A structure explosion response calculation model construction method based on a graph neural network

Abstract

This invention relates to the field of dynamic response calculation for engineering structures, specifically disclosing a method for constructing a structural explosion response calculation model based on graph neural networks. The method includes: encoding and decoding the node and edge features of the graph structure; constructing a spatiotemporal graph processor consisting of multiple stacked spatiotemporal graph tiles, with spatial modeling of a physics-enhanced graph attention network and temporal modeling of gated recurrent units coupled within each tile; integrating physical information into the model in the form of soft or hard constraints; establishing a physics-driven message passing mechanism, including designing a physics-enhanced message function, a wave velocity-aware attention mechanism, and a physics-driven message aggregation and node update method; training the model using a multi-step Rollout training strategy, and validating the model through data accuracy evaluation and physical consistency checks. This invention integrates data-driven and physical mechanisms, solving the problems of time-consuming traditional numerical simulations, weak generalization of purely data-driven models, and insufficient physical consistency.

Description

Technical Field

[0001] This invention relates to the field of engineering structure dynamic response calculation technology, specifically a method for constructing a structural explosion response calculation model based on graph neural networks. Background Technology

[0002] Accurate acquisition of structural explosion response characteristics is a core prerequisite for related analysis work. Due to the high difficulty, cost, and control required for large-scale engineering structural explosion tests, widespread implementation is challenging. High-fidelity numerical simulation has become an important means of obtaining these response characteristics, and reasonable modeling and high-precision calculation are key to accurately acquiring response data.

[0003] Currently, the structural explosion response characteristics are mainly obtained through two methods: one is to simplify the engineering problem extensively, establish an analysis model, and carry out numerical simulation calculations. Although graph neural networks can represent data characteristics with nodes and depict the relationship between elements with links, they have a powerful ability to approximate nonlinear functions and can simulate complex systems without accurately modeling the internal influencing factors of the system; the other is to use deep learning technology to construct a mapping function between input parameters and output response for nonlinear analysis, which provides a new path to balance computational accuracy and efficiency.

[0004] However, the above methods have significant shortcomings: numerical simulations require the construction of detailed models to deal with highly complex nonlinear problems. In scenarios such as structural resilience assessment, sensitivity calculation, and uncertainty analysis, which require hundreds or thousands of calculations, the time and effort are consumed, and the results are heavily dependent on the understanding of the problem, model simplification, and selection of calculation methods. In deep learning, traditional data-driven networks rely on a large amount of high-quality labeled data, which is prone to overfitting due to a lack of physical interpretability and has limited generalization ability. At the same time, they are difficult to adapt to the non-Euclidean, highly dynamic, and multi-source heterogeneous structural characteristics of complex systems. Due to the limitations of training data serialization and gridding, they cannot meet the needs of accurate modeling and simulation.

[0005] To address these prominent issues, overcome the bottlenecks in accuracy, efficiency, and adaptability of existing computational methods, meet the need for efficient and accurate acquisition of structural explosion response characteristics, provide reliable analytical means to reveal the correlation between key structural characteristic parameters and explosion response characteristics, and fill the gap in physical reliability of existing computational methods, it is urgent to propose a more reliable computational model construction method. Summary of the Invention

[0006] To address the aforementioned problems in the prior art, this invention provides a method for constructing a structural explosion response calculation model based on graph neural networks, which effectively solves the problems of weak generalization and insufficient physical consistency, and improves calculation accuracy and efficiency.

[0007] To achieve the above objectives, this invention proposes a method for constructing a structural explosion response calculation model based on graph neural networks, comprising: S1: Node and edge feature encoding and decoding, which maps the input physical features to a high-dimensional feature space through the encoder, and maps the high-dimensional features back to physical quantities through the decoder; S2: Construct a spatiotemporal graph processor, which is composed of multiple stacked spatiotemporal graph tiles. Each spatiotemporal graph tile performs a coupling of spatial modeling based on a physically enhanced graph attention network and temporal modeling based on a gated recurrent unit (GRU) to simulate the process of a node aggregating information from its neighboring nodes. The strength of this process is controlled by a physically driven attention coefficient. S3: Integrate physical information into the model in the form of soft or hard constraints. The soft constraints are achieved by adding a physical residual term to the loss function, and the hard constraints are achieved through model architecture design. S4: Establish a message passing mechanism driven by physical laws, design message functions enhanced by physical information, attention mechanisms for wave speed perception, and physical-driven message aggregation and node update methods, and couple the enhanced message passing mechanism with the time modeling module GRU to form a complete spatiotemporal graph. S5: The model is trained using a multi-step Rollout training strategy and validated through data accuracy evaluation and physical consistency verification.

[0008] Preferably, in S1, the encoder is a shared multilayer perceptron, which performs a nonlinear transformation on the initial features of each node to map them to a high-dimensional feature space, thereby obtaining the initial hidden layer features. ,node The initial high-dimensional features encoded by the encoder satisfy: ; In the formula, For node encoders, For nodes In the The physical state at the time step. For nodes In the The physical state at a time step, ... represents a node. The historical time step physical quantity state sequence; The initial features of each edge are nonlinearly transformed and mapped to a high-dimensional feature space to obtain the encoded edge features. Connecting nodes with neighboring nodes Initial encoding features of edges satisfy: ; In the formula, For edge encoders, For connecting nodes With nodes The initial characteristics of the edges.

[0009] Preferably, in S1, the decoder is a multilayer perceptron (MLP), which decodes the final hidden state of the nodes. Decoding is performed as the increment or absolute value of a physical quantity; where, For nodes The final hidden state, decoded to satisfy: ; In the formula, For nodes In the The increment of physical quantities at a time step. For decoders.

[0010] Preferably, in S2, the specific steps of spatial modeling of the physically-enhanced graph attention network include: employing a graph attention mechanism that allows nodes to dynamically allocate attention to their neighbors based on the edge weights of their physical connections, simulating information propagation in the spatial topology network at a fixed time step; the attention coefficient calculation satisfies: ; In the formula, For nodes For neighboring nodes Attention coefficients, representing neighboring nodes For nodes Information contribution weight, satisfying , The natural exponential function converts the attention score into a non-negative value. Let be a linear rectified activation function with leakage, used to introduce a nonlinear transformation, where 'a' is the attention parameter vector and 'W' is the shared weight matrix. For nodes The current hidden layer feature vector, For neighboring nodes The current hidden layer feature vector, For nodes The current hidden layer feature vector, node For traversing the neighbor set, For connecting nodes with neighboring nodes The encoded feature vector, For nodes With nodes The encoded feature vector, For nodes The set of neighboring nodes; The node aggregation satisfies: ; In the formula, || denotes vector concatenation. It is a non-linear activation function. For nodes Updated node feature vectors after spatial aggregation; The time modeling based on the gated recurrent unit (GRU) is used independently on each node to simulate the dynamic process of a single node, and learns to forget irrelevant historical information and update the current state through its gating mechanism.

[0011] Preferably, in S3, the physical residual term includes residual loss based on the governing equation and physical principle regularization loss; in the residual loss based on the governing equation, at any spatiotemporal point node... In the Time step ( i , t residuals satisfy: ; in, For nodes The corresponding material density, For nodes In the The acceleration at the time step is approximated by the second-order difference between displacement and time. For nodes In the The second-order stress tensor of the time step characterizes the nodes. The three-dimensional stress state at the location, For nodes In the Stress divergence at time step, through nodes with neighboring nodes The weighted average approximation of the projection of the stress difference onto the connection vector satisfies: ; in, For neighboring nodes The stress tensor, For nodes Representative volume, For connecting nodes with neighboring nodes The unit direction vector of the edge, For nodes with neighboring nodes The area represented by the connecting edges between them; The residual loss over the entire spatiotemporal domain satisfies: ; In the formula, Where T is the total number of spatiotemporal points and T is the total number of time steps. This represents the total number of nodes in the structure.

[0012] Preferably, the physical principle regularization loss is divided into a loss term that penalizes predictions that violate the energy dissipation law and a loss term that penalizes stress predictions that exceed the material's dynamic strength. The loss term that penalizes predictions that violate the energy dissipation law is as follows: ; In the formula, This indicates that for all nodes All time steps Summation, covering the entire spacetime domain. For nodes At time step The increase in plastic work, , For nodes At time step The damage energy release rate, , For nodes At time step The increment of the damage variable, ; The penalty for stress prediction exceeding the material's dynamic strength is as follows: ; Where F(·) is the dynamic strength yield surface function, and the input is the node... At time step stress tensor The output is equivalent stress. Let be the dynamic strength limit of the material, and be the inherent mechanical parameter of the material.

[0013] Preferably, the hard constraint is implemented as follows: for displacement boundaries nodes Before the decoder outputs the final value, increment the displacement of this node. Forced to be set as The corresponding incremental replacement network predicts the displacement increment. The corresponding increment is: ; In the formula, For nodes The displacement vector, For nodes The displacement boundary condition vector. For nodes At time step The boundary displacement increment, For nodes In the The displacement boundary condition vector at the time step. For nodes In the The displacement boundary condition vector at the time step.

[0014] Preferably, in S3, the loss function is a weighted sum of data-driven loss and physical constraint loss, satisfying: ; in, For the total loss function, , , For hyperparameters, The error loss between the predicted value and the high-fidelity simulation value, ... represents additional physical constraint loss terms or constitutive constraint loss that can be added as needed. For nodes In the The time step is the displacement vector predicted by the model. For nodes In the The time step is obtained from the high-fidelity reference displacement true value obtained by the finite element method (FEM).

[0015] Preferably, in S4, the message function for enhancing physical information satisfies: ; in, For neighboring nodes Send to node The news For lightweight MLP, For neighboring nodes The stress tensor, n ij To the neighbor node Pointing to node The unit direction vector, For nodes with neighboring nodes Distance-based decay weights, For nodes with neighboring nodes Material consistency weight; The wave velocity sensing attention mechanism is to correlate the calculation of attention weights with the theoretical propagation speed of stress waves in the material, satisfying the following: ; In the formula, For nodes For neighboring nodes Wave speed perception attention coefficient, For nodes For neighboring nodes The eigenvectors of the edges, For nodes For nodes The eigenvectors of the edges, The theoretical wave arrival time, i.e., the time from the stress wave to the node. propagate to neighboring nodes Theoretical time required For the theoretical wave velocity, the stress wave at the node Neighbor nodes The theoretical propagation speed in the material region, For stress waves from nodes propagation to nodes The theoretical time required, where η is the time window width control parameter.

[0016] The physical-driven message aggregation and node update transforms received physical messages into node state updates, simulating Newton's second law. The specific steps of the physical-driven message aggregation and node update include: Physical message aggregation: receiving node Aggregated messages received from all neighbors, forming a combined force: ; In the formula, For nodes The equivalent resultant force vector at a given point is obtained by weighted summation of the physical messages passed by all neighbors; Physics-based node update: This involves aggregating messages and calculating node quality from node density and representative volume. Combine and update the acceleration or velocity of the node: ; In the formula, For nodes Updated velocity vector, For nodes The original velocity vector before the update The time step is the time increment for numerical integration. Calculated from node density and representative volume, For nodes The equivalent acceleration.

[0017] Preferably, in S5, the multi-step Rollout training strategy defines a gradually increasing number of Rollout steps S for the training sample sequence {u0, u1, ..., u...}. T}, input the true values ​​{u0, u1, ..., u} of the first L time steps. L-1 The model performs S-step free prediction to obtain {u} L ,u L+1 ,…,uL+S-1 Multi-step loss prediction satisfy: ; in, Here, represents the loss weight coefficient corresponding to the prediction at step s, set to an incrementing value. s is the single-step index variable within Rollout, used only to iterate through the multi-step prediction process. L is the given true initial time series length, representing the starting time step when the model begins autonomous prediction. Let be the nodal displacement prediction vector output by the model at time step L+s-1. This is the true displacement reference vector corresponding to the L+s-1 time step.

[0018] Therefore, this invention proposes a method for constructing a structural explosion response calculation model based on graph neural networks, which has the following advantages: (1) Deeply integrate prior knowledge of mechanics and core physical laws, and directly embed physical laws such as the law of conservation of momentum, the law of energy dissipation, and the material strength criterion into the model through a dual path of soft constraints and hard constraints and a physical-driven message passing mechanism. This effectively solves the problems of weak generalization ability and insufficient physical consistency of pure data-driven models. The message passing carries clear physical meaning and improves the interpretability of the model.

[0019] (2) By adopting the encoding-processing-decoding spatiotemporal extension paradigm and multi-step Rollout training strategy, the spatiotemporal graph processor efficiently captures the spatiotemporal evolution characteristics of nodes, taking into account both computational accuracy and efficiency, and realizes long-term stable multi-time step full-field response prediction, which is suitable for complex nonlinear scenarios.

[0020] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0021] Figure 1 This is an overall flowchart of the method for constructing a structural explosion response calculation model based on graph neural networks according to the present invention. Detailed Implementation

[0022] To make the technical solutions, advantages, and objectives of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below. The described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the protection scope of this application.

[0023] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0024] like Figure 1 As shown, the present invention provides a method for constructing a structural explosion response calculation model based on a graph neural network, comprising: S1: Node and edge feature encoding and decoding, which maps the input physical features to a high-dimensional feature space through the encoder, and maps the high-dimensional features back to physical quantities through the decoder; The encoder is a shared multilayer perceptron, which performs a nonlinear transformation on the initial features of each node to map them to a high-dimensional feature space, thus obtaining the initial hidden layer features. ,node The initial high-dimensional features encoded by the encoder satisfy: ; In the formula, For node encoders, For nodes In the The physical state at the time step. For nodes In the The physical state at a time step, ... represents a node. The historical time step physical quantity state sequence; The initial features of each edge are nonlinearly transformed and mapped to a high-dimensional feature space to obtain the encoded edge features. Connecting nodes with neighboring nodes Initial encoding features of edges satisfy: ; In the formula, For edge encoders, For connecting nodes With nodes The initial characteristics of the edges.

[0025] The decoder is a multilayer perceptron (MLP), which will output the final hidden state of the nodes. Decoding is performed as the increment or absolute value of a physical quantity; where, For nodes The final hidden state, decoded to satisfy: ; In the formula, For nodes In the The increment of physical quantities at a time step. For decoders.

[0026] S2: Construct a spatiotemporal graph processor, which is composed of multiple stacked spatiotemporal graph tiles. Each spatiotemporal graph tile performs a coupling of spatial modeling based on a physically enhanced graph attention network and temporal modeling based on a gated recurrent unit (GRU), simulating the process by which nodes aggregate information from their neighboring nodes. The strength of this process is controlled by a physically driven attention coefficient. The specific steps for spatial modeling of physically-enhanced graph attention networks include: employing a graph attention mechanism that allows nodes to dynamically allocate attention to their neighbors based on the edge weights of their physical connections, simulating information propagation in the spatial topology network at a fixed time step; and calculating the attention coefficients to satisfy the following: ; In the formula, For nodes For neighboring nodes Attention coefficients, representing neighboring nodes For nodes Information contribution weight, satisfying , The natural exponential function converts the attention score into a non-negative value. Let be a linear rectified activation function with leakage, used to introduce a nonlinear transformation, where 'a' is the attention parameter vector and 'W' is the shared weight matrix. For nodes The current hidden layer feature vector, For neighboring nodes The current hidden layer feature vector, For nodes The current hidden layer feature vector, node For traversing the neighbor set, For connecting nodes with neighboring nodes The encoded feature vector, For nodes With nodes The encoded feature vector, For nodes The set of neighboring nodes; Node aggregation satisfies: ; In the formula, || denotes vector concatenation. It is a non-linear activation function. For nodes Updated node feature vectors after spatial aggregation; The time modeling based on the Gated Recurrent Unit (GRU) is used independently on each node to simulate the dynamic history of a single node, and learns to forget irrelevant historical information and update the current state through its gating mechanism.

[0027] S3: Integrate physical information into the model in the form of soft or hard constraints. Soft constraints are achieved by adding physical residual terms to the loss function, while hard constraints are achieved through model architecture design. The physical residual term includes residual loss based on the governing equation and physical principle regularization loss.

[0028] In the residual loss based on the governing equation, any spatiotemporal node In the Time step ( i , t residuals satisfy: ; in, For nodes The corresponding material density, For nodes In the The acceleration at the time step is approximated by the second-order difference between displacement and time. For nodes In the The second-order stress tensor of the time step characterizes the nodes. The three-dimensional stress state at the location, For nodes In the Stress divergence at time step, through nodes with neighboring nodes The weighted average approximation of the projection of the stress difference onto the connection vector satisfies: ; in, For neighboring nodes The stress tensor, For nodes Representative volume, For connecting nodes with neighboring nodes The unit direction vector of the edge, For nodes with neighboring nodes The area represented by the connecting edges between them; The residual loss over the entire spatiotemporal domain satisfies: ; In the formula, Where T is the total number of spatiotemporal points and T is the total number of time steps. This represents the total number of nodes in the structure.

[0029] The physical principle regularization loss is divided into a loss term that penalizes predictions that violate the energy dissipation law and a loss term that penalizes stress predictions that exceed the material's dynamic strength. The loss term that penalizes predictions that violate the energy dissipation law is as follows: ; In the formula, This indicates that for all nodes All time steps Summation, covering the entire spacetime domain. For nodes At time step The increase in plastic work, , For nodes At time step The damage energy release rate, , For nodes At time step The increment of the damage variable, ; The penalty term for stress prediction exceeding the material's dynamic strength is: ; Where F(·) is the dynamic strength yield surface function, and the input is the node... At time step stress tensor The output is equivalent stress. Let be the dynamic strength limit of the material, and be the inherent mechanical parameter of the material.

[0030] The implementation of hard constraints is as follows: for displacement boundaries nodes Before the decoder outputs the final value, increment the displacement of this node. Forced to be set as The corresponding incremental replacement network predicts the displacement increment. The corresponding increment is: ; In the formula, For nodes The displacement vector, For nodes The displacement boundary condition vector. For nodes At time step The boundary displacement increment, For nodes In the The displacement boundary condition vector at the time step. For nodes In the The displacement boundary condition vector at the time step.

[0031] The loss function is a weighted sum of the data-driven loss and the physical constraint loss, satisfying: ; in, For the total loss function, , , For hyperparameters, The error loss between the predicted value and the high-fidelity simulation value, ... represents additional physical constraint loss terms or constitutive constraint loss that can be added as needed. For nodes In the The time step is the displacement vector predicted by the model. For nodes In the The time step is obtained from the high-fidelity reference displacement true value obtained by the finite element method (FEM).

[0032] Ablation experiments were also conducted to compare the performance of models with and without physical constraints on the test set, especially in extrapolation scenarios. Simultaneously, the momentum and energy of the entire system were checked to ensure they remained conserved within acceptable error ranges, thus completing the physical quantity conservation verification.

[0033] S4: Establish a message passing mechanism driven by physical laws, design message functions enhanced by physical information, attention mechanisms for wave speed perception, and physical-driven message aggregation and node update methods, and couple the enhanced message passing mechanism with the time modeling module GRU to form a complete spatiotemporal graph. The message function for physical information enhancement satisfies: ; in, For neighboring nodes Send to node The news For lightweight MLP, For neighboring nodes The stress tensor, n ij To the neighbor node Pointing to node The unit direction vector, For nodes with neighboring nodes Distance-based decay weights, For nodes with neighboring nodes Material consistency weight; The attention mechanism for wave velocity sensing correlates the calculation of attention weights with the theoretical propagation speed of stress waves in the material, satisfying the following: ; In the formula, For nodes For neighboring nodes Wave speed perception attention coefficient, For nodes For neighboring nodes The eigenvectors of the edges, For nodes For nodes The eigenvectors of the edges, The theoretical wave arrival time, i.e., the time from the stress wave to the node. propagate to neighboring nodes Theoretical time required For the theoretical wave velocity, the stress wave at the node Neighbor nodes The theoretical propagation speed in the material region, For stress waves from nodes propagation to nodes The theoretical time required, where η is the time window width control parameter.

[0034] Physically driven message aggregation and node updates transform received physical messages into node state updates, simulating Newton's second law. The specific steps of physically driven message aggregation and node updates include: Physical message aggregation: receiving node Aggregated messages received from all neighbors, forming a combined force: ; In the formula, For nodes The equivalent resultant force vector at a given point is obtained by weighted summation of the physical messages passed by all neighbors; Physics-based node update: This involves aggregating messages and calculating node quality from node density and representative volume. Combine and update the acceleration or velocity of the node: ; In the formula, For nodes Updated velocity vector, For nodes The original velocity vector before the update The time step is the time increment for numerical integration. Calculated from node density and representative volume, For nodes The equivalent acceleration.

[0035] S5: The model is trained using a multi-step Rollout training strategy and validated through data accuracy evaluation and physical consistency verification.

[0036] In a multi-step Rollout training strategy, the number of Rollout steps S is defined as increasing gradually for a training sample sequence {u0, u1, ..., u...}. T}, input the true values ​​{u0, u1, ..., u} of the first L time steps. L-1 The model performs S-step free prediction to obtain {u} L ,u L+1 ,…,u L+S-1 Multi-step loss prediction satisfy: ; in, Here, represents the loss weight coefficient corresponding to the prediction at step s, set to an incrementing value. s is the single-step index variable within Rollout, used only to iterate through the multi-step prediction process. L is the given true initial time series length, representing the starting time step when the model begins autonomous prediction. Let be the nodal displacement prediction vector output by the model at time step L+s-1. This is the true displacement reference vector corresponding to the L+s-1 time step.

[0037] Data accuracy assessment: The degree of closeness between the model prediction results and the high-fidelity simulation results is quantitatively assessed by setting node-level error and full-field-level error.

[0038] Physical consistency verification: By verifying the global momentum / energy conservation, stress-strain behavior rationality, and boundary condition satisfaction, the model prediction results are verified to meet higher-level physical laws such as global energy conservation (the sum of kinetic energy, strain energy, and dissipated energy should be consistent with the trend of input energy change). This is the key to verifying the reliability of the model.

[0039] Ablation experiments and comparative analysis: Quantify the contribution of each innovative component (such as physical constraints and physical augmentation messaging) to model performance, and compare the long-term prediction RMSE and physical consistency metrics of all models on the test set and the extrapolated test set (parameter range not covered by the training data).

[0040] This invention takes the explosion dynamic response prediction of a commonly used reinforced concrete beam in a certain engineering project as an example. Based on its structural characteristics and the explosion load scenario, a graph neural network model is constructed. The specific implementation process is as follows: The physical characteristics of reinforced concrete beams are encoded by node and edge features. The initial features of the beam, such as node coordinates, material parameters, and edge weights, are mapped to a high-dimensional feature space through a shared multilayer perceptron to obtain the initial hidden layer features and the encoded edge features. After the model training is completed, the final node hidden layer state is mapped back to physical quantities such as displacement and stress through a decoder.

[0041] A spatiotemporal graph processor consisting of multiple stacked spatiotemporal graph tiles is constructed. Each spatiotemporal graph tile is coupled with a physically-enhanced graph attention network and a GRU-gated recurrent unit. The attention weights of nodes are dynamically allocated through the attention mechanism to simulate the spatial propagation of stress waves. By using GRU to capture the temporal evolution characteristics of nodes, the spatiotemporal interaction information of nodes can be effectively extracted.

[0042] The loss function incorporates residual loss based on the momentum conservation equation, energy dissipation law, and regularization loss related to material dynamic strength to form soft constraints; for the displacement boundary nodes of the beam, the displacement increment is forcibly set before the decoder output to achieve hard constraints and ensure that the model meets the core physical laws.

[0043] A physical law-driven message passing mechanism is enabled. Messages with physical meaning, such as bearing stress, are generated through message functions enhanced with physical information. Combined with a wave speed-sensing attention mechanism, the timing characteristics of stress wave propagation are accurately captured. Through physical-driven message aggregation and node updates, the dynamic iteration of node states is completed.

[0044] The model parameters are optimized using a multi-step Rollout training strategy. Data accuracy is evaluated through node-level and global-level error assessments. Physical consistency is verified by global momentum / energy conservation tests and stress-strain behavior rationality tests. The contribution of each innovative component is quantified through ablation experiments.

[0045] Results: The model successfully outputs the full-field displacement and stress dynamic response sequence of the reinforced concrete beam under explosive load for multiple time steps. The error between the prediction results and the high-fidelity simulation results meets the requirements of engineering analysis and strictly follows physical laws such as momentum conservation and non-negative energy dissipation. The boundary conditions are accurately satisfied. In the extrapolation scenario of the uncovered explosive load parameters, it still maintains good generalization ability. Compared with traditional fine numerical simulation, it significantly improves the computational efficiency and provides efficient and reliable technical support for the explosive response analysis of this type of structure.

[0046] Therefore, this invention provides a method for constructing a structural explosion response calculation model based on graph neural networks. This method solves the problems of weak generalization ability and insufficient physical consistency of pure data-driven models, as well as the time-consuming and labor-intensive nature of traditional numerical simulations and their reliance on manual simplification. By integrating physical mechanisms with data-driven approaches, the method improves the interpretability and predictive reliability of the model, achieving high-precision and high-efficiency prediction of the full-field dynamic response across multiple time steps. It also takes into account long-term stability and adaptability to complex nonlinear scenarios, providing reliable support for structural explosion response correlation analysis.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for constructing a structural explosion response calculation model based on graph neural networks, characterized in that, Includes the following steps: S1: Node and edge feature encoding and decoding, which maps the input physical features to a high-dimensional feature space through the encoder, and maps the high-dimensional features back to physical quantities through the decoder; S2: Construct a spatiotemporal graph processor, which is composed of multiple stacked spatiotemporal graph tiles. Each spatiotemporal graph tile performs a coupling of spatial modeling based on a physically enhanced graph attention network and temporal modeling based on a gated recurrent unit (GRU) to simulate the process of a node aggregating information from its neighboring nodes. The strength of this process is controlled by a physically driven attention coefficient. S3: Integrate physical information into the model in the form of soft or hard constraints. The soft constraints are achieved by adding a physical residual term to the loss function, and the hard constraints are achieved through model architecture design. S4: Establish a message passing mechanism driven by physical laws, design message functions enhanced by physical information, attention mechanisms for wave speed perception, and physical-driven message aggregation and node update methods, and couple the enhanced message passing mechanism with the time modeling module GRU to form a complete spatiotemporal graph. S5: The model is trained using a multi-step Rollout training strategy and validated through data accuracy evaluation and physical consistency verification.

2. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 1, characterized in that, In S1, the encoder is a shared multilayer perceptron, which performs a nonlinear transformation on the initial features of each node to map them to a high-dimensional feature space, thus obtaining the initial hidden layer features. ,node The initial high-dimensional features encoded by the encoder satisfy: ； In the formula, For node encoders, For nodes In the The physical state at the time step. For nodes In the The physical state at a time step, ... represents a node. The historical time step physical quantity state sequence; The initial features of each edge are nonlinearly transformed and mapped to a high-dimensional feature space to obtain the encoded edge features. Connecting nodes with neighboring nodes Initial encoding features of edges satisfy: ； In the formula, For edge encoders, For connecting nodes With nodes The initial characteristics of the edges.

3. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 2, characterized in that, In S1, the decoder is a multilayer perceptron (MLP), which converts the final hidden state of the nodes. Decoding is performed as the increment or absolute value of a physical quantity; where, For nodes The final hidden state, decoded to satisfy: ； In the formula, For nodes In the The increment of physical quantities at a time step. For decoders.

4. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 3, characterized in that, In S2, the specific steps for spatial modeling of the physically-enhanced graph attention network include: employing a graph attention mechanism that allows nodes to dynamically allocate attention to their neighbors based on the edge weights of their physical connections, simulating information propagation in the spatial topology network at a fixed time step; the attention coefficient calculation satisfies: ； In the formula, For nodes For neighboring nodes Attention coefficients, representing neighboring nodes For nodes Information contribution weight, satisfying , The natural exponential function converts the attention score into a non-negative value. Let be a linear rectified activation function with leakage, used to introduce a nonlinear transformation, where 'a' is the attention parameter vector and 'W' is the shared weight matrix. For nodes The current hidden layer feature vector, For neighboring nodes The current hidden layer feature vector, For nodes The current hidden layer feature vector, node For traversing the neighbor set, For connecting nodes with neighboring nodes The encoded feature vector, For nodes With nodes The encoded feature vector, For nodes The set of neighboring nodes; The node aggregation satisfies: ； In the formula, || denotes vector concatenation. It is a non-linear activation function. For nodes Updated node feature vectors after spatial aggregation; The time modeling based on the gated recurrent unit (GRU) is used independently on each node to simulate the dynamic process of a single node, and learns to forget irrelevant historical information and update the current state through its gating mechanism.

5. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 4, characterized in that, In S3, the physical residual term includes the residual loss based on the governing equation and the physical principle regularization loss; in the residual loss based on the governing equation, at any spatiotemporal node... In the Time step ( i , t residuals satisfy: ； in, For nodes The corresponding material density, For nodes In the The acceleration at the time step is approximated by the second-order difference between displacement and time. For nodes In the The second-order stress tensor of the time step characterizes the nodes. The three-dimensional stress state at the location, For nodes In the Stress divergence at time step, through nodes with neighboring nodes The weighted average approximation of the projection of the stress difference onto the connection vector satisfies: ； in, For neighboring nodes The stress tensor, For nodes Representative volume, For connecting nodes with neighboring nodes The unit direction vector of the edge, For nodes with neighboring nodes The area represented by the connecting edges between them; The residual loss over the entire spatiotemporal domain satisfies: ； In the formula, Where T is the total number of spatiotemporal points and T is the total number of time steps. This represents the total number of nodes in the structure.

6. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 5, characterized in that, The physical principle regularization loss is divided into a loss term that penalizes predictions that violate the energy dissipation law and a loss term that penalizes stress predictions that exceed the material's dynamic strength. The loss term that penalizes predictions that violate the energy dissipation law is as follows: ； In the formula, This indicates that for all nodes All time steps Summation, covering the entire spacetime domain. For nodes At time step The increase in plastic work, , For nodes At time step The damage energy release rate, , For nodes At time step The increment of the damage variable, ; The penalty for stress prediction exceeding the material's dynamic strength is as follows: ； Where F(·) is the dynamic strength yield surface function, and the input is the node... At time step stress tensor The output is equivalent stress. Let be the dynamic strength limit of the material, and be the inherent mechanical parameter of the material.

7. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 6, characterized in that, The hard constraint is implemented as follows: for displacement boundaries nodes Before the decoder outputs the final value, increment the displacement of this node. Forced to be set as The corresponding incremental replacement network predicts the displacement increment. The corresponding increment is: ； In the formula, For nodes The displacement vector, For nodes The displacement boundary condition vector. For nodes At time step The boundary displacement increment, For nodes In the The displacement boundary condition vector at the time step. For nodes In the The displacement boundary condition vector at the time step.

8. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 7, characterized in that, In S3, the loss function is a weighted sum of data-driven loss and physical constraint loss, satisfying: ； in, For the total loss function, , , For hyperparameters, The error loss between the predicted value and the high-fidelity simulation value, ... represents additional physical constraint loss terms or constitutive constraint loss that can be added as needed. For nodes In the The time step is the displacement vector predicted by the model. For nodes In the The time step is obtained from the high-fidelity reference displacement true value obtained by the finite element method (FEM).

9. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 8, characterized in that, In S4, the message function for enhancing physical information satisfies: ； in, For neighboring nodes Send to node The news For lightweight MLP, For neighboring nodes The stress tensor, n ij To the neighbor node Pointing to node The unit direction vector, For nodes with neighboring nodes Distance-based decay weights, For nodes with neighboring nodes Material consistency weight; The wave velocity sensing attention mechanism is to correlate the calculation of attention weights with the theoretical propagation speed of stress waves in the material, satisfying the following: ； In the formula, For nodes For neighboring nodes Wave speed perception attention coefficient, For nodes For neighboring nodes The eigenvectors of the edges, For nodes For nodes The eigenvectors of the edges, The theoretical wave arrival time, i.e., the time from the stress wave to the node. propagate to neighboring nodes Theoretical time required For the theoretical wave velocity, the stress wave at the node Neighbor nodes The theoretical propagation speed in the material region, For stress waves from nodes propagation to nodes The theoretical time required, where η is the time window width control parameter; The physical-driven message aggregation and node update transforms received physical messages into node state updates, simulating Newton's second law. The specific steps of the physical-driven message aggregation and node update include: Physical message aggregation: receiving node Aggregated messages received from all neighbors, forming a combined force: ； In the formula, For nodes The equivalent resultant force vector at a given point is obtained by weighted summation of the physical messages passed by all neighbors; Physics-based node update: This involves aggregating messages and calculating node quality from node density and representative volume. Combine and update the acceleration or velocity of the node: ； In the formula, For nodes Updated velocity vector, For nodes The original velocity vector before the update The time step is the time increment for numerical integration. Calculated from node density and representative volume, For nodes The equivalent acceleration.

10. The method for constructing a structural explosion response calculation model based on a graph neural network according to claim 9, characterized in that, In S5, the multi-step Rollout training strategy defines a gradually increasing number of Rollout steps S for the training sample sequence {u0, u1, ..., u...}. T }, input the true values ​​{u0, u1, ..., u} of the first L time steps. L-1 The model performs S-step free prediction to obtain {u} L ,u L+1 ,…,u L+S-1 Multi-step loss prediction satisfy: ； in, Here, represents the loss weight coefficient corresponding to the prediction at step s, set to an incrementing value. s is the single-step index variable within Rollout, used only to iterate through the multi-step prediction process. L is the given true initial time series length, representing the starting time step when the model begins autonomous prediction. Let be the nodal displacement prediction vector output by the model at time step L+s-1. This is the true displacement reference vector corresponding to the L+s-1 time step.

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