A Fast Stress Field Calculation Method Based on Graph Network Agent Model

Abstract

This invention discloses a rapid stress field calculation method based on a graph network proxy model. First, a simulation model is created and a training dataset is constructed. Then, mesh information is exported. A graph neural network method based on message aggregation, propagation, and updating is employed, introducing parameters such as unit centroid and volume as node features, and area as edge features to complete the graph construction. Compared with traditional proxy model creation methods, this method fully considers mesh information and improves calculation accuracy. By introducing global features and utilizing external environmental parameters or partial measurement point stress values, rapid and real-time calculation of the structural stress field can be achieved, reducing sensor deployment requirements and hardware costs. This method not only accurately predicts the stress distribution of the structure but also improves calculation efficiency.

Description

Technical Field

[0001] This invention belongs to the field of stress state measurement technology, specifically a method for rapid stress field calculation based on a graph network proxy model. Background Technology

[0002] As engineering problems become increasingly complex, it is crucial to rapidly calculate the stress state (stress field) of structural components such as bearings based on environmental conditions, including external loads, to analyze their reliability and fatigue performance. Traditional methods typically employ finite element analysis (FEM) simulation and actual stress sensor detection for stress state calculation. However, FEM simulation is computationally intensive, time-consuming, and lacks real-time performance; while actual stress sensor detection is limited by the number of measurement points and installation conditions, making it difficult to calculate the entire stress field of the structure. Therefore, it is necessary to develop an alternative stress field calculation method that requires only a small amount of computation while maintaining sufficient accuracy.

[0003] Existing surrogate models include Kriging models (KRG), response surface models (PRS), and radial basis function (RBF) models. These methods approximate the simulation process by fitting an objective function, thus achieving efficient computation. However, when dealing with large-scale datasets, nonlinear relationships, or high-dimensional problems, they typically face problems such as high computational complexity and a high risk of overfitting. Specifically, while Kriging can provide prediction uncertainty, its training and inference processes are relatively slow when dealing with large amounts of data; response surface models perform poorly when dealing with nonlinear relationships and may lead to overfitting as the dimensionality increases; and radial basis function networks, due to their locality limitations, often exhibit insufficient generalization ability when dealing with large-scale problems. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a fast stress field calculation method based on a graph network proxy model, which can not only accurately predict the stress distribution of the structure, but also improve the calculation efficiency.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A fast stress field calculation method based on a graph network proxy model includes the following steps:

[0007] Step 1: Build a simulation model and establish a dataset

[0008] By combining the physical problems of the target stress field with the actual environmental conditions, a finite element simulation model of the structural component is established; the simulation results are then trained in batches using an automated program script and exported as a dataset.

[0009] Step 2: Obtain mesh information based on the simulation model.

[0010] The obtained simulation model is processed and exported in a general format; the mesh information includes node number, node coordinates, element centroid coordinates and element topology information;

[0011] Step 3: Construct a graph network structure using the mesh information from the simulation model.

[0012] The graph network structure is defined as follows:

[0013] G = (V, E)

[0014] Where: V is a set of objects called nodes, defining the centroid of all mesh cells as graph nodes; E is a set of pairs of vertices called edges, defining a graph edge between mesh cells with the same face;

[0015] Graph network structures consist of graph node features and graph edge features; global features are introduced into graph network structures to enhance feature expressiveness and stability.

[0016] Step 4: Training the Graph Network Proxy Model

[0017] A graph network proxy model is trained using a dataset and an encoder-processor-decoder architecture. The encoder embeds the node attribute vectors in the graph network structure into a high-dimensional vector space and generates edge encoded features through non-learning transformation. The processor updates the hidden state of the nodes through a recursive message passing mechanism. The decoder predicts the paradigm equivalence of each node.

[0018] Step 5: Based on environmental conditions, use a surrogate model to quickly calculate the stress field.

[0019] By changing the value of the input global feature, the stress values ​​of all mesh nodes are predicted through a graph network proxy model.

[0020] Furthermore, step one includes the following steps:

[0021] 11) Based on the physical problems of the target stress field and the actual environmental conditions, establish a finite element simulation model of the structural component;

[0022] 12) Mesh the finite element simulation model to ensure the accuracy and efficiency of the calculation results;

[0023] 13) Apply different mechanical loads and boundary conditions to the finite element simulation model to generate simulation data of stress fields under various working conditions; use the measured data of stress measuring points arranged on the structural components to evaluate the simulation data: adjust the boundary conditions to optimize the finite element simulation model, reduce the difference between the simulation data and the measured data, until the simulation data meets the accuracy requirements;

[0024] 14) The simulation results are batch trained and exported as a dataset through an automated program script. The dataset is divided into a training set, a validation set, and a test set. The training set is used to train the graph neural network model, the test set is used to evaluate the generalization performance of the graph neural network model, and the validation set is used to improve hyperparameters and evaluate the graph neural network model to prevent overfitting.

[0025] Furthermore, in step three, two vertices connected by an edge become neighbors, and an adjacency matrix is ​​used. express:

[0026]

[0027] Among them: A ij Represents the adjacency matrix; v i and v j Indicates the boundary e i,j Connect the two vertices; It represents the set of real numbers; n×n represents the dimension.

[0028] Furthermore, in step three, the method for constructing graph node features is as follows: define the centroid of all mesh elements as graph node v. i ∈V; Define the attributes of the graph nodes as The set of real numbers; 1×d v Let represent the dimension of a node attribute; then the node attribute vector is represented as:

[0029] h v =[c,t,v vol ]

[0030] Where: h v A vector of node attributes;

[0031] c is the geometric property of a graph node, and c = [x e ,y e ,z e ], x e y e and z e These are the coordinates of the centroid of the mesh element in the three-dimensional Cartesian coordinate system Oxyz, respectively; t represents the graph node type, using one-hot encoding to represent the mesh element type: if a surface node exists in the mesh element, then this element is also defined as a surface mesh element, and the graph node attribute t is encoded as t = [0,1]; otherwise, it is an internal mesh element, encoded as t = [1,0]; v vol The volume characteristic attribute is used to calculate the volume of each grid cell based on the grid nodes.

[0032] Furthermore, in step three, the method for constructing graph edge features is as follows: define the edge as e. i,j∈E, where i and j are the two connected nodes, and E represents the set of all edges; the graph edge attribute vector is defined as The set of real numbers; 1×d e Let represent the dimension of a node attribute; then the edge attribute vector is represented as:

[0033]

[0034] in: A is the edge attribute vector; e Let be the area of ​​the contact surface between mesh elements, defined as the sum of the areas of the two contact surface elements; Δx, Δy, and Δz are the distances between the centroids of the two mesh elements, and:

[0035] Δx=x j ―x i Δy=y j ―y i Δz=z j ―z i

[0036] Where: x i y i and z i x represents the centroid coordinates of the i-th grid cell; j y j and z j Let be the centroid coordinates of the j-th grid cell.

[0037] Furthermore, in step three, global features are introduced into the graph network structure, represented as follows:

[0038]

[0039] Where: Q is the key global feature, and Represents the set of real numbers; 1×(d v +d Q ) represents the dimension of the global feature; the global feature includes the external load [f x ,f y ,f z ], Measurement point location [x f ,y f ,z f ] and the stress signal at the measuring point [∈ ef1 ,∈ ef2 ...∈ efn ];

[0040] In each layer of the graph network structure, the global feature Q is directly concatenated to the attribute vector of each node. The above yields the enhanced node attribute vector:

[0041]

[0042] in: This represents the enhanced node attribute vector; || indicates the concatenation operation.

[0043] Furthermore, in step four, the encoder is used to embed the node attribute vectors in the graph network structure into a high-dimensional vector space, resulting in:

[0044]

[0045] Among them: MLP en-v For a multilayer perceptron in a node encoder; This represents the hidden state of a node at step t=0; The input vector of a node The dimension is 1×(d v +d θ ); The set of real numbers; d v d represents the feature dimension of a node. θ Represents other feature dimensions related to the node.

[0046] The encoder is used to generate edge-encoded features from edge features through a non-learning transformation, resulting in:

[0047]

[0048] Among them: MLP en―e This refers to a multilayer perceptron in an edge encoder. This represents the hidden state of the edge at step t=0; Represents the edge attribute vector.

[0049] Furthermore, in step four, the method by which the processor updates the hidden state of the node through a recursive message passing mechanism is as follows:

[0050] Calculate v for each node i neighboring nodes The aggregated information being transmitted is defined by the following message aggregation function:

[0051]

[0052] in: It is node v i In the hidden state at step t, describe the feature information of the current node; It is the neighbor node v j The hidden state is used to provide contextual information; e ij It is an edge feature, representing node v i and v j The relationship between them; ΦM It is a message passing function, defined as a multilayer perceptron:

[0053]

[0054] Introducing an attention mechanism to improve message selectivity and model expressiveness:

[0055]

[0056] Where: || denotes vector concatenation operation; α ij It represents the attention weights between nodes, and:

[0057]

[0058] in: This represents the attention score function, used to calculate the correlation score between nodes.

[0059] The hidden state of a node will be based on the received messages. To perform the update, residual connections and layer normalization are introduced during the state update process. The state update formula is as follows:

[0060]

[0061] Where: LayerNorm represents layer normalization; Φ U This is the state update function.

[0062] Furthermore, in step four, the decoder is used to predict the paradigm equivalence of each node, expressed as:

[0063]

[0064] Among them: MLP de It is an MLP for node decoders, used to map processed features to output features, completing the transformation process of encoder-processor-decoder model; This represents the hidden state of the node in step T; This is the processed set of vertices.

[0065] The beneficial effects of this invention are as follows:

[0066] This invention presents a rapid stress field calculation method based on a graph network proxy model. First, a high-quality simulation model is created and a training dataset is constructed. Then, high-quality mesh information is exported. A graph neural network method based on message aggregation, propagation, and updating is employed, introducing parameters such as unit centroid and volume as node features, and area as edge features to complete the graph construction. Compared with traditional proxy model creation methods, this method fully considers mesh information, improving calculation accuracy. By introducing global features and utilizing external environmental parameters or partial stress values ​​from measurement points, rapid and real-time calculation of the structural stress field can be achieved, reducing sensor deployment requirements and hardware costs, and improving calculation efficiency. Furthermore, this method has broad potential in scientific research, solving scientific problems involving high computational demands or time-consuming tasks, such as materials science, structural optimization, and fault prediction. It can also be used for rapid calculation of physical fields such as temperature fields. This method has significant engineering value and promising prospects, promoting the development of digital engineering technology.

[0067] This invention presents a rapid stress field calculation method based on a graph network proxy model. It constructs a novel graph signal and introduces global features as node attributes to capture geometric and boundary conditions. Simultaneously, it utilizes an attention mechanism to overcome the oversmoothing problem common in graph deep learning. Using this method, not only can the stress distribution of a structure be accurately predicted, but the speed is also hundreds of times faster than finite element analysis (FEA) simulators, enabling real-time structural response analysis, calculation, inversion, and structural state monitoring and prediction. In other research fields, this method can also serve as a powerful tool for solving other complex physical problems, such as temperature field calculations, thus promoting scientific development and improving engineering productivity. Attached Figure Description

[0068] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following figures are provided for illustration:

[0069] Figure 1 This is a flowchart of the fast stress field calculation method based on the graph network proxy model of the present invention;

[0070] Figure 2 This is a schematic diagram of the network proxy model. Detailed Implementation

[0071] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0072] This embodiment presents a rapid stress field calculation method based on a graph network proxy model. It utilizes a simulation model to batch simulate the stress field distribution of structural components under different environmental conditions, constructing a training dataset. Stress signals monitored by stress sensors are used to evaluate and optimize the simulation data and model. A basic graph structure is constructed based on the mesh information in the simulation model. A graph network proxy model is trained using message passing and information exchange mechanisms between adjacent vertices. Finally, based on actual environmental information and a limited amount of stress measurement point information, the proxy model is used to achieve rapid stress field calculation. Specifically, as shown... Figure 1 As shown in the figure, the fast stress field calculation method based on the graph network proxy model in this embodiment includes the following steps.

[0073] Step 1: Build a simulation model and establish a dataset

[0074] By combining the physical problems of the target stress field with the actual environmental conditions, a finite element simulation model of the structural component is established; the simulation results are then trained in batches using an automated program script and exported as a dataset.

[0075] Specifically, in this embodiment, the construction of the simulation model includes the following steps.

[0076] 11) In the stage of building the simulation model, a high-precision finite element simulation model of the structural component is established by combining the physical problems of the target stress field and the actual environmental conditions with the finite element analysis (FEA) software.

[0077] 12) By analyzing the stress distribution characteristics and geometry, a suitable mesh generation strategy is selected to mesh the finite element simulation model, ensuring the accuracy and efficiency of the calculation results. In this embodiment, high-quality tetrahedral or hexahedral elements are used for mesh generation, and local mesh refinement rules for key areas are defined to ensure the ability to capture regions with changing stress gradients.

[0078] 13) After constructing a finite element simulation model that can accurately simulate the target stress field, apply different mechanical loads and boundary conditions to the finite element simulation model to generate simulation data of the stress field under various working conditions. Use the measured data of stress measuring points arranged on the structural components to evaluate the simulation data: continuously adjust the boundary conditions to optimize the finite element simulation model, reduce the difference between the simulation data and the measured data, until the simulation data meets the set accuracy requirements.

[0079] 14) The simulation results are batch-trained using automated scripts and exported as a dataset. The dataset is divided into training, validation, and test sets. The training set is used to train the graph neural network model, the test set is used to evaluate the generalization performance of the graph neural network model, and the validation set is used to improve hyperparameters and evaluate the graph neural network model to prevent overfitting. This dataset will provide strong support for subsequent efficient stress field simulations.

[0080] Step 2: Obtain mesh information based on the simulation model.

[0081] The constructed simulation model is used to export the mesh information in a common format (txt or csv). Specifically, the mesh information includes node numbers i = (1, 2...N), node coordinates C = (x, y, z), and element centroid coordinates c = (x...y...z). e ,y e ,z e ) and unit topology information M = [m1, m2, ..., m N Wherein, the coordinates of the nodes and centroids are both in the three-dimensional Cartesian coordinate system Oxyz; M is the node number value that constitutes all mesh elements, m i = [i1,i2,i3...]∈M. This mesh information will serve as the basis for graph data construction in subsequent steps. Simulation runs will verify the mesh quality and the correctness of boundary condition settings, ensuring that the simulation model accurately reflects actual working conditions and laying a reliable foundation for subsequent dataset generation and surrogate model training. The careful design and execution of this process are crucial to the construction and performance of the subsequent graph network model.

[0082] Step 3: Construct a graph network structure using the mesh information from the simulation model.

[0083] In this embodiment, the graph network structure is defined as follows:

[0084] G = (V, E)

[0085] Where: V is a set of objects called nodes, defining the centroid of all mesh elements as graph nodes v. i ∈V; E is a set of paired vertices called edges, defined as a graph edge e between mesh cells with the same face. i,j ∈E.

[0086] Specifically, the two edges e i,j Connected vertices v i and v j Become neighbors and use an adjacency matrix. express:

[0087]

[0088] Among them: A ij Represents the adjacency matrix; v i and v j Indicates the boundary e i,j Connect the two vertices; It represents the set of real numbers; n×n represents the dimension.

[0089] In this embodiment, the graph network structure includes graph node features and graph edge features. During the construction of the graph network structure, it is necessary to construct the graph node features and graph edge features separately.

[0090] (1) Constructing graph node features

[0091] In this embodiment, the method for constructing graph node features is as follows: define the centroid of all mesh cells as graph node v. i ∈V; Define the attributes of the graph nodes as The set of real numbers; 1×d v Let represent the dimension of a node attribute; then the node attribute vector is represented as:

[0092] h v =[c,t,v vol ]

[0093] Where: h v Let be the node attribute vector; c is the geometric attribute of the graph node, and c = [x...]. e ,y e ,z e ], x e y e and z e These are the coordinates of the centroid of the mesh element in the three-dimensional Cartesian coordinate system Oxyz, respectively; t represents the graph node type, using one-hot encoding to represent the mesh element type: if a surface node exists in the mesh element, then this element is also defined as a surface mesh element, and the graph node attribute t is encoded as t = [0,1]; otherwise, it is an internal mesh element, encoded as t = [1,0]; v vol The volume characteristic attribute is used to calculate the volume of each grid cell based on the grid nodes.

[0094] (2) Construct graph edge features

[0095] In this embodiment, the method for constructing graph edge features is as follows: define the edge as e. i,j ∈E, where i and j are the two connected nodes, and E represents the set of all edges; the graph edge attribute vector is defined as The set of real numbers; 1×d e Let represent the dimension of a node attribute; then the edge attribute vector is represented as:

[0096]

[0097] in: A is the edge attribute vector; e Let be the area of ​​the contact surface between mesh elements, defined as the sum of the areas of the two contact surface elements; Δx, Δy, and Δz are the distances between the centroids of the two mesh elements, and:

[0098] Δx=x j ―x i Δy=y j ―y i Δz=z j ―z i

[0099] Where: x i y i and z i x represents the centroid coordinates of the i-th grid cell; j y j and z j Let be the centroid coordinates of the j-th grid cell.

[0100] (3) Introducing global features

[0101] In this embodiment, the graph network structure will be improved by introducing global features to enhance feature representation and stability. By combining global features with vertex or edge features, each layer of the network can perceive the global information of the entire graph, thereby making training more stable, mitigating gradient vanishing and gradient exploding, and improving prediction performance.

[0102] Specifically, global features are introduced into the graph network structure, represented as:

[0103]

[0104] Where: Q is the key global feature, and Represents the set of real numbers; 1×(d v +d Q ) represents the dimension of the global feature; the global feature includes the external load [f x ,f y ,f z ], Measurement point location [x f ,y f ,z f ] and the stress signal at the measuring point [∈ ef1 ,∈ ef2 ...∈ efn ];

[0105] In this embodiment, to simplify the model, in each layer of the graph network structure, the global feature Q is directly concatenated to the attribute vector of each node. The above yields the enhanced node attribute vector:

[0106]

[0107] in: This is the enhanced node attribute vector; || represents the concatenation operation, so that each node can directly refer to the global feature Q without needing to obtain global information through edge propagation.

[0108] Step 4: Training the Graph Network Proxy Model

[0109] In this embodiment, a dataset is used, and a graph network proxy model is trained using an encoder-processor-decoder architecture. Specifically, as shown... Figure 2 As shown, the encoder embeds the node attribute vectors in the graph network structure into a high-dimensional vector space and generates edge-encoded features through non-learning transformation; the processor updates the hidden state of nodes through a recursive message passing mechanism; and the decoder predicts the paradigm equivalence of each node. In this embodiment, the capabilities of a graph neural network (GNN) are utilized to process grid-based data. The model employs the Adam optimizer and a Cosine Annealing learning rate scheduler, with a hidden layer size of 128 and an initial learning rate of 0.001. The architecture consists of three key components: the encoder, the processor, and the decoder, each playing a different role in transforming the input features of the grid vertices into output features. Specifically, the surrogate model can be represented as:

[0110]

[0111] in: The result is the prediction result; Encoder represents the encoder; Processor represents the processor; Decoder represents the decoder.

[0112] (1) Encoder

[0113] In this embodiment, the encoder is used to embed the node attribute vectors in the graph network structure into a high-dimensional vector space, resulting in:

[0114]

[0115] Among them: MLP en-v For a multilayer perceptron in a node encoder; This represents the hidden state of a node at step t=0; The input vector of a node The dimension is 1×(d v +d θ ); The set of real numbers; d v d represents the feature dimension of a node. θ Represents other feature dimensions related to the node.

[0116] For edge features, the encoder is used to generate edge-encoded features through a non-learning transformation, resulting in:

[0117]

[0118] Among them: MLP en―e This refers to a multilayer perceptron in an edge encoder. This represents the hidden state of the edge at step t=0; } represents the edge attribute vector.

[0119] The encoder module enhances the expressive power of nodes.

[0120] (2) Processor

[0121] The processor is the core component of the model architecture, updating the hidden state of nodes through a recursive message passing mechanism. To improve model performance, this embodiment employs an improved graph message passing mechanism, which optimizes convergence speed and significantly reduces error accumulation. The processor progressively updates the hidden state of each node over time steps t = 1, 2, ..., T. The message passing and state update mechanisms are explained in detail below.

[0122] In this embodiment, the processor updates the hidden state of a node through a recursive message passing mechanism.

[0123] The core of message passing is calculating v for each node. i neighboring nodes The aggregated information being transmitted is defined by the following message aggregation function:

[0124]

[0125] in: It is node v i In the hidden state at step t, describe the feature information of the current node; It is the neighbor node v j The hidden state is used to provide contextual information; e ij It is an edge feature, representing node v i and v j The relationship between them; Φ M It is a message passing function, defined as a multilayer perceptron:

[0126]

[0127] Introducing an attention mechanism to improve message selectivity and model expressiveness:

[0128]

[0129] Where: || denotes vector concatenation operation; α ij It represents the attention weights between nodes, and:

[0130]

[0131] in: This represents the attention score function, used to calculate the correlation score between nodes.

[0132] After message passing is complete, the node's hidden state will be based on the received message. To perform the update, residual connections and layer normalization are introduced during the state update process. The state update formula is as follows:

[0133]

[0134] Where: Φ U The state update function is defined as follows:

[0135]

[0136] To accelerate model convergence and improve stability, residual connections and layer normalization are introduced during the state update process. The final improved state update formula is as follows:

[0137]

[0138] Where: LayerNorm represents layer normalization.

[0139] (3) Decoder

[0140] The decoder is used to predict the paradigm equivalence of each node, expressed as:

[0141]

[0142] Among them: MLP de It is an MLP for node decoders, used to map processed features to output features, completing the transformation process of encoder-processor-decoder model; This represents the hidden state of the node in step T; This is the processed set of vertices.

[0143] Step 5: Based on environmental conditions, use a surrogate model to quickly calculate the stress field.

[0144] By changing the value of the input global feature, the stress values ​​of all mesh nodes are predicted through a graph network proxy model.

[0145] After the model training is complete, the input global features are changed. By calculating the value of Q, the stress values ​​of all mesh nodes can be obtained. If the global feature Q is defined as an external environmental parameter or the stress values ​​of some measuring points, the stress field can be quickly calculated by adjusting the model input Q. Specifically, if the global feature Q is defined as the stress values ​​of measuring points, the stress field can be calculated in real time using the real-time input of a small number of measuring point stress signals. Furthermore, by combining this with a 3D visualization program, a 3D cloud map can also be displayed.

[0146] The above-described embodiments are merely preferred embodiments provided to fully illustrate the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A fast stress field calculation method based on a graph network proxy model, characterized in that: Includes the following steps: Step 1: Build a simulation model and establish a dataset By combining the physical problems of the target stress field with the actual environmental conditions, a finite element simulation model of the structural component is established; the simulation results are then trained in batches using an automated program script and exported as a dataset. Step 2: Obtain mesh information based on the simulation model. The obtained simulation model is processed and exported in a general format; the mesh information includes node number, node coordinates, element centroid coordinates and element topology information; Step 3: Construct a graph network structure using the mesh information from the simulation model. The graph network structure is defined as follows: in: It is a set of objects called nodes, defining the centroid of all mesh cells as graph nodes; A graph edge is a pair of vertices called an edge. A graph edge is defined as the existence of grid cells with the same face. The graph network structure includes graph node features and graph edge features; global features are introduced into the graph network structure to enhance feature expressiveness and stability; the global features are external environmental features or stress values ​​of some measurement points; Introducing global features into the graph network structure, represented as: in: As a key global feature, and ; The set of real numbers; The dimension representing the global feature; global features include external loads. Measurement point location and the stress signal at the measuring point ; In each layer of the graph network structure, global features are... The attribute vector is directly concatenated to each node. The above yields the enhanced node attribute vector: in: This is the enhanced node attribute vector; Indicates a splicing operation; Step 4: Training the Graph Network Proxy Model A graph network proxy model is trained using a dataset and an encoder-processor-decoder architecture. The encoder embeds the node attribute vectors in the graph network structure into a high-dimensional vector space and generates edge encoded features through non-learning transformation. The processor updates the hidden state of the nodes through a recursive message passing mechanism. The decoder predicts the paradigm equivalence of each node. Step 5: Based on environmental conditions, use a surrogate model to quickly calculate the stress field. By changing the values ​​of the global features, the stress values ​​of all mesh nodes are predicted using a graph network proxy model.

2. The method for fast stress field calculation based on graph network proxy model according to claim 1, characterized in that: Step one includes the following steps: 11) Based on the physical problems of the target stress field and the actual environmental conditions, establish a finite element simulation model of the structural component; 12) Mesh the finite element simulation model to ensure the accuracy and efficiency of the calculation results; 13) Apply different mechanical loads and boundary conditions to the finite element simulation model to generate simulation data of stress fields under various working conditions; The simulation data was evaluated using measured data from stress measurement points placed on the structural components: boundary conditions were adjusted to optimize the finite element simulation model, and the difference between the simulation data and the measured data was reduced until the simulation data met the accuracy requirements. 14) The simulation results are batch trained and exported as a dataset through an automated program script. The dataset is divided into a training set, a validation set, and a test set. The training set is used to train the graph neural network model, the test set is used to evaluate the generalization performance of the graph neural network model, and the validation set is used to improve hyperparameters and evaluate the graph neural network model to prevent overfitting.

3. The method for fast stress field calculation based on graph network proxy model according to claim 1, characterized in that: In step three, two vertices connected by an edge become neighbors, and an adjacency matrix is ​​used. express: in: Represents the adjacency matrix; and Indicates by edge Connect the two vertices; Represents the set of real numbers; Indicates dimension.

4. The method for fast stress field calculation based on graph network proxy model according to claim 1, characterized in that: In step three, the method for constructing graph node features is as follows: define the centroid of all mesh cells as graph nodes. Define the attributes of the graph nodes as follows: ; The set of real numbers; Let represent the dimension of a node attribute; then the node attribute vector is represented as: in: A vector of node attributes; Let be the geometric properties of the graph nodes, and , , and The centroids of the mesh elements in the three-dimensional Cartesian coordinate system are respectively The coordinate values; For graph node types, one-hot encoding is used to represent mesh cell types: if a mesh cell contains surface nodes, then this cell is also defined as a surface mesh cell. Graph node attributes. Encoded as Conversely, it is an internal grid cell, coded as... ; The volume characteristic attribute is used to calculate the volume of each grid cell based on the grid nodes.

5. The method for fast stress field calculation based on graph network proxy model according to claim 1, characterized in that: In step three, the method for constructing graph edge features is as follows: define an edge as... ,in and For the two nodes to be connected, The graph represents the set of all edges; the graph edge attribute vector is defined as follows: , The set of real numbers; Let represent the dimension of a node attribute; then the edge attribute vector is represented as: in: This is an edge attribute vector; The area of ​​the contact surface between mesh elements is defined as the sum of the areas of the two contact surface elements; , and Let be the distance between the centroids of the two grid cells, and: ， ， in: , and For the first Centroid coordinates of the grid cell; , and For the first Centroid coordinates of the grid cell.

6. The method for fast stress field calculation based on graph network proxy model according to claim 1, characterized in that: In step four, the encoder is used to embed the node attribute vectors in the graph network structure into a high-dimensional vector space, resulting in: in: For a multilayer perceptron in a node encoder; Indicates that the node is The hidden state of the step; The input vector of a node The dimension is ; The set of real numbers; Represents the feature dimension of a node; This represents other feature dimensions related to the node; The encoder is used to generate edge-encoded features from edge features through a non-learning transformation, resulting in: in: This refers to a multilayer perceptron in an edge encoder. Indicates the edge is in The hidden state of the step; Represents the edge attribute vector.

7. The method for fast stress field calculation based on graph network proxy model according to claim 1, characterized in that: In step four, the processor updates the hidden state of the node using a recursive message passing mechanism as follows: Calculate each node neighboring nodes The aggregated information being transmitted is defined by the following message aggregation function: in: It is a node exist The hidden state of the step describes the feature information of the current node; Neighboring nodes The hidden state is used to provide contextual information; Edge features represent nodes and The relationship between them; It is a message passing function, defined as a multilayer perceptron: Introducing an attention mechanism to improve message selectivity and model expressiveness: in: This represents a vector concatenation operation; It represents the attention weights between nodes, and: in: This represents the attention score function, used to calculate the correlation score between nodes; The hidden state of a node will be based on the received messages. To perform the update, residual connections and layer normalization are introduced during the state update process. The state update formula is as follows: in: Representation layer normalization; This is the state update function.

8. The method for fast stress field calculation based on graph network proxy model according to claim 1, characterized in that: In step four, the decoder is used to predict the paradigm equivalence of each node, expressed as: in: It is an MLP for node decoders, used to map processed features to output features, completing the transformation process of encoder-processor-decoder model; For nodes in The hidden state of the step; This is the processed set of vertices.

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