Product structure integration design method and system based on adaptive transfer learning
By employing adaptive transfer learning, an integrated design model for product structure is constructed. Optimization is achieved using online fine-tuning of neural networks and the moving asymptote algorithm, which solves the problems of high computational resource consumption and limited generalization ability in topology optimization for large-scale complex structural design, thus realizing efficient and integrated design and optimization.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2025-09-15
- Publication Date
- 2026-05-19
AI Technical Summary
Existing topology optimization methods consume high computational resources in the design of large-scale complex structures, and machine learning-based methods have limited generalization ability and are difficult to adapt to new practical problems.
An adaptive transfer learning approach is adopted. By constructing an integrated design model of product structure, a neural network model is pre-trained using an offline dataset, and accuracy evaluation and dataset updates are performed in the online stage. The density of fine grid control points is optimized by combining the moving asymptote algorithm, thereby realizing online fine-tuning of the neural network.
It significantly improves the design efficiency and accuracy of topology optimization, reduces computational costs, and achieves integrated design, analysis and optimization of product structure.
Smart Images
Figure CN121257265B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of structural optimization technology, specifically relating to an integrated design method and system for product structure based on adaptive transfer learning. Background Technology
[0002] The integrated design approach employs isogeometric analysis techniques, integrating design, analysis, and optimization processes by sharing geometric models from CAD and CAE. Within this framework, topology optimization can determine the optimal material distribution within the design domain without relying on prior knowledge, thus significantly improving structural performance. However, as an emerging material distribution design method, topology optimization introduces a higher-dimensional design space compared to size and shape optimization, significantly increasing computational resource consumption while providing greater design freedom. Currently, some research has been conducted on accelerating topology optimization, primarily employing strategies such as high-performance computing, approximate models, and multi-scale analysis. However, these methods are mostly applicable to models with relatively simple geometries, and research on accelerating topology optimization for large-scale complex structures still falls short of meeting the needs of practical industrial applications.
[0003] In recent years, machine learning-based intelligent acceleration methods have shown great potential in specific scenarios. However, these methods are generally limited by the scale of training data, typically requiring hundreds of thousands of samples to build a high-precision model. Furthermore, their generalization ability is limited; the trained models often only apply to cases already present or highly similar in the training set, making it difficult to adapt to new real-world problems through fine-tuning. Therefore, how to achieve intelligent integrated design of product structures based on adaptive transfer learning has become a key issue that urgently needs to be addressed. Summary of the Invention
[0004] To address the shortcomings of existing technologies and achieve the goals of improving the accuracy and efficiency of integrated design while reducing costs, this invention adopts the following technical solution:
[0005] The integrated product structure design method based on adaptive transfer learning includes the following steps:
[0006] Step S1: With product structural flexibility as the target, material usage as the constraint, and the relative density of equal geometric unit control points as the design variable, construct an integrated design model for the product structure.
[0007] Step S2: Divide the product structure design domain into equal geometric parts to obtain coarse mesh elements and their internal fine mesh elements; obtain the displacement of the control points of the coarse mesh elements and the relative density of the control points of the fine mesh elements as inputs, and the corresponding sensitivity of the control points of the fine mesh elements as outputs to construct an offline dataset;
[0008] Step S3: Pre-train the neural network model using an offline dataset;
[0009] Step S4: In the online phase, the displacement of the control points of the coarse mesh is solved based on the current product structure. If the correction flag is true, the correction interval is reduced, the displacement and sensitivity of the control points of the fine mesh are solved, and compared with the sensitivity predicted by the neural network model to update the correction flag. An online correction dataset is constructed to correct the neural network model online. If the correction flag is false, the correction interval is increased. Based on the displacement of the control points of the coarse mesh with equal geometry and the relative density of the control points of the fine mesh within it, the sensitivity of the control points of the fine mesh is predicted by the neural network model. The remainder of the current iteration number divided by the iteration interval number is determined. If it is zero, the correction flag is true; otherwise, the correction flag remains unchanged. The relative density of the control points of the fine mesh is updated, and the relative density of the control points of the coarse mesh is obtained. The displacement of the control points of the coarse mesh is solved again until the iteration end condition is met. The integrated design result of the product structure is obtained based on the relative density of the control points of the fine mesh.
[0010] Further, step S4 includes the following steps:
[0011] Step S4.1: Initialize the relative density of coarse and fine mesh control points, the maximum number of iterations for isogeometric topology optimization, the neural network prediction accuracy threshold, the current iteration number, the corrected iteration interval D, and the maximum iteration interval D. max The online correction flag is set to true by default.
[0012] Step S4.2: Construct the global stiffness matrix of the product structure on the coarse mesh, and solve for the displacement of the control points of the coarse mesh elements;
[0013] Step S4.3: Determine the online correction flag. If it is false, input the displacement of the control points of the coarse-grid cells with equal geometry and the relative density of the control points of the fine-grid cells within them into the neural network model to obtain the predicted sensitivity of the fine-grid cell control points. At the same time, reassign the correction iteration interval number, i.e., D = min(D+1, D...). max min() represents the minimum value operation; if true, the sensitivity of the fine mesh unit control points is calculated and the neural network model is corrected online.
[0014] Step S4.4: Determine whether the remainder of the current iteration number divided by the iteration interval number D is 0. If yes, the online correction flag is true; otherwise, the online correction flag remains unchanged.
[0015] Step S4.5: Based on the sensitivity information of the fine grid cell control points, update the relative density of the fine grid cell control points using the moving asymptote algorithm, and obtain the relative density of the coarse grid cell control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine grid control points.
[0016] Step S4.6: Determine if the current iteration number is less than the maximum iteration number of the equal geometry topology optimization. If so, increase the current iteration number and jump to step S4.2; otherwise, stop the equal geometry topology optimization iteration and obtain the integrated design result of the product structure based on the relative density of the control points of the fine mesh unit.
[0017] Further, in step S4.3, calculating the sensitivity of the fine-mesh unit control points and making online corrections to the neural network model includes the following steps:
[0018] Step S4.3.1: Reassign the corrected iteration interval number, i.e., D = max(1, D-1), where max() represents the maximum value operation;
[0019] Step S4.3.2: Construct the global stiffness matrix of the product structure on the fine mesh and solve for the displacement of the control points of the fine mesh elements;
[0020] Step S4.3.3: Calculate the sensitivity y corresponding to the control point of the fine mesh element;
[0021] Step S4.3.4: Predict the sensitivity y of the control points in the fine mesh cell using a neural network model. E ;
[0022] Step S4.3.5: Calculate the prediction error e of the neural network model NN Determine e NN If the value is less than the prediction accuracy threshold ε, the online correction flag is set to true; otherwise, the online correction flag is set to false.
[0023] Step S4.3.6: Using the displacement of the control points of the coarse-grid cells with uniform geometry and the relative density of the control points of the fine-grid cells inside them as inputs, and the sensitivity of the control points of the fine-grid cells as outputs, construct an online correction dataset;
[0024] Step S4.3.7: Retrain the neural network model locally using the online correction dataset.
[0025] Furthermore, the prediction error formula in step S4.3.5 is as follows:
[0026]
[0027] in, and Let N represent the true value and the neural network prediction value of the sensitivity of the i-th fine-mesh cell control point after linear normalization, respectively. r This represents the number of control points in the fine grid, and α and β are the weights of the root mean square error and the maximum absolute error, respectively.
[0028] Furthermore, the neural network model in step S3 is a fully connected neural network model, including an input layer, multiple hidden layers, and an output layer. The input layer is used to input the displacement of control points of coarse-grid cells with equal geometry and the relative density of control points of fine-grid cells within them. The multiple hidden layers are connected sequentially, and feature extraction is performed based on the output results of the previous hidden layer. The output layer is used to output the sensitivity of control points of fine-grid cells. In step S4.3.7, the training parameters of the input layer and some hidden layers on the input side of the neural network model are frozen, and only the training parameters of some hidden layers on the output side of the output layer are opened. The neural network model is then retrained using the Adam optimizer.
[0029] Furthermore, in step S1, the expression for the integrated product structure design model is as follows:
[0030]
[0031] stKU=F
[0032]
[0033] 0<ρ min ≤ρ i,j ≤1, i=1,2,...,N ξ j = 1, 2, ..., N η
[0034] 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 represents the relative density of control points used as design variables. 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.
[0035] Further, step S2 includes the following steps:
[0036] Step S2.1: Divide the product structure design domain into equal geometric meshes to obtain equal geometric coarse mesh elements and element control points. Use a node insertion strategy to refine the equal geometric coarse mesh to obtain equal geometric fine mesh elements and element control points.
[0037] Step S2.2: Solve the integrated design model of the product structure using the isogeometric topology optimization algorithm;
[0038] Step S2.3: In each optimization iteration, record the displacement of the control points of the coarse grid cells with uniform geometry and the relative density of the control points of the fine grid cells inside them as input, and record the sensitivity of the control points of the fine grid cells as output, so as to construct an offline dataset.
[0039] The product structure integrated design system based on adaptive transfer learning includes a product structure integrated design model building module, an offline dataset generation module, a neural network module, and a product structure integrated design generation module. The product structure integrated design method based on adaptive transfer learning is used to sequentially execute the product structure integrated design model building, offline dataset building, neural network model pre-training, and product structure integrated design result generation.
[0040] Furthermore, the integrated product structure design generation module includes an initialization unit, a solution unit, a correction flag judgment unit, a remainder judgment unit, a relative density acquisition unit, and an iteration number judgment unit;
[0041] The initialization unit is used to initialize the relative density of coarse grid control points and fine grid control points, the maximum number of iterations for isogeometric topology optimization, the neural network prediction accuracy threshold, the current iteration number, the correction iteration interval D, and the maximum iteration interval D. max The online correction flag is set to true by default.
[0042] The solving unit is used to construct the global stiffness matrix of the product structure on the coarse grid and solve for the displacement of the control points of the coarse grid unit.
[0043] The correction flag judgment unit is used to judge the online correction flag. If it is false, the displacement of the control point of the coarse-grid unit and the relative density of the control points of the fine-grid unit inside it are input into the neural network model to obtain the predicted sensitivity of the fine-grid unit control point. At the same time, the correction iteration interval is reassigned, i.e., D = min(D+1, D max min() represents the minimum value operation; if true, the sensitivity of the fine mesh unit control points is calculated and the neural network model is corrected online.
[0044] The remainder judgment unit is used to determine whether the remainder of the current iteration number divided by the iteration interval number D is 0. If it is, the online correction flag is true; otherwise, the online correction flag remains unchanged.
[0045] The relative density acquisition unit updates the relative density of the control points of the fine grid cells using the moving asymptote algorithm based on the sensitivity information of the control points of the fine grid cells, and obtains the relative density of the control points of the coarse grid cells based on the generalized inverse matrix of the mapping matrix between the control points of the coarse and fine grid cells.
[0046] The iteration number judgment unit is used to determine whether the current iteration number is less than the maximum iteration number of the equal geometric topology optimization. If so, the current iteration number is increased and the process jumps to step S4.2; otherwise, the equal geometric topology optimization iteration is stopped, and the integrated design result of the product structure is obtained based on the relative density of the control points of the fine mesh unit.
[0047] Furthermore, in the correction flag judgment unit, the calculation of the sensitivity of the fine mesh unit control points and the online correction of the neural network model specifically include: reassigning the correction iteration interval number, i.e., D = max(1, D-1), where max() represents the maximum value operation; constructing the global stiffness matrix of the product structure on the fine mesh and solving for the displacement of the fine mesh unit control points; calculating the sensitivity y corresponding to the fine mesh unit control points; and using the neural network model to predict the sensitivity y of the fine mesh unit control points. NN ; Calculate the prediction error e of the neural network model NN Determine e NN If the error is less than the prediction accuracy threshold ε, the online correction flag is true; otherwise, it is false. The online correction dataset is constructed by taking the displacement of the control points of the coarse grid cells with uniform geometry and the relative density of the control points of the fine grid cells inside them as inputs and the sensitivity of the control points of the fine grid cells as outputs. The neural network model is then locally retrained using the online correction dataset.
[0048] The advantages and beneficial effects of this invention are as follows:
[0049] 1. This invention constructs an integrated design model for product structure. By adopting isogeometric analysis basis functions as shape functions, it fundamentally eliminates the geometric errors caused by the conversion between CAD and CAE models, and realizes the integrated design, analysis and optimization of product structure.
[0050] 2. This invention proposes an intelligent isogeometric topology optimization method based on adaptive transfer learning. By evaluating the prediction accuracy of the current neural network model, the online correction dataset is adaptively updated to fine-tune the neural network model. While ensuring prediction accuracy, the number of calculations of the true value of fine mesh sensitivity is significantly reduced, thereby improving the efficiency of integrated design.
[0051] 3. This invention reduces the dependence on the amount of online training data and the computational cost of generating online training datasets by freezing the parameters of the input layer and some hidden layers of the neural network model, and only opening some trainable parameters of the hidden and output layers. At the same time, it avoids the feature coverage problem caused by global parameter updates during online fine-tuning. 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 offline datasets 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 offline datasets 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 offline datasets in an embodiment of the present invention.
[0057] Figure 4 This is a diagram of the neural network structure constructed in an embodiment of the present invention.
[0058] Figure 5 This is a boundary condition diagram of the circular bend in an embodiment of the present invention.
[0059] Figure 6 This is a schematic diagram of the integrated design result obtained by the method of this embodiment of the invention.
[0060] Figure 7 This is a schematic diagram of the integrated design result obtained by the standard equal geometric 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 integrated product structure design system based on adaptive transfer learning includes an integrated product structure design model building module, an offline dataset generation module, a neural network module, and an integrated product structure design generation module, which execute sequentially as follows: Figure 2 The product structure integration design method based on adaptive transfer learning shown herein includes the following steps:
[0063] Step S1: Construct an integrated design model for the product structure, expressed as follows:
[0064]
[0065] stKU=F
[0066]
[0067] 0<ρ min ≤ρ i,j ≤1, i=1,2,...,N ξ j = 1, 2, ..., N η
[0068] Where c is the product structural flexibility, U and F represent the global displacement and load vectors respectively, K is the global stiffness matrix, and u e and K e N represents the element displacement vector and stiffness matrix, respectively. e The number of geometric units is given by V, which represents the structural volume function. V0 and V represent the total structural volume and material utilization rate of the product, respectively. The relative density ρ at the control points is also mentioned. i,j It is a design variable, N ξ and N η ρ is the number of control points in both directions of the parameter domain. min This is the minimum design variable set to avoid singularity in the stiffness matrix.
[0069] Step S2: Generate an offline dataset using an isogeometric topology optimization algorithm. This dataset takes the displacement of control points in coarse-grid cells and the relative density of control points in fine-grid cells within them as input, and the sensitivity of control points in fine-grid cells as output. The specific steps for generating the offline dataset are as follows:
[0070] Step S2.1: Divide the product structure design domain into equal geometric meshes to obtain equal geometric coarse mesh elements and control points. Use a node insertion strategy to refine the equal geometric coarse mesh to obtain equal geometric fine mesh elements and control points.
[0071] Construct separately Figures 3a to 3c An integrated design model for rectangular, L-shaped, and MBB beam product structures was developed. A double third-order NURBS basis function was used as the shape function to discretize the product structure design domain. The maximum volume fraction was set to 0.4, and the number of discrete grids in the horizontal and vertical directions was set to 100×50, resulting in a coarse NURBS grid for the product structure. A node insertion strategy was then used to refine the coarse grid with a refinement level of 2, resulting in a fine NURBS grid with a number of grids of 200×100.
[0072] Step S2.2: Solve the integrated design model of the product structure using the isogeometric topology optimization algorithm;
[0073] Step S2.3: In each optimization iteration, record the displacement of the control points of the coarse grid cells with uniform geometry and the relative density of the control points of the fine grid cells inside them as inputs, and record the sensitivity of the control points of the fine grid cells as outputs.
[0074] Step S3: Pre-train a neural network model using an offline dataset; specifically, a fully connected neural network model, including an input layer, multiple hidden layers, and an output layer. The input layer is used to input the displacement of control points in coarse-grid cells with equal geometry and the relative density of control points in fine-grid cells within them; multiple hidden layers are connected sequentially, and feature extraction is performed based on the output of the previous hidden layer; the output layer is used to output the sensitivity of control points in fine-grid cells.
[0075] In this embodiment of the invention, a construction is performed as follows: Figure 4 The neural network model shown includes an input layer, four hidden layers, and an output layer. The activation functions are set to [tanh, silu, silu, silu, silu, relu], and the number of neurons in each layer is set to [43, 128, 128, 64, 32, 25]. The loss function is set to root mean square error, the learning rate is 0.005, and the maximum number of iterations is set to 1000. The neural network model is initially trained using the Adam optimizer.
[0076] Step S4: Use an intelligent isogeometric topology optimization algorithm based on adaptive transfer learning to solve the integrated design model and obtain the integrated design result of the product structure;
[0077] In this embodiment of the invention, a double third-order NURBS basis function is used as the shape function discretization, as shown in the figure. Figure 5 The design domain for the circular bend product structure shown has a volume fraction of 0.35, a coarse mesh of 96×48, a refinement level of 2, and a fine mesh of 192×96. A mapping matrix T between the control points of the coarse and fine meshes is constructed. p An intelligent isogeometric topology optimization algorithm based on adaptive transfer learning is used to solve the integrated design model. The specific steps are as follows:
[0078] Step S4.1: Initialize the design variables ρ for coarse and fine grid control points c ,ρ r Maximum number of iterations t in geometric topology optimization max =200, neural network prediction accuracy threshold ε = 0.01, current iteration number t = 1, correction iteration interval D = 5, and maximum iteration interval D max =10, online correction flag F=TRUE;
[0079] Step S4.2: Construct the global stiffness matrix of the product structure on the coarse mesh, and solve for the displacement of the control points of the coarse mesh elements;
[0080] Step S4.3: Determine if the online correction flag F is TRUE. If not, input the displacement of the control points of the coarse-grid elements with equal geometry and the relative density of the control points of the fine-grid elements within them into the neural network model to obtain the predicted sensitivity of the fine-grid element control points. At the same time, reassign the correction iteration interval number, i.e., D = min(D+1, D...). max If so, calculate the sensitivity of the control points of the fine mesh elements and perform online corrections to the neural network model, specifically by executing the following steps:
[0081] Step S4.3.1: Reassign the corrected iteration interval number, i.e., D = max(1, D-1);
[0082] Step S4.3.2: Construct the global stiffness matrix of the product structure on the fine mesh and solve for the displacement of the control points of the fine mesh elements;
[0083] Step S4.3.3: Calculate the sensitivity y corresponding to the control point of the fine mesh element;
[0084] Step S4.3.4: Predict the sensitivity y of the control points in the fine mesh cell using a neural network model. E ;
[0085] Step S4.3.5: Calculate the prediction error e of the neural network model according to the following formula. NN Determine e NN If the prediction accuracy threshold ε is less than ε, then the online correction flag F = FALSE; otherwise, F = TRUE.
[0086]
[0087] in, and These are the true value and the neural network prediction value of the sensitivity of the i-th fine-mesh cell control point after linear normalization, respectively. N r =202×102 is the number of fine grid control points.
[0088] Step S4.3.6: Using the displacement of the control points of the coarse-grid cells with uniform geometry and the relative density of the control points of the fine-grid cells inside them as inputs, and the sensitivity of the control points of the fine-grid cells as outputs, construct an online correction dataset;
[0089] Step S4.3.7: Locally retrain the neural network model using the online corrected dataset;
[0090] Specifically, the training parameters of the input layer and the first two hidden layers in the neural network model are frozen, while the training parameters of the last two hidden layers and the output layer are only opened, and the neural network model is retrained using the Adam optimizer.
[0091] Step S4.4: Determine whether the remainder of the current iteration number t divided by the iteration interval number D is 0. If it is, then the online correction flag F = TRUE; otherwise, the online correction flag remains unchanged.
[0092] Step S4.5: Based on the sensitivity information of the fine grid cell control points, update the relative density of the fine grid cell control points using the moving asymptote algorithm, and obtain the relative density of the coarse grid cell control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine grid control points.
[0093] Step S4.6: Determine if the current iteration number t is less than the maximum iteration number t for isogeometric topology optimization. max If so, then t = t + 1, and jump to step S4.2; otherwise, stop the geometric topology optimization iteration and obtain the integrated design result of the product structure based on the relative density of the control points of the fine mesh unit.
[0094] The final integrated design result obtained using the method of this invention is as follows: Figure 6 As shown. To illustrate the acceleration effect of this method, this implementation example also uses the standard equal-geometric topology optimization method. Figure 5 The example shown is optimized, and the corresponding optimization results are as follows: Figure 7 As shown in the table, the design results obtained by the proposed method and the standard geometric topology optimization method are basically the same. 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 is only 0.84% different from that of the traditional method, while achieving a speedup of 3.13 times in terms of computational efficiency, which significantly improves the solution efficiency of the integrated design model.
[0095] Table 1 Target performance and CPU computation time of design results obtained by different methods.
[0096] Target performance CPU computation time Standard geometric topology optimization method 87.29 3140 seconds The method proposed in this invention 88.03 1004 seconds
[0097] 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 product structure integrated design method based on adaptive transfer learning, characterized in that... Includes the following steps: Step S1: With product structural flexibility as the target, material usage as the constraint, and the relative density of equal geometric unit control points as the design variable, construct an integrated design model for the product structure. Step S2: Perform equal geometric division on the product structure design domain to obtain coarse mesh elements and their internal fine mesh elements; The offline dataset is constructed by taking the displacement of the control points of the coarse mesh and the relative density of the control points of the fine mesh as inputs, and the corresponding sensitivity of the control points of the fine mesh as outputs. Step S3: Pre-train the neural network model using an offline dataset; Step S4: In the online phase, the displacement of the control points of the coarse mesh is calculated based on the current product structure. If the correction flag is true, the number of correction intervals is reduced, and the displacement and sensitivity of the control points of the fine mesh are calculated and compared with the sensitivity predicted by the neural network model to update the correction flag. An online correction dataset is constructed to correct the neural network model online. If the correction flag is false, the number of correction intervals is increased. Based on the displacement of the control points of the coarse mesh with equal geometry and the relative density of the control points of the fine mesh within it, the sensitivity of the control points of the fine mesh is predicted by the neural network model. The remainder of the current iteration number divided by the iteration interval number is determined. If it is zero, the correction flag is true; otherwise, the correction flag remains unchanged. Update the relative density of control points in the fine mesh cells and obtain the relative density of control points in the coarse mesh cells; Return to recalculate the displacement of the control points of the coarse mesh until the iteration termination condition is met, and obtain the integrated design result of the product structure based on the relative density of the control points of the fine mesh.
2. The integrated product structure design method based on adaptive transfer learning according to claim 1, characterized in that: Step S4 includes the following steps: Step S4.1: Initialize the relative density of coarse and fine mesh control points, the maximum number of iterations for isogeometric topology optimization, the neural network prediction accuracy threshold, the current iteration number, the corrected iteration interval D, and the maximum iteration interval D. max The online correction flag is set to true by default. Step S4.2: Construct the global stiffness matrix of the product structure on the coarse mesh, and solve for the displacement of the control points of the coarse mesh elements; Step S4.3: Determine the online correction flag. If it is false, input the displacement of the control points of the coarse-grid cells with equal geometry and the relative density of the control points of the fine-grid cells within them into the neural network model to obtain the predicted sensitivity of the fine-grid cell control points. At the same time, reassign the correction iteration interval number. min() represents the minimum value operation; if true, the sensitivity of the fine mesh unit control points is calculated and the neural network model is corrected online. Step S4.4: Calculate the current iteration number divided by the iteration interval. If the remainder is 0, the online correction flag is true; otherwise, the online correction flag remains unchanged. Step S4.5: Based on the sensitivity information of the fine grid cell control points, update the relative density of the fine grid cell control points using the moving asymptote algorithm, and obtain the relative density of the coarse grid cell control points based on the generalized inverse matrix of the mapping matrix between the coarse and fine grid control points. Step S4.6: Determine if the current iteration number is less than the maximum iteration number for isogeometric topology optimization. If so, increase the current iteration number and jump to step S4.
2. Otherwise, stop the geometric topology optimization iteration and obtain the integrated design result of the product structure based on the relative density of the control points of the fine mesh unit.
3. The integrated product structure design method based on adaptive transfer learning according to claim 2, characterized in that: In step S4.3, the sensitivity of the control points of the fine mesh element is calculated and the neural network model is corrected online, including the following steps: Step S4.3.1: Reassign the corrected iteration interval number, i.e. max() represents the operation of finding the maximum value; Step S4.3.2: Construct the global stiffness matrix of the product structure on the fine mesh and solve for the displacement of the control points of the fine mesh elements; Step S4.3.3: Calculate the sensitivity corresponding to the control points of the fine mesh elements. ; Step S4.3.4: Predict the sensitivity of control points in fine-mesh cells using a neural network model. ; Step S4.3.5: Calculate the prediction error of the neural network model Determine the prediction error Is it less than the prediction accuracy threshold? If yes, the online correction flag is true; otherwise, the online correction flag is false. Step S4.3.6: Using the displacement of the control points of the coarse-grid cells with uniform geometry and the relative density of the control points of the fine-grid cells inside them as inputs, and the sensitivity of the control points of the fine-grid cells as outputs, construct an online correction dataset; Step S4.3.7: Retrain the neural network model locally using the online correction dataset.
4. The integrated product structure design method based on adaptive transfer learning according to claim 3, characterized in that: The prediction error formula in step S4.3.5 is as follows: in, and They represent the th element after linear normalization. The true value of the sensitivity of each fine-grid control point and the predicted value of the neural network. This indicates the number of control points in the fine grid. and It is the weight of the root mean square error and the maximum absolute error.
5. The integrated product structure design method based on adaptive transfer learning according to claim 3, characterized in that: The neural network model in step S3 is a fully connected neural network model, including an input layer, multiple hidden layers, and an output layer. The input layer is used to input the displacement of the control points of the coarse-grid cells with equal geometry and the relative density of the control points of the fine-grid cells inside them. The multiple hidden layers are connected in sequence, and feature extraction is performed based on the output results of the previous hidden layer. The output layer is used to output the sensitivity of the control points of the fine-grid cells. In step S4.3.7, the training parameters of the input layer and some hidden layers on the input side of the neural network model are frozen, and only the training parameters of the output layer and some hidden layers on the output side are opened. The neural network model is then retrained using an optimizer.
6. The integrated product structure design method based on adaptive transfer learning according to claim 1, characterized in that: In step S1, the expression for the integrated product structure design model 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. This represents the relative density of control points used as design variables. 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. The integrated product structure design method based on adaptive transfer learning according to claim 1, characterized in that: Step S2 includes the following steps: Step S2.1: Divide the product structure design domain into equal geometric meshes to obtain equal geometric coarse mesh elements and element control points. Use a node insertion strategy to refine the equal geometric coarse mesh to obtain equal geometric fine mesh elements and element control points. Step S2.2: Solve the integrated design model of the product structure using the isogeometric topology optimization algorithm; Step S2.3: In each optimization iteration, record the displacement of the control points of the coarse grid cells with uniform geometry and the relative density of the control points of the fine grid cells inside them as input, and record the sensitivity of the control points of the fine grid cells as output, so as to construct an offline dataset.
8. A product structure integrated design system based on adaptive transfer learning, comprising a product structure integrated design model construction module, an offline dataset generation module, a neural network module, and a product structure integrated design generation module, characterized in that: The product structure integrated design method based on adaptive transfer learning as described in any one of claims 1 to 7 is used to sequentially execute the product structure integrated design model construction, offline dataset construction, neural network model pre-training, and product structure integrated design result generation.
9. The integrated product structure design system based on adaptive transfer learning according to claim 8, characterized in that: The integrated product structure design and generation module includes an initialization unit, a solution unit, a correction flag judgment unit, a remainder judgment unit, a relative density acquisition unit, and an iteration number judgment unit. The initialization unit is used to initialize the relative density of coarse grid control points and fine grid control points, the maximum number of iterations for isogeometric topology optimization, the neural network prediction accuracy threshold, the current iteration number, the correction iteration interval D, and the maximum iteration interval D. max The online correction flag is set to true by default. The solving unit is used to construct the global stiffness matrix of the product structure on the coarse grid and solve for the displacement of the control points of the coarse grid unit. The correction flag judgment unit is used to judge the online correction flag. If it is false, the displacement of the control point of the coarse-grid unit with equal geometry and the relative density of the control points of the fine-grid unit inside it are input into the neural network model to obtain the predicted sensitivity of the fine-grid unit control point. At the same time, the correction iteration interval is reassigned. min() represents the minimum value operation; if true, the sensitivity of the fine mesh unit control points is calculated and the neural network model is corrected online. The remainder determination unit is used to determine the current iteration number divided by the iteration interval number. If the remainder is 0, the online correction flag is true; otherwise, the online correction flag remains unchanged. The relative density acquisition unit updates the relative density of the control points of the fine grid cells using the moving asymptote algorithm based on the sensitivity information of the control points of the fine grid cells, and obtains the relative density of the control points of the coarse grid cells based on the generalized inverse matrix of the mapping matrix between the control points of the coarse and fine grid cells. The iteration number determination unit is used to determine whether the current iteration number is less than the maximum iteration number of the isogeometric topology optimization. If so, the current iteration number is increased and the process jumps to step S4.
2. Otherwise, stop the geometric topology optimization iteration and obtain the integrated design result of the product structure based on the relative density of the control points of the fine mesh unit.
10. The integrated product structure design system based on adaptive transfer learning according to claim 9, characterized in that: In the correction flag judgment unit, the sensitivity of the fine mesh unit control points is calculated and the neural network model is corrected online. Specifically, this includes reassigning the correction iteration interval number, i.e., the iteration interval number. `max()` represents the maximum value operation; construct the global stiffness matrix of the product structure on the fine mesh, solve for the displacement of the control points of the fine mesh elements; calculate the sensitivity corresponding to the control points of the fine mesh elements. Predicting control point sensitivity of fine-grid cells using a neural network model ; Calculate the prediction error of the neural network model Determine the prediction error Is it less than the prediction accuracy threshold? If yes, the online correction flag is true; otherwise, the online correction flag is false. The online correction dataset is constructed by taking the displacement of the control points of the coarse grid cells with equal geometry and the relative density of the control points of the fine grid cells inside them as inputs and the sensitivity of the control points of the fine grid cells as outputs. The neural network model was locally retrained using an online corrected dataset.