherical particle material is obtained by calculating using Darcy's equation.

[0023] In one embodiment, the macroscopic parameters extracted in step S3 include sample porosity, sample tortuosity, sample pore heterogeneity, and sample fractal dimension, wherein the sample porosity is calculated as follows:

[0024] φ=V void / V all (2)

[0025] In the formula, φ is the porosity of the sample, and V void V is the pore volume. all The total volume of the sample.

[0026] The method for calculating the tortuosity of the specimen is as follows:

[0027]

[0028] In the formula, τ s Let v be the tortuosity of the sample, i be the i-th node in the flow field, N be the total number of nodes in the flow field, and v be the tortuosity of the sample. xi Let v be the flow velocity in the x-direction of the i-th node. yi Let v be the flow velocity in the y-direction of the i-th node. zi Let be the z-direction velocity of the i-th node, where the velocity in each direction is the velocity distribution of the flow field in step S2.2;

[0029] The method for calculating the porosity heterogeneity of the sample is as follows:

[0030]

[0031] In the formula, φ j φ is the porosity of the j-th sub-sample; φ is the overall porosity of the sample.

[0032] The fractal dimension of the sample is calculated as follows:

[0033]

[0034] In the formula, A is R n Any nonempty bounded subset of space; N r (A) represents the minimum number of n-dimensional cubes with side length r required to cover A.

[0035] In one embodiment, the microscale parameters extracted in step S3 include structural feature parameters at the pore scale, the connectivity and flow rate within different samples, and the extraction process includes:

[0036] Based on the maximum sphere algorithm, a pore network model is established, and the average pore coordination number C and average pore radius r are extracted from the pore network model. p Average throat radius r t Average laryngeal length l t As a structural characteristic parameter at the pore scale, the pore network model equates the pores inside the structure to a series of pore bodies and throats, with pore bodies represented by spheres and throats represented by thin rods.

[0037] The complex network method is used to analyze the microstructure and connectivity of the sample. In this method, pores are treated as nodes in the complex network, throats are treated as edges connecting two nodes, and the cross-sectional area of ​​the throat is used as the weight of each edge. The complex network is formed by analyzing and calculating the clustering coefficient, heterogeneity coefficient, and global efficiency index. The obtained indexes are used to determine the connectivity and flow rate of different samples.

[0038] In one implementation, the clustering coefficients of a complex network are calculated as follows:

[0039]

[0040] In the formula, V is the set of nodes in the complex network, a is the node number, k is the number of node degrees, t(G) is the number of triangles formed by nodes and edges in the complex network, and the clustering coefficient index is used to reflect the probability that the neighbors of nodes in the complex network are neighbors of each other.

[0041] The degree heterogeneity coefficient of a complex network is represented by the entropy H of the degree distribution in the complex network, and is calculated as follows:

[0042]

[0043] The entropy of the moderate degree distribution in a complex network is used to represent the non-uniformity of nodes in the network, where P(k) represents the proportion of nodes with a moderate degree of k in the complex network.

[0044] The global efficiency in complex networks is calculated as follows:

[0045]

[0046] In the formula, Z represents the total number of nodes in the complex network; Let node i and node i * The shortest path length between them, global efficiency is used to quantify the connectivity of the pore structure, reflecting the transport capacity and efficiency of fluid in the pore network.

[0047] In one implementation, S4 includes:

[0048] S4.1: Construct a machine learning model dataset based on the extracted macroscopic and microscopic structural parameters and the calculated permeability of spherical granular materials;

[0049] data m (X,Y) (9)

[0050] In the formula, m is the number of samples; X is the sample structure feature parameter; and Y is the target result.

[0051] S4.2: Divide the training dataset from the machine learning model dataset; construct a machine learning model, and train the machine learning model based on the training dataset using the random forest algorithm to obtain a trained penetration rate prediction model. During the training process, R... 2 Values ​​are used to evaluate the fitting accuracy of machine learning models:

[0052]

[0053] In the formula, Y is the model's predicted value. s The target value for each sample in the test dataset; To test the mean of the target values ​​in the dataset, R 2 The size is used to represent the prediction performance of the machine learning model.

[0054] In one embodiment, after step S4.1, the method further includes:

[0055] Data preprocessing of the machine learning model dataset specifically involves: normalizing the input data and mapping the data within the range of [0,1].

[0056]

[0057]

[0058] In the formula, s is the sample number; X′ s and Y′ s The value is the normalized value; X s and Y s These are the first and second values ​​of the sample, respectively; X min X max Y represents the minimum and maximum values ​​of the first sample value. min Y max These are the minimum and maximum values ​​of the second value in the sample, respectively.

[0059] Based on the same inventive concept, a second aspect of the present invention provides a machine learning-based prediction system for the permeability characteristics of spherical particle systems, comprising:

[0060] The sample dataset creation module is used to generate aggregates of particles with different gradations and compress them to obtain calculation samples by using the discrete element method based on the gradation information and compaction degree of spherical particles. Then, the region is segmented to create a sample dataset containing the gradation information of spherical particles, confining pressure, and three-dimensional image structure.

[0061] The permeability calculation module is used to calculate the permeability of samples in the sample dataset based on the lattice Boltzmann method and the D3Q19 lattice model, and to obtain the permeability of spherical granular materials.

[0062] The structural feature extraction module is used to extract structural features from the samples in the sample dataset. The extracted structural features include macroscopic scale parameters and microscopic scale parameters.

[0063] The model training module is used to construct a machine learning model dataset based on the calculated permeability of particulate materials and the extracted structural features, and to divide the machine learning model dataset into a training dataset; to construct a machine learning model, and to train the machine learning model based on the training dataset using the random forest algorithm to obtain a trained permeability prediction model.

[0064] The prediction module is used to predict the permeability of spherical particle systems using a trained permeability prediction model.

[0065] Based on the same inventive concept, a third aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in the first aspect.

[0066] Compared with the prior art, the advantages and beneficial technical effects of the present invention are as follows:

[0067] The method provided by this invention constructs a sample dataset containing gradation information, confining pressure, and three-dimensional image structure of spherical granular materials. This dataset is a particle packing model dataset based on the gradation information of spherical granular materials. This particle packing model can reflect the complex and realistic pore structure inside the granular material, improving the applicability and practical engineering value of the dataset. Furthermore, this invention provides a method for describing the pore structure of samples based on a combination of macroscopic and microscopic scales, extracting structural parameters such as porosity φ and tortuosity τ. s Pore ​​heterogeneity coefficient I d Fractal dimension F d Average porosity coordination number C, average pore radius r p Average throat radius r t Average laryngeal length l t Global clustering coefficient T, entropy H of degree distribution, and global efficiency. This invention uses multi-scale information about the sample structure as input parameters for a machine learning model. This significantly improves the accuracy of sample structure description and overcomes the shortcomings of previous studies, such as incomplete and unrepresentative extraction of sample structural information. Finally, a machine learning model based on the random forest algorithm is used to train a dataset consisting of the sample's structural parameters and permeability to obtain the relationship between sample structure and permeability. When predicting the permeability of particulate materials based on this invention, only the structural parameters need to be input to quickly obtain the permeability value. This invention overcomes the shortcomings of long periods in indoor and field tests and the inability to quickly obtain permeability data, thus improving the timeliness of permeability prediction. Attached Figure Description

[0068] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0069] Figure 1 This is a flowchart of a machine learning-based method for rapid prediction of permeability of particulate materials in an embodiment of the present invention.

[0070] Figure 2 This is a schematic diagram of the gradation curves of five samples selected in an embodiment of the present invention.

[0071] Figure 3 The following are schematic diagrams of three scale models in the embodiments of the present invention, wherein (a) is a schematic diagram of pore structure, (b) is a pore network model, and (c) is a complex network model.

[0072] Figure 4 This is a schematic diagram of the seepage simulation domain and boundary conditions in an embodiment of the present invention.

[0073] Figure 5 This is a schematic diagram of the prediction results of the machine learning model in an embodiment of the present invention. Detailed Implementation

[0074] This invention discloses a rapid prediction method for the permeability characteristics of spherical particle systems based on machine learning. First, a discrete element method is used to generate assemblies of spherical particles with different gradations. By changing the target pressure and the interparticle friction coefficient, particle samples with different densities are generated. The particle samples are then segmented into regions to establish a large-scale sample dataset containing particle material gradation information and three-dimensional image structures. The permeability of the particle samples is then calculated using the lattice Boltzmann method and the D3Q19 lattice model. Next, the structural features of the particle samples at both macroscopic and microscopic scales are extracted. Using the structural feature parameters of the particle material at multiple scales as input and the permeability of the particle samples as output, a large-scale dataset is constructed to train the machine learning model. The machine learning model is then trained, ultimately yielding a model that can accurately and effectively predict permeability based on the structural features of the particle material at multiple scales.

[0075] The method of this invention can generate spherical particle assemblages with different gradation characteristics and densities through numerical simulation. The particle packing reflects the complex pore structure within the spherical particle system. It describes the complex pore structure of particulate materials based on macroscopic and microscopic pore structure characteristics, overcoming the limitation of macroscopic structural parameters in accurately describing the complex internal structure of pores. Simultaneously, a permeability prediction model based on machine learning is constructed based on the extracted structural parameters, solving the problems of long testing times and equipment limitations caused by the large range of particle size variations in traditional seepage tests. Practice has proven that this prediction method is convenient and effective, with high prediction accuracy, and has strong engineering application and promotion value.

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] Example 1

[0078] This invention provides a method for predicting the permeability characteristics of a spherical particle system based on machine learning, comprising:

[0079] S1: Based on the gradation information and compaction degree of spherical granular materials, aggregates of granular materials with different gradations are generated by the discrete element method and compressed to obtain calculation samples. Then, region segmentation is performed to establish a sample dataset containing gradation information of spherical granular materials, confining pressure and three-dimensional image structure.

[0080] S2: Based on the lattice Boltzmann method and the D3Q19 lattice model, the permeability of the samples in the sample dataset is calculated to obtain the permeability of the spherical particle material.

[0081] S3: Extract structural features from the samples in the sample dataset. The extracted structural features include macroscopic scale parameters and microscopic scale parameters.

[0082] S4: Based on the calculated permeability of the particulate material and the extracted structural features, construct a machine learning model dataset and divide it into a training dataset; construct a machine learning model, train it using the random forest algorithm based on the training dataset, and obtain a trained permeability prediction model.

[0083] S5: Predict the permeability of the spherical particle system using a trained permeability prediction model.

[0084] Please see Figure 1 The above is a flowchart of a method for rapid prediction of permeability of particulate materials based on machine learning in an embodiment of the present invention.

[0085] Specifically, by changing the target pressure and the interparticle friction coefficient, particle samples with different densities can be generated; the particle samples are then divided into regions to establish a large-scale sample dataset containing particle material gradation information and three-dimensional image structure.

[0086] Using structural characteristic parameters of granular materials at multiple scales as input and granular sample permeability as output, a machine learning model is trained. The random forest algorithm is used to control and make decisions during the training process, resulting in a well-trained permeability prediction model. Finally, the well-trained permeability prediction model can be used to predict the permeability of spherical particle systems.

[0087] In one implementation, step S1 includes:

[0088] S1.1: Obtain the gradation information of spherical granular materials based on known engineering data;

[0089] S1.2: Based on the gradation information of spherical granular materials, several granular aggregates with different gradations are generated by the discrete element method. The sample in the granular aggregate is compressed according to the degree of compaction to obtain the calculated sample.

[0090] S1.3: Based on the position information of the spherical particles in the calculation sample, the porous region and the solid region are divided, with the value "0" representing the porous phase and the value "1" representing the solid phase, so that the three-dimensional image structure is transformed into a three-dimensional digital matrix form, and a sample dataset containing the gradation information of the spherical particle material, the confining pressure and the three-dimensional image structure is established. The sample dataset is represented in binary file format.

[0091] Specifically, the discrete element method can generate a large number of different graded particle assemblies. The particle assembly sample is then compressed, and the degree of compaction can be set according to the actual situation, such as controlling the target confining pressure to 1 MPa, to obtain the sample used for subsequent simulation calculations.

[0092] Please see Figure 2 This is a schematic diagram of the gradation curves of five samples selected in this embodiment of the invention.

[0093] In one implementation, step S2 includes:

[0094] S2.1: The permeability of the samples in the sample dataset was calculated using the lattice Boltzmann method. The D3Q19 lattice model was selected, and the model was based on the single-relaxation-time BGK model. Specifically, the water flow direction was set as the x-direction, and the entire flow domain space was discretized into lattice points. The fluid motion process was transformed into the collision and migration process of fluid particles. The collision and migration process of fluid particles was realized through iterative evolution based on the distribution function of fluid particles. The evolution process is shown in the following equation:

[0095]

[0096] In the formula, f n Let be the non-equilibrium distribution function of the particle; x is the particle position; e n The velocity of the particle in the nth direction is t; the discrete time is τ; the relaxation time is f. n,eq Let be the particle equilibrium distribution function;

[0097] S2.2: When the flow simulation reaches a steady state, the velocity distribution of the flow field is calculated using formula (1);

[0098] S2.3: Based on the velocity distribution of the calculated flow field, the spherical particle material is obtained by calculating using Darcy's equation.

[0099] Specifically, formula (1) represents the basic principle of the Lattice Boltzmann Method (LBM) calculation, which is the equilibrium function of each grid point in the fluid domain. When the numerical simulation (flow simulation) reaches a steady state, the velocity distribution of the flow field can be obtained by performing statistical calculations on the equilibrium function of each grid point, and then the permeability can be calculated by Darcy's equation.

[0100] Please see Figure 4 This is a schematic diagram of the seepage simulation domain and boundary conditions in an embodiment of the present invention.

[0101] In one embodiment, the macroscopic parameters extracted in step S3 include sample porosity, sample tortuosity, sample pore heterogeneity, and sample fractal dimension, wherein the sample porosity is calculated as follows:

[0102] φ=Vvoid / V all (2)

[0103] In the formula, φ is the porosity of the sample, and V void V is the pore volume. all The total volume of the sample.

[0104] The method for calculating the tortuosity of the specimen is as follows:

[0105]

[0106] In the formula, τ s Let v be the tortuosity of the sample, i be the i-th node in the flow field, N be the total number of nodes in the flow field, and v be the tortuosity of the sample. xi Let v be the flow velocity in the x-direction of the i-th node. yi Let v be the flow velocity in the y-direction of the i-th node. zi Let be the z-direction velocity of the i-th node, where the velocity in each direction is the velocity distribution of the flow field in step S2.2;

[0107] The method for calculating the porosity heterogeneity of the sample is as follows:

[0108]

[0109] In the formula, φ j φ is the porosity of the j-th sub-sample; φ is the overall porosity of the sample.

[0110] The fractal dimension of the sample is calculated as follows:

[0111]

[0112] In the formula, A is R n Any nonempty bounded subset of space; N r (A) represents the minimum number of n-dimensional cubes with side length r required to cover A.

[0113] Specifically, based on the separation results of the porous phase and the solid phase, the ratio of the pore volume to the total volume of the sample can be obtained as the porosity of the sample.

[0114] Based on the formula (Formula 1) in the permeability of step 2, the flow velocity field distribution inside the sample is obtained, and the tortuosity is calculated according to formula (3).

[0115] When calculating the porosity heterogeneity of a sample, the sample is divided into M×M×M sub-samples, and the porosity of each sub-sample is calculated separately to obtain the porosity heterogeneity.

[0116] When calculating the fractal dimension of a sample, the box dimension method is used to calculate the fractal dimension of the sample to reflect the complexity and irregularity of the pore structure.

[0117] In one embodiment, the microscale parameters extracted in step S3 include structural feature parameters at the pore scale, the connectivity and flow rate within different samples, and the extraction process includes:

[0118] Based on the maximum sphere algorithm, a pore network model is established, and the average pore coordination number C and average pore radius r are extracted from the pore network model. p Average throat radius r t Average laryngeal length l t As a structural characteristic parameter at the pore scale, the pore network model equates the pores inside the structure to a series of pore bodies and throats, with pore bodies represented by spheres and throats represented by thin rods.

[0119] The complex network method is used to analyze the microstructure and connectivity of the sample. In this method, pores are treated as nodes in the complex network, throats are treated as edges connecting two nodes, and the cross-sectional area of ​​the throat is used as the weight of each edge. The complex network is formed by analyzing and calculating the clustering coefficient, heterogeneity coefficient, and global efficiency index. The obtained indexes are used to determine the connectivity and flow rate of different samples.

[0120] Please see Figure 3 The figures are schematic diagrams of three scale models in the embodiments of the present invention, wherein (a) is a schematic diagram of pore structure, (b) is a pore network model, and (c) is a complex network model.

[0121] In one implementation, the clustering coefficients of a complex network are calculated as follows:

[0122]

[0123] In the formula, V is the set of nodes in the complex network, a is the node number, k is the number of node degrees, t(G) is the number of triangles formed by nodes and edges in the complex network, and the clustering coefficient index is used to reflect the probability that the neighbors of nodes in the complex network are neighbors of each other.

[0124] The degree heterogeneity coefficient of a complex network is represented by the entropy H of the degree distribution in the complex network, and is calculated as follows:

[0125]

[0126] The entropy of the moderate degree distribution in a complex network is used to represent the non-uniformity of nodes in the network, where P(k) represents the proportion of nodes with a moderate degree of k in the complex network.

[0127] The global efficiency in complex networks is calculated as follows:

[0128]

[0129] In the formula, Z represents the total number of nodes in the complex network; Let node i and node i * The shortest path length between them, global efficiency is used to quantify the connectivity of the pore structure, reflecting the transport capacity and efficiency of fluid in the pore network.

[0130] The microstructure (connectivity, flow rate) of different samples is characterized by the calculated indices of complex networks, thereby obtaining microscale parameters.

[0131] The structural characteristic parameters and permeability calculation results of some samples are shown in Table 1.

[0132] Table 1 shows the structural characteristic parameters and permeability results of some samples.

[0133]

[0134]

[0135] In one implementation, S4 includes:

[0136] S4.1: Construct a machine learning model dataset based on the extracted macroscopic and microscopic structural parameters and the calculated permeability of spherical granular materials;

[0137] data m (X,Y) (9)

[0138] In the formula, m is the number of samples; X is the sample structure feature parameter; and Y is the target result.

[0139] S4.2: Divide the training dataset from the machine learning model dataset; construct a machine learning model, and train the machine learning model based on the training dataset using the random forest algorithm to obtain a trained penetration rate prediction model. During the training process, R... 2 Values ​​are used to evaluate the fitting accuracy of machine learning models:

[0140]

[0141] In the formula, Y is the model's predicted value. s The target value for each sample in the test dataset; To test the mean of the target values ​​in the dataset, R 2 The size is used to represent the prediction performance of the machine learning model.

[0142] Specifically, in the decision-making process of a random forest, starting from the root node, random sampling with replacement is used. The data is then divided into multiple training subsets, which are further split based on their feature parameters to form decision trees. Each decision tree is computed in parallel, and the mode of all decision tree results is used as the prediction result. During training, 80% of the data is selected as the training set, and 20% as the test set. The training set is the dataset used in the machine learning model training process, while the test set is used to evaluate the accuracy of the machine learning model's prediction results. R is used. 2 Values ​​are used to evaluate the fitting accuracy of machine learning models.

[0143] Please see Figure 5 This is a schematic diagram of the prediction results of the machine learning model in an embodiment of the present invention.

[0144] In one embodiment, after step S4.1, the method further includes:

[0145] Data preprocessing of the machine learning model dataset specifically involves: normalizing the input data and mapping the data within the range of [0,1].

[0146]

[0147]

[0148] In the formula, s is the sample number; X′ s and Y′ s The value is the normalized value; X s and Y s These are the first and second values ​​of the sample, respectively; X min X max Y represents the minimum and maximum values ​​of the first sample value. min Y max These are the minimum and maximum values ​​of the second value in the sample, respectively.

[0149] Data preprocessing can improve the accuracy of data samples and increase the convergence speed of machine learning.

[0150] The present invention relates to a method for rapid prediction of permeability characteristics of spherical particle systems based on machine learning, comprising the following five implementation steps:

[0151] 1. Obtain particle material gradation information, generate particle assemblies with different gradations using the discrete element method, compress them under certain conditions to obtain calculation samples, perform region segmentation, and establish a large-scale sample dataset containing particle material gradation information and three-dimensional image structure.

[0152] 2. The permeability of the sample was calculated using the lattice Boltzmann method and the D3Q19 lattice model.

[0153] Third, extract structural feature information and calculate the macroscopic and microscopic parameters of the sample respectively;

[0154] Fourth, a dataset for building a machine learning model is established based on these parameter data results. The machine learning model is then constructed and trained using the random forest algorithm to finally obtain a model that can accurately and effectively predict penetration rates.

[0155] V. Predict the permeability of the spherical particle system using a trained permeability prediction model.

[0156] The beneficial effects of this invention are:

[0157] Numerical simulations can generate spherical particle assemblages with different gradations and densities. The particle packing reflects the complex pore structure within the spherical particle system. By describing the complex pore structure of particulate materials based on macroscopic and microscopic pore structure characteristics, this method overcomes the limitation of macroscopic structural parameters in accurately describing the complex internal pore structure. Furthermore, a machine learning-based permeability prediction model is constructed based on the extracted structural parameters, solving the problems of long testing times and equipment limitations caused by the large range of particle size variations in traditional seepage tests. Practical application has proven that this prediction method is convenient, effective, and has high prediction accuracy, demonstrating strong value for engineering applications.

[0158] Example 2

[0159] Based on the same inventive concept, this embodiment provides a machine learning-based prediction system for the permeability characteristics of spherical particle systems, comprising:

[0160] The sample dataset creation module is used to generate aggregates of particles with different gradations and compress them to obtain calculation samples by using the discrete element method based on the gradation information and compaction degree of spherical particles. Then, the region is segmented to create a sample dataset containing the gradation information of spherical particles, confining pressure, and three-dimensional image structure.

[0161] The permeability calculation module is used to calculate the permeability of samples in the sample dataset based on the lattice Boltzmann method and the D3Q19 lattice model, and to obtain the permeability of spherical granular materials.

[0162] The structural feature extraction module is used to extract structural features from the samples in the sample dataset. The extracted structural features include macroscopic scale parameters and microscopic scale parameters.

[0163] The model training module is used to construct a machine learning model dataset based on the calculated permeability of particulate materials and the extracted structural features, and to divide the machine learning model dataset into a training dataset; to construct a machine learning model, and to train the machine learning model based on the training dataset using the random forest algorithm to obtain a trained permeability prediction model.

[0164] The prediction module is used to predict the permeability of spherical particle systems using a trained permeability prediction model.

[0165] Since the system described in Embodiment 2 of this invention is the same system used to implement the machine learning-based method for predicting the permeability characteristics of a spherical particle system in Embodiment 1 of this invention, those skilled in the art can understand the specific structure and variations of this system based on the method described in Embodiment 1 of this invention, and therefore will not be repeated here. All systems used in the method of Embodiment 1 of this invention fall within the scope of protection of this invention.

[0166] Example 3

[0167] Based on the same inventive concept, the present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed, implements the method described in Embodiment 1.

[0168] Since the computer-readable storage medium described in Embodiment 3 of this invention is the same computer-readable storage medium used in implementing the machine learning-based method for predicting the permeability characteristics of a spherical particle system in Embodiment 1 of this invention, those skilled in the art can understand the specific structure and variations of this computer-readable storage medium based on the method described in Embodiment 1 of this invention, and therefore will not be repeated here. All computer-readable storage media used in the method of Embodiment 1 of this invention fall within the scope of protection of this invention.

[0169] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0170] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0171] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the invention.

[0172] Obviously, those skilled in the art can make various modifications and variations to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations to the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention also intends to include these modifications and variations.

Claims

1. A method for predicting the permeation characteristics of a system of spherical particles based on machine learning, characterized in that, The method comprises the following steps: S1: generating different gradation particle assemblies by discrete element method according to the gradation information of the spherical particle material and the compaction degree, and compressing the particle assemblies to obtain calculation samples, and then performing regional segmentation to establish a sample data set containing the gradation information of the spherical particle material, confining pressure and three-dimensional image structure; S2: calculating the permeability of the samples in the sample data set based on the lattice Boltzmann method and the D3Q19 lattice model to obtain the permeability of the spherical particle material; S3: extracting structural features of the samples in the sample data set, wherein the extracted structural features include macro-scale parameters and micro-scale parameters; S4: constructing a machine learning model data set according to the calculated permeability of the particle material and the extracted structural features, and dividing a training data set from the machine learning model data set; constructing a machine learning model, training the machine learning model based on the training data set and using a random forest algorithm to obtain a trained permeability prediction model; S5: using the trained permeability prediction model to predict the permeability of the spherical particle system; Step S2 comprises: S2.1: The permeability of the sample in the sample data set is calculated by using the lattice Boltzmann method, the D3Q19 lattice model is selected, the model is based on the BGK model with single relaxation time, specifically, the water flow direction is set as The entire basin space is discretized into lattice points in the direction, the movement process of the fluid is converted into the collision and migration process of the fluid particles, the collision and migration process of the fluid particles is realized by iterative evolution based on the distribution function of the fluid particles, and the evolution process is as follows: （1） wherein is the particle non-equilibrium distribution function; is the particle position; is the velocity of the particle in the direction; is the discrete time; is the relaxation time; is the particle equilibrium distribution function; S2.2: calculating the velocity distribution of the flow field by formula (1) when the flow simulation reaches a steady state; S2.3: calculating the permeability of the spherical particle material based on the calculated velocity distribution of the flow field by Darcy equation; S4 comprises: S4.1: constructing a machine learning model data set according to the extracted macro-scale and micro-scale structural parameters and the calculated permeability of the spherical particle material; （9） In the formula is the sample number; is the sample structure feature parameter; is the target result; S4.2: divide the training dataset from the machine learning model dataset; build a machine learning model, train the machine learning model based on the training dataset and using the random forest algorithm, and obtain a trained permeability prediction model, wherein in the training process, the following is adopted value to evaluate the fitting accuracy of the machine learning model: （10） In the formula, is the model prediction value; is the target value of each sample in the test data set; is the mean value of the sample target values in the test data set, The size of is used to represent the prediction effect of the machine learning model.

2. The method of predicting the permeation characteristics of a spheroid particle system based on machine learning of claim 1, wherein, Step S1 comprises: S1.1: obtaining the gradation information of the spherical particle material according to known engineering data; S1.2: generating a plurality of particle assemblies with different gradations by discrete element method according to the gradation information of the spherical particle material, and compressing the samples in the particle assemblies to obtain calculation samples according to the compaction degree; S1.3: dividing the pore region and the solid region according to the position information of the spherical particles in the calculation samples, taking the value "0" to represent the pore phase and the value "1" to represent the solid phase, so that the three-dimensional image structure is converted into a three-dimensional digital matrix form, and a sample data set containing the gradation information of the spherical particle material, the confining pressure and the three-dimensional image structure is established, wherein the sample data set is in the form of a binary file.

3. The method of predicting the permeation characteristics of a spheroidal particle system based on machine learning of claim 1, wherein, The macro-scale parameters extracted in step S3 include sample porosity, sample tortuosity, sample pore heterogeneity and sample fractal dimension, wherein the calculation method of the sample porosity is: （2） wherein is the porosity of the sample, is the pore volume, is the total volume of the sample, The calculation method of the sample tortuosity is: （3） wherein is the tortuosity of the sample, i is the i-th node in the flow field, N is the total number of nodes in the flow field, is the x-direction flow velocity of the i-th node, is the y-direction flow velocity of the i-th node, is the z-direction flow velocity of the i-th node, wherein the flow velocity in each direction is the velocity distribution of the flow field in step S2.2; The calculation method of the sample pore heterogeneity is: （4） wherein porosity of the jthsub-sample; porosity of the entire sample The calculation method of the sample fractal dimension is: （5） wherein is any non-empty bounded subset of is covered by the side length needed is of the minimum number of d-cubes.

4. The method of predicting the permeation characteristics of a spheroid particle system based on machine learning of claim 1, wherein, The micro-scale parameters extracted in step S3 include structural feature parameters in the pore size, the connection mode and the flow degree inside different samples, and the extraction process comprises: Based on the maximum sphere algorithm, a pore network model is established, and the average pore coordination number is extracted from the pore network model. Average pore radius Average laryngeal radius Average larynx length As a structural characteristic parameter at the pore scale, the pore network model equates the pores inside the structure to a series of pore bodies and throats, with pore bodies represented by spheres and throats represented by thin rods. The complex network method is used to analyze the microstructure and connectivity of the sample. In the complex network, the pore points are regarded as nodes, the throat is regarded as the edge connecting two nodes, and the cross-sectional area of the throat is regarded as the weight of each edge. The complex network is formed, and the clustering coefficient, heterogeneity coefficient and global efficiency index are obtained by analyzing the formed complex network. The connectivity mode and flow degree of different samples are obtained by using the obtained indexes.

5. The method of predicting the permeation characteristics of a spheroidal particle system based on machine learning of claim 4, wherein, The calculation method of the clustering coefficient of the complex network is as follows: （6） In the formula, G is a set of nodes in a complex network, a is a node number, k is a node degree number, t(G) is a number of triangles formed by nodes and edges in the complex network, and the clustering coefficient index is used to reflect a probability that neighbors of a node in the complex network are neighbors of each other. Complex network degree heterogeneity coefficient is an entropy of the degree distribution in a complex network is represented, the calculation is performed as follows, （7） The entropy of the degree distribution in complex networks is used to represent the unevenness of nodes in the network, The proportion of nodes with degree value in complex networks. The calculation method of the global efficiency of the complex network is as follows: （8） In the formula, Z is the total number of nodes in the complex network; is the node and the shortest path length between the node is the global efficiency, which is used to quantify the connectivity degree of the pore structure and reflects the transmission ability and efficiency of fluid in the pore network.

6. The method of predicting the permeation characteristics of a spheroid particle system based on machine learning of claim 1, wherein, After step S4.1, the method further comprises: The data preprocessing is performed on the machine learning model dataset, specifically: the input data is normalized, and the data is mapped in the range of [0, 1]. range. （11） （12） wherein is the sample number; and is the normalized value; and are the first and second sample values, respectively; , represent the minimum and maximum values of the first sample values, , are the minimum and maximum values of the second sample values, respectively.

7. A machine learning based system for predicting the permeation characteristics of a spheroidal particle system, characterized in that, The machine learning based prediction method for permeability of a spheroidal particle system according to claim 1 is implemented, and the prediction system comprises: A sample data set establishing module is configured to generate different graded particle assemblies by a discrete element method according to the spheroidal particle material grading information and the compaction degree, to obtain a calculation sample by compression, and to establish a sample data set comprising the spheroidal particle material grading information, the confining pressure and a three-dimensional image structure by region segmentation; A permeability calculation module is configured to calculate the permeability of the sample in the sample data set based on a lattice Boltzmann method and a D3Q19 lattice model, to obtain the permeability of the spheroidal particle material; A structure feature extraction module is configured to extract structure features of the sample in the sample data set, wherein the extracted structure features comprise macro-scale parameters and micro-scale parameters; A model training module is configured to construct a machine learning model data set according to the calculated permeability of the particle material and the extracted structure features, to divide a training data set from the machine learning model data set, to construct a machine learning model, to train the machine learning model based on the training data set and by using a random forest algorithm, and to obtain a trained permeability prediction model; A prediction module is configured to predict the permeability of the spheroidal particle system by using the trained permeability prediction model.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, The program is executed by the processor to implement the method according to any one of claims 1 to 6.

Images