Node intelligent generation method integrating deep learning and topological optimization technology

Abstract

The invention relates to the technical field of computer-aided engineering design, and discloses a node intelligent generation method fusing deep learning and topological optimization technology, and the method comprises the steps: obtaining an initial node geometric model, carrying out topological optimization based on a variable density method, and constructing a three-dimensional node voxelization training data set through data enhancement and voxelization processing; constructing a three-dimensional generative adversarial network, training by using the data set, and executing network parameter constraint by using a composite loss function including adversarial loss, topological regularization loss and diversity constraint loss in training; obtaining a generated voxel model output by the generator, and carrying out space alignment on the generated voxel model and the finite element mesh; in the aligned finite element model, a preset reward coefficient is given to a unit corresponding to the entity area, and quadratic topological optimization calculation is executed through an objective function containing the reward coefficient. According to the method, the discrete three-dimensional matrix is converted into a continuous geometric entity, and the phenomena of model boundary discrete defects and force transfer path fracture are eliminated.

Description

Technical Field

[0001] This invention relates to the field of computer-aided engineering design technology, specifically to a node intelligent generative method that integrates deep learning and topology optimization techniques. Background Technology

[0002] In the field of spatial structures and complex building engineering, nodes, as key components connecting various load-bearing members, directly determine the force transmission efficiency and safety performance of the overall structure through their topological configuration. Traditional node design mainly relies on empirical trial and error or parametric modeling based on specific criteria, making it difficult to achieve optimal material distribution while satisfying complex load boundary conditions. In recent years, topology optimization techniques such as the variable density method based on continuum mechanics have been widely used in node design. These methods, through sensitivity analysis and iterative solutions, can obtain structural configurations with clear force transmission paths. However, such numerical optimization methods consume a great deal of computational resources, and even small changes in initial boundary conditions often require re-execution of the full iteration, making it difficult to meet the real-time requirements of rapid scheme comparison under multiple load conditions in engineering design.

[0003] With the development of artificial intelligence technology, generative design of complex nodes using deep learning models such as generative adversarial networks has become a new technological direction. This type of method attempts to achieve second-level prediction of node configurations by establishing a mapping relationship between boundary condition features and topological morphology. However, in existing technologies, the generation results based on deep learning typically exist in the form of three-dimensional discrete voxel matrices. Their underlying logic lacks physical conservation constraints, leading to the output generated voxel models being highly susceptible to local fractures in force transmission paths within three-dimensional space or the formation of isolated, non-load-bearing material suspension blocks. Furthermore, due to the inherent discrete nature of voxelization, the generated entity boundaries often exhibit a significant stepped serrated effect. This not only reduces the geometric accuracy of the structure but also prevents the model from being directly imported into a finite element analysis environment for mechanical verification due to a lack of boundary continuity, thus limiting the reliable application of generative design in practical engineering manufacturing. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a node intelligent generative method that integrates deep learning and topology optimization techniques. This method solves the problem that in existing node topology optimization designs, the output three-dimensional voxel discrete model lacks constraints on the continuity of physical force transmission paths and surface geometric smoothness, resulting in boundary step-like discrete defects and internal load-bearing material fractures in the generated structure, which cannot directly meet the requirements of finite element continuous medium mechanics analysis.

[0005] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a node intelligent generative method that integrates deep learning and topology optimization techniques, comprising the following steps: An initial node geometric model is obtained, and topology optimization is performed based on the variable density method. The optimized initial node geometric model is then subjected to data augmentation and voxelization to construct a three-dimensional node voxelization training dataset. A three-dimensional generative adversarial network (GAN) containing a generator and a discriminator is constructed. The GAN is trained using the three-dimensional node voxelized training dataset. During the training process, a composite loss function is used to constrain the GAN, which includes adversarial loss, topology regularization loss, and diversity constraint loss. Obtain the generated voxel model output by the generator after training is completed, spatially align the generated voxel model with the finite element mesh, assign a preset reward coefficient to the element corresponding to the solid region in the generated voxel model in the aligned finite element model, and perform secondary topology optimization with an objective function containing the reward coefficient to obtain the final complex node model.

[0006] Through the above technical solution, this invention couples discrete three-dimensional matrix data with a continuous finite element geometric mesh. The voxel distribution output by the network forward propagation initially establishes the main force path. Subsequently, through alignment operations and iterative quadratic density method, the stepped shape of the entity boundary introduced by the previous voxelization transformation is eliminated, and the discrete three-dimensional feature matrix is ​​transformed into a geometric entity that meets the requirements of continuous analysis in finite element mechanics.

[0007] Preferably, when performing topology optimization based on the variable density method, a three-field floating projection method is introduced to decouple the density field into a design field that controls the global material distribution, a filtering field that suppresses the checkerboard effect, and a projection field that maps the continuous density to a discrete distribution of approximately zero and one. This three-field decoupling mechanism constrains the minimum feature size of the solid material and eliminates numerical instability during the optimization iteration process.

[0008] In one specific embodiment, the step of constructing the 3D node voxelized training dataset specifically includes: applying random perturbations to the unit sensitivity during the iterative process of topology optimization based on the variable density method to escape local extrema; performing symmetry processing on the initial node geometric model after topology optimization, and rotating the symmetrically processed initial node geometric model around a fixed axis at preset angle intervals to expand the sample size; performing voxelization processing on the expanded initial node geometric model, converting it into a 3D matrix format suitable for network training, to obtain the 3D node voxelized training dataset. The above steps sequentially generate spatial pose-derived models within a 3D angular range, providing rotational invariance features of the model in 3D space.

[0009] Preferably, the generator comprises a cascaded volumetric transposed convolutional module, residual blocks, and a self-attention mechanism module, used to upsample the input random noise vector layer by layer and map it to a 3D solid structure; the discriminator comprises a volumetric convolutional downsampling layer and a fully connected classification layer, used to extract multi-scale features and output true / false discrimination probabilities; the first network layer of the discriminator uses instance normalization processing, and subsequent network layers combine to use batch normalization processing. The aforementioned residual blocks establish forward bypass connections across network layers to maintain the identity mapping of feature propagation; the self-attention mechanism module calculates the feature correlation matrix between voxel nodes to establish global spatial distance dependencies.

[0010] In one specific embodiment, the topology regularization loss includes at least connectivity loss and continuity loss. The connectivity loss is calculated by taking the first difference of the voxel density field in the three principal directions and extracting the negative correlation of the direction with the largest connectivity as the loss to maximize the consistency of adjacent voxels. The continuity loss is calculated by introducing a mean convolution kernel to calculate the local average density field. The continuity loss includes a first term that uses an exponential function to penalize activated voxels in low-density neighborhoods, and a second term that constrains the local density to tend towards a preset optimal value through a squared difference penalty. The constraints of the above loss function eliminate isolated suspended blocks that do not bear loads in the generated voxel model and force the material to maintain physical continuity along the principal force directions.

[0011] Preferably, the topology regularization loss further includes clustering loss and smoothness loss; the clustering loss minimizes the second moment of the material distribution by extracting the set of active voxels from the generated voxels and calculating the normalized average distance from each active voxel to the geometric centroid of the set of active voxels, thereby forcing the generated voxels to cluster towards the center; the smoothness loss penalizes abrupt changes in the density field by calculating the second difference of the density field using the second-order discrete Laplace operator to eliminate the boundary staircase effect; when configuring the composite loss function, the weight value of the clustering loss is configured to be greater than the weight values ​​of the connectivity loss, the continuity loss, and the smoothness loss. The above weight configuration establishes the dominant role of clustering features in the topology dimensionality reduction process, reducing the overall envelope volume of the generated structure.

[0012] In one specific embodiment, the diversity constraint loss includes a diversity loss and a pattern search loss. The diversity loss calculates the cosine similarity between the feature vectors of generated samples and imposes a penalty when the cosine similarity exceeds a preset similarity threshold. The pattern search loss calculates the spatial distance between generated samples and the potential spatial distance between their corresponding random noise vectors, using exclusion and proportional terms to force the spatial distance to maintain a proportional relationship with the potential spatial distance. This computational mechanism forces the network to expand its search range for different topological forms during parameter updates, reducing the probability of outputting a homogeneous, single structure.

[0013] Preferably, the step of spatially aligning the generated voxel model with the finite element mesh specifically includes: using the generated voxel model as a source point cloud set and the finite element model containing the finite element mesh as the target geometry; constructing a rigid body transformation model including rotation, translation, and fine-tuning scaling operations; constructing an objective function based on the distance field, with the objective of minimizing the sum of the average Euclidean distance from the transformed source point cloud set to the surface of the target geometry and the scaling regularization term, and performing optimization to obtain the optimal transformation parameters to complete the spatial alignment. The aforementioned rigid body transformation based on the distance field unifies the discrete output to the target-defined global coordinate system, eliminating spatial pose deviations.

[0014] In one specific embodiment, the step of optimizing and obtaining the optimal transformation parameters to complete the spatial alignment specifically includes: solving a non-convex optimization problem containing the objective function based on the distance field using a multi-starting point differential evolution strategy to obtain the optimal transformation parameters; and using a nearest neighbor search algorithm to extract the set of solid element indices in the target geometric field based on the optimal transformation parameters to generate a density mask array for identifying solid regions. The density mask array establishes Boolean attribute markers for the finite element mesh, distinguishing between load-bearing regions with solid material and non-solid void regions.

[0015] Preferably, the step of assigning a preset reward coefficient to the elements corresponding to the solid regions in the generated voxel model in the aligned finite element model, and performing secondary topology optimization using an objective function containing the reward coefficient, specifically includes: identifying the solid regions in the finite element model based on the density mask array; for the aligned finite element model, if a finite element element belongs to the solid region, assigning a solid reward coefficient greater than one; if a finite element element does not belong to the solid region, assigning a default reward coefficient equal to one; constructing a variable density objective function containing the solid reward coefficient and the default reward coefficient, wherein the variable density objective function is configured to calculate the reward coefficient of each finite element element, the penalty power of the element relative density, the transpose of the element displacement vector, and the sum of the products of the element stiffness matrix and the element displacement vector; and completing the secondary topology optimization by minimizing the variable density objective function to eliminate boundary discretization defects and obtain the final complex node model. The aforementioned finite element iterative process with a reward coefficient bias applies weighted scaling to the stiffness of the marked entity region, forcing the secondary topology optimization to perform local boundary approximation and smoothing processing on the initial force transmission skeleton output by the three-dimensional generative adversarial network.

[0016] This invention provides an intelligent node generation method that integrates deep learning and topology optimization techniques. It has the following beneficial effects: 1. This invention constructs a 3D generative adversarial network (GAN) containing a generator and a discriminator, and combines it with a quadratic variable density topology optimization method with a reward coefficient bias to transform the discrete 3D voxel matrix output by the network's forward propagation into continuous finite element geometric entities. This process eliminates the stepped, jagged morphology of entity boundaries introduced by simply relying on voxelization transformation, and eliminates isolated non-load-bearing material blocks in the 3D design space, ultimately outputting a complex node geometric model with smooth, continuous boundaries that meets the requirements of continuous physical and mechanical analysis.

[0017] 2. This invention configures a composite loss function during the parameter iteration process of the 3D generative adversarial network. Through the second-order difference and exponential penalty calculation of connectivity loss and continuity loss, it constrains activated voxels to cluster towards high-density neighborhoods and maintain physical connectivity along the predetermined principal force direction. Simultaneously, it utilizes diversity loss and pattern search loss to force the geometric distance change in the output space to maintain a proportional relationship with the noise distance change in the latent space. These constraint mechanisms eliminate the breakage defect in the force transmission path within the generative voxel model and avoid pattern collapse during feature dimensionality reduction, thus reducing the output probability of a single homogeneous topology.

[0018] 3. This invention constructs a non-convex objective function based on a distance field and performs multi-starting-point differential evolution optimization to calculate the optimal rigid body transformation parameters for the generated voxel model to reach the target finite element mesh, eliminating initial pose deviations and generating a density mask array. Based on the density mask array, finite element elements belonging to the solid material region are assigned a solid reward coefficient greater than one. The aforementioned spatial alignment and biasing mechanism performs a weighted scaling operation during the sensitivity analysis stage of element stiffness, forcing subsequent secondary finite element mesh iterations to strictly follow the initial force transmission backbone output by the generated network for material distribution reconstruction. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the overall technical route of the node intelligent generation method of the present invention; Figure 2 This is a schematic diagram of the data augmentation process of the present invention; Figure 3 This is a schematic diagram of the generator network structure of the present invention; Figure 4 This is a schematic diagram of the discriminator network structure of the present invention; Figure 5 This is a schematic diagram of the voxel model space alignment optimization of the present invention; Figure 6 This is a schematic diagram of the preprocessing and dimensions of the K6 node in this invention; Figure 7 This is a schematic diagram of the training loss curve of the K6 node generation model of the present invention; Figure 8This is a schematic diagram of the initial scheme for the K6 node generated by the GAN of this invention; Figure 9 This is a schematic diagram of the post-processed optimized K6 node scheme of the present invention; Figure 10 This is a schematic diagram of the K6 node optimization results based on the reward mechanism post-processing of the present invention; Figure 11 This is a schematic diagram comparing the node generation quality under different topology regularization weight configurations of the present invention. Figure 12 This is a schematic diagram comparing the generated sample morphology under different diversity loss weight configurations of the present invention. Figure 13 This is a schematic diagram of the dimensions of the three-layer rigid frame node model of the present invention; Figure 14 This is a schematic diagram of the loss curve during the training process of the framework nodes of the present invention; Figure 15 This is a schematic diagram of the post-processing results of the framework nodes in this invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] See attached document Figure 1 This invention provides a node intelligent generative method that integrates deep learning and topology optimization techniques, which may include: The initial node geometric model is obtained, and topology optimization is performed based on the variable density method. Data augmentation and voxelization are performed on the node model after topology optimization to construct a three-dimensional node voxelization training dataset. A 3D generative adversarial network (GAN) containing a generator and a discriminator is constructed. The GAN is trained using the aforementioned 3D node voxelized training dataset. During the training process, a composite loss function is used to constrain the GAN, which includes adversarial loss, topology regularization loss, and diversity constraint loss. Obtain the generated voxel model output by the trained generator, spatially align the generated voxel model with the finite element mesh, assign a preset reward coefficient to the element corresponding to the solid region in the generated voxel model in the aligned finite element model, and perform secondary topology optimization with the objective function containing the above reward coefficient to obtain the final complex node model.

[0022] The aforementioned intelligent node generation method, which integrates deep learning and topology optimization techniques, is executed based on an intelligent node generation system. This system includes a dataset construction module, a network training module, and a post-processing optimization module.

[0023] The dataset construction module is used to obtain the initial node geometry model and perform topology optimization based on the variable density method. During the iterative process of topology optimization, the dataset construction module performs sensitivity random perturbation operations and model rotation transformation operations to expand the model sample size.

[0024] The dataset construction module voxelizes the node models after expanding the sample size, converts them into a three-dimensional matrix format suitable for network training, and outputs the aforementioned three-dimensional node voxelized training dataset.

[0025] The generative network training module is used to construct a 3D generative adversarial network. This 3D generative adversarial network includes a generator and a discriminator. The generative network training module obtains the aforementioned 3D node voxelized training dataset and uses this dataset to iteratively train the generator and discriminator alternately.

[0026] During the training process, the generative network training module uses a composite loss function that includes the aforementioned adversarial loss, topological regularization loss, and diversity constraint loss to update the network parameters of the 3D generative adversarial network.

[0027] The post-processing optimization module is used to acquire the generated voxel model output by the generator and process the pose relationship between the generated voxel model and the target finite element mesh. The post-processing optimization module performs spatial alignment operations to eliminate pose deviations.

[0028] The post-processing optimization module extracts density masks to identify solid regions in the finite element model based on the spatial alignment results. The module assigns a preset solid reward coefficient to finite element elements belonging to these solid regions and a default reward coefficient to finite element elements not belonging to these regions.

[0029] The post-processing optimization module performs a second-order topology optimization based on the variable density objective function that includes the above entity reward coefficients and the above default reward coefficients, eliminates boundary discrepancies, and outputs the final complex node model.

[0030] See attached document Figure 2 The dataset construction module obtains the initial node geometric model. It then establishes a parameterized node geometric model, generating initial node designs with different configurations by adjusting the node geometric dimension parameters.

[0031] The dataset construction module performs topology optimization on the initial node geometry model based on the variable density method, calculating the material distribution. During the topology optimization calculation, the module introduces a three-field floating projection method to decouple the single density field into independent design, filter, and projection fields. The design field controls the initial global material distribution, the filter field eliminates numerical instability and suppresses the checkerboard effect in the material distribution, and the projection field maps continuous density variables to discrete density distributions. Through the cascade calculation of these independent physical fields, the module constrains the minimum characteristic size of the material, generating a topology configuration with solid boundaries.

[0032] In the iterative solution phase of topology optimization based on the variable density method, the dataset construction module performs a sensitivity perturbation operation. The dataset construction module calculates the sensitivity values ​​of the objective function with respect to the relative density of each cell and applies random perturbations to these sensitivity values. This random sensitivity perturbation operation changes the current updated values ​​of the cell sensitivity, forcing the topology optimization algorithm to deviate from the predetermined gradient descent path during iterative updates, thus escaping local extrema.

[0033] The dataset construction module obtains the node model after the topology optimization iteration. The dataset construction module then performs symmetry processing on the optimized node model, extracting a proportionally symmetrical geometric model.

[0034] For the symmetrically processed node model, the dataset construction module performs a rotation transformation operation with the Z-axis of the coordinate system as the rotation center. The module sets the rotation angle interval to 60 degrees, generating spatial pose derivative models corresponding to different rotation angles sequentially within a 360-degree circumferential range. This rotation transformation operation equidistantly expands a single input sample into multiple training samples with distinct directions, achieving a uniformly distributed expansion of the dataset sample size and providing spatial rotation invariance features.

[0035] The dataset construction module performs voxelization on the node models after expanding the sample size. The module determines whether the 3D spatial mesh contains solid material, converts the discrete geometric model into a 3D matrix format suitable for network training, and outputs the aforementioned 3D node voxelized training dataset.

[0036] See attached document Figure 3 The generator network training module constructs the generator in the 3D generative adversarial network. The generator adopts a depth transposed convolutional architecture, which includes an input layer, a fully connected projection layer, four cascaded volume transposed convolutional modules, residual blocks, and a self-attention mechanism module.

[0037] The generator obtains a random noise vector with a dimension of 256. The fully connected projection layer receives the random noise vector and maps it into the initial three-dimensional feature tensor.

[0038] Four cascaded volumetric transpose convolutional modules receive the initial 3D feature tensor and perform layer-by-layer upsampling operations. These layer-by-layer upsampling operations expand the spatial resolution of the 3D feature tensor. In the four cascaded volumetric transpose convolutional modules, the number of feature channels decreases sequentially, with the decreasing sequence configured as 256, 128, 64, and 32.

[0039] Within the internal network layers of the volume transposed convolution module, the generator network training module integrates batch normalization and linear rectified activation functions. Batch normalization calculates the mean and variance of the input batch of 3D feature data uniformly, adjusting the feature data distribution to a standard state. The linear rectified activation function performs a non-linear mapping on the normalized feature data.

[0040] The generator network training module embeds residual blocks into the generator's network architecture. These residual blocks establish forward bypass connections across network layers, directly accumulating the inputs of shallow networks to the outputs of deep networks, maintaining the identity mapping state during feature propagation, and avoiding the vanishing feature gradient phenomenon caused by the increase in the number of network layers.

[0041] The generator network training module embeds a self-attention mechanism module at the intermediate network layer of the generator. This self-attention mechanism module calculates the feature correlation matrix between voxel nodes within the 3D feature tensor. Based on this feature correlation matrix, the generator network training module assigns weights to global dependencies in 3D space, establishing connections between structural features between distant local regions.

[0042] See attached document Figure 4 The generative network training module constructs the discriminator in the 3D generative adversarial network. The discriminator consists of four cascaded volumetric convolutional downsampling layers and a fully connected classification layer.

[0043] The discriminator acquires the real sample voxel matrix from the 3D node voxelization training dataset, as well as the generated voxel model matrix output by the generator. Four volumetric convolutional downsampling layers receive the input 3D matrix data and perform multi-level feature extraction and spatial resolution compression operations.

[0044] In the four volumetric convolutional downsampling layers, the geometric dimensions of the volumetric convolution kernel are configured as 4×4×4, and the stride is set to 2. The number of feature channels increases sequentially in the four volumetric convolutional downsampling layers, with the increment sequence configured as 64, 128, 256, and 512.

[0045] The first network layer of the discriminator performs instance normalization. Instance normalization independently calculates the mean and variance of the 3D feature map for a single input sample, eliminating initial contrast differences between different 3D node models. Subsequent volumetric convolutional downsampling layers of the discriminator combine batch normalization with a leaky linear rectified activation function. This leaky linear rectified activation function retains a small gradient at a preset proportion for negative inputs, maintaining the continuous activation state of network nodes.

[0046] The generative network training module introduces a 3D dropout layer after the volumetric convolutional downsampling layer at the end of the discriminator. During the iterative update of network parameters, the 3D dropout layer randomly sets the output matrix of some 3D feature channels to zero according to a preset probability value, severing the fixed connections between specific feature nodes and reducing the network's overfitting to local sample features.

[0047] The fully connected classification layer receives a multi-scale 3D feature tensor processed by four volumetric convolutional downsampling layers. This fully connected classification layer maps the extracted multi-scale 3D feature tensor to scalar values ​​and outputs the probability of determining the authenticity of the current input 3D entity structure.

[0048] See attached document Figure 1 The generative network training module trains the 3D generative adversarial network using a 3D node voxelized training dataset. During training iterations, the module performs constraint update operations on the network parameters. The module calculates a weighted sum of the adversarial loss, topology regularization loss, and diversity constraint loss to construct a composite loss function for evaluating the network output error. The computational model of this composite loss function satisfies the following relationship: ; In the formula, Represents the composite loss function. Indicating resistance to loss, Represents the topological regularization loss. Represents diversity weight, Indicating a loss of diversity, Indicates the search weight of the pattern. This represents the loss from pattern search.

[0049] The generator network training module calculates the adversarial loss described above. It extracts the discriminator's discrimination result against the generator's output feature matrix and calculates the log-expected value of this result using binary cross-entropy. This calculation process establishes a minimax game mechanism to constrain the generator's network weight parameters, resulting in a three-dimensional feature matrix that approximates the true distribution of the training dataset. The specific formula for calculating the adversarial loss is as follows: ; In the formula, This represents the expected value operation. Represents a random noise vector. Describe the prior distribution, This represents the three-dimensional feature matrix output by the generator. This represents the true or false probability of the discriminator's output.

[0050] The network training module calculates the topology regularization loss mentioned above, which specifically includes connectivity loss, continuity loss, clustering loss, and smoothness loss.

[0051] The generative network training module first calculates the connectivity loss. To ensure the continuity of the load transfer path, the module defines connectivity by maximizing the consistency of adjacent voxels. The module calculates the first-order differences in the three principal directions and takes the negative correlation of the direction with the greatest connectivity as the loss. This operation encourages the generated structure to maintain connectivity in at least one principal force direction, and the mathematical expression for its connectivity loss satisfies the following relationship: ; In the formula, Indicates connectivity loss. Indicates the direction of the coordinate axes. Indicates the total number of voxels. An indicator function representing voxel values ​​greater than a preset threshold. This represents a first-order difference operator along a specific coordinate axis.

[0052] The generative network training module calculates the continuity loss. It introduces a mean convolution kernel to calculate the average density field of the local neighborhood. The continuity loss is configured with two penalty mechanisms: the first uses an exponential function to calculate the penalty value for activated voxels in low-density neighborhoods; the second uses the squared difference to calculate the penalty value for local average density deviations from the preset optimal distribution. The continuity loss constrains activated voxels to cluster towards high-density neighborhoods, eliminating isolated, suspended structures in the generated voxel model. The calculation process for the above continuity loss satisfies the following relationship: ; In the formula, Indicates continuous loss. Indicates the total number of voxels. This represents the generated voxel model matrix. Represents the characteristic function, This represents the local average density field matrix.

[0053] The generative network training module calculates the clustering loss. It extracts the set of active voxels from the generated voxel model and calculates the normalized Euclidean distance from the coordinates of each active voxel to the geometric centroid of the set. The clustering loss is calculated using the second moment of the material distribution, and a minimization process is performed to force the discretely distributed voxels to cluster towards the geometric center region, reducing the envelope volume of the overall structure. The specific calculation process for the above clustering loss is as follows: ; In the formula, Represents the clustering loss. Indicates batch size, Indicates the sample number. Indicates the set of activated voxels. Indicates the number of activated voxels. Represents the normalized radius. Represents voxel coordinates, Represents the geometric centroid coordinates. This represents the L2 norm.

[0054] The generative network training module calculates the smoothness loss. It uses the second-order discrete Laplacian operator to calculate the second-order difference values ​​of the density field. The smoothness loss calculates the degree of abrupt change in the spatial distribution of the density field and applies a penalty to eliminate the stepped shape of entity boundaries, reducing the geometric roughness of the generated voxel model surface. The numerical calculation of the above smoothness loss satisfies the following relationship: ; In the formula, Indicates smoothness loss. This represents the second-order discrete Laplace operator.

[0055] When configuring the composite loss function parameters, the network training module sets the weight coefficient of the clustering loss to be greater than the weight coefficients of the connectivity loss, continuity loss, and smoothness loss.

[0056] The generative network training module calculates the diversity loss in the diversity constraint loss. It extracts feature vectors from different generated samples and calculates the cosine similarity between these feature vectors. When the calculated cosine similarity exceeds a preset similarity threshold, a numerical penalty operation is applied to the diversity loss, reducing the probability of the generator outputting a homogeneous structural model. The expression for calculating the diversity loss is as follows: ; In the formula, and Indicates the sample index. Represents the numerical values ​​of the elements in the cosine similarity matrix. This represents the similarity threshold.

[0057] The generative network training module calculates the pattern search loss in the diversity constraint loss. It calculates the spatial distance between generated voxel models and the latent spatial distance between the random noise vectors corresponding to these models. The pattern search loss is calculated through a combination of exclusion and proportional terms, forcing a proportional relationship between the change in distance in the feature output space and the change in distance in the latent noise space. The calculation process of this pattern search loss satisfies the following relationship: ; In the formula, Indicates spatial distance. Indicates potential spatial distance.

[0058] See attached document Figure 5 The post-processing optimization module obtains the generated voxel model output by the generator. It then converts the data format of the generated voxel model into a source point cloud set. Finally, it obtains a finite element model containing a finite element mesh and configures this mesh-containing finite element model as the target geometry.

[0059] The post-processing optimization module constructs a rigid body transformation model for the aforementioned source point cloud set. This rigid body transformation model includes rotation, translation, and fine-tuning scaling operations. The coordinate update calculation process for any point in the source point cloud set after processing by the rigid body transformation model satisfies the following relationship: ; In the formula, Represents the transformed coordinates. This indicates the scaling factor for fine-tuning. Represents the rotation matrix. Indicates rotation Euler angles, Represents any point in the source point cloud set. This represents the translation vector.

[0060] The post-processing optimization module constructs a distance-field-based objective function. This distance-field-based objective function is used to quantify the spatial error after rigid body transformation. The objective function consists of the sum of the average Euclidean distance from the transformed source point cloud to the target geometric surface and a scaling regularization term. The numerical calculation process of the distance-field-based objective function satisfies the following relationship: ; In the formula, This represents the objective function based on the range field. Indicates the number of source point cloud sets. Represents the source point cloud set. The Euclidean distance transformation function represents the geometric field of the target. This indicates the scaling penalty weight.

[0061] The post-processing optimization module employs a multi-starting-point differential evolution strategy to solve the non-convex optimization problem involving the aforementioned distance-field-based objective function. The module generates multiple initial populations in the parameter space and iterates to obtain the optimal transformation parameters that minimize the numerical value of the distance-field-based objective function. These optimal transformation parameters correspond to specific rotation Euler angles, translation vectors, and fine-tuning scaling factors.

[0062] The post-processing optimization module updates the spatial coordinates of the source point cloud set using the above-mentioned optimal transformation parameters, thereby completing the spatial alignment of the generated voxel model with the above-mentioned finite element mesh.

[0063] After spatial alignment, the post-processing optimization module uses a nearest neighbor search algorithm to process the aligned model data. The post-processing optimization module calculates the spatial distance between the aligned source point cloud set and the target geometric field mesh nodes.

[0064] Based on the optimal transformation parameters and nearest neighbor search results, the post-processing optimization module extracts a set of solid element indices from the target geometry. Using this extracted set of solid element indices, the module generates a density mask array for global localization. This density mask array is used in subsequent steps to distinguish between solid and non-solid regions in the aligned finite element model.

[0065] See attached document Figure 6 The post-processing optimization module obtains the density mask array generated in the spatial alignment step. Using this density mask array, the post-processing optimization module performs spatial attribute classification operations on all finite element elements in the finite element model.

[0066] Based on the results of the spatial attribute classification operation described above, the post-processing optimization module identifies the solid and non-solid regions in the finite element model. The post-processing optimization module then performs a reward coefficient allocation operation for each finite element.

[0067] For the aligned finite element model, if any finite element element is contained within the solid region identified by the density mask array, the post-processing optimization module assigns a solid reward coefficient to that finite element element. The value of this solid reward coefficient is set to be greater than one.

[0068] If a finite element is not contained within the aforementioned solid region, the post-processing optimization module assigns a default reward coefficient to that finite element. This default reward coefficient is set to one.

[0069] The post-processing optimization module constructs a variable-density objective function for this node model. This variable-density objective function calculates the sum of parameters for each finite element. The model based on the variable-density objective function, combined with the aforementioned entity reward coefficients and default reward coefficients, establishes a quadratic topology optimization constraint mechanism with spatial location bias.

[0070] The calculation process of the objective function of the above variable density method satisfies the following relationship: ; In the formula, This represents the objective function of the variable density method. This represents the total number of finite element elements. Indicates the number of the finite element. Indicates the reward coefficient. Represents relative density. Indicates the penalty factor. This represents the transpose of the element displacement vector. Represents the element stiffness matrix. This represents the element displacement vector.

[0071] The post-processing optimization module calculates the sensitivity values ​​of the objective function of the variable density method with respect to the relative density of each element. For finite element elements configured with a solid reward coefficient, their element stiffness is subject to a weighted scaling factor greater than one during the calculation process. This weighted scaling operation increases the probability of material retention in the target region during the sensitivity analysis stage.

[0072] The post-processing optimization module performs a minimization operation on the objective function of the variable density method described above. Through this minimization operation, the post-processing optimization module completes the quadratic topology optimization.

[0073] The aforementioned secondary topology optimization operation reconstrains the material's density distribution boundary using a continuous finite element mesh, eliminating boundary discretization defects introduced by the preceding voxelization transformation and spatial alignment. The post-processing optimization module outputs the final complex node model.

[0074] See attached document Figure 7 A typical converging node in a K6-type single-layer spherical reticulated shell structure was selected as the initial verification object. The geometric model of this node includes a central hub and six radially distributed converging members. A three-dimensional design space was established, and predetermined axial tensile, compressive, and bending moment loads were applied to the ends of the six converging members. The central hub region and the ends of the members were designated as fixed non-design regions, while the connection region between the six converging members was designated as the optimization design region for material iteration.

[0075] See attached document Figure 8The generative network training module inputs the design domain parameters and random noise vectors of the K6-type single-layer spherical shell nodes into the generator of the trained 3D generative adversarial network. The generator performs forward computation and outputs a generated voxel model corresponding to the current input conditions. This generated voxel model exhibits a topological feature where the material is radially distributed from the central hub to the six converging members, forming continuous voxel connectivity regions along the load transmission path, and outputting the overall load-bearing backbone configuration.

[0076] See attached document Figure 9 The post-processing optimization module acquires the generated voxel model, discretizes its surface, and converts it into source 3D point cloud data. The module then acquires the original K6-node model containing a continuous finite element mesh and configures it as the target geometry. Finally, the module executes the multi-starting-point differential evolution strategy described above to solve the distance-field-based objective function in the parameter space.

[0077] The post-processing optimization module calculates and obtains the optimal Euler angles for rotation, translation vector, and fine-tuning scaling factor for the model. Using these optimal parameters, the module updates the spatial coordinates of the source 3D point cloud data, completing the pose alignment operation between the generated voxel model and the target geometry.

[0078] See attached document Figure 10 After spatial alignment, the post-processing optimization module uses a nearest neighbor search algorithm to extract the set of entity element indices in the target geometry, generating a density mask array for the K6-type node. The post-processing optimization module then performs spatial attribute classification. For finite element elements contained within the entity regions identified by the density mask array, the post-processing optimization module configures their reward coefficient to 3.0. For finite element elements not contained within these entity regions, the post-processing optimization module configures their reward coefficient to 1.0.

[0079] The post-processing optimization module constructs a variable-density objective function that includes the aforementioned entity reward coefficients and default reward coefficients, and performs an iterative solution operation for quadratic topology optimization. During the iterative solution process, regions configured with high reward coefficients receive higher material retention weights during sensitivity updates, ensuring that the quadratic topology optimization strictly follows the main force transmission configuration of the generated voxel model.

[0080] The post-processing optimization module recalculates the material continuity distribution in the model boundary region by minimizing the objective function of the variable density method. This iterative solution process eliminates the stepped, jagged morphology on the surface of the generated voxel model, outputting a final K6-type single-layer spherical reticulated shell complex node model with a continuous, smooth solid surface. This processing transforms discrete three-dimensional matrix data into a continuous geometric solid that meets the requirements of finite element mechanical analysis.

[0081] See attached document Figure 11The generative network training module establishes multiple independent control training groups. Each control training group adopts the same network hierarchy architecture and initial hyperparameter configuration as the aforementioned 3D generative adversarial network. The generative network training module removes specific constraint terms from the aforementioned composite loss function and performs independent iterative update operations on the network parameters of each control training group using the aforementioned 3D node voxelized training dataset.

[0082] The first control group removes the aforementioned connectivity loss from the composite loss function. The generator network training module is input with a random noise vector and extracts the generated voxel model output from the first control group. This generated voxel model exhibits a geometric feature of voxel distribution fracture along the defined tensile and compressive load transmission path. The absence of the aforementioned connectivity loss prevents the internal material of the model from forming a continuous principal force-bearing topology.

[0083] The second control group removes the aforementioned continuity loss and smoothness loss from the composite loss function. The generative network training module extracts the generated voxel model output by the second control group. This generated voxel model presents as discrete, suspended voxel blocks within local regions of the 3D design space. In the entity boundary regions of the generated voxel model, due to the lack of second-order difference penalty constraints, the density gradient changes drastically, and the entity surface exhibits a dense, stepped, serrated morphology, failing to meet the physical property requirements of material geometric continuity in finite element analysis.

[0084] The third control group removes the clustering loss from the composite loss function. The generator network training module extracts the generated voxel model output by the third control group. The activated voxels in the generated voxel model are distributed divergently in the three-dimensional design space. The calculated overall structural envelope volume exceeds the preset topological boundary constraint limit. The above results indicate that the lack of clustering loss constraint causes the structural material to fail to converge towards the central stress region, increasing redundant non-load-bearing material.

[0085] See attached document Figure 12 The fourth control group removed the aforementioned diversity loss and pattern search loss from the composite loss function. The generative network training module input multiple sets of random noise vectors with distinct means and variances to the network parameters of the fourth control group. Calculation results show that the cosine similarity values ​​among the multiple generated voxel models output by the fourth control group are all greater than 0.95, exceeding the preset homogenization threshold.

[0086] According to the above Figure 12 The scatter plot of the feature distribution shown indicates that the geometric features output by the fourth control group exhibit an extremely concentrated state with a single center in the high-dimensional reduced space. These data results demonstrate that, in the absence of diversity and pattern search constraints, the parameter distribution of the 3D generative adversarial network (GAN) suffers from pattern collapse, and the generator loses its ability to traverse and search the feature space, only able to output unidirectional topological configurations with convergent structures.

[0087] The generative network training module extracts a generative voxel model from the output of a 3D generative adversarial network based on a complete composite loss function as an experimental control group. This experimental control group, under the premise of satisfying the connectivity requirements of the tensile-compressive-bending composite load transfer path, outputs a complex node model with smooth entity boundaries and geometric features converging towards the centroid.

[0088] In the experimental control group, the cosine similarity values ​​of the generated voxel models for different random noise inputs all exhibited a dispersed distribution characteristic of less than 0.6. The above ablation experiments verify that the various constraint mechanisms in this composite loss function have irreplaceable physical and mathematical roles. The adversarial loss, topological regularization loss, and diversity constraint loss, through weighted coupling calculations, construct a multidimensional mathematical optimization boundary for three-dimensional spatial topological features, eliminating the generation probability of isolated materials, jagged boundaries, and homogeneous structures.

[0089] See attached document Figure 13 To verify the generalization ability of the aforementioned 3D generative adversarial network under different geometric boundary conditions, a three-story rigid frame node in a typical building structure was selected as the generalization verification object. The spatial topology of this rigid frame node includes a vertically continuous main load-bearing column and multiple orthogonal or oblique horizontal frame beams. The dataset construction module established the 3D initial design space of this rigid frame node and applied composite boundary conditions including axial compressive load, bidirectional shear force, and spatial bidirectional bending moment to the connection ends of the main load-bearing column and the horizontal frame beams. The cross-sectional extension region of the frame beam and column was set as the fixed non-design region, and the central core area where the column and beam intersect was set as the optimization design region for material iteration.

[0090] See attached document Figure 14 The network training module extracts the feature parameters of the aforementioned composite boundary conditions and combines them with a random noise vector, then inputs them into the 3D generative adversarial network trained using the aforementioned single-layer spherical shell node dataset. Without fine-tuning or retraining the network parameters, the generator's volume transposed convolution module performs cross-domain feature mapping. The generator directly outputs the generated voxel model corresponding to the current rigid frame node.

[0091] In the intersection region of the vertical main load-bearing column and the horizontal frame beam, the aforementioned generated voxel model adaptively generates haunch-shaped connectivity features to resist bidirectional spatial bending moments, and generates a cross-distributed voxel force skeleton in the core area of ​​shear force concentration. These geometric distribution features indicate that the 3D generative adversarial network, through the constraint of a composite loss function, successfully extracts the underlying physical force mechanism and topological mapping relationship, without falling into overfitting to a single structural form.

[0092] See attached document Figure 15The post-processing optimization module obtains the generated voxel model of the three rigidly connected frame nodes and extracts the original continuous finite element mesh of the frame nodes as the target geometry. The post-processing optimization module constructs an objective function based on the distance field and performs spatial alignment operations using a multi-starting-point differential evolution strategy. The post-processing optimization module calculates the optimal parameter set of the spatial Euler transform to eliminate the initial pose deviation between the generated voxel model and the target finite element mesh.

[0093] After completing the 3D spatial alignment, the post-processing optimization module generates a density mask array based on the nearest neighbor search results to distinguish between solid material regions and non-solid void regions within the core area of ​​the frame nodes. The post-processing optimization module assigns a solid reward coefficient greater than one to finite element elements belonging to solid material regions and a default reward coefficient equal to one to finite element elements belonging to non-solid void regions.

[0094] The post-processing optimization module performs a quadratic variable density topology optimization operation, including the aforementioned reward coefficient bias. This quadratic topology optimization operation uses the armholes and cross skeletons of the generated voxel model as the highly sensitive force transmission backbone, and performs finite element iterative calculations under boundary continuity physical constraints. These iterative calculations absolve the surface step effect introduced by the three-dimensional matrix discretization. The post-processing optimization module ultimately outputs a complex solid model of a three-layer rigidly connected frame node that meets the requirements for smooth mechanical transitions.

[0095] The execution results of Example 2 above demonstrate that the node-intelligent generative method based on the aforementioned fusion of deep learning and topology optimization techniques can efficiently predict and reconstruct topological features for novel geometric boundary conditions not included in the training dataset distribution, utilizing a unified generative adversarial network framework and post-processing optimization mechanism. This system possesses zero-shot generalization generation capabilities across configurations and load conditions, and can directly output continuous geometric entity models with engineering manufacturing feasibility.

Claims

1. A node intelligent generative method integrating deep learning and topology optimization techniques, characterized in that, Includes the following steps: An initial node geometric model is obtained, and topology optimization is performed based on the variable density method. The optimized initial node geometric model is then subjected to data augmentation and voxelization to construct a three-dimensional node voxelization training dataset. A three-dimensional generative adversarial network (GAN) containing a generator and a discriminator is constructed. The GAN is trained using the three-dimensional node voxelized training dataset. During the training process, a composite loss function is used to constrain the GAN, which includes adversarial loss, topology regularization loss, and diversity constraint loss. Obtain the generated voxel model output by the generator after training is completed, spatially align the generated voxel model with the finite element mesh, assign a preset reward coefficient to the element corresponding to the solid region in the generated voxel model in the aligned finite element model, and perform secondary topology optimization with an objective function containing the reward coefficient to obtain the final complex node model.

2. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 1, characterized in that, When performing topology optimization based on the variable density method, a three-field floating projection method is introduced to decouple the density field into a design field that controls the global material distribution, a filter field that suppresses the checkerboard effect, and a projection field that maps the continuous density to a discrete distribution of approximately zero and one.

3. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 2, characterized in that, The steps for constructing the 3D node voxelized training dataset specifically include: During the iterative process of topology optimization based on the variable density method, random perturbations are applied to the unit sensitivity to escape local extrema. The initial node geometric model after topology optimization is symmetrically processed, and the symmetrically processed initial node geometric model is rotated around a fixed axis at preset angle intervals to expand the sample size. The initial node geometric model, after expanding the sample size, is voxelized and converted into a three-dimensional matrix format suitable for network training, resulting in the three-dimensional node voxelized training dataset.

4. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 1, characterized in that, The generator includes a cascaded volume transpose convolution module, a residual block, and a self-attention mechanism module, used to upsample the input random noise vector layer by layer and map it into a three-dimensional solid structure. The discriminator includes a volumetric convolutional downsampling layer and a fully connected classification layer, which are used to extract multi-scale features and output the true / false discrimination probability. The first network layer of the discriminator uses instance normalization, and subsequent network layers use batch normalization.

5. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 1, characterized in that, The topology regularization loss includes at least connectivity loss and continuity loss; The connectivity loss is calculated by taking the first difference of the voxel density field in the three principal directions and extracting the negative correlation of the maximum connectivity direction as the loss, in order to maximize the consistency of adjacent voxels. The continuity loss is calculated by introducing a mean convolution kernel to calculate the local average density field. The continuity loss includes a first term that uses an exponential function to penalize activated voxels in low-density neighborhoods, and a second term that constrains the local density to tend towards a preset optimal value by a squared difference penalty term.

6. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 5, characterized in that, The topology regularization loss also includes clustering loss and smoothness loss; The clustering loss is achieved by extracting the set of active voxels from the generated voxels and calculating the normalized average distance from each active voxel to the geometric centroid of the set of active voxels, thereby minimizing the second moment of the material distribution to force the generated voxels to cluster toward the center. The smoothness loss is achieved by using the second-order discrete Laplace operator to calculate the second-order difference of the density field, penalizing abrupt changes in the density field to eliminate the boundary staircase effect. When configuring the composite loss function, the weight value of the clustering loss is configured to be greater than the weight values ​​of the connectivity loss, the continuity loss, and the smoothness loss.

7. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 1, characterized in that, The diversity constraint loss includes diversity loss and pattern search loss; The diversity loss is achieved by calculating the cosine similarity between the feature vectors of the generated samples and imposing a penalty when the cosine similarity exceeds a preset similarity threshold. The pattern search loss calculates the spatial distance between generated samples and the potential spatial distance between corresponding random noise vectors, and uses exclusion and proportional terms to force the spatial distance to maintain a proportional relationship with the potential spatial distance.

8. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 1, characterized in that, The specific steps for spatially aligning the generated voxel model with the finite element mesh include: The generated voxel model is used as the source point cloud set, and the finite element model containing the finite element mesh is used as the target geometric field. Construct a rigid body transformation model that includes rotation, translation, and fine-tuning scaling operations; An objective function based on the distance field is constructed, with the goal of minimizing the sum of the average Euclidean distance from the transformed source point cloud set to the target geometric field surface and the scaling regularization term. The optimal transformation parameters are obtained to complete the spatial alignment.

9. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 8, characterized in that, The step of optimizing the solution to obtain the optimal transformation parameters to complete the spatial alignment specifically includes: A multi-starting-point differential evolution strategy is used to solve the non-convex optimization problem containing the objective function based on the distance field, and to obtain the optimal transformation parameters. Using the nearest neighbor search algorithm, the set of entity unit indices in the target geometric field is extracted based on the optimal transformation parameters, and a density mask array is generated to identify the entity region.

10. The node intelligent generative method integrating deep learning and topology optimization techniques according to claim 9, characterized in that, The step of assigning a preset reward coefficient to the elements corresponding to the solid regions in the generated voxel model in the aligned finite element model, and performing secondary topology optimization using an objective function containing the reward coefficient, specifically includes: The density mask array is used to identify the solid regions in the finite element model; For the aligned finite element model, if any finite element element belongs to the entity region, then an entity reward coefficient with a value greater than one is assigned. If the finite element element does not belong to the entity region, a default reward coefficient of one is assigned. Construct a variable density method objective function that includes the entity reward coefficient and the default reward coefficient. The variable density method objective function is configured to calculate the reward coefficient of each finite element, the penalty power of the element relative density, the transpose of the element displacement vector, and the sum of the products of the element stiffness matrix and the element displacement vector. The quadratic topology optimization is completed by minimizing the objective function of the variable density method, eliminating boundary discrepancies and obtaining the final complex node model.

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