Time-decaying on-line migration of anisotropy smart structure for isogeometric topology optimization
By employing an intelligent isogeometric topology optimization method with time decay online migration, freezing the backbone parameters of the baseline neural network and adding a corrected network head, and combining the time decay buffer dataset and sensitivity bias angle strategy, the problem of high computational cost and unstable prediction in isogeometric topology optimization in irregular structures is solved, achieving efficient model adaptation and accurate design results.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- ZHEJIANG UNIV
- Filing Date
- 2026-03-27
- Publication Date
- 2026-07-14
Smart Images
Figure CN122389110A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of structural optimization technology, specifically involving a method for intelligent geometric topology optimization of irregular structures with time-decayed online migration. Background Technology
[0002] Isogeometric topology optimization, as an advanced design method for irregular structures, utilizes non-uniform rational B-spline basis functions as shape functions, achieving seamless integration of CAD, CAE, and structural optimization. However, while ensuring geometric accuracy and high analytical precision, isogeometric topology optimization also introduces significant computational overhead, especially when dealing with high-resolution mesh sensitivity analysis of irregular structures, where the computational cost is often prohibitive.
[0003] In recent years, deep learning techniques have been introduced into topology optimization to accelerate the iterative process. Early research often employed offline learning models, using large amounts of data to train neural networks to directly predict optimization results or sensitivity. However, these methods have significant limitations: offline models typically struggle to generalize to new design problems with different geometric boundaries or load conditions outside the training set, leading to a substantial drop in prediction accuracy. To address the generalization problem, transfer learning methods are introduced into the online optimization process. Online samples generated during topology optimization iterations are used to retrain the offline-built baseline model, improving its prediction accuracy for specific problems. However, topology optimization is a dynamic iterative process; design variables and physical fields evolve with each iteration, meaning the data distribution from earlier iterations differs significantly from the current iteration's distribution. Simply using historical data for training introduces invalid information, interfering with the model's accurate prediction of the current state and leading to instability or even non-convergence in the optimization process. Summary of the Invention
[0004] To address the shortcomings of existing technologies, this invention proposes a time-decay online migration intelligent geometric topology optimization method for irregular structures, comprising the following steps:
[0005] A time-decaying online migration intelligent geometric topology optimization method for irregular structures includes the following steps:
[0006] Step S1: With the goal of minimizing the flexibility of the irregular structure, the material usage as a constraint, and the relative density of control points of the uniform geometric mesh as a design variable, construct a uniform geometric topology optimization model for the irregular structure.
[0007] Step S2: In the offline pre-training stage, the isogeometric topology optimization algorithm is used to solve multiple sets of preset numerical design examples to generate an offline dataset containing multi-resolution grid features; a benchmark neural network model is pre-trained based on the offline dataset; the benchmark neural network model includes a graph neural network module and a fully connected neural network module;
[0008] Step S3: During the online design phase of the product, the initial design domain of the product is divided into dual-resolution equal geometric meshes to obtain two sets of equal geometric mesh units and corresponding control points with coarse and fine resolutions respectively; based on the benchmark neural network model, the pre-training parameters of its backbone network are frozen, and a correction network head is added to the end of the fully connected neural network module of the benchmark neural network model to complete the initialization of the online neural network model.
[0009] Step S4: Enter the online isogeometric topology optimization iterative process, perform isogeometric analysis on the irregular structure on the coarse resolution mesh; use the online neural network model to predict the sensitivity of the control points on the fine resolution mesh;
[0010] Step S5: Using an online adaptive update strategy based on the sensitivity deviation angle, determine whether the online neural network model needs to be corrected in the current iteration step. If yes, proceed to step S6; otherwise, proceed to step S7.
[0011] Step S6: Perform geometric analysis such as fine-resolution mesh on the irregular structure of the current iteration step to obtain the true values of displacement and sensitivity of the control points corresponding to the fine-resolution mesh; construct an online training dataset using the time decay buffer method, and retrain the parameters of the corrected network head of the online neural network model based on the online training dataset. After the model update is completed, predict the sensitivity of the control points of the fine-resolution mesh through the updated online neural network model; proceed to step S7.
[0012] Step S7: Based on the predicted sensitivity of the fine-resolution grid control points, update the relative density of the fine-resolution grid control points using the moving asymptote algorithm; calculate the updated relative density of the coarse-resolution grid control points using the generalized inverse matrix of the coarse-fine resolution grid control point mapping matrix and complete the update.
[0013] Step S8: Determine whether the current iteration step meets the preset convergence termination condition for isogeometric topology optimization; if the convergence termination condition is not met, return to step S4 and enter the next iteration; if the convergence termination condition is met, output the isogeometric topology optimization design result of the irregular structure based on the relative density of the fine-resolution mesh control points obtained in the final iteration.
[0014] Furthermore, in step S1, the expression for the geometric topology optimization design model for irregular structures is as follows:
[0015]
[0016] in, Indicates the flexibility of irregular structures. 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 irregular 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 three directions of the parameter domain, respectively. This represents the minimum design variable set to avoid singularity in the stiffness matrix.
[0017] Furthermore, the graph neural network module is composed of at least two graph feature extraction units with identical structures stacked sequentially; wherein, the input of one graph feature extraction unit is the coordinate information and relative density information of the global fine-resolution grid control points, and the input of the other graph feature extraction units is the graph features output by the previous graph feature extraction unit; the graph feature extraction unit adopts a deep residual network structure, and its internal structure includes a batch normalization layer, a Point Transformer layer and a graph convolutional network layer sequentially arranged along the data transmission direction.
[0018] Furthermore, the fully connected neural network module is used to concatenate and fuse the displacement of the local coarse-resolution grid cell control point with the graph features extracted by the graph neural network module from the local fine-resolution grid cell, and finally output the sensitivity prediction value of the local fine-resolution grid cell control point; the fully connected neural network module is composed of an input layer, multiple hidden layers with residual connections, and an output layer connected in sequence; the local coarse-resolution grid cell refers to a single NURBS basis function unit under the coarse-resolution grid; the local fine-resolution grid cell refers to the fine-resolution grid cell within the coverage area corresponding to the local coarse-resolution grid cell.
[0019] Furthermore, step S3 includes the following steps:
[0020] Step S3.1: Load the offline pre-trained benchmark neural network model and freeze all the basic parameters of the benchmark model. This makes it untrainable during the online phase;
[0021] Step S3.2: Add a lightweight fully connected neural network, i.e., a correction head, to the intermediate hidden layers of the fully connected neural network module of the baseline model. Its parameters are denoted as ;
[0022] Step S3.3: Extract the frozen intermediate features of the basic neural network model and use them for baseline prediction. At the same time, the correction head receives the intermediate feature map as input and uses it to predict and output a residual correction term.
[0023] Step S3.4: Add the prediction result of the baseline model to the residual correction term of the correction head to obtain the final corrected output of the online model; during the online backpropagation training phase, the gradient only flows to and updates the parameters of the correction head. .
[0024] Furthermore, the online adaptive update strategy based on the sensitivity deviation angle in step S5 is as follows:
[0025] After the online geometric topology optimization iterative process starts, the correction flag is set to true during the initial iteration phase until the sensitivity deviation angle calculated in the current iteration step is less than the preset accuracy threshold; after entering the subsequent iteration phase, the preset number of iteration interval steps is checked. Every preset check iteration interval steps Perform a correction to the online neural network model.
[0026] Furthermore, the formula for calculating the sensitivity deviation angle is as follows:
[0027]
[0028] in, This represents the sensitivity vector of the fine-grid control points predicted by the neural network model. This represents the true sensitivity vector of the fine-mesh control points obtained through isogeometric analysis.
[0029] Furthermore, in step S6, an online training dataset is constructed using a time decay buffer method, including the following steps:
[0030] Step S6.1: Create a structure with a length of Fixed-length queue As a storage structure for buffered datasets, it is specifically designed to store the most recently... Data samples generated through geometric topology optimization iterations such as sub-fine meshes;
[0031] Step S6.2: When the maximum queue length is reached, the queue operates according to the first-in, first-out principle, discarding the oldest data samples to accommodate newly entered data;
[0032] Step S6.3: Assign a time decay penalty coefficient to each data sample in the queue, and calculate the time decay weight based on a monotonically decreasing exponential decay function. ,in For the attenuation rate parameter, The iteration interval corresponding to the sample;
[0033] Step S6.4: Construct the time-decay weighted online loss function, as shown in the following calculation formula:
[0034]
[0035] in, It is an online loss function. It is the root mean square error function.
[0036] The advantages and beneficial effects of this invention are as follows:
[0037] 1. This invention adopts a parameter fine-tuning strategy based on the modified network head. By freezing the pre-training parameters of the backbone network of the benchmark neural network model obtained through offline pre-training, only the added lightweight modified network head is trained to complete the fitting of the sensitivity prediction residual. This effectively avoids the catastrophic forgetting problem in the online transfer learning process, and at the same time significantly reduces the computational load and computing power cost of model training in the online stage.
[0038] 2. This invention proposes a time-decay-based buffered online dataset construction method. Addressing the issue of constantly changing sample data distribution during topology optimization iterations, a fixed-length buffer queue is constructed to store online training samples. A time-decay weighting strategy is introduced, assigning higher weight coefficients to recently highly correlated samples in the iteration sequence, while gradually reducing the weight ratio of earlier samples and updating and eliminating the queue. This allows the online neural network model to continuously adapt to the topology optimization state of the current iteration step, significantly improving the model's sensitivity, prediction stability, and prediction accuracy during dynamic iterations.
[0039] 3. This invention proposes an online adaptive update strategy based on the sensitivity deviation angle. The deviation angle of the sensitivity vector of the control point in the fine-resolution grid is used as the monitoring index for model correction. Combined with the preset number of check iteration intervals, the model correction strategy for the current iteration step is adaptively determined. Under the premise of ensuring the accuracy of topology optimization design, the online solution efficiency of geometric topology optimization models such as irregular structures is greatly improved. Attached Figure Description
[0040] Figure 1 This is a flowchart of the method of the present invention.
[0041] Figure 2a This is a schematic diagram of the boundary conditions (MBB beam) of a numerical design example used to generate an offline dataset in an embodiment of the present invention.
[0042] Figure 2b This is a schematic diagram (rectangle) of the boundary conditions for a numerical design example used to generate an offline dataset in an embodiment of the present invention.
[0043] Figure 2c This is a schematic diagram (L-shaped) of the boundary conditions for a numerical design example used to generate an offline dataset in an embodiment of the present invention.
[0044] Figure 2d This is a schematic diagram of the boundary conditions (circular ring beam) of a numerical design example used to generate an offline dataset in an embodiment of the present invention.
[0045] Figure 3 This is a diagram of the offline benchmark neural network structure constructed in an embodiment of the present invention.
[0046] Figure 4 This is a diagram showing the design domain and boundary conditions of the hook beam irregular structure in this embodiment of the invention.
[0047] Figure 5 This is a diagram of the online neural network structure constructed in an embodiment of the present invention.
[0048] Figure 6 This is a schematic diagram of the geometric topology optimization results obtained by the method of the present invention.
[0049] Figure 7 This is a schematic diagram of the results obtained by the standard equal geometric topology optimization method in an embodiment of the present invention. Detailed Implementation
[0050] 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.
[0051] like Figure 1 As shown, the intelligent geometric topology optimization method for irregular structures with time-decay online migration specifically includes the following steps:
[0052] Step S1: With the goal of minimizing the compliance of the irregular structure, the material usage as a constraint, and the relative density of control points of the uniform geometric mesh as the design variable, construct a uniform geometric topology optimization model for the irregular structure. The model expression is as follows:
[0053]
[0054] in, Indicates the flexibility of irregular structures. 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 irregular 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 three directions of the parameter domain, respectively. This represents the minimum design variable value set to avoid singularity in the stiffness matrix; in this embodiment, it is set to 0.001.
[0055] Step S2: In the offline pre-training stage, the isogeometric topology optimization algorithm is used to solve multiple sets of preset numerical design examples to generate an offline dataset containing multi-resolution grid features; a benchmark neural network model is pre-trained based on the offline dataset; the benchmark neural network model includes a graph neural network module and a fully connected neural network module;
[0056] The graph neural network module is composed of at least two graph feature extraction units with the same structure stacked sequentially. The input of one graph feature extraction unit is the coordinate information and relative density information of the global fine-resolution grid control points, and the input of the other graph feature extraction units is the graph features output by the previous graph feature extraction unit. The graph feature extraction unit adopts a deep residual network structure, and its internal structure includes a batch normalization layer, a PointTransformer layer and a graph convolutional network layer sequentially arranged along the data transmission direction.
[0057] Furthermore, the fully connected neural network module is used to concatenate and fuse the displacement of the local coarse-resolution grid cell control point with the graph features extracted by the graph neural network module from the local fine-resolution grid cell, and finally output the sensitivity prediction value of the local fine-resolution grid cell control point; the fully connected neural network module is composed of an input layer, multiple hidden layers with residual connections, and an output layer connected in sequence; the local coarse-resolution grid cell refers to a single NURBS basis function unit under the coarse-resolution grid; the local fine-resolution grid cell refers to the fine-resolution grid cell within the coverage area corresponding to the local coarse-resolution grid cell.
[0058] This embodiment constructs respectively Figures 2a to 2d The isogeometric topology optimization models of MBB beams, rectangular beams, L-shaped beams, and circular ring beams are used. Third-order NURBS basis functions are employed as the shape function discrete numerical case design domain. The maximum volume fraction is set to 0.4, and the number of discrete grids in the horizontal and vertical directions is set to [values to be filled in]. , , as well as A NURBS coarse mesh was obtained; a node insertion strategy was used to refine the coarse mesh of equal geometry to a refinement level of 4, resulting in mesh numbers of [number missing]. , , as well as NURBS fine mesh; solved using an isogeometric topology optimization algorithm; generated an offline dataset containing multi-resolution mesh features;
[0059] In this embodiment of the invention, a construction is performed as follows: Figure 3 The offline benchmark neural network model shown has the following settings: the number of graph feature extraction units is set to 3, the number of output features is set to 4, and the number of neurons per layer in the fully connected neural network module is set to... Except for the final output layer, the activation function of the entire neural network is the sigmoid linear unit, the activation function of the final output layer is the softplus, the loss function of the neural network is set to root mean square error, the learning rate is 0.005, the maximum number of iterations is set to 1000, and the neural network model is initially trained using the Adam optimizer.
[0060] Step S3: During the online design phase of the product, the initial design domain of the product is divided into dual-resolution equal geometric meshes to obtain two sets of equal geometric mesh units and corresponding control points with coarse and fine resolutions respectively; based on the benchmark neural network model, the pre-training parameters of its backbone network are frozen, and a correction network head is added to the end of the fully connected neural network module of the benchmark neural network model to complete the initialization of the online neural network model.
[0061] Step S3.1: Load the offline pre-trained benchmark neural network model and freeze all the basic parameters of the benchmark model. This makes it untrainable during the online phase.
[0062] Step S3.2: Add a lightweight fully connected neural network, i.e., a correction head, to the intermediate hidden layers of the fully connected neural network module of the baseline model. Its parameters are denoted as .
[0063] Step S3.3: Extract the frozen intermediate features of the basic neural network model and use them for baseline prediction. At the same time, the correction head receives the intermediate feature map as input and uses it to predict and output a residual correction term.
[0064] Step S3.4: Add the prediction result of the baseline model to the residual correction term of the correction head to obtain the final corrected output of the online model; during the online backpropagation training phase, the gradient only flows to and updates the parameters of the correction head. .
[0065] 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 4 The design domain for the irregular hook beam structure shown has a volume fraction of 0.4 and a coarse mesh number of [number missing]. The refinement level is 4, and the number of grid cells in the fine mesh is [number missing]. The maximum number of topology optimization iterations is set to 200; the sensitivity deviation angle accuracy threshold is set to 5°, and the number of iterations is checked to 5; the online dataset is stored using a fixed-length queue of length 5; the decay rate parameter is set to 0.95; and the correction flag is initialized to true.
[0066] In this embodiment of the invention, a construction is performed as follows: Figure 5 The online neural network model shown includes a newly added correction head consisting of four fully connected neural network layers, with the number of neurons in each layer set to [256, 256, 256, 216], the activation function being a sigmoid linear unit, the learning rate being 0.002, the maximum number of iterations being set to 1000, and the neural network model being initially trained using the Adam optimizer.
[0067] Step S4: Enter the online isogeometric topology optimization iterative process, perform isogeometric analysis on the irregular structure on the coarse resolution mesh; use the online neural network model to predict the sensitivity of the control points on the fine resolution mesh;
[0068] Step S5: Using an online adaptive update strategy based on the sensitivity deviation angle, determine whether the online neural network model needs to be corrected in the current iteration step. If yes, proceed to step S6; otherwise, proceed to step S7.
[0069] Step S6: Perform geometric analysis such as fine-resolution mesh on the irregular structure of the current iteration step to obtain the true values of displacement and sensitivity of the control points corresponding to the fine-resolution mesh; construct an online training dataset using the time decay buffer method, and retrain the parameters of the corrected network head of the online neural network model based on the online training dataset. After the model update is completed, predict the sensitivity of the control points of the fine-resolution mesh through the updated online neural network model.
[0070] Step S6.1: Create a structure with a length of Fixed-length queue As a storage structure for buffered datasets, it is specifically designed to store the most recently... Data samples generated through geometric topology optimization iterations such as finer meshes.
[0071] Step S6.2: When the maximum queue length is reached, the queue operates on the first-in, first-out principle, discarding the oldest data sample to accommodate newly entered data.
[0072] Step S6.3: Assign a time decay penalty coefficient to each data sample in the queue, and calculate the time decay weight based on a monotonically decreasing exponential decay function. ,in For the attenuation rate parameter, This represents the iteration interval corresponding to the sample.
[0073] Step S6.4: Construct a time-decay weighted online loss function, the calculation formula of which is shown below:
[0074]
[0075] in, It is an online loss function. It is the root mean square error function.
[0076] Step S7: Based on the predicted sensitivity of the fine-resolution grid control points, update the relative density of the fine-resolution grid control points using the moving asymptote algorithm; calculate the updated relative density of the coarse-resolution grid control points using the generalized inverse matrix of the coarse-fine resolution grid control point mapping matrix and complete the update.
[0077] Step S8: Determine if the current iteration is less than 200; if not, return to step S4 and proceed to the next iteration; if so, output the geometric topology optimization results such as irregular structure based on the final relative density of the fine mesh control points.
[0078] The isogeometric topology optimization results obtained by the method of this invention are 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 4 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 isogeometric topology optimization method are basically the same. Table 1 records the comparison between the proposed method and the standard isogeometric 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 0.25% different from that of the traditional method, while achieving a speedup of 6.924 times in terms of computational efficiency, significantly improving the solution efficiency of the isogeometric topology optimization model.
[0079] Table 1. Target performance and CPU computation time of design results obtained by different methods
[0080] Target performance CPU computation time Standard geometric topology optimization method 1219.72 147011.86 seconds The method proposed in this invention 1222.71 21298.88 seconds
[0081] 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 time-decaying online migration intelligent iso-geometric topology optimization method for irregular structures, characterized in that: Includes the following steps: Step S1: With the goal of minimizing the flexibility of the irregular structure, the material usage as a constraint, and the relative density of control points of the uniform geometric mesh as the design variable, construct a uniform geometric topology optimization model for the irregular structure. Step S2: In the offline pre-training stage, the isogeometric topology optimization algorithm is used to solve multiple sets of preset numerical design examples to generate an offline dataset containing multi-resolution grid features; a benchmark neural network model is pre-trained based on the offline dataset; the benchmark neural network model includes a graph neural network module and a fully connected neural network module; Step S3: During the online design phase of the product, the initial design domain of the product is divided into dual-resolution equal geometric meshes to obtain two sets of equal geometric mesh units and corresponding control points with coarse and fine resolutions respectively; based on the benchmark neural network model, the pre-training parameters of its backbone network are frozen, and a correction network head is added to the end of the fully connected neural network module of the benchmark neural network model to complete the initialization of the online neural network model. Step S4: Enter the online isogeometric topology optimization iterative process, perform isogeometric analysis on the irregular structure on the coarse resolution mesh; use the online neural network model to predict the sensitivity of the control points on the fine resolution mesh; Step S5: Using an online adaptive update strategy based on the sensitivity deviation angle, determine whether the online neural network model needs to be corrected in the current iteration step. If yes, proceed to step S6; otherwise, proceed to step S7. Step S6: Perform geometric analysis such as fine-resolution mesh on the irregular structure of the current iteration step to obtain the true values of displacement and sensitivity of the control points corresponding to the fine-resolution mesh; construct an online training dataset using the time decay buffer method, and retrain the parameters of the corrected network head of the online neural network model based on the online training dataset. After the model update is completed, predict the sensitivity of the control points of the fine-resolution mesh through the updated online neural network model; proceed to step S7. Step S7: Based on the predicted sensitivity of the fine-resolution grid control points, update the relative density of the fine-resolution grid control points using the moving asymptote algorithm; calculate the updated relative density of the coarse-resolution grid control points using the generalized inverse matrix of the coarse-fine resolution grid control point mapping matrix and complete the update. Step S8: Determine whether the current iteration step meets the preset convergence termination condition for isogeometric topology optimization; if the convergence termination condition is not met, return to step S4 and enter the next iteration; if the convergence termination condition is met, output the isogeometric topology optimization design result of the irregular structure based on the relative density of the fine-resolution mesh control points obtained in the final iteration.
2. The time-decay online migration intelligent geometric topology optimization method for irregular structures according to claim 1, characterized in that: In step S1, the expression for the geometric topology optimization design model for irregular structures is as follows: in, Indicates the flexibility of irregular structures. 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 irregular 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 three directions of the parameter domain, respectively. This represents the minimum design variable set to avoid singularity in the stiffness matrix.
3. The time-decay online migration intelligent geometric topology optimization method for irregular structures according to claim 1, characterized in that: The graph neural network module is composed of at least two graph feature extraction units with the same structure stacked sequentially. The input of one graph feature extraction unit is the coordinate information and relative density information of the global fine-resolution grid control points, and the input of the other graph feature extraction units is the graph features output by the previous graph feature extraction unit. The graph feature extraction unit adopts a deep residual network structure, and its internal structure includes a batch normalization layer, a PointTransformer layer and a graph convolutional network layer sequentially arranged along the data transmission direction.
4. The time-decay online migration intelligent geometric topology optimization method for irregular structures according to claim 1, characterized in that: The fully connected neural network module is used to stitch together and fuse the displacement of the control points of the local coarse-resolution grid cells and the graph features extracted by the graph neural network module from the local fine-resolution grid cells, and finally output the sensitivity prediction value of the control points of the local fine-resolution grid cells. The fully connected neural network module is composed of an input layer, multiple hidden layers with residual connections, and an output layer connected in sequence. The local coarse-resolution grid cell refers to a single NURBS basis function unit under the coarse-resolution grid. The local fine-resolution grid cell refers to the fine-resolution grid cell within the coverage area corresponding to the local coarse-resolution grid cell.
5. The time-decay online migration intelligent geometric topology optimization method for irregular structures according to claim 1, characterized in that: Step S3 includes the following steps: Step S3.1: Load the offline pre-trained benchmark neural network model and freeze all the basic parameters of the benchmark model. This makes it untrainable during the online phase; Step S3.2: Add a lightweight fully connected neural network, i.e., a correction head, to the intermediate hidden layers of the fully connected neural network module of the baseline model. Its parameters are denoted as ; Step S3.3: Extract the frozen intermediate features of the basic neural network model and use them for baseline prediction. At the same time, the correction head receives the intermediate feature map as input and uses it to predict and output a residual correction term. Step S3.4: Add the prediction results of the baseline model to the residual correction term of the correction head to obtain the final corrected output of the online model; During the online backpropagation training phase, gradients only flow to and update the parameters of the correction head. .
6. The method for intelligent geometric topology optimization of irregular structures with time-decayed online migration according to claim 1, characterized in that: The online adaptive update strategy based on the sensitivity deviation angle in step S5 is as follows: After the online geometric topology optimization iteration process is started, the correction flag will be set to true in the initial iteration phase until the sensitivity deviation angle calculated in the current iteration step is less than the preset accuracy threshold. After entering the subsequent iteration stage, the preset check iteration interval number of steps is set. Every preset check iteration interval steps Perform a correction to the online neural network model.
7. The time-decay online migration intelligent geometric topology optimization method for irregular structures according to claim 6, characterized in that: The formula for calculating the sensitivity deviation angle is as follows: in, This represents the sensitivity vector of the fine-grid control points predicted by the neural network model. This represents the true sensitivity vector of the fine-mesh control points obtained through isogeometric analysis.
8. The time-decay online migration intelligent geometric topology optimization method for irregular structures according to claim 1, characterized in that: In step S6, an online training dataset is constructed using a time decay buffering method, including the following steps: Step S6.1: Create a structure with a length of Fixed-length queue As a storage structure for buffered datasets, it is specifically designed to store the most recently... Data samples generated through geometric topology optimization iterations such as sub-fine meshes; Step S6.2: When the maximum queue length is reached, the queue operates according to the first-in, first-out principle, discarding the oldest data samples to accommodate newly entered data; Step S6.3: Assign a time decay penalty coefficient to each data sample in the queue, and calculate the time decay weight based on a monotonically decreasing exponential decay function. ,in For the attenuation rate parameter, The iteration interval corresponding to the sample; Step S6.4: Construct the time-decay weighted online loss function, as shown in the following calculation formula: in, It is an online loss function. It is the root mean square error function.