Particle crushing simulation method and system based on KAN neural network

Abstract

The invention relates to the technical field of particle crushing simulation, in particular to a particle crushing simulation method and system based on a KAN neural network. The method comprises the following steps: constructing a single-particle discrete element simulation model, and simulating particle crushing strength through the single-particle discrete element simulation model; adjusting the positions of the loaded particles to obtain a plurality of stress states, and analyzing the characteristic strength indexes 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 balanced sampling to obtain an enhanced data set; and training a KAN neural network which introduces a learnable activation function by using the enhanced data set to obtain a particle crushing simulation model, and completing particle crushing simulation through the particle crushing simulation model. The device can accurately simulate the crushing behavior of the two-dimensional circular particles in a complex stress state, and is suitable for particle crushing research and engineering application in the fields of geotechnical engineering, powder technology and the like.

Description

Technical Field

[0001] This invention relates to the field of particle crushing simulation technology, and specifically to a particle crushing simulation method and system based on a KAN neural network. Background Technology

[0002] In existing particle breakage simulation technologies, accurate particle breakage criteria are a prerequisite for many numerical simulation methods. For example, the Discrete Element Method (DEM) is an important tool for simulating particle breakage, and commonly used methods include the Bound Particle Model (BPM) and the Fragmentation Replacement Method (FRM). BPM simulates particle breakage behavior by constructing a single-particle model from mutually bonded sub-particles and by detecting the failure of inter-particle bonds. It can realistically reproduce crack propagation and stress distribution, but its computational cost is high. FRM, on the other hand, determines whether a particle has broken based on a specified particle breakage criterion, and then uses a group of sub-particles to replace the original broken particles to simulate the particle breakage process. However, the simulation accuracy is highly dependent on the form of the chosen particle breakage criterion.

[0003] Currently, commonly used particle failure criteria include: maximum contact force criterion, average contact force criterion, maximum principal stress criterion, average principal stress criterion, maximum shear stress criterion, and maximum tensile stress criterion. However, a single particle failure criterion is difficult to apply to all stress states. Under certain specific stress states, particles will still fail, but the characteristic strengths of particles proposed by a single particle failure criterion cannot accurately characterize the critical failure strength of particles. For example, under two-dimensional orthogonal contact force conditions, the characteristic strength corresponding to the maximum shear stress of particles is always 0, which has a significant impact on the accuracy of simulations. Under complex stress conditions, the characteristic strengths on which traditional criteria rely exhibit significant variability at the critical state. Without introducing complex correction coefficients, the criterion is prone to overestimating or underestimating the critical strength, thus failing to accurately reflect the particle breakage behavior.

[0004] In existing particle numerical simulation methods such as discrete element method, the characteristic intensity defined by the traditional particle failure criterion is difficult to accurately reflect the critical stress state of particles under complex stress conditions and cannot effectively indicate the actual moment of particle breakage, which is an urgent problem to be solved. Summary of the Invention

[0005] To address the shortcomings of existing methods and the needs of practical applications, and in order to solve the aforementioned problems, this invention provides a particle breakage simulation method based on a KAN neural network, comprising the following steps: A single-particle discrete element simulation model is constructed to simulate particle breakage intensity. The position of the loaded particle is adjusted to obtain various stress states. Traditional failure criteria are used to analyze the characteristic strength indices under these stress states to obtain an initial dataset. The initial dataset is then processed through rotation enhancement, exchange enhancement, and equilibrium sampling to obtain an enhanced dataset. A KAN neural network with a learnable activation function is trained using the enhanced dataset to obtain a particle breakage simulation model. This model is then used to complete the particle breakage simulation.

[0006] This invention presents a particle breakage criterion based on a KAN neural network. Utilizing the property proven by the Kolmogorov-Arnold theorem that a multivariate continuous function can be represented as a composite of a finite number of univariate continuous functions and binary addition operations, a learnable activation function is introduced to enhance the model's flexibility and expressive power. It comprehensively considers the complex stress state of particles and the characteristic intensity forms in various existing traditional criteria, significantly improving its adaptability to complex loading conditions and effectively increasing simulation accuracy. It can accurately simulate the breakage behavior of two-dimensional circular particles under complex stress states, and is suitable for particle breakage research and engineering applications in fields such as geotechnical engineering and powder technology.

[0007] Optionally, the construction of a single-particle discrete element simulation model, and the simulation of particle breakage intensity using the single-particle discrete element simulation model, includes the following steps: Based on a specified porosity, sub-particles of the same diameter are randomly generated within the range of large circular particles; all sub-particles are simulated to be in equilibrium using discrete element method (DEM) simulation, and the bonding between particles is activated to bind all sub-particles into a whole; the breaking strength of the single-particle model is optimized by adjusting the bonding strength and bonding stiffness parameters to obtain a single-particle DEM simulation model, and the breaking strength of the particles is simulated using the single-particle DEM simulation model.

[0008] This invention first generates sub-particles of the same diameter with a specified porosity to recreate the internal structure of real particles, laying the foundation for a realistic physical model. Then, it uses discrete element method (DEM) to achieve sub-particle equilibrium and activate bonding, constructing a complete single-particle entity to simulate the structural integrity of real particles. Finally, it optimizes bonding parameters to calibrate the fracture strength, ensuring the model's fracture characteristics match those of real particles. This provides an accurate and reliable foundation for subsequent multi-stress state simulations, augmented dataset construction, and KAN model training, avoiding simulation deviations caused by model structural or strength distortions, and ensuring that particle fracture simulation accurately reflects real fracture patterns.

[0009] Optionally, the analysis of the characteristic strength index under the stress state using traditional failure criteria includes the following steps: Based on the maximum contact force criterion, the first characteristic strength index under the stress state is analyzed; based on the average contact force criterion, the second characteristic strength index under the stress state is analyzed; based on the maximum principal stress criterion, the third characteristic strength index under the stress state is analyzed; based on the average principal stress criterion, the fourth characteristic strength index under the stress state is analyzed; based on the maximum shear stress criterion, the fifth characteristic strength index under the stress state is analyzed; based on the maximum tensile stress criterion, the sixth characteristic strength index under the stress state is analyzed.

[0010] This invention extracts multi-dimensional feature intensity indicators using six traditional failure criteria to comprehensively capture key information about particle stress: the maximum and average contact force criterion reflects local contact stress characteristics, the maximum and average principal stress criterion reflects the overall stress distribution, and the maximum shear stress and tensile stress criterion focuses on the critical state under different failure mechanisms. This invention overcomes the limitations of a single criterion, characterizing the complex stress state of particles from local to global perspectives and from different mechanical mechanism dimensions. It provides rich and comprehensive input features for subsequent dataset construction, enabling the KAN neural network to learn stress-fracture correlation patterns that more closely resemble reality, laying a data foundation for improving the accuracy of particle fracture simulation.

[0011] Optionally, the first characteristic strength index under the stress state, based on the maximum contact force criterion, satisfies the following formula: in, Indicates the first characteristic intensity index. Indicates particle diameter, This represents the normal contact force at the i-th contact. This indicates the total number of contacts of the tested particles.

[0012] Optionally, the second characteristic strength index under the stress state, based on the average contact force criterion, satisfies the following formula: in, This represents the second characteristic intensity index. Indicates particle diameter, This indicates the total number of contacts of the tested particles.

[0013] Optionally, the third characteristic strength index under the stress state, based on the maximum principal stress criterion, satisfies the following formula: in, This represents the third characteristic intensity index. Indicates particle volume, This indicates the total number of contacts of the tested particles. Indicates contact force. This represents the vector from the point of force application to the center of the particle.

[0014] Optionally, the rotational enhancement satisfies the following formula: in, Indicates the lateral position after rotation enhancement. Indicates the lateral position before rotational enhancement. Indicates the angle of random rotation. Indicates the longitudinal position before rotational enhancement. This indicates the longitudinal position after rotation enhancement.

[0015] Optionally, the exchange enhancement includes the following steps: The order of the particles is randomly shuffled to obtain a new order; data is then exchanged based on the old and new orders.

[0016] Optionally, the KAN neural network with a learnable activation function satisfies the following formula: in, This represents a complex nonlinear functional relationship that needs to be approximated. This represents the learnable function matrix of the Lth layer. This represents the input features.

[0017] The KAN neural network of this invention, through a multi-layered nested structure of learnable function matrices, replaces the traditional fixed activation function with a learnable activation function. This allows it to flexibly adapt to the complex correlation between feature intensity indicators and the crushing state in particle crushing, breaking through the limitations of traditional neural network fitting capabilities. Through hierarchical iterative learnable function matrices, it can layer by layer explore the deep mechanical correlation between multi-dimensional features, accurately approximating the nonlinear crushing law of particles under complex stress. It provides strong model support for determining the crushing state using multiple feature intensity indicators, avoids the bias of a single criterion, and ensures the accuracy of critical state determination in subsequent particle crushing simulations. This is the core technical link for improving the overall simulation accuracy.

[0018] Secondly, to efficiently execute the particle crushing simulation method based on a KAN neural network provided by this invention, this invention also provides a particle crushing simulation system based on a KAN neural network, including a processor, an input device, an output device, and a memory. The processor, input device, output device, and memory are interconnected. The memory stores a computer program containing program instructions. The processor is configured to call the program instructions to execute the particle crushing simulation method based on a KAN neural network as described in the first aspect of this invention. The particle crushing simulation system based on a KAN neural network of this invention has a compact structure and stable performance, and can stably execute the particle crushing simulation method based on a KAN neural network provided by this invention, further improving the overall applicability and practical application capability of this invention. Attached Figure Description

[0019] Figure 1 A flowchart of a particle breakage simulation method based on a KAN neural network is provided in this embodiment of the invention; Figure 2 This is a schematic diagram of force state generation provided in an embodiment of the present invention; Figure 3 This is a framework diagram of a particle crushing simulation system based on a KAN neural network, provided for an embodiment of the present invention. Detailed Implementation

[0020] Specific embodiments of the present invention will now be described in detail. It should be noted that the embodiments described herein are for illustrative purposes only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the invention. However, it will be apparent to those skilled in the art that these specific details are not necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been specifically described to avoid obscuring the invention.

[0021] Throughout this specification, references to "an embodiment," "an embodiment," "an example," or "an example" mean that a particular feature, structure, or characteristic described in connection with that embodiment or example is included in at least one embodiment of the invention. Therefore, the phrases "in an embodiment," "in an embodiment," "an example," or "an example" appearing in various places throughout the specification do not necessarily refer to the same embodiment or example. Furthermore, specific features, structures, or characteristics can be combined in one or more embodiments or examples in any suitable combination and / or sub-combination. Moreover, those skilled in the art will understand that the illustrations provided herein are for illustrative purposes and are not necessarily drawn to scale.

[0022] Please see Figure 1To address the aforementioned problems, this invention provides a particle breakage simulation method based on a KAN neural network, such as... Figure 1 As shown, in one embodiment, the method includes the following steps: S1. Construct a single-particle discrete element simulation model to simulate particle breakage intensity.

[0023] In this embodiment, the construction of a single-particle discrete element simulation model, and the simulation of particle breakage intensity using the single-particle discrete element simulation model, includes the following steps: S11. Randomly generate sub-particles of the same diameter within the range of large round particles based on the specified porosity.

[0024] By specifying a porosity of 0.01, sub-particles of the same diameter are randomly generated within the range of large spherical particles. For a single particle model with a diameter of 2 mm, approximately 9600 sub-spheres are generated to ensure that the sub-particles are distributed sufficiently uniformly and that the internal pores are sufficiently few.

[0025] S12. Simulate all sub-particles in equilibrium using discrete element method, and activate the adhesion between particles to bond all sub-particles into a whole.

[0026] Run discrete element simulation until all sub-particles are in equilibrium, then activate the bonding between particles to bind all sub-particles together as a whole.

[0027] S13. Adjust the bonding strength and bonding stiffness parameters to optimize the crushing strength of the single particle model and obtain the single particle discrete element simulation model. Simulate the particle crushing strength through the single particle discrete element simulation model.

[0028] Specifically, the crushing strength of a single-particle model is optimized by adjusting the bond strength and bond stiffness parameters. The bond strength parameter describes the maximum stress that the bond between sub-particles can withstand, while the bond stiffness parameter describes the bond's ability to resist deformation.

[0029] Furthermore, the parameters of the discrete element single-particle model were calibrated using a trial-and-error method based on the results of single-particle compression tests of real particles.

[0030] S2. Adjust the position of the loaded particles to obtain various stress states, and use traditional failure criteria to analyze the characteristic strength indexes under the stress states to obtain the initial dataset.

[0031] like Figure 2 As shown, by adjusting the position of the loaded particles, the complex stress state of the tested particles is simulated. Taking the stress state under the action of 4 loaded particles as an example, the following process is used to establish data samples of a single particle breaking under this stress state.

[0032] (1) Generation of loading particle position: For two-dimensional particles, the position of the loading particle can be represented by the polar coordinate angle of the center of the circle relative to the center of the measured particle. First, the first loading particle is randomly generated, and then the second particle is randomly generated in the remaining area that does not overlap with the first loading particle, until all particles are generated, which is regarded as a force state. According to the above method, a force state is generated each time until enough force states are collected.

[0033] (2) Generating features and labels for the dataset: The features of the dataset consist of two parts. The first part is the direct force state information, including the positions of the four loaded particles. , And the magnitude of force The second part analyzes the characteristic strength indices of the corresponding stress states under traditional failure criteria.

[0034] Furthermore, the analysis of the characteristic strength index under the stress state using traditional failure criteria includes the following steps: S21. Based on the maximum contact force criterion, analyze the first characteristic strength index under the stress state.

[0035] Specifically, the first characteristic strength index under the stress state, based on the maximum contact force criterion, satisfies the following formula: in, Indicates the first characteristic intensity index. Indicates particle diameter, This represents the normal contact force at the i-th contact. This indicates the total number of contacts of the tested particles.

[0036] S22. Based on the average contact force criterion, analyze the second characteristic strength index under the stress state.

[0037] Specifically, the second characteristic strength index under the stress state, analyzed based on the average contact force criterion, satisfies the following formula: in, This represents the second characteristic intensity index. Indicates particle diameter, This indicates the total number of contacts of the tested particles.

[0038] S23. Based on the maximum principal stress criterion, analyze the third characteristic strength index under the stress state.

[0039] Specifically, the third characteristic strength index under the stress state, based on the maximum principal stress criterion, satisfies the following formula: in, This represents the third characteristic intensity index. Indicates particle volume, This indicates the total number of contacts of the tested particles. Indicates contact force. This represents the vector from the point of force application to the center of the particle.

[0040] S24. Based on the mean principal stress criterion, analyze the fourth characteristic strength index under the stress state.

[0041] Specifically, based on the mean principal stress criterion, the fourth characteristic strength index under the stress state is analyzed and satisfies the following formula: in, The characteristic strength of the mean principal stress criterion is the fourth characteristic strength index. Indicates the maximum principal stress. This represents the minimum principal stress.

[0042] S25. Based on the maximum shear stress criterion, analyze the fifth characteristic strength index under the stress state.

[0043] Specifically, based on the maximum shear stress criterion, the fifth characteristic strength index under the stress state is analyzed and satisfies the following formula: in, This represents the intensity index of the fifth characteristic.

[0044] S26. Based on the maximum tensile stress criterion, analyze the sixth characteristic strength index under the stress state.

[0045] Specifically, based on the maximum tensile stress criterion, the sixth characteristic strength index under the stress state is analyzed and satisfies the following formula: in, This represents the sixth characteristic strength index.

[0046] Furthermore, positive samples represent the critical breakage state, labeled 1, while negative samples represent the unbreakable state, labeled 0. Positive samples are sampled by taking the maximum value of each contact force in a single-particle breakage model as the critical contact force, calculating input features such as critical characteristic intensity, and assigning a label of 1. Negative samples are sampled by selecting the period from the start of the simulation to the moment the maximum contact force occurs as the sampling range. Within this range, Latin hypercube sampling is used; that is, based on the number of negative samples to be sampled, the sampling range is divided into M small regions. A random sample is taken from each small region, and the contact forces at that moment are used to calculate the input features of the negative sample, which are then labeled 0, thus obtaining the initial dataset.

[0047] S3. The initial dataset is processed by rotation enhancement, exchange enhancement, and balanced sampling to obtain an enhanced dataset.

[0048] In this embodiment, the rotation enhancement is achieved by generating a random rotation angle. The position of the loaded particles is uniformly rotated by this angle to obtain new position coordinates, satisfying the following formula: in, Indicates the lateral position after rotation enhancement. Indicates the lateral position before rotational enhancement. Indicates the angle of random rotation. Indicates the longitudinal position before rotational enhancement. This indicates the longitudinal position after rotation enhancement.

[0049] Furthermore, the exchange enhancement includes the following steps: First, the order of the particles is randomly shuffled to obtain a new order.

[0050] Data augmentation is achieved by exchanging the order of contact force information. Taking the case of four loaded particles as an example, the original order 1, 2, 3, 4 is randomly shuffled, resulting in a new order of 3, 2, 1, 4.

[0051] Secondly, data is exchanged according to the old and new order. Taking the above exchange order as an example, the data exchange satisfies: 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.

[0052] 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.

[0053] 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: 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: 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.

[0054] The final complete network can be represented as: in, This represents a complex nonlinear functional relationship that needs to be approximated. This represents the learnable function matrix of the Lth layer. This represents the input features.

[0055] Furthermore, the training and prediction process of the model is as follows: (1) Establishment of neural network model: The KAN model is adopted. The nodes and data feature dimensions of the input layer are determined. The number of output layers is 1. The number and number of hidden layers are used as hyperparameters and determined through repeated experiments and verifications. The output layer is finally scaled to [0,1] by the Sigmoid function and transformed into a binary classification result of 0 or 1 with a threshold of 0.5.

[0056] (2) Model Training: The dataset will be divided into three parts: training set, test set, and validation set. Features will be standardized, and data will be scaled to [0,1]. The loss function used is the binary cross-entropy loss function, and the optimizer is the Adam algorithm. During training, the hyperparameters adjusted include: the number and size of hidden layers, the number of iterations, the batch size, and the optimizer parameters. Through trial and error, the model with the highest test accuracy is selected to obtain the trained model. (3) Model prediction: After the artificial neural network model is trained, it can be used for prediction. First, the data to be predicted is preprocessed in the same way as the training data. Then, the preprocessed data to be predicted is input into the trained neural network model to obtain the model's prediction result. The above methods are integrated into a discrete element method (DEM) simulation platform to achieve dynamic, high-precision simulation of particle breakage. The specific steps are as follows: (1) Discrete element numerical simulation calculation: Generate the corresponding discrete element model according to the required task, such as a one-dimensional compression test. Set appropriate particle properties and contact properties between particles for discrete element particles, and start discrete element numerical simulation calculation.

[0057] (2) During the simulation, the stress state of the particles is monitored at regular time steps (e.g., 100 steps). The maximum contact force criterion is used for preliminary detection to select particles that meet the critical strength and critical particle size. The input characteristics are calculated based on the stress state of the particles at this time.

[0058] (3) For the particles screened out in the initial detection, their input features are fed into the machine learning prediction model to obtain a prediction of the breakage state. When the obtained breakage state is 1, the breakage operation is performed to generate fragments and replace the original particles.

[0059] (4) Iterative process: Repeat the above process until the simulation ends, and finally output the particle crushing process and particle size distribution results.

[0060] Please see Figure 3In an embodiment, to efficiently execute the particle breakage simulation method based on a KAN neural network provided by this invention, this invention also provides a particle breakage simulation system based on a KAN neural network, comprising: an input device, an output device, a processor, and a memory, wherein the input device, output device, processor, and memory are interconnected, and the memory contains program instructions for the steps of the particle breakage simulation method based on a KAN neural network. The particle breakage simulation system based on a KAN neural network of this invention has a compact structure and stable performance, and can stably execute the particle breakage simulation method based on a KAN neural network of this invention, further improving the overall applicability and practical application capability of this invention.

[0061] In this embodiment, the processor may be a central processing unit, but it can also be other general-purpose processors, digital signal processors, application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (OPGs), other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor. Input devices can be used to acquire data. Output devices can be used to output the results obtained by storing program instructions contained in a computer program in the memory provided by this invention. The memory may include read-only memory and random access memory (RAM), and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory (RAM).

[0062] In one possible implementation, the memory may include a stored program area and a stored data area. The stored program area may store the operating system and applications required for at least one function; the stored data area may store data created during use. Furthermore, the memory may include read-only memory and random access memory, and provides instructions and data to the processor. The memory stores the operating system and operating instructions, executable modules, or data structures, or subsets thereof, or extended sets thereof. The operating instructions may include various operation instructions for implementing various operations. The operating system may include various system programs for implementing various basic tasks and handling hardware-based tasks.

[0063] The embodiment also provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of the particle crushing simulation method based on the KAN neural network described above.

[0064] The storage medium can include various media that can store program code, such as USB flash drives, portable hard drives, read-only memory, random access memory, magnetic disks, or optical disks.

[0065] In summary, this invention, based on a KAN neural network-based particle breakage criterion, utilizes the property proven by the Kolmogorov-Arnold theorem that a multivariate continuous function can be expressed as a composite of a finite number of univariate continuous functions and binary addition operations. By introducing a learnable activation function, the flexibility and expressive power of the model are enhanced. It comprehensively considers the complex stress state of particles and the characteristic intensity forms in various existing traditional criteria, significantly improving the adaptability to complex loading conditions and effectively improving simulation accuracy. It can accurately simulate the breakage behavior of two-dimensional circular particles under complex stress states, and is suitable for particle breakage research and engineering applications in fields such as geotechnical engineering and powder technology.

[0066] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention, and they should all be covered within the scope of the present invention.

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.

2. The method of claim 1, wherein, 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; activating the adhesion between particles to bond all sub-particles into a whole by simulating that all sub-particles are in a balanced state through discrete element simulation; adjusting adhesion strength and adhesion 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.

3. 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.

4. The KAN neural network-based particle breakage simulation method according to claim 3, 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.

5. The method of claim 3, wherein the KAN neural network is trained using a training dataset comprising a plurality of training samples, each training sample comprising a plurality of input parameters and a corresponding output parameter. 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.

6. The KAN neural network-based particle breakage simulation method according to claim 3, 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, denotes a third characteristic intensity indicator, denotes a particle volume, denotes a total number of contacts of the particle under test, denotes a contact force, denotes a vector from the point of force application to the particle center.

7. The KAN neural network-based particle breakage simulation method according to claim 1, wherein, The method of 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.

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

9. The method of claim 1, wherein the KAN neural network-based particle breakage simulation method is characterized by, 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.

10. A KAN neural network-based particle breakage simulation system, characterized by, The particle breakage simulation system based on a 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, and the program instructions are used to execute the particle breakage simulation method based on a KAN neural network according to any one of claims 1-9.

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