A heterogeneous graph data representation method for structural explosion dynamic response analysis

Abstract

This invention relates to the field of structural explosion dynamic response calculation, specifically disclosing a heterogeneous graph data representation method for structural explosion dynamic response analysis. The method includes: establishing and validating a high-fidelity finite element baseline model of the structural explosion response, and obtaining a baseline data source for the structural explosion response; establishing and implementing an adaptive sampling algorithm based on physical field gradients to adaptively select key nodes representing the structural dynamic characteristics from the finite element mesh nodes; establishing a multi-attribute graph edge linking and weight quantization method to construct a multi-attribute weighted graph; and establishing an automated construction and storage method for spatiotemporal graph datasets to generate a spatiotemporal sequence graph dataset for training a graph neural network. This invention overcomes the limitations of traditional neural networks on the serialization and meshing of training data, achieving automated, high-fidelity conversion from continuous, heterogeneous finite element simulation data to sparse, discrete graph structure data with well-defined topological relationships, as well as data size simplification and increased physical information density.

Description

Technical Field

[0001] This invention relates to the field of structural explosion dynamics technology, specifically to a heterogeneous graph data characterization method for structural explosion dynamic response analysis. Background Technology

[0002] Accurate analysis of the dynamic response characteristics of structures during explosions is a core prerequisite for ensuring engineering safety and optimizing structural design. Due to inherent challenges such as the difficulty, high cost, and complex control of large-scale engineering structural explosion tests, high-fidelity numerical simulation has become the primary and effective means of studying the dynamic response characteristics of structures during explosions. Reasonable modeling and high-precision calculation are key to accurately obtaining these structural response characteristics.

[0003] In practical engineering scenarios such as structural toughness assessment, sensitivity calculation, and uncertainty analysis, hundreds or thousands of repeated calculations are often required, which places high demands on both the accuracy and efficiency of numerical simulation. This makes the research and optimization of related technologies of great practical engineering value.

[0004] Currently, the relevant core technology solutions mainly fall into two categories: Firstly, there is traditional numerical simulation analysis. This involves extensive simplification of specific engineering problems to establish corresponding analytical models for calculating structural responses. Its core reliance is on the engineer's understanding of the engineering problem, their ability to construct simplified models, and their experience in selecting computational methods. For highly complex nonlinear problems such as structural explosion responses, more refined numerical models are needed to ensure analytical accuracy. However, the computational process of refined numerical simulation is time-consuming and labor-intensive, making it difficult to meet efficiency requirements in scenarios requiring high-frequency repetitive calculations, and thus unsuitable for practical applications of parametric analysis and optimization design.

[0005] Secondly, traditional deep learning modeling. With the deep integration of deep learning and structural engineering, the modeling and analysis mode combining physical information and data-driven approaches has introduced a new paradigm for structural dynamics calculations due to its efficient nonlinear analysis capabilities. Numerical analysis models essentially establish mapping functions between input parameters and output responses, which aligns closely with the analytical logic of deep learning, providing a feasible path to address the challenge of balancing accuracy and efficiency in traditional structural mechanics response calculations.

[0006] However, the above two types of technical solutions still have obvious shortcomings in practical applications: Traditional numerical simulation analysis techniques rely on human experience for simplification, are highly subjective, and have extremely high computational costs for detailed models. They cannot be directly applied to scenarios that require a lot of repetitive calculations, making it difficult to balance accuracy and efficiency. For traditional deep learning modeling techniques, on the one hand, their data-driven network models rely on a large number of high-quality labeled datasets and are prone to overfitting due to a lack of physical interpretability, resulting in limited model generalization ability; on the other hand, complex structure explosion systems generally have structural characteristics such as non-Euclidean, highly dynamic, and multi-source heterogeneous. Traditional neural networks are limited by the requirements of training data serialization and gridding, and cannot adapt to the highly dynamic characteristics of complex data in time, space and other dimensions, making it difficult to achieve accurate modeling and simulation.

[0007] Compared to traditional neural networks, graph neural networks can not only represent the characteristics of data elements in the form of nodes, but also depict the correlation between different elements through information transmission between links. They have a powerful ability to approximate nonlinear functions and can achieve accurate simulation of complex systems without the need for precise modeling of internal influencing factors. This provides a new feasible path for modeling and simulating complex systems such as the dynamic response of structural explosions.

[0008] Against this backdrop, the current technology system lacks a data analysis method that can efficiently connect high-fidelity physical models and graph neural networks. It cannot transform complex, heterogeneous, dynamic, and continuous gridded finite element simulation data into sparse, discretized graph structure data with clear topological relationships, thus making it difficult to fully leverage the advantages of graph neural networks.

[0009] Therefore, there is an urgent need to develop a high-precision and high-efficiency heterogeneous graph data representation method to solve the data conversion problem between high-fidelity physical models and graph neural networks, laying the foundation for the subsequent construction of graph neural network proxy models that integrate physical mechanisms and data-driven approaches, thereby efficiently and accurately obtaining structural explosion response characteristics. Summary of the Invention

[0010] To address the aforementioned problems in the prior art, this invention provides a heterogeneous graph data characterization method for structural explosion dynamic response analysis. This method effectively solves the technical challenge of directly using high-fidelity finite element simulation data for graph neural network training, significantly improving data utilization efficiency and the prediction accuracy and physical reliability of subsequent proxy models.

[0011] To achieve the above objectives, this invention proposes a heterogeneous graph data characterization method for structural explosion dynamic response analysis, comprising: S1: Establish and verify a high-fidelity finite element benchmark model of the structural explosion response, and obtain the benchmark data source for the explosion response; S2: Establish and implement an adaptive sampling algorithm based on physical field gradients to adaptively select key nodes representing the dynamic characteristics of the structure from the finite element mesh nodes; S3: Establish a multi-attribute graph edge linking and weight quantification method, construct a graph topology connecting key nodes, quantify the strength of physical interactions between nodes through edge attributes, and construct a multi-attribute weighted graph containing the physical laws of structural internal force transmission and stress wave propagation. S4: Establish an automated method for constructing and storing spatiotemporal graph datasets, converting unstructured result files generated by parameterized high-fidelity simulations into spatiotemporal sequence graph datasets for training graph neural networks.

[0012] Preferably, in S1, the specific steps for establishing and verifying a high-fidelity finite element baseline model of the structural explosion response and obtaining the explosion response data source include: S11. Construct a structure-air-explosive finite element model and use the multi-material arbitrary Lagrange-Euler MM-ALE algorithm to simulate the detonation process of the explosive, the propagation of the shock wave and the coupling process of the structural dynamic response. Set boundary constraints and define the contact or fluid-structure interaction between the structure and the air. S12. Set key variables of the model to form a parameter space. The key variables include explosion scene parameters and structural parameters. By comparing with experimental data in published literature or verified analytical solutions, verify the accuracy and reliability of the benchmark model. S13. After the explosion simulation is completed, extract the physical field information of displacement, velocity, acceleration, stress, equivalent plastic strain, maximum principal stress, and damage variables of the model nodes, and identify the nodes and regions with severe and critical responses.

[0013] Preferably, in S2, the specific steps for establishing and implementing the adaptive sampling algorithm based on the physical field gradient include: S21. Select representative physical fields and perform filtering preprocessing; S22, for each finite element mesh node Calculate importance weights ; S23. Use systematic sampling or K-Means clustering algorithm to perform probability sampling based on node importance weights; S24. Post-processing is performed using a hierarchical sampling strategy and minimum distance constraints. S25. Perform algorithm verification on the graph structure data obtained by adaptive sampling.

[0014] Preferably, in S22, the importance weight The calculations include: S221. Calculation of finite element mesh nodes using the central difference method. Gradient vector in physical field I and its amplitude The calculation formula is: ; ; In the formula, Represents the physical field I along First-order rate of change in the axial direction, Represents the physical field I along First-order rate of change in the axial direction, Represents the physical field I along First-order rate of change in the axial direction; S222. Weights are constructed using a nonlinear mapping function, wherein the nonlinear mapping function is: ; ; in, Importance weight The minimum value, Importance weight The maximum value, This represents the maximum value of the gradient magnitude. This represents the minimum value of the gradient magnitude. It is a nonlinear control factor. For scaling parameters, For translation parameters, These are the normalized weight values ​​in the [0,1] interval; S223, Computation Node Probability of being selected : ; In the formula, N is the total number of grid nodes.

[0015] Preferably, in S24, the hierarchical sampling strategy is as follows: set a threshold T. high For all normalized weight values ​​in the interval [0,1] Deterministic sampling is performed on the nodes, and probabilistic sampling is used to extract nodes from the remaining nodes, with uniform random sampling in a flat region with extremely low weights; a minimum Euclidean distance is set. Apply distance constraints when the distance between two selected nodes is less than [a certain value]. When this happens, nodes with lower weights are discarded.

[0016] Preferably, in S25, the specific steps for algorithm verification of the graph structure data obtained by adaptive sampling include: inputting the graph structure data obtained by adaptive sampling into a GNN model for training, and comparing its prediction results with those of the model obtained by uniform sampling. The comparison indicators include the root mean square error (RMSE) of the response in the key region, the mean absolute error (MAE) of the overall response, and the information entropy of the dataset.

[0017] Preferably, step S3 specifically includes: S31. Construct physics-driven graph edge topology links; S32. Link correction based on material consistency; S33. Quantize and calculate the weights of multiple attribute edges; S34. Integrate information to construct graph data G containing physical laws: ; In the formula, For the set of nodes for adaptive sampling, For a set of edges in a physics-driven topological link, The node feature matrix contains static and dynamic attributes such as coordinates, elastic modulus, density, and initial damage. This is an edge attribute matrix, containing the overall weight, the weight of each factor, and the edge type; S35. Perform algorithm comparison and verification.

[0018] Preferably, in S31, the construction of the physical-driven graph edge topology link includes: establishing the initial link using the Delaunay triangulation algorithm, while setting the search radius R and deleting edges with a side length greater than R; In S32, the link is modified as follows: if two nodes belong to different material regions or are separated by a known interface, then the direct connection between them is deleted, or a special interface edge attribute is assigned.

[0019] Preferably, in S33, the quantization calculation of multi-attribute edge weights is as follows: Define nodes With nodes Spatial distance factor between Force transmission path factor Material consistency factor The connection nodes are obtained by weighted geometric mean fusion. With nodes edge Overall weight The formula is: ; in, , , For hyperparameters, Used to identify a one-sided topological relationship between two related structural nodes, i.e., a representative node With nodes A specific edge is formed; The spatial distance factor Using exponential decay or power-law decay models: in, For nodes coordinates For nodes coordinates It is the attenuation coefficient; The force transmission path factor The calculation process is as follows: Calculate the edge vectors: ; Get edges Unit vector of principal stress direction at midpoint Consistency in calculation direction: ; In the formula, edge vectors and principal stress direction vector The included angle, It is the cosine of the angle between the edge direction and the principal stress direction; Mapping consistency to weights When the direction of the edge is completely aligned with the direction of the principal stress, When perpendicular, the value is 0.5; when completely opposite, the value is 0. The material consistency factor The calculation is as follows: if node and nodes If they are the same type of material, then If they belong to different materials, then a penalty weight is assigned. If seams or cracks exist, assign a lower weight. .

[0020] Preferably, step S4 specifically includes: S41. Load the node mapping table and extract the physical quantities of the specified nodes in the mapping table in parallel at all time steps, ensuring that all physical quantities are extracted at the same time step. S42. Based on the high-frequency components of the explosion shock wave Determine the Nyquist frequency and maximum sampling time interval Linear interpolation or cubic spline interpolation is used to resample the original physical quantities of non-uniform time steps to a time step of 1. For a uniform time series with intervals of , the calculation formula is: ; In the formula, X resampled [n] represents the physical quantity value at the nth uniform time step; interp(·) is the linear interpolation or cubic spline interpolation operator; T original This array, representing the original time step vector from a high-fidelity simulation output, is typically non-uniform; X original Is with T originalA one-to-one correspondence of physical quantity numerical vectors; S43. Pre-construct a static graph topology, create a graph snapshot for each time step of each working condition, assemble the physical quantities of all nodes at the corresponding time into a node feature matrix, and then stack the graph snapshots of all time steps in chronological order to form a spatiotemporal graph sequence. The assembly of the physical quantities of all nodes at the corresponding time into a node feature matrix is ​​as follows: ; in, Let be the node feature matrix corresponding to time t, where t is the time identifier corresponding to the time step. Here, N is the node index, and N is the total number of nodes. For nodes At any moment eigenvectors; node At any moment eigenvectors It includes static properties and dynamic response quantities. The static properties include coordinates, elastic modulus, density, and initial damage. The dynamic response quantities include displacement, velocity, stress, strain, and damage variables. ; in, For nodes Three-dimensional spatial coordinates, For nodes At time t Directional shift, For nodes At time t Directional normal stress, For nodes von Mises equivalent stress at time t For nodes The damage variable at time t, This is the matrix transpose symbol; The process involves stacking the snapshots of all time steps in chronological order to form a spatiotemporal graph sequence. for: ; In the formula, For a moment The corresponding image snapshot, , ... These are the moments arranged in chronological order. This represents the total number of time steps. S44. Connect the above steps using a Python script, input a list of paths to the parameterized simulation results files, and output a dataset file divided into training / validation / test sets.

[0021] Therefore, this invention proposes a heterogeneous graph data characterization method for structural explosion dynamic response analysis, the advantages of which are as follows: (1) To realize the automated and high-fidelity conversion of complex, heterogeneous, and continuous finite element simulation data into sparse, discrete graph structure data with clear topological relationships, encode mechanical laws into graph topology and attributes, simplify the data scale while improving the density of physical information, and provide key technical support for the application of graph neural networks in the field of structural explosion.

[0022] (2) By using an adaptive sampling algorithm based on physical field gradient and a multi-attribute weighted graph construction containing stress wave propagation and internal force transmission laws, the basic principles of structural mechanics are directly encoded into the topology and attributes of the graph data, so that the generated graph data itself becomes a physical information carrier.

[0023] 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

[0024] Figure 1 This is an overall flowchart of a heterogeneous graph data characterization method for structural explosion dynamic response analysis according to the present invention; Figure 2 This is a schematic diagram of an adaptive sampling algorithm based on physical field gradients for a heterogeneous graph data characterization method for structural explosion dynamic response analysis according to the present invention. Detailed Implementation

[0025] 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.

[0026] 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.

[0027] like Figures 1-2 As shown, the present invention provides a heterogeneous graph data characterization method for structural explosion dynamic response analysis, comprising: S1: Establish and verify a high-fidelity finite element baseline model of the structural explosion response, and obtain the explosion response data source. Specific steps include: S11. Construct a structure-air-explosive finite element model and use the multi-material arbitrary Lagrange-Euler MM-ALE algorithm to simulate the detonation process of the explosive, the propagation of the shock wave and the coupling process of the structural dynamic response. Set boundary constraints and define the contact or fluid-structure interaction between the structure and the air. S12. Set key variables of the model to form a parameter space. Key variables include explosion scenario parameters (such as explosive equivalent and detonation location) and structural parameters (such as geometric dimensions and reinforcement ratio). By comparing with experimental data in published literature or verified analytical solutions, verify the accuracy and reliability of the benchmark model and ensure that the error of key response indicators is within an acceptable range. S13. After the explosion simulation is completed, extract the physical field information of displacement, velocity, acceleration, stress, equivalent plastic strain, maximum principal stress, and damage variables of the model nodes, and identify the nodes and regions with severe and critical responses.

[0028] S2: Establish and implement an adaptive sampling algorithm based on physical field gradients to adaptively select key nodes from the finite element mesh nodes; The specific steps for establishing and implementing an adaptive sampling algorithm based on physical field gradients include: S21. Select representative physical fields (such as the maximum principal stress field and the equivalent plastic strain field) and perform filtering preprocessing to smooth numerical fluctuations; S22, for each finite element mesh node Calculate importance weights ; Importance weight The calculations include: S221. Calculate nodes using the central difference method. Gradient vector in physical field I and its amplitude The calculation formula is: ; ; In the formula, Represents the physical field I along First-order rate of change in the axial direction, Represents the physical field I along First-order rate of change in the axial direction, Represents the physical field I along First-order rate of change in the axial direction; S222. Weights are constructed using a nonlinear mapping function, which is: ; ; in, Importance weight The minimum value, Importance weight The maximum value, This represents the maximum value of the gradient magnitude. This represents the minimum value of the gradient magnitude. It is a nonlinear control factor. For scaling parameters, For translation parameters, These are the normalized weight values ​​in the [0,1] interval; S223, Computation Node Probability of being selected : ; In the formula, For nodes The weight of represents the proportion of the total weight, where N is the total number of grid nodes.

[0029] S23. Use systematic sampling or K-Means clustering algorithm to perform probability sampling based on weights; S24. Post-processing is performed using a hierarchical sampling strategy and minimum distance constraints. The stratified sampling strategy sets a threshold T. high For all normalized weight values ​​in the interval [0,1] Deterministic sampling is performed on the nodes, and probabilistic sampling is used to extract nodes from the remaining nodes, with uniform random sampling in a flat region with extremely low weights; a minimum Euclidean distance is set. Apply distance constraints when the distance between two selected nodes is less than [a certain value]. When this happens, nodes with lower weights are discarded.

[0030] S25. Perform algorithm verification on the graph structure data obtained by adaptive sampling.

[0031] The specific steps for algorithm verification of graph structure data obtained by adaptive sampling include: inputting the graph structure data obtained by adaptive sampling into a GNN model for training, and comparing its prediction results with those of a model obtained by uniform sampling. The comparison metrics include the root mean square error (RMSE) of the response in the key region, the mean absolute error (MAE) of the overall response, and the information entropy of the dataset.

[0032] S3: Establish a multi-attribute graph edge linking and weight quantification method, construct a graph topology connecting key nodes, quantify the strength of physical interactions between nodes through edge attributes, and construct a multi-attribute weighted graph containing physical laws. Specifically, it includes: S31. Constructing physics-driven graph edge topology links; The construction of physics-driven graph edge topology links includes: using the Delaunay triangulation algorithm to establish initial links, while setting the search radius R, deleting edges with a side length greater than R, and eliminating excessively far non-physical connections. S32. Link correction based on material consistency: If two nodes belong to different material regions or are separated by a known interface (such as structural joints or cracks), delete the direct connection between them or assign special interface edge properties.

[0033] S33. Quantize and calculate the weights of multiple attribute edges; In S33, the quantization calculation of multi-attribute edge weights is as follows: Define nodes With nodes Spatial distance factor between Force transmission path factor Material consistency factor The connection nodes are obtained by weighted geometric mean fusion. With nodes edge Overall weight The formula is: ; in, , , For hyperparameters, Used to identify a one-sided topological relationship between two related structural nodes, i.e., a representative node With nodes A specific edge is formed; Spatial distance factor Using exponential decay or power-law decay models: in, For nodes coordinates For nodes coordinates It is the attenuation coefficient; Force transmission path factor The calculation process is as follows: Calculate the edge vectors: ; Get edges Unit vector of principal stress direction at midpoint Consistency in calculation direction: ; In the formula, edge vectors and principal stress direction vector The included angle, It is the cosine of the angle between the edge direction and the principal stress direction; Mapping consistency to weights When the direction of the edge is completely aligned with the direction of the principal stress, When perpendicular, the value is 0.5; when completely opposite, the value is 0. The material consistency factor The calculation is as follows: if node and nodes If they are the same type of material, then If they belong to different materials, then a penalty weight is assigned. If seams or cracks exist, assign a lower weight. .

[0034] S34. Integrate information to construct graph data G containing physical laws: ; In the formula, For the set of nodes for adaptive sampling, For a set of edges in a physics-driven topological link, The node feature matrix contains static and dynamic attributes such as coordinates, elastic modulus, density, and initial damage. This is an edge attribute matrix, containing the overall weight, the weight of each factor, and the edge type; S35. Perform algorithm comparison and verification.

[0035] S4: Establish an automated method for constructing and storing spatiotemporal graph datasets, generating spatiotemporal sequence graph datasets suitable for training graph neural networks from the large number of unstructured result files generated by parameterized high-fidelity simulations. Specifically, this includes: S41. Load the node mapping table and extract the physical quantities of the specified nodes in the mapping table in parallel at all time steps, ensuring that all physical quantities are extracted at the same time step. S42. Based on the high-frequency components of the explosion shock wave Determine the Nyquist frequency and maximum sampling time interval Linear interpolation or cubic spline interpolation can be used to interpolate non-uniform time steps. The original physical quantities were resampled to For a uniform time series with intervals of , the calculation formula is: ; In the formula, X resampled [n] represents the physical quantity value at the nth uniform time step; interp(·) is the linear interpolation or cubic spline interpolation operator; T original This array, representing the original time step vector from a high-fidelity simulation output, is typically non-uniform; Xoriginal Is with T original A one-to-one correspondence of physical quantity numerical vectors.

[0036] S43. Pre-construct a static graph topology, create a graph snapshot for each time step of each working condition, assemble the physical quantities of all nodes at the corresponding time into a node feature matrix, and then stack the graph snapshots of all time steps in chronological order to form a spatiotemporal graph sequence.

[0037] The physical quantities of all nodes at the corresponding time point are assembled into a node characteristic matrix as follows: ; in, Let be the node feature matrix corresponding to time t, where t is the time identifier corresponding to the time step. Here, N is the node index, and N is the total number of grid nodes. For nodes At any moment eigenvectors; node At any moment eigenvectors It includes static properties and dynamic response quantities. The static properties include coordinates, elastic modulus, density, and initial damage. The dynamic response quantities include displacement, velocity, stress, strain, and damage variables. ; in, For nodes Three-dimensional spatial coordinates, For nodes At time t Directional shift, For nodes At time t Directional normal stress, For nodes von Mises equivalent stress at time t For nodes The damage variable at time t, This is the matrix transpose symbol; Stack the snapshots of all time steps in chronological order to form a spatiotemporal graph sequence. for: ; In the formula, For a moment The corresponding image snapshot, , ... These are the moments arranged in chronological order. This represents the total number of time steps. S44. Connect the above steps using a Python script, input a list of paths to the parameterized simulation results files, and output a dataset file divided into training / validation / test sets.

[0038] This invention takes the dynamic response analysis of a reinforced concrete frame structure under near-field explosion as an example, and combines common structural parameters and explosion scenarios in engineering. The specific implementation process is as follows: S1: Construction and Verification of High-Fidelity Finite Element Benchmark Model Construct a three-dimensional finite element model of a single-span reinforced concrete frame structure using air and explosives. The frame span is 6m, the story height is 3m, the beam cross-section is 300mm×500mm, the column cross-section is 400mm×400mm, and the concrete strength grade is C30 (elastic modulus 30GPa, density 2400kg / m³). 3 (Compressive strength 30MPa), longitudinal reinforcement uses HRB400 (elastic modulus 206GPa, density 7850kg / m³). 3 The yield strength is 400 MPa); the explosive is TNT with an equivalent of 2 kg, and the detonation point is located at the bottom surface of the frame beam at the mid-span (contact explosion).

[0039] The MM-ALE algorithm was used to simulate detonation and shock wave propagation. The outer boundary of the air domain was set as a non-reflective boundary condition, and the fluid-structure interaction algorithm was used to simulate the transfer of explosive load between the frame concrete and the air. Parameter settings were used to form a parameter space (3×2×3=18 sets of working conditions) for the explosive equivalent (1kg, 2kg, 3kg), detonation location (mid-span beam, column base), and frame reinforcement ratio (1.0%, 1.5%, 2.0%). The accuracy of the model was verified by comparing it with data such as the mid-span displacement time history, column base strain response, and concrete fracture range from the "Close-range Explosion Test of C30 Reinforced Concrete Frame" in published literature, ensuring that the error was within 8%.

[0040] After the simulation is completed, physical field information such as displacement, maximum principal stress, equivalent plastic strain, and damage variables of all nodes are extracted to identify areas with severe response, such as the mid-span of the beam and the base of the column.

[0041] S2: Adaptive sampling implementation based on physical field gradient: The maximum time history values ​​of the principal stress field and the equivalent plastic strain field are selected as the core physical fields, and Gaussian filtering (standard deviation) is applied. Smoothing data fluctuations. A non-linear control factor is used when calculating node importance weights. Scaling parameters Translation parameters The formula is normalized to obtain Set the weight threshold T high 90th percentile ( ), deterministic sampling is performed on the nodes in this region, and probabilistic sampling is performed on the remaining nodes according to weight proportions, for those with low physical field gradients ( In flat regions, uniform random sampling is performed at a sampling rate of 3% to ensure global connectivity of the graph structure. Minimum Euclidean distance. m, remove redundant nodes.

[0042] Ultimately, the original 180,000+ finite element mesh nodes were reduced to 2,500 key nodes. Verification showed that this sampling scheme reduced the RMSE of the key region by 18%, the MAE of the entire field by 14%, and the information entropy of the dataset by 9% compared to uniform sampling.

[0043] S3: Construction of Multi-Attribute Weighted Graphs Initial topological links were generated based on Delaunay triangulation. Edges exceeding R=0.8m (corresponding to 1.6 times the beam section height) were then removed to eliminate excessively long non-physical connections. During link correction, direct connections between concrete and air nodes were removed, and edges between reinforced and concrete nodes were assigned the "interface edge" attribute. The initial weight was set to 0.3 and optimized as a learnable parameter during subsequent training to simulate the bond-slip effect between reinforced and concrete.

[0044] Edge weights are calculated using a weighted geometric mean formula, with hyperparameters... (Spatial distance factor) (Force transmission path factor) (Material consistency factor); Spatial distance factor adopts an exponential decay model, with a decay coefficient. ; The force transmission path factor is obtained by calculating the cosine of the angle between the edge vector and the principal stress direction at the midpoint of the edge; the material consistency factor is set according to the node material type: 1 between concrete nodes, 1 between steel nodes, 0.3 between steel and concrete nodes (determined empirically based on the elastic modulus ratio and bond strength), and 0.2 between concrete and air nodes (simulating pressure transmission loss).

[0045] By integrating a node set of 2500 key nodes, an edge set of approximately 7500 edges, a node feature matrix, and an edge attribute matrix, a multi-attribute weighted graph G containing physical laws is constructed.

[0046] S4: Automated Construction of Spatiotemporal Graph Datasets Load the graph node ID-finite element mesh node ID mapping table, and use a Python script to read 18 sets of LS-DYNA.d3plot files with different working conditions in parallel. Extract the physical quantities of 2500 key nodes in all time steps within 0-50ms to ensure the spatiotemporal alignment of displacement, stress, damage and other data.

[0047] The dominant frequency of the explosion shock wave Set the Nyquist frequency Maximum sampling time interval Cubic spline interpolation was used to resample the non-uniform time step data into 5000 uniform time steps (corresponding to a total duration of 50ms).

[0048] For each time step, a graph snapshot is created, and a node feature matrix (2500×12 dimensions, including: 3D coordinates, concrete strength reduction factor, elastic modulus, density, initial damage, current step triaxial displacement, and current step damage variable) is assembled and stacked in chronological order to form a spatiotemporal graph sequence G (5000 graph snapshots). The entire process is connected by a script, taking the simulation result file paths of 18 working conditions as input, and outputting an HDF5 format dataset divided into training set (12 sets), validation set (3 sets), and test set (3 sets), which can be directly called for training of graph neural networks.

[0049] This embodiment successfully constructed a high-fidelity finite element baseline model through a four-step process, reducing more than 180,000 mesh nodes to 2,500 key nodes. The RMSE of the key region response was reduced by 18% compared with uniform sampling, and the MAE of the whole field was reduced by 14%. A multi-attribute weighted graph containing 2,500 nodes and about 7,500 edges was formed, and finally a standardized HDF5 format spatiotemporal graph dataset containing 18 working conditions and 100 time steps was generated.

[0050] Comparative verification shows that the GNN model trained on this dataset has an error of less than 12% compared with the high-fidelity simulation results in predicting stress response in key areas, with a single forward inference time of only 0.3 seconds (about 2000 times more efficient than traditional finite element calculations). It achieves both automated high-fidelity conversion of complex finite element simulation data to graph structure data and a balance between data size reduction and physical information density enhancement, significantly improving the accuracy, efficiency, and physical interpretability of subsequent models.

[0051] Therefore, this invention provides a heterogeneous graph data representation method for structural explosion dynamic response analysis, which solves the data conversion problem between high-fidelity physical models and graph neural networks. By embedding physical information into the graph structure design, the mechanical laws such as stress wave propagation and internal force transmission contained in the continuous medium mechanics model are encoded into the topology and properties of the graph. This breaks through the limitations of traditional neural networks on the serialization and gridding of training data, and realizes the automated and high-fidelity conversion of complex, heterogeneous, dynamic, and continuous gridded finite element simulation data into sparse, discretized graph structure data with clear topological relationships, achieving a balance between data scale reduction and physical information density enhancement.

[0052] 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 heterogeneous graph data characterization method for structural explosion dynamic response analysis, characterized in that, Includes the following steps: S1: Establish and verify a high-fidelity finite element benchmark model of the structural explosion response, and obtain the benchmark data source for the explosion response; S2: Establish and implement an adaptive sampling algorithm based on physical field gradients to adaptively select key nodes representing the dynamic characteristics of the structure from the finite element mesh nodes; S3: Establish a multi-attribute graph edge linking and weight quantification method, construct a graph topology connecting key nodes, quantify the strength of physical interactions between nodes through edge attributes, and construct a multi-attribute weighted graph containing the physical laws of structural internal force transmission and stress wave propagation. S4: Establish an automated method for constructing and storing spatiotemporal graph datasets, converting unstructured result files generated by parameterized high-fidelity simulations into spatiotemporal sequence graph datasets for training graph neural networks.

2. The heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 1, characterized in that, In S1, the specific steps for establishing and verifying a high-fidelity finite element baseline model of the structural explosion response and obtaining the explosion response data source include: S11. Construct a structure-air-explosive finite element model and use the multi-material arbitrary Lagrange-Euler MM-ALE algorithm to simulate the detonation process of the explosive, the propagation of the shock wave and the coupling process of the structural dynamic response. Set boundary constraints and define the contact or fluid-structure interaction between the structure and the air. S12. Set key variables of the model to form a parameter space. The key variables include explosion scene parameters and structural parameters. By comparing with experimental data in published literature or verified analytical solutions, verify the accuracy and reliability of the benchmark model. S13. After the explosion simulation is completed, extract the physical field information of displacement, velocity, acceleration, stress, equivalent plastic strain, maximum principal stress, and damage variables of the model nodes, and identify the nodes and regions with severe and critical responses.

3. The heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 2, characterized in that, In S2, the specific steps for establishing and implementing the adaptive sampling algorithm based on the physical field gradient include: S21. Select representative physical fields and perform filtering preprocessing; S22, for each finite element mesh node Calculate importance weights ; S23. Use systematic sampling or K-Means clustering algorithm to perform probability sampling based on node importance weights; S24. Post-processing is performed using a hierarchical sampling strategy and minimum distance constraints. S25. Perform algorithm verification on the graph structure data obtained by adaptive sampling.

4. The heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 3, characterized in that, In S22, importance weights The calculations include: S221. Calculation of finite element mesh nodes using the central difference method. Gradient vector in physical field I and its amplitude The calculation formula is: ； ； In the formula, Represents the physical field I along First-order rate of change in the axial direction, Represents the physical field I along First-order rate of change in the axial direction, Represents the physical field I along First-order rate of change in the axial direction; S222. Weights are constructed using a nonlinear mapping function, wherein the nonlinear mapping function is: ； ； in, Importance weight The minimum value, Importance weight The maximum value, This represents the maximum value of the gradient magnitude. This represents the minimum value of the gradient magnitude. It is a nonlinear control factor. For scaling parameters, For translation parameters, These are the normalized weight values ​​in the [0,1] interval; S223, Computation Node Probability of being selected : ； In the formula, N is the total number of grid nodes.

5. The heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 3, characterized in that, In S24, the hierarchical sampling strategy is as follows: set a threshold T. high For all normalized weight values ​​in the interval [0,1] Deterministic sampling is performed on the nodes, and probabilistic sampling is used to extract nodes from the remaining nodes, with uniform random sampling in a flat region with extremely low weights; a minimum Euclidean distance is set. Apply distance constraints when the distance between two selected nodes is less than [a certain value]. When this happens, nodes with lower weights are discarded.

6. The heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 3, characterized in that, In S25, the specific steps for algorithm verification of the graph structure data obtained by adaptive sampling include: inputting the graph structure data obtained by adaptive sampling into a GNN model for training, and comparing its prediction results with those of the model obtained by uniform sampling. The comparison indicators include the root mean square error (RMSE) of the response in the key region, the mean absolute error (MAE) of the overall response, and the information entropy of the dataset.

7. The heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 6, characterized in that, Step S3 specifically includes: S31. Construct physics-driven graph edge topology links; S32. Link correction based on material consistency; S33. Quantize and calculate the weights of multiple attribute edges; S34. Integrate information to construct graph data G containing physical laws: ； In the formula, For the set of nodes for adaptive sampling, For a set of edges in a physics-driven topological link, The node feature matrix contains static and dynamic attributes such as coordinates, elastic modulus, density, and initial damage. This is an edge attribute matrix, containing the overall weight, the weight of each factor, and the edge type; S35. Perform algorithm comparison and verification.

8. The heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 7, characterized in that, In S31, the construction of physics-driven graph edge topology links includes: using the Delaunay triangulation algorithm to establish initial links, while setting the search radius R and deleting edges with a side length greater than R; In S32, the link is modified as follows: if two nodes belong to different material regions or are separated by a known interface, then the direct connection between them is deleted, or a special interface edge attribute is assigned.

9. A heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 7, characterized in that, In S33, the quantization calculation of multi-attribute edge weights is as follows: Define nodes With nodes Spatial distance factor between Force transmission path factor Material consistency factor The connection nodes are obtained by weighted geometric mean fusion. With nodes edge Overall weight The formula is: ； in, , , For hyperparameters, Used to identify a one-sided topological relationship between two related structural nodes, i.e., a representative node With nodes A specific edge is formed; The spatial distance factor Using exponential decay or power-law decay models: in, For nodes coordinates For nodes coordinates It is the attenuation coefficient; The force transmission path factor The calculation process is as follows: Calculate the edge vectors: ; Get edges Unit vector of principal stress direction at midpoint Consistency in calculation direction: ； In the formula, edge vectors and principal stress direction vector The included angle, It is the cosine of the angle between the edge direction and the principal stress direction; Mapping consistency to weights When the direction of the edge is completely aligned with the direction of the principal stress, When perpendicular, the value is 0.5; when completely opposite, the value is 0. The material consistency factor The calculation is as follows: if node and nodes If they are the same type of material, then If they belong to different materials, then a penalty weight is assigned. If seams or cracks exist, assign a lower weight. .

10. A heterogeneous graph data characterization method for structural explosion dynamic response analysis according to claim 9, characterized in that, Step S4 specifically includes: S41. Load the node mapping table and extract the physical quantities of the specified nodes in the mapping table in parallel at all time steps, ensuring that all physical quantities are extracted at the same time step. S42. Based on the high-frequency components of the explosion shock wave Determine the Nyquist frequency and maximum sampling time interval Linear interpolation or cubic spline interpolation is used to resample the original physical quantities of non-uniform time steps to a time step of 1. For a uniform time series with intervals of , the calculation formula is: ； In the formula, X resampled [n] represents the physical quantity value at the nth uniform time step; interp(·) is the linear interpolation or cubic spline interpolation operator; T original This array, representing the original time step vector from a high-fidelity simulation output, is typically non-uniform; X original Is with T original A one-to-one correspondence of physical quantity numerical vectors; S43. Pre-construct a static graph topology, create a graph snapshot for each time step of each working condition, assemble the physical quantities of all nodes at the corresponding time into a node feature matrix, and then stack the graph snapshots of all time steps in chronological order to form a spatiotemporal graph sequence. The assembly of the physical quantities of all nodes at the corresponding time into a node feature matrix is ​​as follows: ； in, Let be the node feature matrix corresponding to time t, where t is the time identifier corresponding to the time step. Here, N is the node index, and N is the total number of nodes. For nodes At any moment eigenvectors; node At any moment eigenvectors It includes static properties and dynamic response quantities. The static properties include coordinates, elastic modulus, density, and initial damage. The dynamic response quantities include displacement, velocity, stress, strain, and damage variables. ； in, For nodes Three-dimensional spatial coordinates, For nodes At time t Directional shift, For nodes At time t Directional normal stress, For nodes von Mises equivalent stress at time t For nodes The damage variable at time t, This is the matrix transpose symbol; The process involves stacking the snapshots of all time steps in chronological order to form a spatiotemporal graph sequence. for: ； In the formula, For a moment The corresponding image snapshot, , ... These are the moments arranged in chronological order. This represents the total number of time steps. S44. Connect the above steps using a Python script, input a list of paths to the parameterized simulation results files, and output a dataset file divided into training / validation / test sets.

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