Electromagnetic tomography reconstruction method and system based on graph convolutional neural network

Abstract

The present application relates to a method and system for electromagnetic tomography reconstruction based on graph convolutional neural network, the method comprising: carrying out grid division on the to-be-measured region of the target image, obtaining a plurality of grid units and constructing a topological graph; constructing an electromagnetic characteristic unit based on the nodes and edges in the topological graph, calculating the conductivity distribution and the corresponding current density distribution of the electromagnetic characteristic unit, and obtaining the node features in the topological graph; constructing the node features into a node feature matrix and inputting the node feature matrix into a pre-trained graph convolutional neural network model to output a feature map; counting the distribution of feature values in the feature map, combining the concentration degree and the change range of the electromagnetic characteristics in different regions, obtaining the mixing state of the multiphase flow in the stirring process, and completing the electromagnetic tomography reconstruction of the target image. The present application effectively mines the complex relationship of non-euclidean data in the to-be-measured region, and provides strong support for state monitoring, flow behavior analysis and process optimization in the mixing and stirring process of multiphase flow.

Description

Technical Field

[0001] This invention relates to the field of electrical tomography technology, and in particular to an electromagnetic tomography reconstruction method and system based on graph convolutional neural networks. Background Technology

[0002] Electromagnetic tomography (EMT), as a non-invasive method for detecting multiphase flows, has shown great potential in monitoring multiphase flows in metallurgical processes due to its advantages such as fast response speed and no interference with the measured medium. Based on the principle of electromagnetic induction, it collects electromagnetic property information of the multiphase flow medium by arranging sensors around the measured area, and then reconstructs an image of the internal multiphase flow distribution. However, traditional EMT image reconstruction algorithms have many limitations and cannot meet the complex and variable multiphase flow detection requirements of metallurgical processes. When facing harsh environments such as high temperatures and strong electromagnetic interference in metallurgical processes, existing algorithms have low imaging accuracy, resulting in an inability to clearly present the actual state of the multiphase flow. When detecting multiphase flows, it is difficult to accurately distinguish the distribution and flow characteristics of each phase, thus affecting the effective control of the metallurgical process. This not only increases production costs but may also lead to unstable product quality. Therefore, developing high-precision EMT reconstruction algorithms has become an urgent need to promote the intelligent and efficient development of metallurgical processes. Summary of the Invention

[0003] The purpose of this invention is to provide an electromagnetic tomography reconstruction method and system based on graph convolutional neural networks, which can perform continuous, non-invasive, and real-time imaging detection of metallurgical multiphase flow processes, effectively uncover complex relationships in non-Euclidean data, improve the accuracy of electromagnetic tomography, and accurately monitor the mixing state of multiphase flow.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] Electromagnetic tomography reconstruction methods based on graph convolutional neural networks include:

[0006] The target image is divided into grids to obtain several grid cells and a topology map is constructed.

[0007] Electromagnetic property units are constructed based on the nodes and edges in the topology graph. The conductivity distribution and corresponding current density distribution of the electromagnetic property units are calculated to obtain the node characteristics in the topology graph.

[0008] The node features are constructed into a node feature matrix and input into a pre-trained graph convolutional neural network model to output a feature map;

[0009] The distribution of feature values ​​in the feature map is statistically analyzed, and the concentration and variation range of electromagnetic properties in different regions are combined to obtain the mixing state of the multiphase flow during the stirring process, thus completing the electromagnetic tomography reconstruction of the target image.

[0010] Optionally, the test region of the target image is divided into grids to obtain several grid cells and construct a topology map, including:

[0011] The target image is divided into grids by a hybrid grid method to obtain several grid cells. The hybrid grid method uses a dense structured network, and the parameters of the dense structured network are adaptively adjusted according to the different shapes and sizes of the target image.

[0012] The topology graph is constructed by recording the geometric information and connection relationships of each grid cell through discretization.

[0013] Optionally, electromagnetic property units are constructed based on the nodes and edges in the topology graph, and the conductivity distribution and corresponding current density distribution of the electromagnetic property units are calculated to obtain the node characteristics in the topology graph, including:

[0014] The electromagnetic property unit is constructed based on the edges constructed from the feature nodes and feature point descriptors in the topology graph. During the construction process, the differences in electromagnetic properties of different media are considered, and a weighted average method is used to fuse the electromagnetic properties of adjacent nodes.

[0015] The conductivity distribution of each electromagnetic property unit is calculated by numerical analysis, and the corresponding current density distribution is calculated by combining the conductivity distribution with Maxwell's equations to obtain the characteristics of each node in the topology graph.

[0016] Optionally, the electromagnetic coupling effect between adjacent electromagnetic property units is also considered during the construction process, and the coupling coefficient is incorporated into the calculation of the conductivity distribution. The coupling coefficient is:

[0017]

[0018] Where k is the coupling coefficient, x1∈[x 1a x 1b ],y1∈[y 1a y 1b ],z1∈[z 1a , z 1b ] represents the region of the first unit volume; x2∈[x 2a x 2b ],y2∈[y 2a y 2b ],z2∈[z 2a , z 2b] represents the region of the second unit volume; μ0 is the magnetic permeability.

[0019] Optionally, the node features are constructed into a node feature matrix and input into a pre-trained graph convolutional neural network model to output a feature map, including:

[0020] The node features are filtered and sorted to construct a node feature matrix;

[0021] The node feature matrix is ​​input into the graph convolutional neural network model, and the features between non-Euclidean distances in the region to be tested are extracted through convolutional layers to obtain feature information and output feature maps. The graph convolutional neural network model adopts a residual connection structure, which is constructed by adding skip connections between the convolutional layers. The graph convolutional neural network model is trained using an electromagnetic tomography dataset.

[0022] Optionally, before inputting the node feature matrix into the graph convolutional neural network model, the node feature matrix is ​​further normalized so that each feature dimension in the node feature matrix has the same scale.

[0023] Optionally, constructing the electromagnetic tomography dataset includes:

[0024] The test region of the sample image is discretized, and the boundary conditions between the excitation source and the sensor are defined. The conductivity distribution of the sample is then calculated.

[0025] And the sample current density distribution corresponding to the sample conductivity distribution;

[0026] The sample conductivity distribution and the corresponding sample current density distribution are input into the electromagnetic tomography forward problem model. By solving Maxwell's equations and discretizing the sample conductivity distribution into pixel values ​​to generate sample image grayscale values, an electromagnetic tomography dataset containing conductivity distribution and current density is constructed.

[0027] Optionally, statistically analyzing the distribution of feature values ​​in the feature map includes:

[0028] The DBSCAN clustering algorithm is used to classify the feature values ​​in the feature map by setting the neighborhood radius and the minimum number of samples. The probability density estimation method is then used to calculate the probability distribution of the feature values ​​in different intervals, as well as the boundaries and ranges of different electromagnetic property regions, based on the classification results.

[0029] The present invention also provides an electromagnetic tomography reconstruction system based on graph convolutional neural networks, comprising:

[0030] The module is used to divide the test area of ​​the target image into grids, obtain several grid cells, and construct a topology graph.

[0031] The calculation module is used to construct electromagnetic property units based on the nodes and edges in the topology graph, calculate the conductivity distribution and corresponding current density distribution of the electromagnetic property units, and obtain the node features in the topology graph.

[0032] The reconstruction module is used to construct the node features into a node feature matrix and input it into a pre-trained graph convolutional neural network model to output a feature map.

[0033] The analysis module is used to statistically analyze the distribution of feature values ​​in the feature map and, in conjunction with the concentration and variation range of electromagnetic properties in different regions, obtain the mixing state of the multiphase flow during the stirring process.

[0034] Optionally, the system further includes a training module for constructing an electromagnetic tomography dataset and training a graph convolutional neural network model using the electromagnetic tomography dataset, wherein the electromagnetic tomography dataset includes:

[0035] The test area of ​​the sample image is discretized, and the boundary conditions between the excitation source and the sensor are defined. The sample conductivity distribution and the sample current density distribution corresponding to the sample conductivity distribution are calculated.

[0036] The sample conductivity distribution and the corresponding sample current density distribution are input into the electromagnetic tomography forward problem model. By solving Maxwell's equations and discretizing the sample conductivity distribution into pixel values ​​to generate sample image grayscale values, an electromagnetic tomography dataset containing conductivity distribution and current density is constructed.

[0037] The beneficial effects of this invention are as follows:

[0038] (1) The electromagnetic tomography reconstruction method and system based on graph convolutional neural network proposed in this invention can perform intelligent imaging and non-invasive online monitoring of multiphase flow in metallurgical process, and can intuitively display the mixing state of multiphase flow in molten pool.

[0039] (2) The electromagnetic tomography reconstruction method and system based on graph convolutional neural network proposed in this invention can mine the features between non-Euclidean data in the area to be tested, and can more accurately reconstruct the multiphase flow distribution image and clearly present the actual state of multiphase flow.

[0040] (3) The electromagnetic tomography reconstruction method and system based on graph convolutional neural network proposed in this invention can be applied to the fields of multiphase flow in metallurgical processes, oil, natural gas and chemical pipeline transportation. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a flowchart of the electromagnetic tomography reconstruction method based on graph convolutional neural networks according to an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of the electromagnetic tomography reconstruction system based on graph convolutional neural networks according to an embodiment of the present invention. Detailed Implementation

[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0045] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] This embodiment provides an electromagnetic tomography reconstruction method based on graph convolutional neural networks, such as... Figure 1 As shown, it includes:

[0047] The target image is divided into grids to obtain several grid cells and a topology map is constructed.

[0048] Electromagnetic property units are constructed based on the nodes and edges in the topology graph. The conductivity distribution and corresponding current density distribution of the electromagnetic property units are calculated to obtain the node characteristics in the topology graph.

[0049] The node features are constructed into a node feature matrix and input into a pre-trained graph convolutional neural network model to output a feature map;

[0050] The distribution of feature values ​​in the feature map is statistically analyzed, and the concentration and variation range of electromagnetic properties in different regions are combined to obtain the mixing state of the multiphase flow during the stirring process, thus completing the electromagnetic tomography reconstruction of the target image.

[0051] Specifically, this embodiment can perform intelligent imaging and non-invasive online monitoring of multiphase flow in metallurgical processes, and can intuitively display the mixing state of multiphase flow in the molten pool; it can mine the characteristics between non-Euclidean data in the area to be measured, and can more accurately reconstruct the multiphase flow distribution image, clearly presenting the actual state of multiphase flow; it can be applied to multiphase flow in metallurgical processes, pipeline transportation in oil, natural gas, and chemical industries.

[0052] Further, the test region of the target image is divided into grids to obtain several grid cells and construct a topology map, including:

[0053] The target image is divided into grids by a hybrid grid method to obtain several grid cells. The hybrid grid method uses a dense structured network, and the parameters of the dense structured network are adaptively adjusted according to the different shapes and sizes of the target image.

[0054] The topology graph is constructed by recording the geometric information and connection relationships of each grid cell through discretization.

[0055] Specifically, this embodiment uses a hybrid mesh method to divide the test area of ​​the target image into meshes. A dense structured network is employed to divide the continuous fluid region into small units while maintaining boundary layer resolution. The geometric information and connectivity of each unit are recorded through discretization to construct a topological graph. During mesh division, the parameters of the dense structured network are adaptively adjusted for test areas of different shapes and sizes.

[0056] Furthermore, based on the nodes and edges in the topology graph, electromagnetic characteristic units are constructed, and the conductivity distribution and corresponding current density distribution of the electromagnetic characteristic units are calculated to obtain the node characteristics in the topology graph, including:

[0057] The electromagnetic property unit is constructed based on the edges constructed from the feature nodes and feature point descriptors in the topology graph. During the construction process, the differences in electromagnetic properties of different media are considered, and a weighted average method is used to fuse the electromagnetic properties of adjacent nodes.

[0058] The conductivity distribution of each electromagnetic property unit is calculated by numerical analysis, and the corresponding current density distribution is calculated by combining the conductivity distribution with Maxwell's equations to obtain the characteristics of each node in the topology graph.

[0059] Specifically, this embodiment constructs electromagnetic characteristic units based on the edges built from feature nodes and feature point descriptors in the topology graph. During the construction process, the differences in electromagnetic properties of different media are comprehensively considered, and a weighted average method is used to fuse the electromagnetic properties of adjacent nodes, making the constructed electromagnetic characteristic units more accurately reflect the actual situation. The conductivity distribution of each electromagnetic characteristic unit is calculated using numerical analysis. Based on the conductivity distribution and combined with Maxwell's equations, the corresponding current density distribution is calculated to obtain the characteristics of each node in the topology graph.

[0060] When constructing electromagnetic property units, the electromagnetic coupling effect between adjacent electromagnetic property units is considered. By modifying the calculation model to incorporate the coupling coefficient, the conductivity distribution can be calculated more accurately. It is assumed that the region of the first unit volume is: x1∈[x 1a x 1b ],y1∈[y 1a y 1b ],z1∈[z 1a , z 1b The region of the second unit volume is x2∈[x 2a x 2b ],y2∈[y 2a y 2b ],z2∈[z 2a , z 2b The coupling coefficient is calculated as follows:

[0061]

[0062] Furthermore, the node features are constructed into a node feature matrix and input into a pre-trained graph convolutional neural network model to output a feature map, including:

[0063] The node features are filtered and sorted to construct a node feature matrix;

[0064] The node feature matrix is ​​input into the graph convolutional neural network model, and the features between non-Euclidean distances in the region to be tested are extracted through convolutional layers to obtain feature information and output feature maps. The graph convolutional neural network model adopts a residual connection structure, which is constructed by adding skip connections between the convolutional layers. The graph convolutional neural network model is trained using an electromagnetic tomography dataset.

[0065] Before inputting the node feature matrix into the graph convolutional neural network model, the node feature matrix is ​​normalized so that each feature dimension in the node feature matrix has the same scale.

[0066] Constructing the electromagnetic tomography dataset includes:

[0067] The test area of ​​the sample image is discretized, and the boundary conditions between the excitation source and the sensor are defined. The sample conductivity distribution and the sample current density distribution corresponding to the sample conductivity distribution are calculated.

[0068] The sample conductivity distribution and the corresponding sample current density distribution are input into the electromagnetic tomography forward problem model. By solving Maxwell's equations and discretizing the sample conductivity distribution into pixel values ​​to generate sample image grayscale values, an electromagnetic tomography dataset containing conductivity distribution and current density is constructed.

[0069] Specifically, in this embodiment, the node feature matrix of the topology graph is calculated based on the features of each node in the topology graph. Before calculating the node feature matrix, the node features are filtered and sorted to remove redundant and interfering features, retain key features, and improve computational efficiency and model performance. The node feature matrix is ​​input into a preset graph convolutional neural network model. The convolutional layers of the preset graph convolutional neural network model extract features between non-Euclidean distances in the region under test to obtain feature information and output feature map.

[0070] The pre-defined graph convolutional neural network model employs a residual connection structure, adding skip connections between convolutional layers to alleviate the vanishing gradient problem and enhance the model's ability to learn complex features. The specific structure is as follows:

[0071] y = F(x) + x;

[0072] Where: x is the input, F(x) is the convolutional layer transformation, and y is the output.

[0073] Before inputting the node feature matrix into the preset graph convolutional neural network model, the node feature matrix is ​​normalized to ensure that each feature dimension has the same scale, thereby improving the stability and convergence speed of model training.

[0074]

[0075] Where: X norm The original node feature matrix, μ x σ is the mean. x The standard deviation is denoted as .

[0076] The construction of the electromagnetic tomography dataset includes:

[0077] (1) The region is discretized using the hybrid mesh method, and the unknown boundary conditions between the excitation source and the sensor are defined. When defining the boundary conditions, the interference factors in the actual measurement environment are fully considered, and the virtual boundary method or adaptive boundary condition setting method is adopted to improve the accuracy of the boundary conditions. The conductivity distribution of each electromagnetic property unit in the sample to be measured region is calculated to obtain the conductivity distribution of the sample;

[0078] (2) The sample current density distribution and sample sensitivity corresponding to the sample conductivity distribution are calculated using numerical analysis. During the calculation process, numerical methods such as the finite element method or finite difference method are employed, combined with iterative optimization algorithms, to improve the accuracy and stability of the calculation results.

[0079] (3) Input the sample conductivity distribution and the corresponding sample current density distribution into the electromagnetic tomography forward problem model, solve Maxwell's equations, and discretize the sample conductivity distribution into pixel values ​​to generate sample image gray values, and construct an electromagnetic tomography dataset containing conductivity distribution-current density.

[0080] Specifically, the electromagnetic tomography (EMT) dataset is obtained by calculating the sample area to be tested using the forward problem model. This dataset includes pairs of "conductivity distribution - current density" based on the sample conductivity distribution and corresponding current density distribution of the sample area to be tested. During dataset construction, different types of sample data can be classified and labeled to facilitate subsequent model training and feature analysis.

[0081] The sample conductivity distribution is discretized into pixel values ​​to generate sample image grayscale values. These grayscale values ​​are then reconstructed by inputting the electromagnetic tomography dataset into an initial convolutional neural network model to obtain the predicted image grayscale values. Furthermore, preprocessing is performed on the input sample current density distribution to improve data quality and the model's generalization ability.

[0082] When the data dimension of the sample current density is smaller than that of the output data, the data dimension is expanded. Methods such as interpolation or Generative Adversarial Networks (GANs) are used to expand the data dimension. During the expansion process, the characteristics and distribution of the data are kept unchanged to ensure the quality of the expanded data.

[0083] Furthermore, the distribution of feature values ​​in the feature map is statistically analyzed, including:

[0084] The DBSCAN clustering algorithm is used to classify the feature values ​​in the feature map by setting the neighborhood radius and the minimum number of samples. The probability density estimation method is then used to calculate the probability distribution of the feature values ​​in different intervals, as well as the boundaries and ranges of different electromagnetic property regions, based on the classification results.

[0085] Specifically, this embodiment statistically analyzes the distribution of different feature values ​​in the feature graph, uses the probability density estimation method to accurately calculate the probability distribution of feature values ​​in different intervals, and obtains the mixing state of multiphase flow during the stirring process by combining the concentration and variation range of electromagnetic properties in different regions with fuzzy logic algorithm.

[0086] The DBSCAN clustering algorithm is employed to classify feature values ​​and determine the boundaries and ranges of regions with different electromagnetic properties by setting the neighborhood radius ∈ and the minimum number of samples MinPts. An adaptive adjustment strategy is used when setting the neighborhood radius and the minimum number of samples, dynamically determining the optimal parameters based on the density and distribution characteristics of the dataset to improve the clustering effect.

[0087] This embodiment also provides an electromagnetic tomography reconstruction system based on graph convolutional neural networks, such as... Figure 2 As shown, it includes:

[0088] The module is used to divide the test area of ​​the target image into grids, obtain several grid cells, and construct a topology graph.

[0089] The calculation module is used to construct electromagnetic property units based on the nodes and edges in the topology graph, calculate the conductivity distribution and corresponding current density distribution of the electromagnetic property units, and obtain the node features in the topology graph.

[0090] The reconstruction module is used to construct the node features into a node feature matrix and input it into a pre-trained graph convolutional neural network model to output a feature map.

[0091] The analysis module is used to statistically analyze the distribution of feature values ​​in the feature map and, in conjunction with the concentration and variation range of electromagnetic properties in different regions, obtain the mixing state of the multiphase flow during the stirring process.

[0092] Specifically, the construction module is used to partition each node in the target image's test region using a hybrid mesh method, construct edges based on feature nodes and feature point descriptors in the topology graph, and build a topology graph based on the connections between each node and edge. The construction module has the function of automatically detecting the shape and size of the test region, and intelligently selecting the optimal mesh partitioning strategy and parameters based on the detection results.

[0093] The calculation module is specifically used to construct pixel units based on each node in the topology graph and its two corresponding neighboring nodes. It calculates the dielectric constant distribution of each pixel unit using numerical analysis, and then calculates the corresponding conductivity based on the dielectric constant distribution, thus obtaining the characteristics of each node in the topology graph. The calculation module employs parallel computing technology to improve computational efficiency, and also has error detection and correction functions to ensure the accuracy of the calculation results.

[0094] The reconstruction module is specifically used to construct electromagnetic property units based on the edges constructed from the feature nodes and feature point descriptors in the topology graph, calculate the conductivity distribution of each electromagnetic property unit, calculate the corresponding current density based on the conductivity distribution, and obtain the features of each node in the topology graph; obtain the node feature matrix based on each feature vector, and input the node feature matrix into the graph convolutional neural network to obtain the output feature map.

[0095] The analysis module is specifically used to statistically analyze the distribution of different feature values ​​in the feature map. It uses probability density estimation methods to accurately calculate the probability distribution of feature values ​​in different intervals. Based on the concentration and variation range of electromagnetic properties in different regions, and combined with fuzzy logic algorithms, it obtains the mixing state of multiphase flow during the stirring process.

[0096] The electromagnetic tomography reconstruction system based on graph convolutional neural networks provided in this embodiment further includes a training module. The training module is used to construct an electromagnetic tomography dataset and train a graph convolutional neural network model using the electromagnetic tomography dataset. Constructing the electromagnetic tomography dataset includes:

[0097] The test area of ​​the sample image is discretized, and the boundary conditions between the excitation source and the sensor are defined. The sample conductivity distribution and the sample current density distribution corresponding to the sample conductivity distribution are calculated.

[0098] The sample conductivity distribution and the corresponding sample current density distribution are input into the electromagnetic tomography forward problem model. By solving Maxwell's equations and discretizing the sample conductivity distribution into pixel values ​​to generate sample image grayscale values, an electromagnetic tomography dataset containing conductivity distribution and current density is constructed.

[0099] The training module is specifically used to randomly generate a large number of diverse sample test regions using Monte Carlo simulation based on different flow patterns and corresponding descriptive parameters, thereby increasing the richness of the dataset. The generated sample test regions are preprocessed, including outlier removal and standardization, to ensure the data quality input into the electromagnetic tomography forward problem model. The training module has an intelligent function to evaluate the quality of the generated samples, automatically adjusting the parameters of the Monte Carlo simulation based on the diversity of the samples and their matching degree with the actual situation, thus generating higher-quality samples.

[0100] The training module also calculates the dielectric constant distribution of each pixel unit in the sample's test region using the finite difference method, and calculates the corresponding sample conductivity distribution. Then, it calculates the sample current density distribution and sample sensitivity corresponding to the sample conductivity distribution using numerical analysis. The sample conductivity distribution and the corresponding sample current density distribution are input into the electromagnetic tomography forward problem model. By solving Maxwell's equations and discretizing the sample conductivity distribution into pixel values ​​to generate sample image grayscale values, an electromagnetic tomography dataset containing conductivity distribution and current density is constructed. During the calculation process, the training module employs a high-precision numerical calculation library to improve calculation accuracy, and the calculation results are verified multiple times to ensure the reliability of the model.

[0101] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. An electromagnetic tomography reconstruction method based on graph convolutional neural networks, characterized in that, include: The target image is divided into grids to obtain several grid cells and a topology map is constructed. Electromagnetic property units are constructed based on the nodes and edges in the topology graph. The conductivity distribution and corresponding current density distribution of the electromagnetic property units are calculated to obtain the node characteristics in the topology graph. Electromagnetic property units are constructed based on the nodes and edges in the topology graph. The conductivity distribution and corresponding current density distribution of the electromagnetic property units are calculated to obtain the node characteristics in the topology graph, including: The electromagnetic property unit is constructed based on the edges constructed from the feature nodes and feature point descriptors in the topology graph. During the construction process, the differences in electromagnetic properties of different media are considered, and a weighted average method is used to fuse the electromagnetic properties of adjacent nodes. The conductivity distribution of each electromagnetic property unit is calculated by numerical analysis, and the corresponding current density distribution is calculated by combining the conductivity distribution with Maxwell's equations to obtain the characteristics of each node in the topology graph. The electromagnetic coupling effect between adjacent electromagnetic property units is also considered during the construction process, and the coupling coefficient is incorporated into the calculation of conductivity distribution. The coupling coefficient is: ； in, The coupling coefficient is... , , , represents the region of the first unit volume; , , , which is the region of the second unit volume; Permeability; The node features are constructed into a node feature matrix and input into a pre-trained graph convolutional neural network model to output a feature map; The distribution of feature values ​​in the feature map is statistically analyzed, and the concentration and variation range of electromagnetic properties in different regions are combined to obtain the mixing state of the multiphase flow during the stirring process, thus completing the electromagnetic tomography reconstruction of the target image.

2. The electromagnetic tomography reconstruction method based on graph convolutional neural networks according to claim 1, characterized in that, The target image is divided into grids to obtain several grid cells and a topology map is constructed, including: The target image is divided into grids by a hybrid grid method to obtain several grid cells. The hybrid grid method uses a dense structured network, and the parameters of the dense structured network are adaptively adjusted according to the different shapes and sizes of the target image. The topology graph is constructed by recording the geometric information and connection relationships of each grid cell through discretization.

3. The electromagnetic tomography reconstruction method based on graph convolutional neural networks according to claim 1, characterized in that, The node features are constructed into a node feature matrix and input into a pre-trained graph convolutional neural network model to output a feature map, including: The node features are filtered and sorted to construct a node feature matrix; The node feature matrix is ​​input into the graph convolutional neural network model, and the features between non-Euclidean distances in the region to be tested are extracted through convolutional layers to obtain feature information and output feature maps. The graph convolutional neural network model adopts a residual connection structure, which is constructed by adding skip connections between the convolutional layers. The graph convolutional neural network model is trained using an electromagnetic tomography dataset.

4. The electromagnetic tomography reconstruction method based on graph convolutional neural networks according to claim 3, characterized in that, Before inputting the node feature matrix into the graph convolutional neural network model, the node feature matrix is ​​normalized to ensure that each feature dimension in the node feature matrix has the same scale.

5. The electromagnetic tomography reconstruction method based on graph convolutional neural networks according to claim 3, characterized in that, Constructing the electromagnetic tomography dataset includes: The test area of ​​the sample image is discretized, and the boundary conditions between the excitation source and the sensor are defined. The sample conductivity distribution and the sample current density distribution corresponding to the sample conductivity distribution are calculated. The sample conductivity distribution and the corresponding sample current density distribution are input into the electromagnetic tomography forward problem model. By solving Maxwell's equations and discretizing the sample conductivity distribution into pixel values ​​to generate sample image grayscale values, an electromagnetic tomography dataset containing conductivity distribution and current density is constructed.

6. The electromagnetic tomography reconstruction method based on graph convolutional neural networks according to claim 1, characterized in that, The distribution of feature values ​​in the feature map is statistically analyzed, including: The DBSCAN clustering algorithm is used to classify the feature values ​​in the feature map by setting the neighborhood radius and the minimum number of samples. The probability density estimation method is then used to calculate the probability distribution of the feature values ​​in different intervals, as well as the boundaries and ranges of different electromagnetic property regions, based on the classification results.

7. An electromagnetic tomography reconstruction system based on graph convolutional neural networks, used to implement the method as described in any one of claims 1-6, characterized in that, include: The module is used to divide the test area of ​​the target image into grids, obtain several grid cells, and construct a topology graph. The calculation module is used to construct electromagnetic property units based on the nodes and edges in the topology graph, calculate the conductivity distribution and corresponding current density distribution of the electromagnetic property units, and obtain the node features in the topology graph. The reconstruction module is used to construct the node features into a node feature matrix and input it into a pre-trained graph convolutional neural network model to output a feature map. The analysis module is used to statistically analyze the distribution of feature values ​​in the feature map and, in conjunction with the concentration and variation range of electromagnetic properties in different regions, obtain the mixing state of the multiphase flow during the stirring process.

8. The electromagnetic tomography reconstruction system based on graph convolutional neural networks according to claim 7, characterized in that, The system further includes a training module for constructing an electromagnetic tomography dataset and training a graph convolutional neural network model using the electromagnetic tomography dataset. Constructing the electromagnetic tomography dataset includes: The test area of ​​the sample image is discretized, and the boundary conditions between the excitation source and the sensor are defined. The sample conductivity distribution and the sample current density distribution corresponding to the sample conductivity distribution are calculated. The sample conductivity distribution and the corresponding sample current density distribution are input into the electromagnetic tomography forward problem model. By solving Maxwell's equations and discretizing the sample conductivity distribution into pixel values ​​to generate sample image grayscale values, an electromagnetic tomography dataset containing conductivity distribution and current density is constructed.

Images