Neural network-based product structure and geometry topology optimization method and system

Abstract

The application discloses a product structure isoparametric topology optimization method and system based on a neural network, and belongs to the field of structure optimization. First, a product structure isoparametric topology optimization model is constructed. An isoparametric topology optimization algorithm is adopted, the spatial coordinates and relative density of fine-grid control points and the displacement and sensitivity of coarse-grid control points are taken as inputs, the sensitivity of fine-grid control points is taken as output, and a training data set is generated. Subsequently, a graph convolutional neural network model with multi-resolution information extraction capability is trained by using the data set. The model comprises a graph convolution module for extracting global stiffness information and a full-connection module for local information fusion. Finally, the trained neural network model is integrated into an isoparametric topology optimization solving process, the sensitivity of fine-grid control points is directly predicted by the neural network, thereby avoiding isoparametric analysis with high calculation cost at the fine-grid level, and the calculation efficiency of product structure isoparametric topology optimization is significantly improved.

Description

Technical Field

[0001] This invention belongs to the field of structural optimization, specifically relating to methods and systems for geometric topology optimization of product structures based on neural networks. Background Technology

[0002] Equivalent geometric topology optimization uses spline basis functions as shape functions, which can accurately characterize geometric boundaries with complex curvatures and achieve the unification of CAD models, CAE models and topology optimization models. It shows significant advantages in geometric continuity and numerical analysis accuracy, but it also leads to a more complex numerical calculation process, which significantly increases the computational cost of topology optimization.

[0003] With the rapid development of computer hardware technology and artificial intelligence, computational mechanics is gradually shifting from traditional methods relying on rigorous mathematical derivations to heuristic intelligent methods based on soft computing. Some existing technologies have begun to explore the introduction of machine learning and other techniques into the field of topology optimization. However, most current research focuses on end-to-end mapping methods from boundary conditions to topology optimization results, which typically require large amounts of training data. Furthermore, because topology optimization results are highly sensitive to boundary conditions, their generalization ability is poor when facing optimization problems outside the training set, often resulting in unsatisfactory performance. In addition, existing machine learning-based topology optimization research is mainly based on the traditional finite element analysis framework. Therefore, how to perform isogeometric topology optimization based on neural networks for product structures is of significant importance and application value. Summary of the Invention

[0004] To address the shortcomings of existing technologies and achieve the goals of improving the accuracy and efficiency of product structure design while reducing costs, this invention adopts the following technical solution:

[0005] Geometric topology optimization methods for product structures based on neural networks include the following steps:

[0006] Step S1: With product structural flexibility as the objective, material usage as the constraint, and the relative density of control points of equal geometric units as the design variable, construct a geometric topology optimization model of the product structure.

[0007] Step S2: Discretize the design domain of the product structure to obtain the coarse mesh of the product structure, then refine the coarse mesh, and perform isogeometric topology optimization on the coarse and fine meshes to obtain an offline dataset with the spatial coordinates and relative density of the fine mesh control points, the displacement and sensitivity of the coarse mesh control points as input data, and the sensitivity of the fine mesh control points as output data.

[0008] Step S3: Train a neural network model using an offline dataset;

[0009] Step S4: Apply the trained neural network model online to the isogeometric topology optimization of the product structure to obtain the density distribution results of the product structure topology optimization.

[0010] Furthermore, step S2 specifically includes the following steps:

[0011] Step S2.1: Use the double third-order NURBS basis functions as shape functions to discretize the design domain of the product structure and obtain the NURBS coarse mesh of the product structure;

[0012] Step S2.2: Refine the NURBS coarse mesh of the product structure using an equal geometric node insertion strategy to obtain the NURBS fine mesh and the mapping matrix between the fine mesh and the coarse mesh control points;

[0013] Step S2.3: Perform isogeometric analysis on both coarse and fine meshes to obtain the displacements of the control points for the two mesh resolutions;

[0014] Step S2.4: Calculate the sensitivity of coarse-grid control points and fine-grid control points;

[0015] Step S2.5: Use the spatial coordinates and relative density of the fine-grid control points, the displacement and sensitivity of the coarse-grid control points as input data, and the sensitivity of the fine-grid control points as output data to construct an offline training dataset;

[0016] Step S2.6: Based on the sensitivity information of the fine-mesh control points, update the relative density on the fine-mesh control points using the moving asymptote algorithm, and calculate the relative density of the coarse-mesh control points based on the mapping matrix;

[0017] Step S2.7: Determine whether the convergence condition of the isogeometric topology optimization is met. If not, jump to step S2.3. If it is met, stop the isogeometric topology optimization iteration.

[0018] Furthermore, the NURBS coarse grid of the product structure refined by the equal geometric node insertion strategy involves inserting nodes into the coarse grid node vector to obtain a refined node vector. The control points of the fine grid are formed by linearly combining the control points of the coarse grid. The coarse grid control points are mapped to the fine grid control points through the difference matrix. Each control point of the fine grid is the result of a weighted average of multiple coarse grid control points around it. Each row in the interpolation matrix corresponds to the weighting coefficient required for a fine grid control point. The weighting coefficient is obtained by recursively calculating the ratio of the fine grid node vector value to the coarse grid node vector value. The mapping relationship between the relative density of coarse and fine grid control points is established based on the difference matrix.

[0019] Furthermore, the coarse mesh node vector Ξ={ξ1,ξ2,...,ξ} j ,...,ξn+p+1}, where n represents the number of coarse grid control points in the parameter domain, p represents the order of the NURBS basis functions, and the refined node vector. N Refine Indicates the degree of refinement; the control point matrix of the finer mesh. Using a coarse grid control point matrix P = {P1, P2, ..., P...} n} T The linear combination forms the following, and the specific mapping relationship is as follows:

[0020]

[0021] Among them, T p This indicates mapping coarse grid control point P to fine grid control point P. The interpolation matrix, ξ j This represents the value of the j-th node in the coarse grid node vector Ξ. Represents fine mesh node vectors The value of the i-th node. Let represent the value of the element in the i-th row and j-th column of the q-th order interpolation matrix. This represents the fine grid control points obtained by refining the coarse grid, where P represents the coarse grid control points.

[0022] Furthermore, the neural network model in step S3 includes a global stiffness information extraction neural network module and a local information fusion neural network module;

[0023] The global stiffness information extraction neural network module is specifically a graph convolutional neural network model, including a graph convolutional input layer, a graph convolutional hidden layer, and a graph convolutional aggregation layer. The outputs of the input layer and the hidden layer are connected to the aggregation layer through knowledge jumps. The graph convolutional input layer receives global fine-grid control point information through the message propagation mechanism of the graph convolutional neural network. The graph convolutional hidden layer performs a weighted sum of the neighborhood information around each fine-grid control point in the feature dimension according to the adjacency matrix, and performs nonlinear feature mapping through an activation function. The graph convolutional aggregation layer aggregates the outputs of each layer node passed through the jump connections in the feature dimension. The aggregation operations include concatenation, average pooling, and max pooling.

[0024] The local information fusion neural network module is specifically a fully connected neural network model, including a fully connected input layer, multiple fully connected hidden layers, and a fully connected output layer. The fully connected input layer acquires the displacement and sensitivity at the local coarse element control points, as well as the feature information extracted by the global stiffness information extraction neural network module at the local fine element control points. The local coarse element refers to a single NURBS element under a coarse mesh; the local fine element refers to multiple fine elements obtained by subdividing a single coarse element through a node insertion strategy. The fully connected output layer is used to output the sensitivity at the local fine element control points.

[0025] Furthermore, step S4 specifically includes the following steps:

[0026] Step S4.1: Use NURBS basis functions as shape functions to discretize the product structure design domain, and combine the equal geometric node insertion strategy to obtain the NURBS coarse and fine grid control points of the product structure, as well as the mapping matrix of the coarse and fine grid control points. Due to the message propagation mechanism of graph convolutional neural networks, the number of grids in the application case and the case of generating the training set does not need to be the same, only the degree of refinement needs to be the same.

[0027] Step S4.2: Perform isogeometric analysis on the product structure on the coarse mesh and calculate the sensitivity corresponding to the control points of the coarse mesh;

[0028] Step S4.3: Input the coordinates and relative density of the control points of the fine mesh of the product structure, and the displacement and sensitivity of the control points of the coarse mesh into the trained neural network model to obtain the sensitivity of the control points of the fine mesh;

[0029] Step S4.4: Based on the sensitivity information of the fine-mesh control points, update the relative density on the fine-mesh control points using the moving asymptote algorithm, and calculate the relative density of the coarse-mesh control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine-mesh control points.

[0030] Step S4.5: Determine whether the convergence condition of the isogeometric topology optimization is met. If not, jump to step S4.2. If it is met, stop the isogeometric topology optimization iteration and obtain the isogeometric topology optimization density distribution result.

[0031] Furthermore, the geometric topology optimization model expression for the product structure in step S1 is as follows:

[0032]

[0033] Where c represents the product structural flexibility, U and F represent the global displacement and load vectors respectively, K represents the global stiffness matrix, and u e and K e N represents the element displacement vector and stiffness matrix, respectively. e V represents the number of equal geometric elements, V represents the structural volume function, and V0 and ρ represents the total volume of the product structure and the material utilization rate, respectively. i,j N is used as a design variable to represent the relative density of control points. ξ and N η ρ represents the number of control points in the two directions of the parameter domain, respectively. min This represents the minimum design variable set to avoid singularity in the stiffness matrix.

[0034] A product structure and other geometric topology optimization system based on neural networks includes a product structure and other geometric topology optimization model construction module, an offline dataset generation module, a neural network module, and a product structure and other geometric topology optimization generation module. Using the aforementioned neural network-based product structure and other geometric topology optimization method, the system sequentially constructs a product structure and other geometric topology optimization model, generates an offline dataset, constructs a neural network model, and generates product structure and other geometric topology optimization results.

[0035] Furthermore, the offline dataset generation module includes a coarse mesh generation unit, a mapping matrix generation unit, an isogeometric analysis unit, a sensitivity calculation unit, an offline training dataset construction unit, a relative density generation unit, and a judgment unit;

[0036] The coarse mesh generation unit uses a double third-order NURBS basis function as the shape function to discretize the design domain of the product structure and obtain the NURBS coarse mesh of the product structure.

[0037] The mapping matrix generation unit uses an equal geometric node insertion strategy to refine the NURBS coarse mesh of the product structure, and obtains the NURBS fine mesh and the mapping matrix between the fine mesh and the coarse mesh control points.

[0038] The isogeometric analysis unit performs isogeometric analysis on both coarse and fine meshes to obtain the displacement of the control points of the two resolution meshes.

[0039] The sensitivity calculation unit is used to calculate the sensitivity of coarse grid control points and fine grid control points;

[0040] The offline training dataset construction unit takes the spatial coordinates and relative density of fine-grid control points, the displacement and sensitivity of coarse-grid control points as input data, and the sensitivity of fine-grid control points as output data to construct a set of offline training datasets.

[0041] The relative density generation unit updates the relative density on the fine grid control points using the moving asymptote algorithm based on the sensitivity information of the fine grid control points, and calculates the relative density of the coarse grid control points based on the mapping matrix.

[0042] The judgment unit is used to determine whether the convergence condition of the isogeometric topology optimization is met. If it is not met, the process returns to the isogeometric analysis unit. If it is met, the isogeometric topology optimization iteration stops.

[0043] Furthermore, the product structure and other geometric topology optimization generation module includes product structure discrete units, coarse mesh and other geometric analysis units, fine mesh sensitivity generation module, relative density generation module, and density distribution generation module;

[0044] The product structure discrete unit uses NURBS basis functions as shape functions to discretize the product structure design domain. Combined with the equal geometric node insertion strategy, the NURBS coarse and fine grid control points of the product structure, as well as the mapping matrix of the coarse and fine grid control points, are obtained. Due to the message propagation mechanism of graph convolutional neural networks, the number of grids in the application case and the case of generating the training set does not need to be the same, only the degree of refinement needs to be the same.

[0045] The coarse-mesh iso-geometric analysis unit performs iso-geometric analysis on the product structure on the coarse mesh and calculates the sensitivity corresponding to the coarse-mesh control points;

[0046] The fine mesh sensitivity generation module inputs the coordinates and relative density of the control points of the fine mesh of the product structure, and the displacement and sensitivity of the control points of the coarse mesh into the trained neural network model to obtain the sensitivity of the fine mesh control points.

[0047] The relative density generation module updates the relative density on the fine grid control points using the moving asymptote algorithm based on the sensitivity information of the fine grid control points, and calculates the relative density of the coarse grid control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine grid control points.

[0048] The density distribution generation module determines whether the convergence condition of the isogeometric topology optimization is met. If it is not met, it returns to the coarse mesh isogeometric analysis unit. If it is met, it stops the isogeometric topology optimization iteration and obtains the isogeometric topology optimization density distribution result.

[0049] The advantages and beneficial effects of this invention are as follows:

[0050] 1. This invention constructs a graph convolutional neural network model for multi-resolution information extraction. This model includes a global stiffness information extraction module, which can effectively process graph structure data such as control points in isogeometric topology optimization. At the same time, a local prediction strategy is introduced, which aggregates the feature information of local coarse and fine grid control points through a fully connected neural network, thereby reducing the dependence on large-scale offline datasets, significantly reducing the computational cost of data generation, and improving engineering applicability and efficiency.

[0051] 2. This invention integrates the trained neural network model into the solution process of isogeometric topology optimization. Based on the isogeometric analysis results on the coarse mesh, it directly predicts the sensitivity information of the control points on the fine mesh, thereby avoiding the high computational cost of isogeometric analysis at the fine mesh level, significantly reducing the computational overhead in the optimization process, and greatly improving the overall computational efficiency of isogeometric topology optimization. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the system structure according to an embodiment of the present invention.

[0053] Figure 2 This is a flowchart of a method according to an embodiment of the present invention.

[0054] Figure 3a This is a schematic diagram (rectangle) of the product structure boundary conditions used to generate the dataset in an embodiment of the present invention.

[0055] Figure 3b This is a schematic diagram (L-shaped) of the product structure boundary conditions used to generate the dataset in an embodiment of the present invention.

[0056] Figure 3c This is a schematic diagram of the product structure boundary conditions (MBB beam) used to generate the dataset in an embodiment of the present invention.

[0057] Figure 4 This is a schematic diagram of the graph convolutional neural network structure for multi-resolution information extraction in an embodiment of the present invention.

[0058] Figure 5 This is a schematic diagram illustrating the boundary condition settings for a serpentine product structure example in an embodiment of the present invention.

[0059] Figure 6 This is a diagram showing the topology optimization results of the serpentine product structure in an embodiment of the present invention.

[0060] Figure 7 This is a schematic diagram of the topology optimization results obtained by using the standard equal geometry topology optimization method in an embodiment of the present invention. Detailed Implementation

[0061] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0062] like Figure 1 As shown, the product structure and other geometric topology optimization system based on neural networks includes a product structure and other geometric topology optimization model building module, an offline dataset generation module, a neural network module, and a product structure and other geometric topology optimization generation module, employing methods such as... Figure 2 The product structure and other geometric topology optimization method based on neural networks shown in the diagram sequentially constructs a product structure and other geometric topology optimization model, generates an offline dataset, constructs a neural network model, and generates product structure and other geometric topology optimization results. The method specifically includes the following steps:

[0063] Step S1: Construct a geometric topology optimization model of the product structure; the expression for the geometric topology optimization model of the product structure is as follows:

[0064]

[0065] Where c represents the product structural flexibility, U and F represent the global displacement and load vectors respectively, K represents the global stiffness matrix, and u e and K e N represents the element displacement vector and stiffness matrix, respectively. e V represents the number of equal geometric elements, V represents the structural volume function, and V0 and ρ represents the total volume of the product structure and the material utilization rate, respectively. i,j N is used as a design variable to represent the relative density of control points. ξ and N η ρ represents the number of control points in the two directions of the parameter domain, respectively. min This represents the minimum design variable set to avoid singularity in the stiffness matrix.

[0066] Step S2: Generate a training dataset using an isogeometric topology optimization algorithm. This dataset takes the spatial coordinates and relative density of fine-grid control points, the displacement and sensitivity of coarse-grid control points as input, and the sensitivity of fine-grid control points as output. Specifically, it includes the following steps:

[0067] Step S2.1: Discretize the shapes using bi-third-order NURBS (Non-uniform rational B-spline) basis functions as shape functions. Figures 3a to 3c The design domains for rectangular product structures, L-shaped product structures, and MBB beam product structures are set with a maximum volume fraction of 0.4 and a horizontal and vertical discrete grid number of 100×50 to obtain the NURBS coarse grid of the product structures.

[0068] Step S2.2: Refine the NURBS coarse mesh of the product structure using an equal geometric node insertion strategy, with a refinement level of 2, to obtain a NURBS fine mesh with a mesh size of 200×100 and a mapping matrix T of the coarse and fine mesh control points. p ;

[0069] The NURBS coarse mesh of the product structure is refined using an equal-geometric node insertion strategy, as follows: Given a coarse mesh node vector Ξ={ξ1,ξ2,...,ξ n+p+1}, where n represents the number of coarse grid control points in the parameter domain, p represents the order of the NURBS basis functions, and the refined node vector obtained after inserting nodes is: Make Where N Refin Indicates the level of refinement; control points for finer grids. Control points P = {P1, P2, ..., P} are defined by a coarse grid. n} T The linear combination forms the following, and the specific mapping relationship is as follows:

[0070]

[0071] Among them, T p This indicates mapping coarse grid control point P to fine grid control point P. The interpolation matrix.

[0072] The mapping relationship between the relative densities of control points in coarse and fine meshes is ρ r =T p ρ c , where ρ r ρ represents the vector composed of the relative densities of the control points in the fine mesh. c This is a vector composed of the relative densities of the coarse grid control points;

[0073] Step S2.3: Perform isogeometric analysis on both coarse and fine meshes to obtain the displacement of control points on both resolution meshes;

[0074] Step S2.4: Calculate the sensitivity of the control points for coarse and fine meshes;

[0075] Step S2.5: Record the spatial coordinates and relative density of the fine-grid control points, the displacement and sensitivity of the coarse-grid control points as input, and the sensitivity of the fine-grid control points as output to generate an offline training dataset;

[0076] Step S2.6: Based on the sensitivity information of the fine-mesh control points, update the relative density on the fine-mesh control points using the moving asymptote algorithm, and calculate the relative density of the coarse-mesh control points based on the mapping matrix of the coarse and fine-mesh control points;

[0077] Step S2.7: The convergence condition for isogeometric topology optimization is whether the maximum number of iterations has been reached. The maximum number of iterations is set to 100. Determine whether the convergence condition for isogeometric topology optimization is met. If the convergence condition is not met, jump to step S2.3. If it is met, stop the isogeometric topology optimization iteration.

[0078] Step S3: Build and train as follows Figure 4 The graph convolutional neural network model for multi-resolution information extraction shown includes a graph convolutional neural network module for global stiffness information extraction and a fully connected neural network module for local information fusion.

[0079] The graph convolutional neural network module for global stiffness information extraction includes a graph convolutional input layer, multiple graph convolutional hidden layers, knowledge skip connections, and a graph convolutional aggregation layer. The graph convolutional input layer receives global fine-grid control point information via the message propagation mechanism of the graph convolutional neural network. The graph convolutional hidden layers perform a weighted sum of the neighborhood information surrounding each fine-grid control point along the feature dimension based on the adjacency matrix, and perform nonlinear feature mapping through an activation function. The knowledge skip connections directly connect the outputs of each node in the graph convolutional neural network module to the aggregation layer. The graph convolutional aggregation layer aggregates the outputs of each node passed through the skip connections along the feature dimension. The aggregation operations include concatenation, average pooling, and max pooling.

[0080] The fully connected neural network module for local information fusion includes a fully connected input layer, multiple fully connected hidden layers, and a fully connected output layer. The fully connected input layer receives the displacement and sensitivity at the local coarse unit control points, and the feature information extracted by the graph convolutional neural network module at the local fine unit control points. The local coarse unit refers to a single NURBS unit under a coarse grid; the local fine unit refers to multiple fine units obtained by subdividing a single coarse unit through a node insertion strategy. The fully connected output layer is used to output the sensitivity at the local fine unit control points.

[0081] In this embodiment of the invention, the structural parameters of the graph convolutional neural network module for global stiffness information extraction of the neural network model are as follows: the module includes an input layer, two hidden layers, and an aggregation layer, with activation functions set to [silu,silu,silu,relu] and the number of feature channels being [4,4,4,4]. The fully connected neural network module for local information fusion has six layers, with activation functions set to [tanh,silu,silu,silu,silu,relu] and the number of neurons in each layer being [8,128,128,64,32,4]. The loss function of the neural network is set to root mean square error, the learning rate is 0.005, and the maximum number of iterations is set to 1000.

[0082] Step S4: Apply the trained neural network model online. Figure 5 The illustrated solution process for the isogeometric topology optimization of the serpentine product structure efficiently obtains the density distribution results of the product structure topology optimization. The specific steps are as follows:

[0083] Step S4.1: Discretize the serpentine product structure design domain using NURBS basis functions as shape functions. Combine the equal geometric node insertion strategy to obtain the NURBS coarse and fine grid control points of the serpentine product structure, as well as the mapping matrix of the coarse and fine grid control points. The coarse grid has a grid number of 150×50 and a refinement level of 2. The fine grid has a grid number of 300×100. Due to the message propagation mechanism of graph convolutional neural networks, the number of grids in the application case and the case generated in the training set do not need to be the same. They only need to be the same in terms of refinement level.

[0084] Step S4.2: Perform isogeometric analysis on the product structure on the coarse mesh and calculate the sensitivity corresponding to the control points of the coarse mesh;

[0085] Step S4.3: Input the coordinates and relative density of the control points of the fine mesh of the product structure, and the displacement and sensitivity of the control points of the coarse mesh into the trained neural network model to obtain the sensitivity of the control points of the fine mesh;

[0086] Step S4.4: Based on the sensitivity information of the fine-mesh control points, update the relative density on the fine-mesh control points using the moving asymptote algorithm, and calculate the relative density of the coarse-mesh control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine-mesh control points.

[0087] Step S4.5: The convergence condition for isogeometric topology optimization is whether the maximum number of iterations has been reached. The maximum number of iterations is set to 200. Determine whether the convergence condition for isogeometric topology optimization is met. If the convergence condition is not met, jump to step S4.2. If it is met, stop the isogeometric topology optimization iteration and obtain the isogeometric topology optimization density distribution result as follows. Figure 6 As shown;

[0088] To illustrate the acceleration effect of this invention, this embodiment also employs a standard isogeometric topology optimization method. Figure 5 The serpentine beam shown is optimized with a discrete mesh size of 300×100. The resulting isogeometric topology optimization density distribution is as follows: Figure 7 As shown in the table, the density distribution results obtained by the proposed method are similar to those of the standard geometric topology optimization method, verifying the feasibility of the proposed method. Table 1 records the comparison between the proposed method and the standard geometric topology optimization method in terms of final target performance and CPU computation time. The results show that the target performance of the proposed method deviates from that of the standard method by only 0.77%, while achieving a 4.6-fold speedup in terms of computational efficiency, significantly improving the solution efficiency of topology optimization.

[0089] Table 1 Target performance and CPU computation time of topology optimization results obtained by different methods.

[0090] Target performance CPU computation time Standard geometric topology optimization method 581.1377 4823 seconds The method proposed in this invention 585.6256 1024 seconds

[0091] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing the geometric topology of product structures based on neural networks, characterized in that... Includes the following steps: Step S1: With product structural flexibility as the objective, material usage as the constraint, and the relative density of control points of equal geometric units as the design variable, construct a geometric topology optimization model of the product structure. Step S2: Discretize the design domain of the product structure to obtain the coarse mesh of the product structure, then refine the coarse mesh, and perform isogeometric topology optimization on the coarse and fine meshes to obtain an offline dataset with the spatial coordinates and relative density of the fine mesh control points, the displacement and sensitivity of the coarse mesh control points as input data, and the sensitivity of the fine mesh control points as output data. Step S3: Train a neural network model using an offline dataset; the neural network model includes a global stiffness information extraction neural network module and a local information fusion neural network module; The global stiffness information extraction neural network module is specifically a graph convolutional neural network model, including a graph convolutional input layer, a graph convolutional hidden layer, and a graph convolutional aggregation layer. The outputs of the input layer and the hidden layer are connected to the aggregation layer through knowledge jumps. The input layer receives global fine-grid control point information; the hidden layer performs a weighted sum of the neighborhood information around each fine-grid control point in the feature dimension according to the adjacency matrix, and performs non-linear feature mapping through an activation function; the aggregation layer aggregates the outputs of each layer passed through the jump connections in the feature dimension. The local information fusion neural network module is specifically a fully connected neural network model, including a fully connected input layer, a fully connected hidden layer, and a fully connected output layer. The input layer acquires the displacement and sensitivity at the local coarse unit control points, as well as the feature information extracted by the global stiffness information extraction neural network module at the local fine unit control points. The local coarse unit refers to a single NURBS basis function unit under a coarse mesh; the local fine unit refers to multiple fine units obtained by subdividing a single coarse unit through a node insertion strategy. The fully connected output layer is used to output the sensitivity at the local fine unit control points. Step S4: Apply the trained neural network model online to the isogeometric topology optimization of the product structure to obtain the density distribution results of the product structure topology optimization.

2. The method for optimizing the geometric topology of product structures based on neural networks according to claim 1, characterized in that: Step S2 specifically includes the following steps: Step S2.1: Use isogeometric basis functions as shape functions to discretize the design domain of the product structure and obtain the coarse mesh of the product structure; Step S2.2: Refine the coarse mesh of the product structure using an equal geometric node insertion strategy to obtain the fine mesh and the mapping matrix between the control points of the fine mesh and the coarse mesh; Step S2.3: Perform isogeometric analysis on both the coarse and fine meshes to obtain the displacements of the control points on both meshes; Step S2.4: Calculate the sensitivity of coarse-grid control points and fine-grid control points; Step S2.5: Use the spatial coordinates and relative density of the fine-grid control points, the displacement and sensitivity of the coarse-grid control points as input data, and the sensitivity of the fine-grid control points as output data to construct an offline training dataset; Step S2.6: Based on the sensitivity information of the fine-mesh control points, update the relative density on the fine-mesh control points using the moving asymptote algorithm, and calculate the relative density of the coarse-mesh control points based on the mapping matrix; Step S2.7: Determine whether the convergence condition of the isogeometric topology optimization is met. If not, jump to step S2.

3. If it is met, stop the isogeometric topology optimization iteration.

3. The method for optimizing the geometric topology of product structures based on neural networks according to claim 2, characterized in that: The aforementioned equal-geometric node insertion strategy refines the NURBS coarse grid of the product structure by inserting nodes into the coarse grid node vector to obtain a refined node vector. The control points of the fine grid are formed by linearly combining the control points of the coarse grid. The coarse grid control points are mapped to the fine grid control points through a difference matrix. Each control point of the fine grid is the result of a weighted average of multiple coarse grid control points around it. Each row in the interpolation matrix corresponds to the weighting coefficient required for a fine grid control point. The weighting coefficient is obtained by recursively calculating the ratio of the fine grid node vector value to the coarse grid node vector value. A mapping relationship between the relative density of coarse and fine grid control points is established based on the difference matrix.

4. The method for optimizing the geometric topology of product structures based on neural networks according to claim 3, characterized in that: coarse grid node vector n represents the number of control points in the coarse mesh of the parameter domain, p represents the order of the NURBS basis functions, and the refined node vector. , , Indicates the degree of refinement; the control point matrix of the finer mesh. Control point matrix through coarse grid The linear combination forms the following, and the specific mapping relationship is as follows: in, This indicates the use of coarse grid control points. Mapped to fine mesh control points The interpolation matrix, Represents the coarse grid node vector The value of the j-th node in the middle. Represents fine mesh node vectors The value of the i-th node. Let represent the value of the element in the i-th row and j-th column of the q-th order interpolation matrix. This represents the control points obtained by refining the coarse mesh. This represents the coarse grid control points.

5. The method for optimizing the geometric topology of product structures based on neural networks according to claim 1, characterized in that: Step S4 specifically includes the following steps: Step S4.1: Discretize the product structure design domain using the isogeometric basis functions as shape functions, and obtain the coarse and fine grid control points of the product structure, as well as the mapping matrix of the coarse and fine grid control points, by combining the isogeometric node insertion strategy. Step S4.2: Perform isogeometric analysis on the product structure on the coarse mesh and calculate the sensitivity corresponding to the control points of the coarse mesh; Step S4.3: Input the coordinates and relative density of the control points of the fine mesh of the product structure, and the displacement and sensitivity of the control points of the coarse mesh into the trained neural network model to obtain the sensitivity of the control points of the fine mesh; Step S4.4: Based on the sensitivity information of the fine-mesh control points, update the relative density on the fine-mesh control points using the moving asymptote algorithm, and calculate the relative density of the coarse-mesh control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine-mesh control points. Step S4.5: Determine whether the convergence condition of the isogeometric topology optimization is met. If not, jump to step S4.

2. If it is met, stop the isogeometric topology optimization iteration and obtain the isogeometric topology optimization density distribution result.

6. The method for optimizing the geometric topology of product structures based on neural networks according to claim 1, characterized in that: The geometric topology optimization model expression for the product structure in step S1 is as follows: in, Indicates the flexibility of the product structure. and These represent the global displacement and load vectors, respectively. Represents the global stiffness matrix. and These represent the element displacement vector and stiffness matrix, respectively. Indicates the number of equal geometric units. Represents the structural volume function. and These represent the total volume of the product structure and the material utilization rate, respectively. As a design variable to represent the relative density of control points and These represent the number of control points in the two directions of the parameter domain, respectively. This represents the minimum design variable set to avoid singularity in the stiffness matrix.

7. A product structure and other geometric topology optimization system based on neural networks, comprising a product structure and other geometric topology optimization model construction module, an offline dataset generation module, a neural network module, and a product structure and other geometric topology optimization generation module, characterized in that: The product structure and other geometric topology optimization method based on neural networks as described in any one of claims 1 to 6 is used to sequentially construct a product structure and other geometric topology optimization model, generate an offline dataset, construct a neural network model, and generate product structure and other geometric topology optimization results.

8. The product structure and geometric topology optimization system based on neural networks according to claim 7, characterized in that: The offline dataset generation module includes a coarse grid generation unit, a mapping matrix generation unit, an isogeometric analysis unit, a sensitivity calculation unit, an offline training dataset construction unit, a relative density generation unit, and a judgment unit; The coarse mesh generation unit uses equal geometric basis functions as shape functions to discretize the design domain of the product structure and obtain the coarse mesh of the product structure. The mapping matrix generation unit uses an equal geometric node insertion strategy to refine the coarse mesh of the product structure, thereby obtaining a fine mesh and a mapping matrix between the fine mesh and the control points of the coarse mesh. The isogeometric analysis unit performs isogeometric analysis on both coarse and fine meshes to obtain the displacements of the control points on both coarse and fine meshes. The sensitivity calculation unit is used to calculate the sensitivity of coarse grid control points and fine grid control points; The offline training dataset construction unit takes the spatial coordinates and relative density of fine-grid control points, the displacement and sensitivity of coarse-grid control points as input data, and the sensitivity of fine-grid control points as output data to construct a set of offline training datasets. The relative density generation unit updates the relative density on the fine grid control points using the moving asymptote algorithm based on the sensitivity information of the fine grid control points, and calculates the relative density of the coarse grid control points based on the mapping matrix. The judgment unit is used to determine whether the convergence condition of the isogeometric topology optimization is met. If it is not met, the process returns to the isogeometric analysis unit. If it is met, the isogeometric topology optimization iteration stops.

9. The product structure and geometric topology optimization system based on neural networks according to claim 7, characterized in that: The product structure and other geometric topology optimization generation module includes product structure discrete units, coarse mesh and other geometric analysis units, fine mesh sensitivity generation module, relative density generation module, and density distribution generation module; The product structure discrete unit uses equal geometric basis functions as shape functions to discretize the product structure design domain, and combines equal geometric node insertion strategy to obtain coarse and fine grid control points of the product structure, as well as the mapping matrix of coarse and fine grid control points. The coarse-mesh iso-geometric analysis unit performs iso-geometric analysis on the product structure on the coarse mesh and calculates the sensitivity corresponding to the coarse-mesh control points; The fine mesh sensitivity generation module inputs the coordinates and relative density of the control points of the fine mesh of the product structure, and the displacement and sensitivity of the control points of the coarse mesh into the trained neural network model to obtain the sensitivity of the fine mesh control points. The relative density generation module updates the relative density on the fine grid control points using the moving asymptote algorithm based on the sensitivity information of the fine grid control points, and calculates the relative density of the coarse grid control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine grid control points. The density distribution generation module determines whether the convergence condition of the isogeometric topology optimization is met. If it is not met, it returns to the coarse mesh isogeometric analysis unit. If it is met, it stops the isogeometric topology optimization iteration and obtains the isogeometric topology optimization density distribution result.

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