Structural modal calculation method based on embedded physical information graph neural network

Abstract

This application relates to a structural modal calculation method based on an embedded physical information graph neural network, which specifically includes: dividing the physical structure into a mesh to obtain the input layer node features and adjacency matrix of the graph convolutional neural network; converting the physical information into digital information; using the input layer node features and adjacency matrix as input layer data to construct a graph convolutional neural network structure; applying hard constraints to the boundary conditions of the graph convolutional neural network, embedding first physical information, and forcing the output layer node features to satisfy the boundary conditions in a hard-coded form; constructing an orthogonality module, embedding second physical information, and forcing the output layer node features to satisfy the mode shape orthogonality condition in a hard-coded form; embedding third physical information based on the node features that satisfy the boundary conditions and mode shape orthogonality condition to construct a loss function based on the Rayleigh quotient; and iteratively solving for the mode shapes and modal frequencies of the structure according to the loss function.

Description

Technical Field

[0001] This application relates to the field of computer technology, and in particular to a structural modality calculation method based on an embedded physical information graph neural network. Background Technology

[0002] Structural modal parameters, as one of the dynamic properties of a structure, are fundamental to dynamic analysis. Modal analysis plays a crucial role in fields such as mechanical engineering, aerospace, and civil engineering. For example, the dynamic design of mechanical mechanisms, the solution of structural dynamic response based on the modal superposition method, and the health monitoring of engineering structures all rely on modal calculations.

[0003] Traditional technologies offer various schemes for calculating structural modal parameters. While these theories and methods are numerous, they still have many shortcomings that need improvement. For example, finite element method-based modal calculations require a high level of theoretical knowledge from the operator and are complex to process. Artificial intelligence-based modal calculations can only perform calculations on simple structures and cannot be extended to structures with complex topological relationships. Furthermore, calculations involving multiple vibration modes face numerous constraints and difficulties in parameter tuning. Common neural network-based calculation methods are data-driven, requiring extensive experimentation and model acquisition of labeled data, which is extremely costly for some complex problems.

[0004] It is evident that there is currently no traditional technology that can calculate the structural modal parameters for multiple vibration modes of structures with complex topological relationships. Summary of the Invention

[0005] Therefore, it is necessary to provide a structural modality calculation method based on an embedded physical information graph neural network for complex topological relationships, addressing the aforementioned technical problems.

[0006] Firstly, this application provides a structural modality calculation method based on an embedded physical information graph neural network. The method includes:

[0007] The physical structure is divided into grids to obtain the input layer node features and adjacency matrix of the graph convolutional neural network;

[0008] Using the input layer node features and the adjacency matrix as input layer data, a graph convolutional neural network structure is constructed.

[0009] Hard constraints are imposed on the boundary conditions of the graph convolutional neural network, and the first physical information is embedded in the form of hard encoding to force the node features of the output layer to satisfy the boundary conditions.

[0010] Construct an orthogonality module to embed second physical information so that the node features of the output layer are forced to satisfy the mode orthogonality condition;

[0011] Based on the node characteristics that satisfy the boundary conditions and mode orthogonality conditions, a loss function based on the Ruili quotient is constructed by embedding third physical information.

[0012] The loss function is used to iteratively solve for the mode shapes and modal frequencies of the structure.

[0013] In one embodiment, the step of meshing the physical structure to obtain the input layer node features and adjacency matrix of the graph convolutional neural network includes:

[0014] Obtain the modal order of the structure to be determined;

[0015] Based on the desired modal order, determine the mesh density;

[0016] The physical structure is meshed according to the mesh density to generate multiple elements;

[0017] Obtain the node position coordinates of each element after mesh generation, as well as the topological relationship between elements and nodes;

[0018] The input layer node features of the graph convolutional neural network are obtained based on the node position coordinates, and the adjacency matrix of the graph convolutional neural network is obtained based on the topological relationship between the units and nodes.

[0019] In one embodiment, constructing a graph convolutional neural network structure using the input layer node features and the adjacency matrix as input layer data includes:

[0020] Based on the input layer node features and the adjacency matrix, the input layer input data of the graph convolutional neural network is constructed.

[0021] An MLP (Multi-Layer Perceptron) layer is constructed after the output layer of the graph convolutional neural network, forming a graph convolutional neural network structure that includes input / output layers, hidden layers, output layers, and the MLP.

[0022] In one embodiment, applying hard constraints to the boundary conditions of the graph convolutional neural network, and embedding first physical information in a hard-coded form to force the node features of the output layer to satisfy the boundary conditions, includes:

[0023] Select the mode shape calculation value of the node at the boundary from the node characteristics;

[0024] The modal calculation values ​​of the nodes at the boundary are forcibly replaced with the constraint values ​​that the nodes at the boundary should satisfy, and the first physical information is embedded in the form of hard coding to force the node features of the output layer to satisfy the boundary conditions.

[0025] In one embodiment, constructing the orthogonality module to embed second physical information to force the node features of the output layer to satisfy the mode orthogonality condition includes:

[0026] The node features of the output layer are transformed using the Schmidt orthogonalization method to embed second physical information, thereby forcing the transformed node features of the output layer to satisfy the mode orthogonality constraint.

[0027] In one embodiment, the construction of a loss function based on the Ruili quotient by embedding third physical information based on node features that satisfy boundary conditions and mode orthogonality conditions includes:

[0028] Based on the node features that satisfy the boundary conditions and modal orthogonality conditions, a node feature matrix is ​​generated;

[0029] The node feature matrix is ​​deformed so that the calculated values ​​of the same order vibration mode in each spatial direction are merged into the same column, thus obtaining the transformed node feature matrix;

[0030] Based on the feature matrix of the transformed nodes, a loss function based on the Ruili quotient is constructed by embedding third physical information.

[0031] In one embodiment, the step of constructing a loss function based on Ruili quotient by embedding third physical information according to the transformed node feature matrix includes:

[0032] The kinetic and potential energy of the structural system are calculated based on the node characteristics in the node matrix corresponding to each vibration mode.

[0033] Based on the potential energy and kinetic energy, the energy constraint of the Ruili quotient when the structure vibrates in each mode is obtained.

[0034] Based on the energy constraints of the Ruili business and the weight coefficients corresponding to different preset constraint terms, a loss function is constructed.

[0035] In one embodiment, the iterative solution of the structural mode shapes and modal frequencies based on the loss function includes:

[0036] Based on the loss function, iteratively solve for the structural mode shapes and modal frequencies corresponding to the point where the loss function converges to its minimum value.

[0037] Secondly, this application also provides a structural modality calculation device based on an embedded physical information graph neural network. The device includes:

[0038] The partitioning module is used to partition the physical structure into a grid, thereby obtaining the input layer node features and adjacency matrix of the graph convolutional neural network.

[0039] The core construction module is used to construct a graph convolutional neural network structure using the input layer node features and the adjacency matrix as input layer data.

[0040] The first physical information embedding module is used to apply hard constraints to the boundary conditions of the graph convolutional neural network and embed the first physical information in the form of hard encoding so that the node features of the output layer are forced to meet the boundary conditions.

[0041] The second physical information embedding module is used to construct the orthogonality module, so as to embed the second physical information to force the node features of the output layer to satisfy the mode orthogonality condition.

[0042] The third physical information embedding module is used to embed third physical information to construct a loss function based on the Ruili quotient based on the node features that satisfy the boundary conditions and mode orthogonality conditions.

[0043] The iterative solution module is used to iteratively solve the mode shapes and modal frequencies of the structure according to the loss function.

[0044] Thirdly, this application also provides a computer device. The computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to perform the following steps:

[0045] The physical structure is divided into grids to obtain the input layer node features and adjacency matrix of the graph convolutional neural network;

[0046] Using the input layer node features and the adjacency matrix as input layer data, a graph convolutional neural network structure is constructed.

[0047] Hard constraints are imposed on the boundary conditions of the graph convolutional neural network, and the first physical information is embedded in the form of hard encoding to force the node features of the output layer to satisfy the boundary conditions.

[0048] Construct an orthogonality module to embed second physical information so that the node features of the output layer are forced to satisfy the mode orthogonality condition;

[0049] Based on the node characteristics that satisfy the boundary conditions and mode orthogonality conditions, a loss function based on the Ruili quotient is constructed by embedding third physical information.

[0050] The loss function is used to iteratively solve for the mode shapes and modal frequencies of the structure.

[0051] Fourthly, this application also provides a computer-readable storage medium. The computer-readable storage medium stores a computer program thereon, which, when executed by a processor, performs the following steps:

[0052] The physical structure is divided into grids to obtain the input layer node features and adjacency matrix of the graph convolutional neural network;

[0053] Using the input layer node features and the adjacency matrix as input layer data, a graph convolutional neural network structure is constructed.

[0054] Hard constraints are imposed on the boundary conditions of the graph convolutional neural network, and the first physical information is embedded in the form of hard encoding to force the node features of the output layer to satisfy the boundary conditions.

[0055] Construct an orthogonality module to embed second physical information so that the node features of the output layer are forced to satisfy the mode orthogonality condition;

[0056] Based on the node characteristics that satisfy the boundary conditions and mode orthogonality conditions, a loss function based on the Ruili quotient is constructed by embedding third physical information.

[0057] The loss function is used to iteratively solve for the mode shapes and modal frequencies of the structure.

[0058] Fifthly, this application also provides a computer program product. The computer program product includes a computer program that, when executed by a processor, performs the following steps:

[0059] The physical structure is divided into grids to obtain the input layer node features and adjacency matrix of the graph convolutional neural network;

[0060] Using the input layer node features and the adjacency matrix as input layer data, a graph convolutional neural network structure is constructed.

[0061] Hard constraints are imposed on the boundary conditions of the graph convolutional neural network, and the first physical information is embedded in the form of hard encoding to force the node features of the output layer to satisfy the boundary conditions.

[0062] Construct an orthogonality module to embed second physical information so that the node features of the output layer are forced to satisfy the mode orthogonality condition;

[0063] Based on the node characteristics that satisfy the boundary conditions and mode orthogonality conditions, a loss function based on the Ruili quotient is constructed by embedding third physical information.

[0064] The loss function is used to iteratively solve for the mode shapes and modal frequencies of the structure.

[0065] The aforementioned method, apparatus, computer equipment, storage medium, and computer program product for structural modal calculation based on an embedded physical information graph neural network (PLM) involves meshing the physical structure to obtain the input layer node features and adjacency matrix of the graph convolutional neural network (GNN), converting physical information into digital information, and constructing the GNN structure using the input layer node features and adjacency matrix as input layer data. Hard constraints are applied to the boundary conditions of the GNN, embedding first physical information to force the output layer node features to satisfy the boundary conditions through hard encoding. An orthogonality module is constructed, embedding second physical information to force the output layer node features to satisfy the modal orthogonality condition through hard encoding. Based on the node features satisfying the boundary and modal orthogonality conditions, third physical information is embedded to construct a loss function based on the Rayleigh quotient. The loss function is used to iteratively solve for the modal shapes and modal frequencies of the structure. Throughout this process, only the Rayleigh quotient is introduced as the network's loss function; other mode-related physical conditions, such as boundary conditions and modal orthogonality, are directly encoded into the neural network through hard constraints and do not need to participate in network iteration. The modal orthogonality is enforced by embedding an orthogonalization module into the network structure and transforming the feature space. This hard-coded constraint method reduces network constraints and lowers the difficulty of parameter tuning. Through multiple iterations, modal parameters of structures with complex topological relationships can be calculated. Furthermore, the proposed model is purely physics-driven and does not rely on any labeled data, thus significantly reducing modeling costs and expanding its application scope in practical engineering. Attached Figure Description

[0066] Figure 1 This is an application environment diagram of a structural modality calculation method based on an embedded physical information graph neural network in one embodiment.

[0067] Figure 2 This is a flowchart illustrating a structural mode calculation method based on an embedded physical information graph neural network in one embodiment.

[0068] Figure 3 This is a schematic diagram of the core structure of a convolutional neural network;

[0069] Figure 4 A schematic diagram illustrating the process of applying the first physical information;

[0070] Figure 5 This is a schematic diagram of a sub-process of S100 in one embodiment;

[0071] Figure 6 This is a schematic diagram of the structural network partitioning;

[0072] Figure 7 This is a schematic diagram of the merging and transformation of vibration modes of the same order;

[0073] Figure 8 This is a schematic diagram of a convolutional neural network architecture.

[0074] Figure 9 This is a schematic diagram of the three-dimensional truss geometry model;

[0075] Figure 10 This is a schematic diagram of the upper horizontal longitudinal bracing / lower horizontal longitudinal bracing of a three-dimensional truss;

[0076] Figure 11 This is a schematic diagram of the lateral connection system of a three-dimensional truss.

[0077] Figure 12 Schematic diagram of the calculation curves for different vibration modes;

[0078] Figure 13 This is a structural block diagram of a structural modality calculation device based on an embedded physical information graph neural network in one embodiment;

[0079] Figure 14 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0081] The structural modality calculation method based on an embedded physical information graph neural network provided in this application can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be integrated onto server 104, or it can be located in the cloud or on another network server. Terminal 102 sends a structural modal parameter calculation request to server 104. This request specifies the structure to be calculated, such as structure A. Upon receiving the request, server 104 performs mesh generation on the physical structure, obtaining the input layer node features and adjacency matrix of a graph convolutional neural network (GNN). It converts the physical information into digital information, using the input layer node features and adjacency matrix as input layer data to construct the GNN structure. Hard constraints are applied to the boundary conditions of the GNN, embedding first physical information to force the output layer node features to satisfy the boundary conditions through hard encoding. An orthogonality module is constructed, embedding second physical information to force the output layer node features to satisfy the modal orthogonality condition. Based on the node features satisfying the boundary and modal orthogonality conditions, a third physical information is embedded to construct a loss function based on the Rayleigh quotient. The loss function is used to iteratively solve for the mode shapes and modal frequencies of the structure. Furthermore, server 104 can feed back the obtained mode shapes and modal frequencies to terminal 102. The terminal 102 can be, but is not limited to, various personal computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle systems. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster consisting of multiple servers.

[0082] In one embodiment, such as Figure 2 As shown, a structural modality calculation method based on an embedded physical information graph neural network is provided, which is then applied to... Figure 1 Taking server 104 as an example, the following steps are included:

[0083] S100: The physical structure is divided into grids to obtain the input layer node features and adjacency matrix of the graph convolutional neural network.

[0084] The physical structure refers to the physical structure to be determined, i.e., the physical structure for which structural modal parameters need to be generated. Meshing the physical structure can be based on the modal order to be determined; the higher the modal order, the denser the mesh. After meshing, multiple elements and their corresponding nodes are obtained. Based on the node coordinates and the relationships between elements and nodes, the input data for the subsequent graph convolutional neural network (Graph Convolutional Neural Network) can be obtained. Specifically, based on the position coordinates of each node in the meshed structure, the input layer node features of the Graph Convolutional Neural Network can be obtained. Based on the relationships between the elements and nodes in the meshed structure, the adjacency matrix of the Graph Convolutional Neural Network can be obtained. This converts physical information into digital information in the form of a graph representation.

[0085] S200: Construct a graph convolutional neural network structure using the input layer node features and adjacency matrix as input layer data.

[0086] This section describes the construction of the core structure of a graph convolutional neural network. The features of the input layer nodes and the adjacency matrix are used as input data for feature extraction within the graph convolutional neural network. Generally, a graph convolutional neural network contains an input layer, hidden layers, and an output layer. Specifically, here, the features of the input layer nodes and the adjacency matrix are used as input data.

[0087] In practical applications, after obtaining the input layer node features X and adjacency matrix A of the graph convolutional neural network (GCN) in S100, X and A need to be input into the GCN for feature extraction. Furthermore, since GCNs typically have 2 to 3 layers, too many layers can hinder feature extraction. Therefore, to improve the feature extraction capability of the network structure constructed in this application, an MLP layer is added after the graph convolutional layers. The MLP layer's hyperparameters are flexible and can be adjusted according to the complexity of the problem, thereby improving the network's feature extraction and processing capabilities. Specifically, the powerful feature extraction capability of the MLP is used here to compensate for the weak feature processing capability of traditional GCNs due to the limitation on the number of layers. The construction of the network's input layer, hidden layers, output layer, and MLP layer is as follows... Figure 3 As shown.

[0088] S300: Apply hard constraints to the boundary conditions of the graph convolutional neural network, embedding the first physical information in a hard-coded form to force the node features of the output layer to satisfy the boundary conditions.

[0089] To ensure that the node features of the output layer can obtain the desired solution after multiple iterations, the node features must satisfy the corresponding boundary conditions, i.e., the first physical information. Unlike traditional neural networks that impose constraints through loss functions, this application uses hard coding to force the output node features to satisfy the corresponding boundary conditions. The physical conditions related to the boundary conditions no longer participate in the network iteration.

[0090] In one embodiment, applying hard constraints to the boundary conditions of the graph convolutional neural network and embedding first physical information in a hard-coded form to force the node features of the output layer to meet the boundary conditions includes: selecting the mode shape calculation value of the node at the boundary from the node features; forcibly replacing the mode shape calculation value of the node at the boundary with the constraint value that the node at the boundary should satisfy in a preset manner, and embedding the first physical information in a hard-coded form to force the node features of the output layer to meet the boundary conditions.

[0091] Specifically, such as Figure 4 The boundary condition application process shown in the figure can be represented as follows: The output layer node features of the convolutional neural network can be expressed as follows: Figure 4 The matrix shown is in the form of a matrix. The calculated value of the j-th mode shape representing the i-th node; where (i = 1, ..., N; j = 1, ..., n); These represent the 1st, i-th, and nth mode shapes, respectively. Calculate the x, y, z directions for the j-th mode shape at the boundary node. These are the constraint values ​​that the nodes at the boundary must satisfy. After obtaining the node characteristics output by the network, the modal values ​​of the nodes at the boundary are selected. Force it to be replaced with constraint value Immediately This yields the modified node features, which satisfy the corresponding boundary conditions.

[0092] S400: Construct an orthogonality module to embed second physical information so that the node features of the output layer are forced to satisfy the mode orthogonality condition.

[0093] In addition to satisfying boundary conditions, the node characteristics of the network output layer also need to satisfy the mode shape orthogonality condition, i.e., the second physical information. According to relevant theories of structural dynamics, the mode shapes of a structure are orthogonal with respect to the mass matrix and stiffness matrix.

[0094] S500: Based on the node characteristics that satisfy the boundary conditions and mode orthogonality conditions, a loss function based on the Ruili quotient is constructed by embedding third physical information.

[0095] After obtaining the node features that satisfy the boundary conditions and orthogonality conditions, a loss function can be constructed based on these features. Specifically, the above processing includes the embedding of three types of physical information: boundary conditions, modal orthogonality, and Rayleigh quotient. Boundary conditions and modal orthogonality are embedded using hard constraints, while the Rayleigh quotient is embedded using soft constraints.

[0096] S600: Iteratively solve the mode shapes and modal frequencies of the structure based on the loss function.

[0097] During the iterative solution process, the convergence value of the loss is continuously calculated. When the loss converges to the minimum value, the mode shapes and modal frequencies of each order are obtained.

[0098] The aforementioned structural modal calculation method based on an embedded physical information graph neural network involves meshing the physical structure to obtain the input layer node features and adjacency matrix of the graph convolutional neural network (GNN). This converts the physical information into digital information, which is then used as input layer data to construct the GNN structure. Hard constraints are applied to the boundary conditions of the GNN, embedding first physical information to force the output layer node features to satisfy the boundary conditions through hard encoding. An orthogonality module is constructed, embedding second physical information to force the output layer node features to satisfy mode shape orthogonality conditions through hard encoding. Based on the node features satisfying the boundary and mode shape orthogonality conditions, third physical information is embedded to construct a loss function based on the Rayleigh quotient. The loss function is then used to iteratively solve for the mode shapes and frequencies of each order of the structure. Throughout this process, only the Rayleigh quotient is introduced as the network's loss function; other mode-related physical conditions, such as boundary conditions and mode orthogonality, are directly encoded into the neural network through hard constraints, without participating in network iteration. The modal orthogonality is enforced by embedding an orthogonalization module into the network structure and transforming the feature space. This hard-coded constraint method reduces network constraints and lowers the difficulty of parameter tuning. Through multiple iterations, modal parameters of structures with complex topological relationships can be calculated. Furthermore, the proposed model is purely physics-driven and does not rely on any labeled data, thus significantly reducing modeling costs and expanding its application scope in practical engineering.

[0099] like Figure 5 As shown, in one embodiment, S100 includes:

[0100] S110: Obtain the modal order of the structure to be determined;

[0101] S120: Determine the mesh density based on the order of the modes to be determined;

[0102] S130: Mesh the physical structure according to the mesh density to generate multiple elements;

[0103] S140: Obtain the node position coordinates of each element after mesh generation, as well as the topological relationship between elements and nodes;

[0104] S150: Obtain the input layer node features of the graph convolutional neural network based on the node position coordinates, and obtain the adjacency matrix of the graph convolutional neural network based on the topological relationship between the units and nodes.

[0105] like Figure 6 As shown, the structure to be determined is first divided into multiple elements. The mesh density depends on the order of the mode to be determined. The higher the order of the mode to be determined, the denser the mesh. Figure 6 In, (x i ,y i Let F be the coordinates of the i-th node. xi ,F yi M i The horizontal reaction force, vertical reaction force, and bending moment at the i-th constraint point represent the constraint conditions at the i-th boundary.

[0106] By using the position coordinates of each node in the meshed structure, the node features of the input layer of the graph convolutional neural network are obtained.

[0107]

[0108] Based on the relationship between each unit and node in the network structure after partitioning, the adjacency matrix of the graph convolutional neural network is obtained, i.e.

[0109]

[0110] As shown in equation (2), if the i-th node and the j-th node are located in the same cell, then the element A in the i-th row and j-th column... ij =1, because this application intends to use an undirected graph to construct the network structure, at this time the element A in the j-th row and i-th column is... ji =1; If the i-th node and the j-th node are not in the same cell, then the element A in the i-th row and j-th column is 1. ij =0, element A in row j and column i = 0 ji =0.

[0111] In one embodiment, constructing an orthogonality module to embed second physical information to force the node features of the output layer to satisfy the mode orthogonality condition includes:

[0112] The node features of the output layer are transformed using the Schmidt orthogonalization method to embed second physical information, thereby forcing the transformed node features of the output layer to satisfy the mode orthogonality constraint.

[0113] The Schmidt orthogonalization method is a technique in linear algebra used to transform a set of linearly independent vectors into a set of orthogonal vectors. In neural networks, the features of the output layer nodes typically represent the model's predictions or decision-making processes; orthogonalizing these features ensures that they do not interfere with each other.

[0114] In addition to satisfying boundary conditions, the node features of the network output layer also need to satisfy the modal orthogonality condition. According to relevant theories of structural dynamics, the mode shapes of a structure are orthogonal with respect to the mass matrix and stiffness matrix. Unlike traditional neural networks that construct network constraints through loss functions, this application uses the Schmidt orthogonalization method to transform the output layer node features, forcing the transformed node features to satisfy the modal orthogonality constraint, thereby embedding physical information. The Schmidt orthogonalization method is shown below:

[0115]

[0116] In the formula, To force the satisfaction of the first and (i+1)th order mode shapes corresponding to the node characteristics after boundary condition processing, For the modified node features Node features after orthogonal transformation; The first, i-th, and (i+1)-th mode shapes corresponding to the modified nodal features. The component in the j-th unit; M j Let be the element mass matrix of the j-th element.

[0117] After the characteristic transformations as shown in equations (3) and (4), the mode components that satisfy orthogonality can be obtained.

[0118] In one embodiment, based on the node features that satisfy the boundary conditions and the modal orthogonality conditions, the loss function based on the Ruili quotient is constructed by embedding third physical information, including:

[0119] Based on the node features that satisfy the boundary conditions and mode orthogonality conditions, a node feature matrix is ​​generated; the node feature matrix is ​​transformed so that the calculated values ​​of the same mode in each spatial direction are merged into the same column to obtain the transformed node feature matrix; based on the transformed node feature matrix, third physical information is embedded to construct a loss function based on the Ruili quotient.

[0120] For nodes that satisfy the boundary conditions and orthogonality conditions, an orthogonal transformation is performed, the specific transformation being as follows: Figure 7 As shown, the calculated values ​​of the same vibration mode in the x, y, and z directions are combined into the same column.

[0121] In one embodiment, constructing a loss function based on the Ruili quotient by embedding third physical information according to the transformed node feature matrix includes:

[0122] The kinetic and potential energy of the structural system are calculated based on the node characteristics in the node matrix corresponding to each mode of vibration. Based on the potential and kinetic energy, the energy constraint of the Ruili quotient when the structure vibrates in each mode of vibration is obtained. According to the energy constraint of the Ruili quotient and the weight coefficients corresponding to different preset constraint terms, the loss function is constructed.

[0123] First, obtain the node feature component corresponding to the j-th mode shape in the network output layer features. Use this component to calculate the potential energy of the overall structural system when the structure vibrates with the j-th mode shape as calculated.

[0124]

[0125] In the formula, E j E represents the potential energy of the structural system corresponding to the calculated value of the j-th mode shape. j,i K represents the potential energy of the i-th element of the structure corresponding to the calculated value of the j-th mode; i Let be the element stiffness matrix of the i-th element; The calculated value for the j-th mode shape The component of the i-th element; e is the number of elements in the structural system.

[0126] Then, using the node feature components corresponding to the j-th mode shape in the above network output layer features, the kinetic energy of the overall structural system when the structure vibrates with the calculated value of the j-th mode shape is calculated.

[0127]

[0128] In the formula, V j V represents the kinetic energy of the structural system corresponding to the calculated value of the j-th mode shape. j,i M represents the kinetic energy of the i-th element of the structure corresponding to the calculated value of the j-th mode; i Let be the unit mass matrix of the i-th unit.

[0129] Based on the above calculated values ​​of structural potential energy and kinetic energy, the Rayleigh quotient for the structure vibrating with the calculated value of the j-th mode shape is:

[0130]

[0131] If the order of the mode shape to be determined is n, then the loss function should include the Rayleigh quotients corresponding to the modes from order 1 to n, as shown in equation (10):

[0132]

[0133] In the formula, λ k This is the weight coefficient corresponding to the k-th constraint.

[0134] Because the calculated Rayleigh quotient is greater when the structure vibrates in higher-order modes than when it vibrates in lower-order modes, the weighting coefficients should be set to satisfy λ. k <λ k+1 After the above processing steps, the resulting graph convolutional neural network architecture is as follows: Figure 8 As shown.

[0135] In one embodiment, iteratively solving for the mode shapes and modal frequencies of the structure based on the loss function includes:

[0136] Based on the loss function, iteratively solve for the structural mode shapes and modal frequencies corresponding to the convergence of the loss function to the minimum value.

[0137] After multiple iterative calculations, when the loss in the formula converges to its minimum value, the calculated values ​​of each mode shape are... This represents the actual mode shape of the structure. When the calculation converges, the calculated value of the j-th mode shape can be obtained. The corresponding Rayleigh quotient R_q j Corresponding to the j-th mode shape, the j-th modal frequency is:

[0138]

[0139] To explain in detail the data processing process of the structural modal calculation method based on the embedded physical information graph neural network of this application, the following will use a three-dimensional truss as an example to illustrate the data processing process of this application.

[0140] like Figure 9 The image shows a three-dimensional truss geometric model; a planar schematic diagram of the structure is shown below. Figure 10 , Figure 11 As shown.

[0141] like Figure 10 , Figure 11 The dimensions of the three-dimensional truss components are shown. Furthermore, the cross-sectional area of ​​the components is A = 0.005 m². 2 Material density dens = 7860 kg / m³ 3 The elastic modulus E = 2.1e11pa.

[0142] The truss shown in the figure is simulated using rod elements, and the element stiffness matrix and element mass matrix are shown in equations (12) and (13).

[0143]

[0144]

[0145] Based on the GCN-based modal computation framework of this application, the calculated frequency values ​​of the structure are shown in the table.

[0146] Table 1 Calculated Frequency Values

[0147]

[0148] As shown in the table above, the frequency calculation values ​​obtained based on the modal calculation framework of this application have an error of less than 0.2% compared with the finite element method, which can meet the engineering requirements.

[0149] Based on the modal calculation framework proposed in this application, the calculated mode shape curves are as follows: Figure 12 As shown.

[0150] The Modality Decision Criterion (MAC) is a mathematical tool for comparing two vectors. If two vectors are completely equal, the MAC should be 1, and vice versa.

[0151] Table 2 MAC Calculation Values

[0152] Modal order MAC 1 99.99％ 2 99.99％ 3 99.99％ 4 99.99％ 5 99.99％ 6 99.99％

[0153] As shown in Table 2, the MAC values ​​based on the modal calculation framework proposed in this example are all above 99%, which verifies the accuracy of the algorithm.

[0154] Overall, in different embodiments, the core improvements and effects of the structural modality calculation method based on embedded physical information graph neural networks in this application mainly include the following:

[0155] (1) A graph network modal computation framework with embedded physical information is proposed. During training, this framework does not require any labeled data to construct the network's loss function. Instead, it guides the network training by embedding physical knowledge into the neural network architecture. In this way, it is not necessary to obtain labeled data based on a large number of field experiments and numerical simulations, which reduces the investment of manpower and material resources, greatly reduces the cost of building the network, and expands the application scope of the model in practical engineering.

[0156] (2) A modal computation framework based on GCN is proposed. An orthogonality module is introduced into the framework, which forces the output layer node features of the network to meet the mode orthogonality condition and embeds relevant physical information. By modifying the output layer node features, the boundary conditions are hard-coded, and the relevant physical information is no longer reflected in the loss function in the form of soft constraints. This reduces the number of network constraints, lowers the difficulty of parameter tuning, improves the accuracy of modal computation, and makes it possible to solve multiple mode shapes.

[0157] (3) Based on the ability of graph convolutional neural networks to process non-Euclidean data, it makes it possible to perform modal calculations on neural networks with complex topological relationships, thus solving the problem that traditional PINN-based methods can only calculate the vibration modes of structures with relatively simple topological relationships.

[0158] (4) This application solves the problem that the feature extraction capability of graph convolutional neural networks (GCN) is limited because the number of layers is not easy to set too many by adding a multilayer perceptron (MLP) to the output layer of the graph network and taking advantage of the MLP’s strong fitting ability for nonlinear functions.

[0159] (5) This application uses a neural network to solve the modalities of a system with complex topological relationships by using the Rayleigh quotient as the objective function. This solves the problem that the Rayleigh quotient-based method can only estimate the frequency of structures with relatively simple topological relationships and cannot be further applied and promoted.

[0160] It should be understood that although the steps in the flowcharts of the above embodiments are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the above embodiments may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0161] Based on the same inventive concept, this application also provides a structural modality calculation device based on an embedded physical information graph neural network for implementing the structural modality calculation method based on an embedded physical information graph neural network as described above. The solution provided by this device is similar to the implementation scheme described in the above method. Therefore, the specific limitations of one or more embodiments of the structural modality calculation device based on an embedded physical information graph neural network provided below can be found in the limitations of the structural modality calculation method based on an embedded physical information graph neural network described above, and will not be repeated here.

[0162] In one embodiment, such as Figure 13 As shown, a structural modality calculation device based on an embedded physical information graph neural network is provided, comprising:

[0163] The partitioning module 100 is used to partition the physical structure into a grid to obtain the input layer node features and adjacency matrix of the graph convolutional neural network.

[0164] The core construction module 200 is used to construct a graph convolutional neural network structure using the input layer node features and the adjacency matrix as input layer data.

[0165] The first physical information embedding module 300 is used to apply hard constraints to the boundary conditions of the graph convolutional neural network and embed the first physical information in the form of hard encoding so that the node features of the output layer are forced to meet the boundary conditions.

[0166] The second physical information embedding module 400 is used to construct an orthogonality module to embed the second physical information so that the node features of the output layer are forced to satisfy the mode orthogonality condition.

[0167] The third physical information embedding module 500 is used to embed third physical information to construct a loss function based on the Ruili quotient based on the node features that satisfy the boundary conditions and mode orthogonality conditions.

[0168] The iterative solution module 600 is used to iteratively solve the mode shapes and modal frequencies of the structure according to the loss function.

[0169] In one embodiment, the partitioning module 100 is further configured to obtain the desired modal order of the structure; determine the mesh partitioning density based on the desired modal order; partition the physical structure into multiple units according to the mesh partitioning density; obtain the node position coordinates of each unit after mesh partitioning, as well as the topological relationship between the units and nodes; obtain the input layer node features of the graph convolutional neural network according to the node position coordinates, and obtain the adjacency matrix of the graph convolutional neural network according to the topological relationship between the units and nodes.

[0170] In one embodiment, the core construction module 200 is further configured to construct input data for the input layer of the graph convolutional neural network based on the input layer node features and the adjacency matrix; and to add an MLP layer after the output layer of the graph convolutional neural network to form a graph convolutional neural network structure including an input layer, a hidden layer, an output layer and an MLP.

[0171] In one embodiment, the first physical information embedding module 300 is further configured to select the mode shape calculation value of the node at the boundary in the node features; forcibly replace the mode shape calculation value of the node at the boundary with the constraint value that the node at the boundary should satisfy in a preset manner, and embed the first physical information in a hard-coded form so that the node features of the output layer are forced to satisfy the boundary conditions.

[0172] In one embodiment, the second physical information embedding module 400 is further configured to perform feature transformation on the node features of the output layer based on the Schmitt orthogonalization method, so as to embed the second physical information to force the node features of the transformed output layer to satisfy the mode orthogonality constraint.

[0173] In one embodiment, the third physical information embedding module 500 is further configured to generate a node feature matrix based on node features that satisfy boundary conditions and mode orthogonality conditions; deform the node feature matrix so that the calculated values ​​of the same mode shape in each spatial direction are merged into the same column to obtain a transformed node feature matrix; and embed the third physical information to construct a loss function based on the Ruili quotient according to the transformed node feature matrix.

[0174] In one embodiment, the third physical information embedding module 500 is further used to calculate the kinetic and potential energy of the structural system based on the node characteristics in the node matrix corresponding to each mode of vibration; based on the potential and kinetic energy, the energy constraint of the Ruili quotient when the structure vibrates in each mode of vibration is obtained; and according to the energy constraint of the Ruili quotient and the weight coefficients corresponding to different preset constraint terms, a loss function is constructed.

[0175] In one embodiment, the iterative solution module 600 is further configured to iteratively solve the structural mode shapes and modal frequencies corresponding to the minimum value of the loss function.

[0176] The modules in the aforementioned structural modality computing device based on embedded physical information graph neural networks can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the operations corresponding to each module.

[0177] In one embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 14 As shown, the computer device includes a processor, memory, and a network interface connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores preset data. The network interface communicates with external terminals via a network connection. When executed by the processor, the computer program implements a structural modality calculation method based on an embedded physical information graph neural network.

[0178] Those skilled in the art will understand that Figure 14 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0179] In one embodiment, a computer device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the above-described structural modality calculation method based on an embedded physical information graph neural network.

[0180] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the above-described structural modality calculation method based on an embedded physical information graph neural network.

[0181] In one embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the above-described structural modality calculation method based on an embedded physical information graph neural network.

[0182] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM). The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0183] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0184] The above embodiments are merely illustrative of several implementation methods of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A structural modality calculation method based on an embedded physical information graph neural network, characterized in that, The method includes: The physical structure is meshed to obtain the input layer node features and adjacency matrix of the graph convolutional neural network; the physical structure is the physical structure for which structural modal parameters need to be generated; the physical structure includes a three-dimensional truss. Using the input layer node features and the adjacency matrix as input layer data, a graph convolutional neural network structure is constructed. Hard constraints are imposed on the boundary conditions of the graph convolutional neural network, and the first physical information is embedded in the form of hard encoding to force the node features of the output layer to satisfy the boundary conditions. Construct an orthogonality module to embed second physical information so that the node features of the output layer are forced to satisfy the mode orthogonality condition; Based on the node characteristics that satisfy the boundary conditions and mode orthogonality conditions, a loss function based on the Ruili quotient is constructed by embedding third physical information. The mode shapes and modal frequencies of the structure are solved iteratively based on the loss function. The step of dividing the physical structure into a grid to obtain the input layer node features and adjacency matrix of the graph convolutional neural network includes: constructing the input layer input data of the graph convolutional neural network based on the input layer node features and adjacency matrix; and adding an MLP layer after the output layer of the graph convolutional neural network to form a graph convolutional neural network structure including an input layer, a hidden layer, an output layer, and an MLP. The input layer node features are represented as follows: In the formula, (x i y i ) represents the coordinates of the i-th node, where i = 1 to 5; The adjacency matrix is ​​represented as: In the formula, if the i-th node and the j-th node are in the same unit, then the element in the i-th row and j-th column is 1; if the i-th node and the j-th node are not in the same unit, then the element in the i-th row and j-th column is 0. The step of applying hard constraints to the boundary conditions of the graph convolutional neural network and embedding first physical information in a hard-coded form to force the node features of the output layer to meet the boundary conditions includes: selecting the mode shape calculation value of the node at the boundary from the node features; forcibly replacing the mode shape calculation value of the node at the boundary with the constraint value that the node at the boundary should satisfy in a preset manner, and embedding first physical information in a hard-coded form to force the node features of the output layer to meet the boundary conditions; the first physical information is the physical information that the node needs to satisfy the corresponding boundary conditions. The boundary conditions include the constraint conditions at the i-th boundary, wherein the constraint conditions at the i-th boundary are the horizontal reaction force, vertical reaction force, and bending moment at the i-th constraint. The construction of the orthogonality module, which embeds second physical information to force the node features of the output layer to satisfy the modal orthogonality condition, includes: performing feature transformation on the node features of the output layer based on the Schmitt orthogonalization method, and embedding second physical information to force the transformed node features of the output layer to satisfy the modal orthogonality constraint; the second physical information is the physical information that the node features need to satisfy the corresponding modal orthogonality condition; The computational process of feature transformation of the node features in the output layer based on the Schmitt orthogonalization method is represented as follows: In the formula, To force the satisfaction of the first and (i+1)th order mode shapes corresponding to the node characteristics after boundary condition processing, The modified node features are the node features after orthogonal transformation; The first, i-th, and (i+1)-th mode shapes corresponding to the modified nodal features. The component in the j-th unit; M j Let be the element mass matrix of the j-th element; The method of constructing a loss function based on the Ruili quotient by embedding third physical information based on node features that satisfy boundary conditions and modal orthogonality conditions includes: generating a node feature matrix based on node features that satisfy boundary conditions and modal orthogonality conditions; transforming the node feature matrix so that the calculated values ​​of the same order mode in each spatial direction are merged into the same column to obtain a transformed node feature matrix; and constructing a loss function based on the Ruili quotient by embedding third physical information based on the transformed node feature matrix; wherein the third physical information is the physical information that the node features must satisfy the corresponding Ruili quotient. The loss function based on the Ruili quotient is constructed as follows: Obtain the node feature components corresponding to the j-th mode shape in the network output layer features. When calculating the vibration of the structure with the j-th mode shape using the node feature components, the potential energy of the overall structural system is as follows: In the formula, E j E represents the potential energy of the structural system corresponding to the calculated value of the j-th mode shape. j,i K represents the potential energy of the i-th element of the structure corresponding to the calculated value of the j-th mode; i Let be the element stiffness matrix of the i-th element; The calculated value for the j-th mode shape The component of the i-th element; e is the number of elements in the structural system. In the formula, V j V represents the kinetic energy of the structural system corresponding to the calculated value of the j-th mode shape. j,i M represents the kinetic energy of the i-th element of the structure corresponding to the calculated value of the j-th mode; i Let be the unit mass matrix of the i-th unit; Based on the calculated potential and kinetic energies, the Rayleigh quotient for the structure vibrating with the calculated j-th mode shape is obtained using the following formula: If the order of the mode shape to be determined is n, then the loss function should include the Rayleigh quotients corresponding to the modes from order 1 to n, as shown in equation (10): In the formula, λ k This is the weight coefficient corresponding to the k-th constraint.

2. The method according to claim 1, characterized in that, The process of dividing the physical structure into a grid to obtain the input layer node features and adjacency matrix of the graph convolutional neural network includes: Obtain the modal order of the structure to be determined; Based on the desired modal order, determine the mesh density; The physical structure is meshed according to the mesh density to generate multiple elements; Obtain the node position coordinates of each element after mesh generation, as well as the topological relationship between elements and nodes; The input layer node features of the graph convolutional neural network are obtained based on the node position coordinates, and the adjacency matrix of the graph convolutional neural network is obtained based on the topological relationship between the units and nodes.

3. The method according to claim 1, characterized in that, The step of constructing a loss function based on the Ruili quotient by embedding third physical information according to the feature matrix of the transformed nodes includes: The kinetic and potential energy of the structural system are calculated based on the nodal characteristics in the nodal matrix corresponding to each mode of vibration. Based on the potential energy and kinetic energy, the energy constraint of the Ruili quotient when the structure vibrates in each mode is obtained. Based on the energy constraints of the Ruili business and the weight coefficients corresponding to different preset constraint terms, a loss function is constructed.

4. The method according to claim 1, characterized in that, The iterative solution of the structural mode shapes and modal frequencies based on the loss function includes: Based on the loss function, iteratively solve for the structural mode shapes and modal frequencies corresponding to the point where the loss function converges to its minimum value.

5. A structural modality calculation device based on an embedded physical information graph neural network, characterized in that, Based on the method of any one of claims 1 to 4, the apparatus comprises: A partitioning module is used to partition the physical structure into a mesh to obtain the input layer node features and adjacency matrix of the graph convolutional neural network; the physical structure is the physical structure for which structural modal parameters need to be generated. The core construction module is used to construct a graph convolutional neural network structure using the input layer node features and the adjacency matrix as input layer data. The first physical information embedding module is used to apply hard constraints to the boundary conditions of the graph convolutional neural network and embed the first physical information in the form of hard encoding so that the node features of the output layer are forced to meet the boundary conditions. The second physical information embedding module is used to construct the orthogonality module, so as to embed the second physical information to force the node features of the output layer to satisfy the mode orthogonality condition. The third physical information embedding module is used to embed third physical information to construct a loss function based on the Ruili quotient based on the node features that satisfy the boundary conditions and mode orthogonality conditions. The iterative solution module is used to iteratively solve for the mode shapes and modal frequencies of the structure according to the loss function; The partitioning module is also used to construct the input data of the input layer of the graph convolutional neural network based on the node features of the input layer and the adjacency matrix; and to add an MLP layer after the output layer of the graph convolutional neural network to form a graph convolutional neural network structure including an input layer, a hidden layer, an output layer and an MLP. The first physical information embedding module is further used to apply hard constraints to the boundary conditions of the graph convolutional neural network, embedding the first physical information in a hard-coded form to force the node features of the output layer to meet the boundary conditions, including: selecting the mode shape calculation value of the node at the boundary from the node features; forcibly replacing the mode shape calculation value of the node at the boundary with the constraint value that the node at the boundary should satisfy in a preset manner, embedding the first physical information in a hard-coded form to force the node features of the output layer to meet the boundary conditions; the first physical information is the physical information that the node needs to satisfy the corresponding boundary conditions. The second physical information embedding module is also used in the construction orthogonality module to embed the second physical information so that the node features of the output layer are forced to meet the mode orthogonality condition. This includes: performing feature transformation on the node features of the output layer based on the Schmitt orthogonalization method, so as to embed the second physical information so that the transformed node features of the output layer are forced to meet the mode orthogonality constraint; the second physical information is the physical information that the node features need to meet the corresponding mode orthogonality condition. The third physical information embedding module is also used to construct a loss function based on the Ruili quotient by embedding the third physical information based on the node features that satisfy the boundary conditions and mode orthogonality conditions. This includes: generating a node feature matrix based on the node features that satisfy the boundary conditions and mode orthogonality conditions; transforming the node feature matrix so that the calculated values ​​of the same order mode in each spatial direction are merged into the same column to obtain a transformed node feature matrix; and constructing a loss function based on the Ruili quotient by embedding the third physical information based on the transformed node feature matrix. The third physical information is the physical information that the node features must satisfy the corresponding Ruili quotient.

6. The apparatus according to claim 5, characterized in that, The partitioning module is also used to obtain the desired modal order of the structure; determine the mesh partitioning density based on the desired modal order; partition the physical structure into multiple units according to the mesh partitioning density; obtain the node position coordinates of each unit after mesh partitioning, as well as the topological relationship between units and nodes; obtain the input layer node features of the graph convolutional neural network based on the node position coordinates, and obtain the adjacency matrix of the graph convolutional neural network based on the topological relationship between units and nodes.

7. The apparatus according to claim 5, characterized in that, The third physical information embedding module is also used to calculate the kinetic and potential energy of the structural system based on the node characteristics in the node matrix corresponding to each mode of vibration; based on the potential and kinetic energy, the energy constraint of the Ruili quotient when the structure vibrates in each mode of vibration is obtained; and based on the energy constraint of the Ruili quotient and the weight coefficients corresponding to different preset constraint terms, a loss function is constructed.

8. The apparatus according to claim 5, characterized in that, The iterative solution module is also used to iteratively solve for the structural mode shapes and modal frequencies corresponding to the minimum value of the loss function.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.

Images