Granular material hopper reverse optimization method combining graph neural network and discrete element method

Abstract

The invention discloses a particle material hopper reverse optimization method combining a graph neural network and a discrete element method, and the method comprises the steps: simulating and generating a data set through the discrete element method, training a graph neural network model, and employing a multi-component loss function optimization model containing data loss and semi-physical loss; the shape of the hopper is parameterized through a quadratic Bezier curve, the average particle speed serves as a discharging rate optimization target, and parameters are updated through an Adam optimizer; the particle density is introduced to control the mixing degree, and inverse design is achieved by setting the separation distance and the mixing coefficient. According to the method, the unloading efficiency and the particle mixing uniformity are remarkably improved, the adaptability and the calculation efficiency of the model are enhanced, an accurate and efficient particle material treatment solution is provided, and the method has a wide industrial application prospect.

Description

Technical Field

[0001] The present invention relates to the technical field of granular material processing, and particularly to a reverse optimization method for a granular material hopper that combines a graph neural network and the discrete element method. Background Art

[0002] In many industrial fields such as chemical engineering and pharmaceuticals, the flow characteristics of granular materials are crucial for the production process. As a key device for granular material processing, the design of the hopper directly affects product quality, production efficiency, and cost. Traditional hopper design methods mainly rely on empirical rules and simplified physical models. However, for complex or novel hopper geometries, these traditional methods often cannot accurately predict the granular flow behavior, resulting in design results that cannot meet the requirements of modern industry for efficient and precise control of granular motion.

[0003] With the development of computer simulation technology, the discrete element method (DEM) and the continuum model have become important tools for studying the behavior of granular materials. The discrete element method (DEM) can directly track the motion of particles and provide relatively accurate simulation results of granular flow. However, DEM has a high computational cost, especially when dealing with inverse problems and performing multiple iterative optimizations, its computational efficiency is low, so it is not suitable for the multiple optimization processes in hopper shape design. On the other hand, although the continuum model can capture some key features of hopper flow, it also faces problems such as high computational cost and low efficiency, and its application is limited in the optimization process of complex shapes.

[0004] In recent years, the application of machine learning technology in the field of fluid mechanics has received extensive attention, especially the graph neural network (GNN). GNN has demonstrated excellent capabilities in simulating granular dynamics, and can effectively handle data associations and pattern recognition in complex systems, thus providing new possibilities for the optimized design of hopper granular flow. However, existing GNN-based research mainly focuses on forward prediction models, and its application in reverse optimization design is still in the exploratory stage, and related methods and technologies still need to be further studied and improved. Summary of the Invention

[0005] Object of the Invention: Aiming at the problems existing in the prior art, the present invention provides a reverse optimization method for a granular material hopper that combines a graph neural network and the discrete element method. By combining the graph neural network and the reverse optimization strategy, the optimized design of the hopper shape and particle properties is realized, the discharging efficiency is improved, the degree of particle mixing is controlled, and a more efficient and precise solution is provided for the granular material processing process.

[0006] Technical Solution: The present invention provides a reverse optimization method for a granular material hopper that combines a graph neural network and the discrete element method, including the following steps:

[0007] S1. Data acquisition: Use the discrete element method to simulate and generate a hopper particle flow dataset containing particle flow information under different hopper shapes and different initial conditions. Divide the hopper particle flow dataset into a training set, a test set, and a validation set.

[0008] S2. Construction and optimization of the graph neural network framework model: Represent the granular material system as a graph structure, where nodes represent particles and edges represent the interactions between particles. Construct a graph neural network framework model containing an encoding module, a message passing module, and a decoding module and optimize it. Specifically: The encoding module is used to transform the state information of particles to form the node features of the graph. The message passing module updates the state of each node by aggregating the information of neighboring nodes. The decoding module maps the processed node features back to the output format. The optimized model with strong generalization ability can effectively predict the dynamic characteristics of particle flow under different working conditions.

[0009] S3. Optimal design of hopper shape: Parameterize the hopper shape using quadratic Bezier curves to clarify the relationship between the hopper geometric parameters and the curve control points. Set the maximization of the discharge rate as the optimization goal, where the discharge rate is defined by the average velocity of particles in a specific area of the hopper. Calculate the vertical velocity of particles in this area and find its average value. At the same time, optimize considering the constraints of particle stagnation or "bridging" phenomena.

[0010] The geometric parameters of the hopper include the inlet diameter, outlet diameter, height, etc. Parameterize the hopper to obtain the key parameters that can smoothly control the hopper shape. Calculate the gradient of this parameter through the reverse optimization framework and iteratively optimize this parameter until the preset goal is achieved.

[0011] S4. Control of particle mixing degree and property inference: In the graph neural network framework model constructed in S2, reintroduce the particle density property so that the graph neural network framework model can learn the influence of particle density on the mixing degree. Define the sum of the Euclidean distances between particles, and use the normalized separation distance obtained as the mixing coefficient to measure the particle mixing degree. According to the target mixing coefficient, use the trained graph neural network framework model for inverse design, predict the required particle density ratio, and guide the selection of particle properties in actual production based on this ratio. Among them, the closer the mixing coefficient is to 0, the more uniform the particle mixing is.

[0012] Furthermore, in S1, regard the hopper particle flow dataset as the motion state of the real granular fluid, and divide the dataset into a training set, a test set, and a validation set according to the ratio of 10:1:1. The training set is used to train the model, the test set is used to test the accuracy of the model, and the validation set is used to verify the performance of the model.

[0013] Furthermore, in the training data, the positions and quantities of the initial particles are randomly distributed and noise is added. This step is used to simulate the uncertainties in the real environment and enhance the robustness of the model.

[0014] Furthermore, in S2, the training set data is input into the graph neural network framework model for training. A multi-component loss function including data loss and semi-physical loss is adopted, and the model parameters are optimized through the backpropagation algorithm.

[0015] The expression of the data loss is:

[0016]

[0017] Where, and represent the true values, a i and x i represent the predicted acceleration and position vectors, and γ is the weight factor.

[0018] The calculation expression of the semi-physical loss is:

[0019]

[0020] Where, m i is the mass of the i-th particle, and λ is the weight factor.

[0021] In this step, the data loss is used to measure the difference between the prediction results and the true particle acceleration and position. The semi-physical loss is based on Newton's third law to constrain the total internal force of the system, enabling the model to capture the motion law of the particles without directly obtaining the internal force data. By minimizing the total value of the loss function, the model parameters are optimized to improve the prediction accuracy and the accuracy of the model.

[0022] Furthermore, in S3, the hopper shape is parameterized using a quadratic Bezier curve, and the formula is:

[0023]

[0024] Where, the parameters P 0 and P 2 are fixed, P 1 is the optimization parameter, determining the relationship between geometric parameters such as the inlet diameter, outlet diameter, and height and the curve control points, and taking the control point coordinates as the optimization parameters.

[0025] Furthermore, in S3, the Adam optimizer is used to perform reverse optimization on the target. By calculating the gradient of the optimization target, the parameters of the hopper shape are iteratively updated until the convergence condition is met.

[0026] Furthermore, in S4, the Euclidean distance formula is used to calculate the separation distance, specifically:

[0027]

[0028] where a and b represent two different particulate components, N a and N b represent the number of particles of the two components respectively, ||a i -b j || 2 represents the Euclidean distance between particle a i and particle b j , min j ||a i -b j || 2 represents the distance from particle a i to the nearest particle in component b, min i ||b j -a i || 2 represents the distance from particle b j to the nearest particle in component a. This step can effectively study the mixing of particles with different properties in the hopper, thereby precisely controlling the particle flow and mixing degree, and further improving the uniformity and processing efficiency of the particle material flow.

[0029] Advantages: The present invention generates a data set through DEM simulation, trains a graph neural network (GNN) model, and optimizes the model using a multi-component loss function including data loss and semi-physical loss; the hopper shape is parameterized by a quadratic Bezier curve, and the average particle velocity is used as the optimization target for the discharge rate, and the Adam optimizer is used to update the parameters; the particle density is introduced to control the mixing degree, and inverse design is achieved by setting the separation distance and mixing coefficient. Compared with the prior art, the specific advantages are as follows:

[0030] (1) By optimizing the hopper shape and controlling its discharge speed, the inclined wall of the hopper forms a smooth convex shape, significantly increasing the vertical average velocity of the particles during the discharging process, reducing the velocity loss caused by the collision of the particles with the wall surface, and thus improving the discharging efficiency. The experimental results show that the discharging efficiency of the optimized hopper can be increased by about 40%.

[0031] (2) The model of the present invention can accurately predict the required particle density ratio to achieve the mixing condition according to the set target mixing coefficient, thereby effectively guiding the selection of particle properties, ensuring the uniform mixing of particles with different properties in the hopper, and improving the stability of product quality.

[0032] (3) The model based on the Graph Neural Network (GNN) can adapt to different initial conditions and particle properties, has good generalization ability, and has excellent prediction performance for unseen data. This model can be widely applied to different particle material processing scenarios and provide flexible solutions for various industrial needs. For example, when processing two-component particles with different density ratios, although the density ratio randomly varies between 1:1 and 1:9, the model can still accurately predict the changes in the motion state of the particles.

[0033] (4) Compared with the traditional Discrete Element Method (DEM), although the method of the present invention requires a certain amount of time in the training stage (for example, it takes about 5 hours to complete 100,000 iterations of training), in practical applications, such as in the process of hopper shape optimization, its calculation efficiency is significantly improved. The GNN-based method only needs about 20 minutes to complete the optimization, while the genetic algorithm based on DEM requires 8 hours, and the calculation speed is increased by 24 times. This method can quickly solve complex particle material processing problems, reduce the calculation cost, and significantly improve the production efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a schematic diagram showing the particle state update process, including three modules: encoding, message passing, and decoding. V represents particles, E represents the connections between particles, and G represents the graph structure composed of V and E;

[0035] Figure 2 (a) is a schematic diagram of the hopper geometric structure; (b) illustrates that the hopper is parameterized as a quadratic Bezier curve;

[0036] Figure 3 It is a schematic diagram of the inverse design structure model based on GNS;

[0037] Figure 4 It shows the evolution process of the hopper shape from the initial conical shape to the final optimized shape;

[0038] Figure 5 It is to compare the changes in the velocity field before and after optimization;

[0039] Figure 6 (a) Hopper dimensions (cm) before optimization, bridging phenomenon occurs for aluminum and acrylic particles; (b) Hopper dimensions (cm) after optimization, calculate the average velocity of the marked particles;

[0040] Figure 7 (a) shows the average error distribution of the optimization results relative to the DEM method at different slope angles, (b) shows the change in MSE of the model at different training iteration times, and the error bars represent the standard deviation;

[0041] Figure 8Parameter inversion process of particle density ratio when the initial density ratio is 1:9 and the target mixing coefficient is 0.2 (ρ1:ρ2 = blue particles: orange particles);

[0042] Figure 9 For the experimental verification of property inversion, (a) represents the real experiment, (b) represents the DEM simulation, and (c) represents the model prediction;

[0043] Figure 10 Flow chart of the particle material hopper reverse optimization method combining graph neural network and discrete element method of the present invention. Detailed implementation manners

[0044] The present invention will be further described below in conjunction with the accompanying drawings and detailed implementation manners.

[0045] Embodiment 1:

[0046] This embodiment provides a particle material hopper reverse optimization method combining graph neural network and discrete element method, specifically as follows:

[0047] 1. Data preparation: Use DEM simulation to generate hopper particle flow data. Set the initial slope angle of the hopper to 40°, and randomly initialize parameters such as particle density, quantity, and friction coefficient. A total of 350 working conditions are generated. Divide the data set into a training set, a test set, and a validation set according to 10:1:1. Randomly distribute the initial positions and quantities of particles in the training data, and add noise to simulate real-world uncertainties.

[0048] 2. Model training and optimization: As Figure 1 shown, construct a GNS model. This graph neural network architecture is divided into three main parts: input state (X 0 to X n ), graph neural network (GNS(d θ ), and feature vector processing (including encoding, message passing, and decoding). In the encoding stage, the input particle material state is converted into a feature vector where G represents the graph structure composed of particles, containing information about the particles themselves and the interactions between particles; in the message passing stage, node features and edge features are updated, and the node features contain information about the interactions between particles; in the decoding stage, the updated feature vector is converted back into the physical state of the particle material. Use this network framework to input the training set data for training, adopt a multi-component loss function including data loss and semi-physical loss, and optimize the model parameters through the backpropagation algorithm. The expression of the loss function is:

[0049]

[0050] where and represents the true value, a i and x i represent the predicted acceleration and position vectors, γ is the weight factor, and is determined to be optimal at 0.6 in the experiment; the calculation expression of the semi-physical loss is:

[0051]

[0052] where m i is the mass of the i-th particle, and λ is the weight factor.

[0053] 3. Hopper shape parameterization: As Figure 2 shown, use a quadratic Bézier curve to parameterize the hopper shape, and the formula is:

[0054]

[0055] where the parameters P 0 and P 2 are fixed, P 1 is the optimization parameter. Determine the relationship between geometric parameters such as the inlet diameter, outlet diameter, and height and the curve control points, and use the control point coordinates as the optimization parameters. Set the optimization goal to maximize the discharge rate, and calculate the average velocity of the particles in a specific area of the hopper as the measure of the discharge rate.

[0056] 4. Shape optimization: Its optimization framework is as Figure 3 shown. First, define the initial positions of the particles and the initial shape of the hopper, and set the initial parameters. Select the particles in the target area, calculate their vertical velocities and take the average. Load the trained model and perform forward propagation calculations to obtain preliminary results. Calculate the gradient through the gradient function and update the parameters to optimize the velocity distribution. At the same time, add a penalty term to constrain the hopper shape to prevent unreasonable shapes such as concave shapes. Iteratively update the hopper shape parameters, calculate the gradient according to the optimization goal, and use the Adam optimizer to adjust the parameters until the discharge rate reaches the optimum or meets the convergence condition.

[0057] 5. Result verification and analysis: Figure 4 shows the iterative optimization process of the hopper, Figure 5 shows the change in the particle velocity field before and after optimization. Conduct experimental verification on the optimized hopper shape as Figure 6 shown. Conduct discharge experiments using particles of different materials (such as steel balls, aluminum balls, acrylic balls), and record the average discharge velocities of the particles of different materials in the hopper. The experimental results are shown in Table 1.

[0058] Table 1 Comparison of velocities before and after optimization

[0059]

[0060] Note: In the table, "bridging phenomenon" occurred in the hoppers made of aluminum and acrylic materials before optimization, and normal discharging was impossible. As shown in Figure 6 (a), normal discharging can be achieved in the optimized hopper.

[0061] By comparing the discharging efficiency of the hopper before and after optimization, the consistency between the experimental results and the model prediction was analyzed. It was observed that the shape of the hopper after optimization changed from the initial straight inclination to a more curved form, significantly reducing the pressure of the particles on the wall surface and improving the discharging efficiency. The experimental results were consistent with the model prediction, verifying the effectiveness of the method. Figure 7 (a) shows the average error of the optimization results relative to the DEM method at different slope angles, and (b) shows the change of MSE of the model at different training iteration times. The error bars represent the standard deviation.

[0062] Embodiment 2:

[0063] This embodiment provides an inversion of the properties of different component particles in a granular material hopper by combining a graph neural network and the discrete element method, specifically as follows:

[0064] 1. Data generation and preprocessing: For the case of binary particle mixing, a dataset was generated by DEM simulation. The particle density ratio (varying from 1:1 to 1:9), quantity, and other relevant parameters were randomly initialized to ensure data diversity. The training set, test set, and validation set were also divided in the same way. The particle density attribute was added to the nodes of the graph structure to enable the GNN model to learn the influence of density on particle flow.

[0065] 2. Model training and calculation of mixing coefficient: The GNN model was trained using the processed dataset. The training process was similar to that of Embodiment 1, and the multi-component loss function was used to optimize the model parameters. The separation distance was defined to measure the degree of particle mixing. The Euclidean distance between different component particles was calculated based on the particle positions, and the separation distance was calculated according to the formula and normalized to obtain the mixing coefficient to quantify the uniformity of particle mixing. The Euclidean distance formula for calculating the separation distance is specifically:

[0066]

[0067] where a and b represent two different particle components, N a and N b represent the particle quantities of the two components respectively, ||a i -b j || 2 represents the Euclidean distance between particle a i and particle b j , and min j ||a i -bj || 2 Represents the distance, in min, from particle a i to the nearest particle in component b i ||b j -a j || 2 Represents the distance from particle b j to the nearest particle in component a.

[0068] 3. Property inversion: Set the target mixing coefficient, e.g., 0.2, and use the trained GNN model for inverse design. Iteratively predict the required particle density ratio, and the process is as Figure 8 shown. As Figure 9 shown in the real experiment for comparing the effectiveness of the verification method, perform mixing experiments using particles of different materials (such as steel, aluminum, glass, acrylic). Adopt the optimized hopper shape to ensure the smooth flow of particles without Figure 6 the "bridging" phenomenon shown in (a). Compare the experimental results, DEM simulation results, and model prediction results to verify the accuracy of the model in particle property inference and mixing control. The experimental results show that the model can effectively guide the selection of the appropriate particle density ratio to achieve the target mixing degree, which is consistent with the model prediction, proving the feasibility of the method in practical applications.

[0069] In summary, the particle material hopper reverse optimization method combining graph neural network and discrete element method of the present invention exhibits good performance in hopper shape optimization and particle mixing control, effectively improving the unloading efficiency, controlling the particle discharge speed and the mixing degree, providing reliable technical support for particle material processing, and can be widely applied to related industrial fields such as chemical industry and pharmaceuticals.

[0070] The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose is to enable those familiar with this technology to understand the content of the present invention and implement it accordingly, and shall not be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit and essence of the present invention shall be covered within the protection scope of the present invention.

Claims

1. A method for reverse optimization of a granular material hopper combining graph neural network and discrete unit method, characterized in that: The following steps are involved: S1. Data acquisition: using the discrete element method to simulate and generate a hopper particle flow data set containing particle flow information under different hopper shapes and different initial conditions, and dividing the hopper particle flow data set into a training set, a test set, and a validation set; S2. Construction and optimization of graph neural network framework model: The particle material system is represented as a graph structure, where nodes represent particles and edges represent interactions between particles; a graph neural network framework model including an encoding module, a message passing module, and a decoding module is constructed and optimized, where: the encoding module is used to convert the state information of the particles to form the node features of the graph; The message passing module updates the state of each node by aggregating the information of neighboring nodes; the decoding module maps the processed node features back to the output format; S3. Hopper shape optimization design: Use quadratic Bezier curves to parameterize the hopper shape and clarify the relationship between the hopper geometric parameters and the curve control points; set the maximization of the discharge rate as the optimization goal, where the discharge rate is defined by the average velocity of the particles in a specific area of ​​the hopper, calculate the vertical velocity of the particles in the area and find its average value, and consider the constraints of particle stagnation or "bridging" phenomenon for optimization; S4. Particle mixing degree control and attribute inference: In the graph neural network framework model constructed in S2, the particle density attribute is reintroduced so that the graph neural network framework model can learn the influence of particle density on the mixing degree: define the sum of the Euclidean distances between particles, and use the separation distance calculated by normalization as the mixing coefficient to measure the particle mixing degree; according to the target mixing coefficient, use the trained graph neural network framework model for reverse design to predict the required particle density ratio, and use this ratio to guide the selection of particle attributes in actual production.

2. The inverse optimization method for a granular material hopper combining a graph neural network and a discrete unit method according to claim 1 is characterized in that: In S1, the hopper particle flow dataset is used as the motion state of the real particle fluid, and the dataset is divided into a training set, a test set and a validation set in a ratio of 10:1:1, wherein the training set is used to train the model, the test set is used to test the accuracy of the model, and the validation set is used to verify the performance of the model.

3. The particle material hopper reverse optimization method combining graph neural network and discrete unit method according to claim 2 is characterized in that: In the training data, the positions and numbers of initial particles are randomly distributed, and noise is added.

4. The particle material hopper reverse optimization method combining graph neural network and discrete unit method according to claim 1 is characterized in that: In S2, the training set data is input into the graph neural network framework model for training, a multi-component loss function including data loss and semi-physical loss is used, and the model parameters are optimized through a back propagation algorithm; The expression of the data loss is: in, and represents the true value, a i and x i represents the predicted acceleration and position vector, and γ is the weight factor; The calculation expression of the semi-physical loss is: Among them, m i is the mass of the ith particle, and λ is the weight factor.

5. The inverse optimization method for a granular material hopper combining a graph neural network and a discrete unit method according to claim 1, characterized in that: In S3, the hopper shape is parameterized using a quadratic Bezier curve, and the formula is: Among them, parameters P0 and P2 are fixed, P1 is the optimization parameter, and the relationship between geometric parameters such as inlet diameter, outlet diameter and height and the curve control points is determined, and the coordinates of the control points are used as optimization parameters.

6. The particle material hopper reverse optimization method combining graph neural network and discrete unit method according to claim 1, characterized in that: In S3, the Adam optimizer is used to perform reverse optimization on the target. By calculating the gradient of the optimization target, the parameters of the hopper shape are iteratively updated until the convergence conditions are met.

7. The inverse optimization method for a granular material hopper combining a graph neural network and a discrete unit method according to claim 1, characterized in that: In S4, the Euclidean distance formula is used to calculate the separation distance, specifically: Among them, a and b represent two different particle components, N a and N b Respectively represent the number of particles of the two components, ||a i -b j ||2 indicates particle a i With particles b j The Euclidean distance between j ||a i -b j ||2 indicates particle a i Distance to the nearest particle in component b, min i ||b j -a i ||2 indicates particle b j The distance to the nearest particle in component a.

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