A method and system for simulating particle breakage based on a KAN neural network

Abstract

The present application relates to the technical field of particle breakage simulation, and in particular to a particle breakage simulation method and system based on a KAN neural network. The method comprises the following steps: constructing a single-particle discrete element simulation model, simulating particle breakage strength through the single-particle discrete element simulation model; adjusting the position of a loaded particle to obtain a plurality of stress states, analyzing characteristic strength indicators in the stress states using a traditional failure criterion to obtain an initial data set; processing the initial data set through rotation enhancement, exchange enhancement and balanced sampling to obtain an enhanced data set; training a KAN neural network with a learnable activation function using the enhanced data set to obtain a particle breakage simulation model, and completing particle breakage simulation simulation through the particle breakage simulation model. The present application can accurately simulate the breakage behavior of two-dimensional circular particles under complex stress states, and is suitable for particle breakage research and engineering application in the fields of geotechnical engineering and powder technology.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of particle breakage simulation, and particularly relates to a particle breakage simulation method and system based on a KAN neural network. BACKGROUND

[0002] In the existing particle breakage simulation technology, an accurate particle breakage criterion is a prerequisite for many numerical simulation methods. The discrete element method (DEM) is an important tool for simulating particle breakage. Common methods include the bonded particle model (BPM) and the fragment replacement method (FRM). The BPM forms a single particle model by bonding sub-particles together and simulates the particle breakage behavior by breaking the bond between particles. It can truly reproduce crack propagation and stress distribution, but the calculation cost is high. The FRM uses a specified particle breakage criterion to determine whether a particle breaks, and then uses a group of sub-particles to replace the original particle that has broken to simulate the particle breakage process. However, the simulation accuracy is highly dependent on the form of the selected particle breakage criterion.

[0003] The commonly used particle breakage criteria include the maximum contact force criterion, the average contact force criterion, the maximum principal stress criterion, the average principal stress criterion, the maximum shear stress criterion, and the maximum tensile stress criterion. However, a single particle breakage criterion cannot be applied to all stress states. In some specific stress states, particles may still break, but the characteristic strength proposed by a single particle breakage criterion cannot well represent the critical breakage strength of the particles. For example, in a two-dimensional orthogonal contact force state, the characteristic strength corresponding to the maximum shear stress of the particle is always 0, which greatly affects the simulation accuracy. Under complex stress conditions, the characteristic strength relied on by traditional criteria shows significant variability at the critical state. If complex correction coefficients are not introduced, the criterion may overestimate or underestimate the critical strength, making it difficult to accurately reflect the particle breakage behavior.

[0004] In the existing particle numerical simulation methods such as discrete element method, the characteristic strength defined by the traditional particle breakage criterion cannot accurately reflect the critical stress state of particles under complex stress conditions, and cannot effectively indicate the real particle breakage time, which is a problem that needs to be solved. SUMMARY

[0005] To address the deficiencies of the existing methods and the needs of practical applications, and to solve the above problems, on the one hand, the present application provides a particle breakage simulation method based on a KAN neural network, comprising the following steps:

[0006] A single-particle discrete element simulation model is constructed to simulate particle breakage strength; a position of a loaded particle is adjusted to obtain a plurality of stress states, a characteristic strength index under the stress state is analyzed by using a traditional failure criterion to obtain an initial data set; the initial data set is processed by rotation enhancement, exchange enhancement and balance sampling to obtain an enhanced data set; a KAN neural network with a learnable activation function is trained by using the enhanced data set to obtain a particle breakage simulation model, and particle breakage simulation simulation is completed by using the particle breakage simulation model.

[0007] The particle breakage criterion based on the KAN neural network uses the property that a multivariate continuous function can be represented as a composite of a finite number of univariate continuous functions and binary addition operations proved by the Kolmogorov-Arnold theorem, introduces a learnable activation function, enhances the flexibility and expression ability of the model, comprehensively considers the complex stress state of the particle and the characteristic strength form in the existing various traditional criteria, significantly improves the adaptability to complex loading conditions, effectively improves the simulation precision, can accurately simulate the breakage behavior of a two-dimensional circular particle under a complex stress state, and is suitable for particle breakage research and engineering application in the fields of geotechnical engineering and powder technology.

[0008] Optionally, the construction of the single-particle discrete element simulation model to simulate the particle breakage strength comprises the following steps:

[0009] Sub-particles with the same diameter are randomly generated in the range of a circular large particle based on a specified porosity; the discrete element simulation is used to make all the sub-particles in a balanced state, and the adhesion between the particles is activated to bond all the sub-particles into a whole; the breakage strength of the single-particle model is optimized by adjusting the adhesion strength and adhesion stiffness parameters to obtain a single-particle discrete element simulation model, and the particle breakage strength is simulated by using the single-particle discrete element simulation model.

[0010] The present application first generates sub-particles with the same diameter according to a specified porosity, restores the internal structure of the real particle, and lays a foundation for a physical model that fits the actual situation; then the sub-particles are balanced and the adhesion is activated by using the discrete element to construct a complete single-particle entity and simulate the structural integrity of the real particle; finally, the adhesion parameters are optimized to calibrate the breakage strength, so that the breakage characteristics of the model match the real particle. The present application provides an accurate and reliable basis for subsequent multi-stress state simulation, enhanced data set construction and KAN model training, avoids simulation deviation caused by model structure or strength distortion, and ensures that the particle breakage simulation can accurately reflect the real breakage rule.

[0011] Optionally, the analysis of the characteristic strength index under the stress state by using the traditional failure criterion comprises the following steps:

[0012] analyze a first characteristic strength index under the stress state based on a maximum contact force criterion; analyze a second characteristic strength index under the stress state based on an average contact force criterion; analyze a third characteristic strength index under the stress state based on a maximum principal stress criterion; analyze a fourth characteristic strength index under the stress state based on an average principal stress criterion; analyze a fifth characteristic strength index under the stress state based on a maximum shear stress criterion; analyze a sixth characteristic strength index under the stress state based on a maximum tensile stress criterion.

[0013] The multi-dimensional characteristic strength indexes are extracted through six traditional failure criteria to comprehensively capture the key information of the stress of the particles: the maximum and average contact force criteria reflect the local contact stress characteristics, the maximum and average principal stress criteria embody the overall stress distribution, and the maximum shear stress and tensile stress criteria focus on the critical state under different failure mechanisms. The application breaks through the limitation of a single criterion, describes the complex stress state of the particles from the local to the overall and from different mechanical mechanism dimensions, provides rich and comprehensive input features for subsequent data set construction, enables the KAN neural network to learn more realistic stress-breaking correlation rules, and lays a data foundation for improving the accuracy of particle breaking simulation.

[0014] Optionally, the first characteristic strength index under the stress state based on the maximum contact force criterion satisfies the following formula:

[0015]

[0016] wherein, the first characteristic strength index is represented by F1, the particle diameter is represented by D, the normal contact force of the i th contact is represented by Fi, the total number of contacts of the measured particle is represented by N.

[0017] Optionally, the second characteristic strength index under the stress state based on the average contact force criterion satisfies the following formula:

[0018]

[0019] wherein, the second characteristic strength index is represented by F2, the particle diameter is represented by D, the total number of contacts of the measured particle is represented by N.

[0020] Optionally, the third characteristic strength index under the stress state based on the maximum principal stress criterion satisfies the following formula:

[0021]

[0022] wherein, represents the third characteristic intensity index, represents the particle volume, represents the total contact number of the measured particle, represents the contact force, represents the vector from the force point to the particle center.

[0023] Optionally, the rotation enhancement satisfies the following formula:

[0024]

[0025] wherein, represents the transverse position after rotation enhancement, represents the transverse position before rotation enhancement, represents the angle of random rotation, represents the longitudinal position before rotation enhancement, represents the longitudinal position after rotation enhancement.

[0026] Optionally, the exchange enhancement comprises the following steps:

[0027] Randomly rearranging the order of the particles to obtain a new order; exchanging data according to the new and old orders.

[0028] Optionally, the KAN neural network introducing a learnable activation function satisfies the following formula:

[0029]

[0030] wherein, represents a complex nonlinear function relationship to be approximated, represents the learnable function matrix of the Lth layer, represents the input feature.

[0031] The KAN neural network of the present application can replace the traditional fixed activation function with a learnable activation function through a multi-layer learnable function matrix nesting structure, can flexibly adapt to the complex association between the characteristic intensity index and the crushing state in particle crushing, can break through the limitations of the fitting ability of the traditional neural network, can mine the deep mechanical association between multi-dimensional features layer by layer through the hierarchical iterative learnable function matrix, and can accurately approximate the nonlinear crushing law under the complex stress of particles; can provide strong model support for using multiple characteristic intensity indexes to determine the crushing state, can avoid single criterion deviation, can guarantee the accuracy of the critical state determination in the subsequent particle crushing simulation, and is the core technical link for improving the overall simulation accuracy.

[0032] In a second aspect, to enable efficient execution of the particle crushing simulation method provided by the present application, the present application further provides a KAN neural network-based particle crushing simulation system, comprising a processor, an input device, an output device and a memory, which are connected to each other, wherein the memory is configured to store a computer program, the computer program comprises program instructions, and the processor is configured to invoke the program instructions to execute the KAN neural network-based particle crushing simulation method according to the first aspect of the present application. The KAN neural network-based particle crushing simulation system of the present application has a compact structure and stable performance, and can stably execute the KAN neural network-based particle crushing simulation method provided by the present application, thereby further improving the overall applicability and practical application capability of the present application. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 A KAN neural network-based particle crushing simulation method flowchart provided by an embodiment of the present application;

[0034] Figure 2 A force state generation schematic diagram provided by an embodiment of the present application;

[0035] Figure 3 A KAN neural network-based particle crushing simulation system framework diagram provided by an embodiment of the present application. DETAILED DESCRIPTION

[0036] The specific embodiments of the present application will be described in detail below, and it should be noted that the embodiments described herein are only used for illustration and do not limit the present application. In the following description, a large number of specific details are set forth in order to provide a thorough understanding of the present application. However, it is obvious to those skilled in the art that the specific details need not be used to implement the present application. In other instances, well-known circuits, software or methods have not been specifically described in order to avoid obscuring the present application.

[0037] Throughout the specification, the references to "one embodiment", "an embodiment", "one example" or "an example" mean that a particular feature, structure or characteristic described in connection with the embodiment or example is included in at least one embodiment of the present application. Therefore, the phrases "in one embodiment", "in an embodiment", "one example" or "an example" appearing throughout the specification do not necessarily all refer to the same embodiment or example. In addition, specific features, structures or characteristics can be combined in any appropriate combination and / or subcombination in one or more embodiments or examples. In addition, those skilled in the art should understand that the diagrams provided herein are for illustrative purposes only and the diagrams are not necessarily drawn to scale.

[0038] Please refer toFigure 1 To solve the above problems, the application provides a granular breakage simulation method based on a KAN neural network, as shown in Figure 1 The method comprises the following steps in one embodiment, as shown in

[0039] S1, a single-particle discrete element simulation model is constructed, and the breakage strength of the particles is simulated through the single-particle discrete element simulation model.

[0040] In an embodiment, the single-particle discrete element simulation model is constructed, and the breakage strength of the particles is simulated through the single-particle discrete element simulation model, comprising the following steps:

[0041] S11, sub-particles of the same diameter are randomly generated within the range of the circular large particles based on a specified porosity.

[0042] Sub-particles of the same diameter are randomly generated within the range of the circular large particles by specifying the porosity as 0.01, and for a single-particle model of 2 mm in diameter, about 9600 sub-spheres are formed to ensure that the sub-particle distribution is uniform enough and the internal porosity is few enough.

[0043] S12, all sub-particles are bonded as a whole by activating the inter-particle bonding through discrete element simulation in an equilibrium state.

[0044] The discrete element simulation is run until all sub-particles are in an equilibrium state, and the inter-particle bonding is activated to bond all sub-particles as a whole.

[0045] S13, the breakage strength of the single-particle model is optimized by adjusting the bonding strength and bonding stiffness parameters to obtain a single-particle discrete element simulation model, and the breakage strength of the particles is simulated through the single-particle discrete element simulation model.

[0046] Specifically, the breakage strength of the single-particle model is optimized by adjusting the bonding strength and bonding stiffness parameters, wherein the bonding strength parameter describes the maximum stress that the inter-particle bonding can withstand, and the bonding stiffness parameter describes the ability of the bonding to resist deformation.

[0047] Further, the parameters of the discrete element single-particle model are calibrated based on the single-particle compression test results of the real particles using a trial-and-error method.

[0048] S2, the position of the loaded particles is adjusted to obtain a variety of stress states, and the characteristic strength index under the stress state is analyzed using a traditional failure criterion to obtain an initial data set.

[0049] As shown in Figure 2 The complex stress state of the measured particles is simulated by adjusting the position of the loaded particles, and the data sample of the single-particle breakage under the stress state is established through the following process taking the stress state under the action of four loaded particles as an example.

[0050] (1) Loading particle position generation: for two-dimensional particles, the loading particle position can be represented by the polar angle at the center of the circle relative to the center of the measured particle circle. The first loading particle is randomly generated, and the second particle is randomly generated in the remaining area that does not overlap with the first loading particle, and so on until all particles are generated, which is regarded as a stress state. According to the above method, a stress state is generated each time until enough stress states are collected.

[0051] (2) Generation of data set features and labels: the feature part of the data set includes two parts. The first part is the direct stress state information, including the positions of the four loading particles , and the force size ; the second part is the characteristic strength index of the corresponding stress state analyzed by the traditional failure criterion.

[0052] Further, the characteristic strength index of the stress state analyzed by the traditional failure criterion comprises the following steps:

[0053] S21, based on the maximum contact force criterion, analyzing the first characteristic strength index of the stress state.

[0054] Specifically, the first characteristic strength index of the stress state analyzed based on the maximum contact force criterion satisfies the following formula:

[0055]

[0056] wherein, represents the first characteristic strength index, represents the particle diameter, represents the normal contact force of the i-th contact, represents the total number of contacts of the measured particle.

[0057] S22, based on the average contact force criterion, analyzing the second characteristic strength index of the stress state.

[0058] Specifically, the second characteristic strength index of the stress state analyzed based on the average contact force criterion satisfies the following formula:

[0059]

[0060] wherein, represents the second characteristic strength index, represents the particle diameter, represents the total number of contacts of the measured particle.

[0061] S23, based on the maximum principal stress criterion, analyzing the third characteristic strength index of the stress state.

[0062] Specifically, the third characteristic strength index under the stress state is analyzed based on the maximum principal stress criterion, and the following formula is satisfied:

[0063]

[0064] wherein, represents the third characteristic strength index, represents the particle volume, represents the total contact number of the measured particle, represents the contact force, represents the vector from the force action point to the particle center.

[0065] S24, the fourth characteristic strength index under the stress state is analyzed based on the average principal stress criterion.

[0066] Specifically, the fourth characteristic strength index under the stress state is analyzed based on the average principal stress criterion, and the following formula is satisfied:

[0067]

[0068] wherein, represents the characteristic strength of the average principal stress criterion, i.e. the fourth characteristic strength index, represents the maximum principal stress, represents the minimum principal stress.

[0069] S25, the fifth characteristic strength index under the stress state is analyzed based on the maximum shear stress criterion.

[0070] Specifically, the fifth characteristic strength index under the stress state is analyzed based on the maximum shear stress criterion, and the following formula is satisfied:

[0071]

[0072] wherein, represents the fifth characteristic strength index.

[0073] S26, the sixth characteristic strength index under the stress state is analyzed based on the maximum tensile stress criterion.

[0074] Specifically, the sixth characteristic strength index under the stress state is analyzed based on the maximum tensile stress criterion, and the following formula is satisfied:

[0075]

[0076] wherein, represents the sixth characteristic strength index.

[0077] Further, the positive sample represents the breakage critical state, and the label is 1; the negative sample represents the unbroken state, and the label is 0. The sampling method of the positive sample is that, in a single particle breakage model, the maximum value of each contact force is taken as the critical contact force, the critical characteristic strength and other input characteristics are calculated, and the label is 1. The sampling method of the negative sample is that, the sampling range is selected from the start time of the simulation to the time when the maximum contact force appears, and Latin hypercube sampling is used in the sampling range, that is, according to the number of negative samples to be sampled, the sampling range is evenly divided into M small regions, and random sampling is performed in each small region. The input characteristics of the negative sample are calculated according to the contact force at this time, and the label is 0, to obtain the initial data set.

[0078] S3, processing the initial data set by rotation enhancement, exchange enhancement and balance sampling to obtain an enhanced data set.

[0079] In the embodiment, the rotation enhancement is performed by generating a random rotation angle to uniformly rotate the position of the loaded particle by the angle to obtain new position coordinates, which satisfy the following formula:

[0080]

[0081] wherein, represents the transverse position after rotation enhancement, represents the transverse position before rotation enhancement, represents the random rotation angle, represents the longitudinal position before rotation enhancement, represents the longitudinal position after rotation enhancement.

[0082] Further, the exchange enhancement includes the following steps:

[0083] First, the order of the particles is randomly disturbed to obtain a new order.

[0084] The order of the contact force information is exchanged to perform data enhancement. Taking the case of four loaded particles as an example, the original order 1, 2, 3, and 4 is randomly disturbed, and the new order is obtained as 3, 2, 1, and 4.

[0085] Second, data exchange is performed according to the new and old orders. Taking the above exchange order as an example, the data exchange satisfies:

[0086]

[0087]

[0088]

[0089]

[0090] By employing the two data augmentation methods described above, positive and negative samples can be upsampled and downsampled respectively to ensure class balance in the dataset. First, the dataset is split into positive and negative sample datasets. Then, using the two data augmentation methods, samples are sampled a specified number of times, and augmentation is performed through rotation and swapping to obtain augmented datasets of arbitrary size. The size of both the augmented positive and negative sample datasets is set to N. Rotation augmentation is then performed to obtain positive and negative samples of size N, maintaining their original size. The positive and negative sample datasets are then swapped for augmentation. Finally, the positive and negative sample datasets are recombine to obtain a class-balanced augmented dataset.

[0091] S4. Use the augmented dataset to train a KAN neural network with a learnable activation function to obtain a particle breakage simulation model, and use the particle breakage simulation model to complete the particle breakage simulation.

[0092] Based on the KAN neural network, a learnable activation function is introduced to improve the model's flexibility and expressive power. The structure consists of a multi-layer neural network architecture with an output layer, several hidden layers, and an output layer. The expression for any layer is as follows:

[0093]

[0094] In the formula, It is the first The output of the j-th neuron in layer l is the input of layer l. It is the output of the i-th neuron in the l-th layer. It is a learnable univariate function, connected to the first... The path from neuron j in layer l to neuron i in layer l is typically parameterized by B-splines and basis functions, and can be represented as:

[0095]

[0096]

[0097]

[0098] In the formula, w is a learnable scaling factor, and spline(x) is a B-spline function responsible for learning complex nonlinear behavior. These are simple SiLU basis functions that guarantee the function's behavior outside the spline range. These are the basis functions of the spline function. These are the learnable basis function coefficients.

[0099] The final complete network can be represented as:

[0100]

[0101] wherein, represents a complex nonlinear function relationship to be approximated, represents a learnable function matrix of the Lth layer, represents an input feature.

[0102] Further, the training and prediction process of the model is as follows:

[0103] (1) Establishment of a neural network model: the nodes of the input layer are determined according to the data feature dimension, the number of output layer is 1, the number and layer of hidden layer are taken as hyperparameters, which are determined through repeated experiments and verification, the output layer is finally scaled to [0, 1] through Sigmoid function, and the threshold 0.5 is used to convert it into two classification results of 0 or 1.

[0104] (2) Training of the model: the data set will be divided into three parts: training set, test set and validation set, and the features will be standardized, the data will be scaled to [0, 1], the loss function used is binary cross entropy loss function, and the optimizer is Adam algorithm. In the training process, the adjusted hyperparameters include: the number and size of hidden layer, the number of iterations, the size of data batch, and the parameters of the optimizer. Through trial and error method, the model with the highest test accuracy is selected to obtain the trained model

[0105] (3) Prediction of the model: after the artificial neural network model is trained, the model can be used for prediction operation. First, the same preprocessing operation is performed on the data to be predicted as the training data, and then the preprocessed data to be predicted is input into the trained neural network model to obtain the prediction result of the model

[0106] Integrate the above method into the discrete element simulation platform to realize dynamic high-precision simulation of particle crushing. The specific steps are as follows:

[0107] (1) Discrete element numerical simulation calculation: generate the corresponding discrete element model according to the required task, for example, one-dimensional compression test, set appropriate particle properties and inter-particle contact properties for the discrete element particles, and start the discrete element numerical simulation calculation.

[0108] (2) During the simulation, monitor the stress state of the particles every certain time step (such as 100 steps), first use the maximum contact force criterion for preliminary detection, select particles that meet the critical strength and critical particle diameter, and calculate the input features according to the stress state of the particles at this time.

[0109] (3) For the first detection of the screened particles, the characteristics are input into the machine learning prediction model to obtain the prediction of the crushing state. When the obtained crushing state is 1, the crushing operation is performed to generate fragments and replace the original particles.

[0110] (4) Loop iteration: repeat the above process until the simulation ends, and finally output the crushing process and particle size distribution results of the particles.

[0111] Please refer to Figure 3 In the embodiment, in order to efficiently execute the particle crushing simulation method based on the KAN neural network provided by the present application, the present application further provides a particle crushing simulation system based on the KAN neural network, which comprises an input device, an output device, a processor, and a memory. The input device, the output device, the processor, and the memory are connected to each other. The memory contains program instructions for the steps of the particle crushing simulation method based on the KAN neural network. The particle crushing simulation system based on the KAN neural network has a compact structure and stable performance, can stably execute the particle crushing simulation method based on the KAN neural network, and further improves the overall applicability and practical application ability of the present application.

[0112] In the embodiment, the processor can be a central processing unit, and can also be other general-purpose processors, digital signal processors, application-specific integrated circuits, ready-to-program gate arrays or other programmable logic devices, discrete gate or transistor logic, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. The input device can be used to obtain data information. The output device can be used to output the results obtained by the program instructions contained in the computer program stored in the memory provided by the present application. The memory can include read-only memory and random access memory, and provide instructions and data to the processor. Part of the memory can also include non-volatile random access memory.

[0113] In a possible implementation, the memory can include a program storage area and a data storage area, wherein the program storage area can store an operating system and application programs required by at least one function, etc.; the data storage area can store data created during use. In addition, the memory can include read-only memory and random access memory, and provide instructions and data to the processor. The memory stores an operating system and operation instructions, executable modules or data structures, or subsets thereof, or an expanded set thereof, wherein the operation instructions can include various operation instructions for implementing various operations. The operating system can include various system programs for implementing various basic tasks and processing hardware-based tasks.

[0114] The embodiment also provides a storage medium, which stores a computer program, and the computer program is executed by a processor to implement the steps of the particle crushing simulation method based on the KAN neural network.

[0115] The storage medium can include a U disk, a mobile hard disk, a read-only memory, a random access memory, a magnetic disk or an optical disk, and various media capable of storing program codes.

[0116] To sum up, the particle crushing criterion based on the KAN neural network uses the property that a multivariate continuous function can be represented as a finite number of univariate continuous functions and a binary addition operation proved by the Kolmogorov-Arnold theorem, introduces a learnable activation function, enhances the flexibility and expression ability of the model, comprehensively considers the complex stress state of the particle and the characteristic strength form in the existing various traditional criteria, significantly improves the adaptability to the complex loading condition, effectively improves the simulation precision, can accurately simulate the crushing behavior of the two-dimensional circular particle under the complex stress state, and is suitable for the particle crushing research and engineering application in the fields of geotechnical engineering and powder technology.

[0117] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that: it can still modify the technical solutions recorded in the above embodiments, or make equivalent replacement for part or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application, and they should be covered in the scope recorded in the present application.

Claims

1. A method for simulating particle breakage based on a KAN neural network, characterized by, The method comprises the following steps: constructing a single-particle discrete element simulation model, simulating particle breakage strength through the single-particle discrete element simulation model; adjusting the position of the loaded particles to obtain various stress states, analyzing characteristic strength indicators in the stress states by using a traditional failure criterion to obtain an initial data set; processing the initial data set through rotation enhancement, exchange enhancement and balance sampling to obtain an enhanced data set; training a KAN neural network with a learnable activation function by using the enhanced data set to obtain a particle breakage simulation model, and completing particle breakage simulation simulation through the particle breakage simulation model; The method of constructing a single-particle discrete element simulation model, simulating particle breakage strength through the single-particle discrete element simulation model, comprises the following steps: randomly generating sub-particles with the same diameter within the range of circular large particles based on a specified porosity; connecting all sub-particles as a whole by activating the bonding between particles through discrete element simulation of all sub-particles in a balanced state; adjusting bonding strength and bonding stiffness parameters to optimize the breakage strength of the single-particle model to obtain a single-particle discrete element simulation model, and simulating particle breakage strength through the single-particle discrete element simulation model; The rotation enhancement satisfies the following formula: wherein, represents the lateral position after rotation enhancement, represents the lateral position before rotation enhancement, represents the angle of random rotation, represents the longitudinal position before rotation enhancement, represents the longitudinal position after rotation enhancement.

2. The method of claim 1, wherein the KAN neural network-based particle breakage simulation method is characterized by, The method of analyzing characteristic strength indicators in the stress states by using a traditional failure criterion comprises the following steps: analyzing a first characteristic strength indicator in the stress states based on a maximum contact force criterion; analyzing a second characteristic strength indicator in the stress states based on an average contact force criterion; analyzing a third characteristic strength indicator in the stress states based on a maximum principal stress criterion; analyzing a fourth characteristic strength indicator in the stress states based on an average principal stress criterion; analyzing a fifth characteristic strength indicator in the stress states based on a maximum shear stress criterion; analyzing a sixth characteristic strength indicator in the stress states based on a maximum tensile stress criterion.

3. The KAN neural network-based particle breakage simulation method according to claim 2, characterized in that, The method of analyzing a first characteristic strength indicator in the stress states based on a maximum contact force criterion satisfies the following formula: wherein, denotes the first characteristic intensity indicator, denotes the particle diameter, denotes the normal contact force of the i-th contact, denotes the total number of contacts of the particle under test.

4. The KAN neural network-based particle breakage simulation method according to claim 2, characterized by, The method of analyzing a second characteristic strength indicator in the stress states based on an average contact force criterion satisfies the following formula: wherein, denotes a second characteristic intensity indicator, denotes a particle diameter, denotes the total number of contacts of the measured particle.

5. The KAN neural network-based particle breakage simulation method according to claim 2, wherein, The method of analyzing a third characteristic strength indicator in the stress states based on a maximum principal stress criterion satisfies the following formula: wherein, represents a third characteristic intensity indicator, represents a particle volume, represents a total number of contacts of the particle under test, represents a contact force, represents a vector from the point of force application to the particle center.

6. The KAN neural network-based particle breakage simulation method according to claim 1, wherein, The exchange enhancement comprises the following steps: randomly shuffling the order of the particles to obtain a new order; performing data exchange according to the new and old orders.

7. The KAN neural network-based particle breakage simulation method according to claim 1, wherein, The KAN neural network with a learnable activation function satisfies the following formula: wherein, represents a complex nonlinear function relationship to be approximated, represents an Lth layer learnable function matrix, represents an input feature.

8. A KAN neural network-based particle breakage simulation system, characterized by, The particle breakage simulation system based on the KAN neural network comprises an input device, an output device, a processor and a memory, which are connected to each other, the memory comprises program instructions for executing the particle breakage simulation method based on the KAN neural network according to any one of claims 1-7.

Images