Mechanical structure lightweight topology optimization method based on generative adversarial network

Abstract

The present application relates to the technical field of topology optimization, in particular to a mechanical structure lightweight topology optimization method based on a generative adversarial network.The present application constructs a generative adversarial network by acquiring source domain mechanical data and target domain agricultural machinery data, introduces a physical mechanism loss and aligns feature distribution to obtain shared features; the features are input into a heterogeneous double-flow branch: a skeleton branch generates a skeleton voxel field through a geometric graph neural network and a differentiable materialization layer, a shell branch generates a shell voxel field through three-dimensional convolution, and the two are output as an overall structure after weighted superposition. In the time domain, the Fourier neural operator is used to predict the impact response, and in the frequency domain, the frequency bandgap loss is calculated, and the cooperative dynamic loss is generated by the Pareto dynamic weighting. Finally, the process constraint is introduced by using the global casting draw projection layer and the welding gun envelope convolution kernel, and the network parameters are updated to convergence. The present application does not depend on massive data, and improves the dynamic performance and manufacturing feasibility of the structure in harsh environments.

Description

Technical Field

[0001] This invention relates to the field of topology optimization technology, specifically to a method for lightweight topology optimization of mechanical structures based on generative adversarial networks. Background Technology

[0002] With the development of modern agricultural machinery towards larger scale, intelligence, and higher efficiency, lightweight design of agricultural machinery equipment has become a key technical approach to improve fuel economy, reduce soil compaction, and lower manufacturing costs. Topology optimization, as a structural design method that finds the optimal material distribution under given design space, load, and boundary conditions, is widely used in the lightweight design of mechanical structures. Although traditional topology optimization methods are theoretically mature, they typically rely on high-density finite element mesh generation and iterative sensitivity analysis, resulting in low computational efficiency, long design cycles, and difficulty in responding to changes in design parameters in real time.

[0003] To address the low computational efficiency of traditional methods, topology optimization using generative adversarial networks (GANs) has become a research hotspot in recent years. By learning the mapping relationship between design variables and the optimal structure, it achieves rapid end-to-end structure prediction. However, despite progress in general machinery and passenger vehicles, applying these technologies to lightweight design of agricultural machinery structures still faces significant technical bottlenecks, primarily in three aspects: First, existing GAN-based topology optimization heavily relies on massive amounts of high-quality training data. However, agricultural machinery products are diverse, with small batch sizes and a lack of standardized historical design databases, representing a typical "small sample" scenario. Without large-scale, high-fidelity data, existing GAN models are prone to overfitting or pattern collapse, making it difficult to generate topologies with practical engineering value. Second, agricultural machinery operates in extremely harsh environments, often accompanied by strong dynamic impacts and high-frequency vibrations. Existing technologies often focus on maximizing stiffness under static or quasi-static conditions, such as introducing static stress and deformation as physical constraints into the loss function. Third, when considering manufacturing constraints, existing technologies often emphasize optimization geared towards additive manufacturing. However, due to cost control constraints, large structural components of agricultural machinery mainly rely on traditional processes such as casting and welding. The structures generated by existing GAN models often contain a large number of irregular cavities, undercuts, or complex curved surfaces, which not only fail to meet the draft angle and minimum wall thickness requirements in the casting process, but also make it impossible for the welding torch to reach them.

[0004] In summary, how to construct a topology optimization method that can meet the complex dynamic impact resistance requirements of agricultural machinery by using traditional casting or welding processes under the condition of lacking large-scale training data is a core technical problem that urgently needs to be solved in this field.

[0005] To address this, a lightweight topology optimization method for mechanical structures based on generative adversarial networks is proposed. Summary of the Invention

[0006] The purpose of this invention is to provide a lightweight topology optimization method for mechanical structures based on generative adversarial networks (GANs). This invention constructs a GAN by acquiring source domain mechanical data and target domain agricultural machinery data, introducing a physical mechanism loss and aligning feature distributions to obtain shared features. These features are then input into heterogeneous dual-stream branches: the skeleton branch generates a skeleton voxel field through a geometric graph neural network and a differentiable materialization layer, while the shell branch generates a shell voxel field through 3D convolution. The two are then weighted and superimposed to output the overall structure. In the time domain, Fourier neural operators are used to predict the impact response, and in the frequency domain, the frequency bandgap loss is calculated, generating a co-dynamic loss through Pareto dynamic weighting. Finally, a global casting draft projection layer and a welding torch envelope convolution kernel are used to introduce process constraints, updating the network parameters until convergence. This invention does not rely on massive amounts of data, improving the dynamic performance and manufacturing feasibility of the structure in harsh environments.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A lightweight topology optimization method for mechanical structures based on generative adversarial networks includes: We acquire source domain mechanical structure data and target domain agricultural machinery data to construct a generative adversarial network; during the pre-training stage, we introduce physical mechanism loss as a regularization term; and we align the feature distributions of the source and target domains to obtain a shared feature vector. The shared feature vectors are input into the skeleton branch and the shell branch respectively; the skeleton branch uses a geometric graph neural network to generate a topological skeleton graph and maps it to a skeleton voxel field through a differentiable skeleton materialization layer; the shell branch uses three-dimensional convolution to generate a shell voxel field; the skeleton voxel field and the shell voxel field are weighted and superimposed using a learnable weighted mask to output the overall structure voxel field. In the time domain, a transient impact surrogate model is constructed using Fourier neural operators to calculate impact energy loss; in the frequency domain, the frequency bandgap loss is calculated; and a co-dynamic loss is generated by combining impact energy loss and frequency bandgap loss through Pareto dynamic weighting. By forcing the overall structure's voxel field to exhibit a monotonically non-decreasing distribution along the demolding direction through a global casting draft projection layer, welding assembly penalties are generated using the welding torch envelope convolution kernel. The parameters of the generative adversarial network are then updated until convergence by combining the cooperative dynamics loss, the welding assembly penalty term, and the adversarial loss of the generative adversarial network.

[0008] Preferably, the generative adversarial network includes a shared feature extractor, a domain discriminator, and a physical residual module; the source domain data is selected from a three-dimensional voxel model of a general mechanical load-bearing structure and its corresponding stress field data, and the target domain data is selected from sparse simulation geometric samples of agricultural machinery structures. The physical mechanism loss is constructed using a meshless physical information neural network strategy. Specifically, the coordinates of configuration points are randomly sampled in the continuous design domain space. The partial derivatives of the density field output by the network with respect to the spatial coordinates are calculated using automatic differentiation technology. These derivatives are then substituted into the partial differential equations of equilibrium in continuous medium mechanics, and the L2 norm of the equation residuals is calculated as the physical mechanism loss. Align the feature distributions of the source and target domains and use the maximum mean difference algorithm; in the regenerating kernel Hilbert space, minimize the distance between the feature distributions of the source and target domains, and force the shared feature extractor to ignore the differences in geometric scale between agricultural machinery and automobiles, retaining only the topological features of force flow transmission.

[0009] Preferably, the skeleton branch employs a geometric graph neural network, with the input being an initial graph constructed from hard points within the design domain as nodes, and the output being updated node coordinates and edge connectivity attributes. The differentiable skeleton materialization layer adopts an implicit function mapping method based on a distance field: each edge output by the graph network is modeled as a cylindrical segment with a preset radius, and each node is modeled as a sphere; the minimum geometric distance from any voxel center point in space to the skeleton centerline is calculated, and a density decay distribution is constructed using a smooth sigmoid function to convert the geometric distance into a voxel density value between 0 and 1; when multiple skeleton segments overlap at a certain point in space, a soft maximization operator is used to aggregate the local voxel density, maintaining the continuity of gradient backpropagation.

[0010] Preferably, the shell branch uses a U-Net 3D convolutional network with skip connections to generate an initial shell field; after the initial shell field, a morphological convolutional layer is connected in series, and erosion and dilation operations are performed sequentially using spherical structural elements with a diameter equal to the minimum wall thickness of the casting to filter out geometric features smaller than the minimum wall thickness; The learnable weighted mask is generated by a convolutional attention module connected in parallel; the convolutional attention module simultaneously receives the skeleton voxel field and the shell voxel field as input channels and outputs a spatial weight matrix with the same size as the voxel field. The weighted superposition operation is as follows: at each voxel position in space, the values ​​of the weight matrix are used as coefficients to linearly interpolate the skeleton voxel density and the shell voxel density. The weight distribution is automatically adjusted through training to preserve skeleton features in stress concentration areas and shell features in boundary areas.

[0011] Preferably, the specific steps for constructing a transient impact proxy model in the time domain include: processing the time-varying resistance data during agricultural machinery operation into a continuous time function input; constructing a Fourier neural operator as an impact response predictor: the Fourier neural operator performs a convolution operation on the input geometric field and load function in the frequency domain space, learning the nonlinear operator mapping from structural geometric parameters to the transient stress distribution across the entire field, avoiding the numerical integration solution process; using historical experimental data to supervise the training of the Fourier neural operator, learning real-time inference capabilities; the calculated impact energy loss is defined as the ratio of the integral of the predicted transient stress field modulus within the impact time window to the total mass of the structure, serving as a meshless index for evaluating the structure's impact resistance efficiency.

[0012] Preferably, the calculation of the frequency bandgap loss specifically involves constructing a frequency domain feature prediction neural operator using a three-dimensional encoder-decoder architecture. The input is the overall structure voxel field, and the output is a tensor with six channels, each channel representing the displacement field of the first six modal modes of the structure. The operator is trained under supervision using historical modal analysis data to learn the nonlinear mapping relationship from geometric topology to modal modes. For each predicted modal displacement field, the corresponding global modal kinetic energy and modal potential energy are calculated using the voxel integration method, and the natural frequency value of the corresponding order is approximately solved by substituting it into the Rayleigh quotient formula. The frequency bandgap range is set to the idling excitation frequency range of the agricultural machinery diesel engine. A potential energy penalty function is constructed, which generates an exponentially increasing loss value when the estimated frequency falls within the frequency bandgap range, and zero otherwise. The Pareto dynamic weighting employs a multi-objective gradient descent algorithm: during backpropagation, the angle between the impact energy loss gradient and the frequency bandgap loss gradient is monitored in real time. When a gradient conflict is detected, a common descent direction is found by solving a quadratic programming problem, and the weights of the two are dynamically adjusted to achieve collaborative optimization of multi-physics objectives.

[0013] Preferably, the specific working principle of the global casting draft projection layer is as follows: the demolding direction of the casting process is defined as the positive Z-axis direction; the global casting draft projection layer is constructed as a differentiable geometric morphology operator: performing a cumulative max pooling operation along the Z-axis direction on the overall structure voxel field, forcing the generation network to actively generate a structural shape that is easy to demold; The specific steps for generating the welding assembly penalty include: defining the rigid space occupancy of the welding torch and its connecting rod as a three-dimensional geometric convolution kernel; identifying the set of voxels at the interface between the skeleton field and the shell field as the area to be welded; performing a binary cross-correlation operation on the overall structural voxel field using the three-dimensional geometric convolution kernel: traversing each voxel position in space, calculating the cumulative sum of the product of the welding torch envelope voxel value and the structural density voxel value within the coverage area of ​​the convolution kernel; when the cumulative sum is non-zero, determining that geometric interference has occurred; calculating the total cumulative sum at all areas to be welded as the welding assembly penalty term, characterizing the geometric interference volume when the welding torch touches the welding point; and by minimizing the welding assembly penalty term, forcing the generation network to automatically reserve free space around the welding point that conforms to the welding torch's movement trajectory by adjusting its geometric shape.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: 1. This invention significantly overcomes the bottleneck of existing deep learning topology optimization methods' reliance on massive amounts of high-fidelity training data by introducing physical mechanism loss and cross-domain feature transfer mechanisms. In specific industrial scenarios lacking standardized historical data, this invention utilizes the force flow transmission laws of general mechanical structures for pre-training and combines physical equation constraints for small-sample fine-tuning. This enables the generator network to converge and generate high-quality structures that conform to physical logic even with limited samples, reducing data acquisition costs and improving the model's generalization ability and design reliability under unknown operating conditions.

[0015] 2. This invention effectively solves the technical challenge of traditional static topology optimization in simultaneously considering transient shock resistance and steady-state vibration damping performance by constructing a time-frequency coordinated dynamic evaluation system. By combining a transient surrogate model constructed using Fourier neural operators with frequency domain analysis based on a meshless method, millisecond-level response prediction of structures under complex dynamic loads is achieved. Furthermore, the optimal balance between shock absorption and vibration damping frequency design is found through a Pareto dynamic weighting mechanism, significantly improving the dynamic robustness and fatigue life of mechanical structures in harsh operating environments.

[0016] 3. This invention achieves integrated collaborative design of structural performance and manufacturing process through the deep integration of heterogeneous dual-flow generation architecture and global multi-process projection technology. Unlike existing technologies that often focus only on single manufacturing constraints or require cumbersome post-processing, this invention utilizes a differentiable skeleton materialization technology to organically integrate the topological skeleton with the envelope shell. Furthermore, through global casting draft projection and welding torch envelope convolution, geometric undercuts are eliminated in real-time during the generation process, and welding space is reserved. This ensures that the generated complex topological structure can directly meet the stringent process requirements of casting demolding and welding assembly without manual repair, significantly shortening the development cycle from design to manufacturing. Attached Figure Description

[0017] Figure 1A flowchart of a lightweight topology optimization method for mechanical structures based on generative adversarial networks provided in an embodiment of the present invention; Figure 2 This is a diagram of a heterogeneous dual-stream generation network architecture provided in an embodiment of the present invention; Figure 3 A flowchart for time-frequency coordination and process constraint evaluation provided in an embodiment of the present invention. Detailed Implementation

[0018] 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.

[0019] Please see Figures 1 to 3 This invention provides a lightweight topology optimization method for mechanical structures based on generative adversarial networks, the technical solution of which is as follows: A lightweight topology optimization method for mechanical structures based on generative adversarial networks includes: We acquire source domain mechanical structure data and target domain agricultural machinery data to construct a generative adversarial network; during the pre-training stage, we introduce physical mechanism loss as a regularization term; and we align the feature distributions of the source and target domains to obtain a shared feature vector. The shared feature vectors are input into the skeleton branch and the shell branch respectively; the skeleton branch uses a geometric graph neural network to generate a topological skeleton graph and maps it to a skeleton voxel field through a differentiable skeleton materialization layer; the shell branch uses three-dimensional convolution to generate a shell voxel field; the skeleton voxel field and the shell voxel field are weighted and superimposed using a learnable weighted mask to output the overall structure voxel field. In the time domain, a transient impact surrogate model is constructed using Fourier neural operators to calculate impact energy loss; in the frequency domain, the frequency bandgap loss is calculated; and a co-dynamic loss is generated by combining impact energy loss and frequency bandgap loss through Pareto dynamic weighting. By forcing the overall structure's voxel field to exhibit a monotonically non-decreasing distribution along the demolding direction through a global casting draft projection layer, welding assembly penalties are generated using the welding torch envelope convolution kernel. The parameters of the generative adversarial network are then updated until convergence by combining the cooperative dynamics loss, the welding assembly penalty term, and the adversarial loss of the generative adversarial network.

[0020] Example 1: This embodiment addresses the lightweight design of tractor drawbars in the agricultural machinery field. As a key component connecting the tractor and implements, the drawbar endures long-term abrupt resistance (impact load) during plowing and high-frequency engine vibration. Furthermore, its production volume is relatively small compared to passenger cars, and it is primarily manufactured using casting processes. This invention proposes a mechanical structure topology optimization method based on physical perception transfer and global collaboration of heterogeneous geometric fields. This method designs a lightweight structure that satisfies both impact resistance and vibration damping performance, and can be directly cast without extensive post-processing.

[0021] As one embodiment of the present invention, refer to Figure 1 Flowchart of a lightweight topology optimization method for mechanical structures based on generative adversarial networks, referencing Figure 2 Heterogeneous dual-stream generation network architecture diagram, refer to Figure 3 Flowchart for time-frequency coordination and process constraint evaluation.

[0022] Furthermore, the generative adversarial network includes a shared feature extractor, a domain discriminator, and a physical residual module; the source domain data is selected from a three-dimensional voxel model of a general mechanical load-bearing structure and its corresponding stress field data, and the target domain data is selected from sparse simulation geometric samples of agricultural machinery structures. The physical mechanism loss is constructed using a meshless physical information neural network strategy. Specifically, the coordinates of configuration points are randomly sampled in the continuous design domain space. The partial derivatives of the density field output by the network with respect to the spatial coordinates are calculated using automatic differentiation technology. These derivatives are then substituted into the partial differential equations of equilibrium in continuous medium mechanics, and the L2 norm of the equation residuals is calculated as the physical mechanism loss. Align the feature distributions of the source and target domains and use the maximum mean difference algorithm; in the regenerating kernel Hilbert space, minimize the distance between the feature distributions of the source and target domains, and force the shared feature extractor to ignore the differences in geometric scale between agricultural machinery and automobiles, retaining only the topological features of force flow transmission.

[0023] The shared feature extractor comprises a five-layer 3D convolutional network with kernel sizes of 7×7×7, 5×5×5, 3×3×3, 3×3×3, and 1×1×1, and the number of kernels in each layer being 32, 64, 128, 256, and 512, respectively. The activation function is a rectified linear unit. The shared feature vector dimension is set to 512, which is determined by the convergence speed and feature representation capability of balanced domain transfer learning.

[0024] The physical mechanism loss is calculated using a meshless physical information neural network strategy. The physical mechanism loss is equal to the product of the reciprocal of the total number of placement points and the sum of the absolute values ​​of the physical residuals at all placement points. Specifically, at each placement point... Above, calculate the density field prediction value. The Laplace operator and the equivalent stress value at that point The absolute value of the sum, finally... The absolute values ​​of these configuration points are averaged.

[0025] In the reproducing kernel Hilbert space, a Gaussian kernel function is chosen. This kernel function is expressed as a negative exponential function of the squared Euclidean distance between two sample points x and y, and is scaled by a bandwidth parameter. The bandwidth parameter is equal to 1 divided by two times... ; The weight is set to the average of the standard deviations of each feature dimension. During pre-training, the weights for physical mechanism loss, adversarial loss, and alignment loss are set to 0.7, 1.0, and 0.5 respectively. The Adam optimizer is used with an initial learning rate of 0.0001, which decays to 0.95 every 10 iterations. The loss function change is less than 0.5 for 100 consecutive iterations. Convergence is determined at that time.

[0026] Specifically, the source domain database contains 50,000 sets of topological morphologies of general mechanical structures such as I-beams and box girders, along with their displacement contour maps under varying loads from 10MPa to 100MPa. The target domain agricultural machinery data contains only 50 sets of preliminarily calibrated tractor drawbar simulation samples, with a geometric space dimension of 1200mm × 800mm × 600mm. During the pre-training phase, the physical mechanism loss is calculated by randomly scattering the coordinates of 10,000 placement points within the drawbar design space and using the Laplacian operator to automatically differentiate the density field gradient. The maximum mean difference algorithm maps the feature vectors of the source and target domains into a 512-dimensional regenerating kernel Hilbert space during the mapping process. Experimental data show that, with only 50 sets of target domain samples, after 200 iterations, the L2 norm of the physical mechanism residual of the model decreased from the initial 1.5 to 0.02, and the Pearson correlation coefficient between the generated topology and the high-fidelity finite element calculation results reached 0.94. Through transfer learning, the model has the ability to extract specific topological features of agricultural machinery from general mechanical laws, thus solving the model collapse problem under small sample training.

[0027] This invention significantly overcomes the bottleneck of deep learning topology optimization's reliance on massive amounts of high-quality data by introducing physical mechanism loss and cross-domain feature transfer mechanisms. In "small sample" scenarios such as agricultural machinery, which lack standardized historical designs, the force flow transmission laws of general mechanical structures are used as prior knowledge for pre-training, and the residuals of physical equations are combined as hard constraints for fine-tuning, enabling the generated network to converge even under limited sample conditions. This method ensures that the generated topology strictly follows the equilibrium equations of continuum mechanics, not only reducing the cost of expensive simulation data acquisition but also significantly improving the model's generalization ability and design reliability when facing new and complex working conditions, avoiding the overfitting phenomenon that traditional pure data-driven models are prone to in small sample scenarios.

[0028] Furthermore, the skeleton branch employs a geometric graph neural network, with the input being an initial graph constructed from hard points within the design domain as nodes, and the output being updated node coordinates and edge connectivity attributes. The differentiable skeleton materialization layer adopts an implicit function mapping method based on a distance field: each edge output by the graph network is modeled as a cylindrical segment with a preset radius, and each node is modeled as a sphere; the minimum geometric distance from any voxel center point in space to the skeleton centerline is calculated, and a density decay distribution is constructed using a smooth sigmoid function to convert the geometric distance into voxel density values ​​between 0 and 1; when multiple skeleton segments overlap at a certain point in space, a soft maximization operator is used to aggregate local voxel densities to maintain the continuity of gradient backpropagation.

[0029] The preset radius is set according to the overall size of the mechanical structure and the expected load. In this embodiment, its value range is preferably 15mm to 45mm to ensure that the frame can meet the structural stiffness requirements without causing material redundancy.

[0030] Specifically, there are 12 hard points connecting the traction frame (such as pin holes and support fixing points), which are used as the initial nodes of the geometric graph neural network. The network output contains the edge connection attributes of 24 key load-bearing paths, with the predicted radius of each edge ranging from 15mm to 45mm. The differentiable skeleton materialization layer discretizes the design space into a 128×128×128 voxel mesh, with each voxel having an edge length of 10mm. For any voxel point in the mesh, the Euclidean distance to the nearest skeleton centerline is calculated. When this distance is less than 30mm, the density value generated using the Sigmoid function approaches 1; when the distance is greater than 50mm, the density value rapidly decays to 0. Through the soft maximization operator, at the nodes of the traction frame subjected to multi-directional forces, the three intersecting cylindrical segments are automatically and smoothly merged. This distance field-based method ensures that the gradient of the voxel density field of the skeleton structure can be smoothly transmitted to the weight parameters of the graph neural network when the shape of the skeleton structure changes, thereby realizing end-to-end collaborative optimization from discrete graph topology to continuous voxel field, enabling the skeleton structure to automatically adjust its thickness according to the force distribution.

[0031] This invention organically unifies discrete topological skeleton optimization with continuous voxel space representation through differentiable skeleton materialization technology. Utilizing implicit function mapping, it can transform the skeleton parameters output by the graph network into a high-quality density distribution field in real time, maintaining differentiability throughout the process. It allows the system to dynamically adjust the connection relationships and cross-sectional dimensions of the structure during optimization, ensuring that the skeleton morphology can be refined according to complex force flow transmission requirements. Through the aggregation of soft maximization operators, it solves the geometric interference and gradient breakage problems at the convergence of multiple branches, providing a stable main load-bearing framework for the subsequently generated structure, significantly improving the flexibility and computational stability of structure generation.

[0032] When generating a topological skeleton graph using a geometric graph neural network, a stress guidance module is introduced: the initial stress tensor field is obtained; the principal stress vector direction at each spatial location is calculated, and a guidance vector field reflecting the force flow trend is constructed; the position of the skeleton nodes is iteratively updated using the guidance vector field, thereby inducing the alignment of the principal stress traces along the skeleton edges.

[0033] In the lightweight design of the bridge frame for large combine harvesters, the bridge frame needs to withstand alternating impact forces from the header (peak load reaching 80kN). The initial hard point is set at the header connecting pin position. In this embodiment, a physical guidance module automatically offsets 24 predicted key nodes in the skeleton branches by 15mm-30mm along the stress gradient direction based on the high-stress cloud map predicted by a physical information neural network. Experimental data shows that, compared with the structure generated by the initial geometry, the local stress concentration factor at key stress points of the optimized skeleton structure decreases from 2.8 to 1.45. Through this dynamic adjustment, the skeleton is not merely a line connecting hard points, but evolves into a physically aware "force-flow spine," improving the overall fatigue strength of the structure by 22% while reducing weight by 12%.

[0034] This invention addresses the technical challenges of rigid node positions and difficulty in accurately matching complex mechanical boundaries in traditional graph neural networks during topology optimization by introducing a physical stress guidance mechanism. When dealing with multi-condition impacts on agricultural machinery, this approach ensures that the main framework of the material always develops along the optimal force flow path, eliminating the problem of excessive stress caused by improper geometric node settings from a fundamental physical logic perspective. This not only improves the structure's load-bearing efficiency and dynamic reliability but also significantly enhances the generator network's physical generalization ability to unknown conditions, ensuring the safety of lightweight solutions under extreme operating conditions.

[0035] Furthermore, the shell branch uses a U-Net 3D convolutional network with skip connections to generate an initial shell field; after the initial shell field, a morphological convolutional layer is connected in series, and erosion and dilation operations are performed sequentially using spherical structural elements with a diameter equal to the minimum wall thickness of the casting to filter out geometric features smaller than the minimum wall thickness. The learnable weighted mask is generated by a convolutional attention module connected in parallel; the convolutional attention module simultaneously receives the skeleton voxel field and the shell voxel field as input channels and outputs a spatial weight matrix with the same size as the voxel field. The weighted superposition operation is as follows: at each voxel position in space, the values ​​of the weight matrix are used as coefficients to linearly interpolate the skeleton voxel density and the shell voxel density. The weight distribution is automatically adjusted through training to preserve skeleton features in stress concentration areas and shell features in boundary areas.

[0036] The shared feature vector is projected onto the skeleton branch and the shell branch through two parallel projection layers, respectively. The skeleton branch projection layer is a fully connected layer that compresses the 512-dimensional features to the node feature dimension of the graph neural network, which is 256 dimensions. The shell branch projection layer uses a three-dimensional deconvolution layer to expand the 512-dimensional features to the spatial dimension.

[0037] The geometric graph neural network adopts a graph isomorphic network architecture, containing three graph convolutional layers. Hard point locations within the design domain are represented by nodes in the initial graph. Node features include three-dimensional coordinate information (x, y, z) and the boundary condition type encoding for each hard point (fixed support, sliding support, free end, etc.). The topological connections of the initial graph are determined based on geometric proximity and engineering experience: the Euclidean distance between all pairs of hard points is calculated, and initial connections are established between hard point pairs whose distance is less than 40% of the diagonal length of the design domain.

[0038] In each graph convolution operation, node feature updates are achieved through a specific message passing and aggregation process. Specifically, the node updates at the 1st layer... The hidden layer characteristics of a layer are derived from its current layer (the first layer). The features of a node are determined by both its own characteristics and those of its neighborhood. First, the algorithm sums and aggregates the feature vectors of all its neighboring nodes; simultaneously, it uses a learnable weight parameter... Weighted scaling (i.e., multiplying by) the node's own characteristics. This is done by adjusting the ratio of self-information to neighborhood information in feature fusion. Then, the weighted self-features are added to the aggregated neighborhood features to obtain the fused composite vector. Finally, this vector is input into a multilayer perceptron for nonlinear transformation and feature extraction, thus completing the information transfer for that layer.

[0039] The initial density distribution of spatial voxel points p in the differentiable skeleton materialization layer. It is constructed using a logistic regression function based on distance decay. This function uses the minimum Euclidean distance from point p to the centerline of the skeleton as the independent variable, and defines the boundary of the entity through a preset radius R (between 15 and 45 mm). The temperature parameter is precisely set to 10, its physical meaning being to control the "hardness" of the boundary: this value ensures that the density value remains constant at a distance from the boundary. Within a very small space of mm, it can produce a significant decay from 0.73 to 0.27, thus forming a clear geometric profile while maintaining the continuous differentiability of the function.

[0040] When multiple skeleton segments overlap in space, a soft maximization operator with a temperature parameter is used for aggregation to fuse the density contributions of each part. The aggregated total density depends on the exponential sum of the independent density contributions of each skeleton segment. Here, the temperature parameter is set to a minimum value of 0.01. This configuration serves a dual purpose: firstly, it makes the aggregation result highly approximate to the maximum value among the individual density components (i.e., hard maximization), ensuring the accuracy of the solid volume; secondly, by preserving a small smoothing effect, it ensures that sufficient gradient signals can be transmitted during backpropagation, thereby supporting end-to-end parameter optimization.

[0041] The shell branch adopts a U-Net network with an encoder-decoder architecture. The encoder consists of four three-dimensional convolutional layers (with 32, 64, 128, and 256 convolutional kernels, a kernel size of 3×3×3, and a stride of 2), and the decoder consists of four corresponding three-dimensional transposed convolutional layers. Skip connections are established between the layers.

[0042] The learnable weighted mask is generated by a parallel convolutional attention module, which comprises two branches: a channel attention branch that learns the importance weights of each input channel through global average pooling and two fully connected layers; and a spatial attention branch that learns the weights of each spatial location through element-wise operations. The final weight matrix generation process employs a strategy of feature fusion and nonlinear mapping. Specifically, the system first uses a concatenation operation to merge the skeleton density field and the shell density field along the channel dimension, forming a multi-source feature representation. This feature is then input into the convolutional layer to capture spatial local correlations and extract fused features. Finally, the convolutional output is processed using a sigmoid activation function, strictly constraining the values ​​to the [0,1] interval, thereby determining the weight allocation for each location in space, allowing it to represent the contribution of different geometric components in the form of probability or proportion.

[0043] Specifically, the U-Net network comprises four layers of downsampling and upsampling processes, preserving the fine geometric features of the traction frame edges through skip connections. Morphological convolutional layers use spherical structural elements with a diameter of 20 mm (corresponding to two voxel diameters) to simulate the minimum wall thickness constraint in the casting process. The spatial weight matrix output by the convolutional attention module shows that in the pin-shaft connection area of ​​the traction frame, the weight coefficients are tilted towards the skeleton features (weight ratio 0.85:0.15), enhancing the core tensile stiffness; while in the outer protective area of ​​the traction frame, the weights are tilted towards the shell features (weight ratio 0.2:0.8), generating a closed shell with a constant wall thickness of 20 mm. Through this weighted superposition, the core load-bearing ribs and the outer thin-walled shell are seamlessly integrated in the final voxel model of the traction frame. Experimental comparisons show that the structure generated by this heterogeneous dual-flow architecture, compared to the structure generated by a single convolutional network, has an 18% higher torsional stiffness under the same weight, and the geometry completely eliminates weak points with a thickness less than 20 mm, ensuring smooth flow of molten metal in the casting mold.

[0044] This invention employs a heterogeneous dual-stream generation architecture and an attention-based collaborative mechanism to achieve the classification design and deep integration of "skeleton load-bearing" and "shell envelope" in mechanical structures. By combining the U-Net network with morphological convolutional layers, minimum wall thickness constraints in the manufacturing process are enforced from the initial generation stage, preventing the formation of sharp edges or slender forks that cannot be cast. The learnable weighted mask acts like an experienced engineer, intelligently identifying the stress distribution characteristics of the structure: strengthening skeleton features along the main load-bearing paths where stress concentration is required to ensure overall stiffness, and preserving shell features in areas where geometric topological integrity needs to be maintained to enhance torsional resistance. This integrated design method not only optimizes the mechanical efficiency of material distribution but also ensures that the generated complex topological model has extremely high process feasibility, eliminating the need for tedious manual post-processing.

[0045] Furthermore, the specific steps for constructing a transient impact proxy model in the time domain include: processing the time-varying resistance data during agricultural machinery operation into a continuous time function input; constructing a Fourier neural operator as an impact response predictor: the Fourier neural operator performs a convolution operation on the input geometric field and load function in the frequency domain space, learning the nonlinear operator mapping from structural geometric parameters to the transient stress distribution across the entire field, avoiding the numerical integration solution process; using historical experimental data to supervise the training of the Fourier neural operator, learning real-time inference capabilities; the calculated impact energy loss is defined as the ratio of the integral of the predicted transient stress field modulus within the impact time window to the total mass of the structure, serving as a meshless index for evaluating the structure's impact resistance efficiency.

[0046] The specific steps for constructing the Fourier neural operator as an impact response predictor include: sampling the continuous time-varying resistance signal during agricultural machinery operation at equal intervals with a frequency of 100Hz, converting it into a discrete time series. Subsequently, a one-dimensional fully connected layer is used to map this sequence to a high-dimensional space, increasing the feature dimension to provide richer semantic features for subsequent frequency domain deep learning.

[0047] In the core convolutional layer of the Fourier neural operator, the input geometric voxel density field and time-varying load are first mapped to the frequency domain through three-dimensional and one-dimensional Fast Fourier Transforms, respectively. Then, the convolution theorem is used to perform element-wise multiplication of their frequency domain representations, efficiently capturing the convolutional relationship between the geometric structure and the dynamic load. This product result is further transformed nonlinearly through two fully connected layers, aiming to learn and model the deep mapping logic from "structure-load coupling" to "complex stress response".

[0048] The processed frequency domain information is converted back to the original time-space domain using an inverse fast Fourier transform. The result is a transient stress tensor, which consists of six independent components that fully describe the mechanical state of the structure as it evolves over time in three-dimensional space, including three normal stress components (along the coordinate axes) and three shear stress components (transplane shear effects).

[0049] Impact energy loss is defined as the cumulative stress intensity per unit mass within the impact window. Specifically, the calculation first uses the von Mises criterion to synthesize a scalar equivalent stress from the six complex stress components: the sum of the squares of the differences in the three normal stresses and the sum of the squares of six times the shear stress, then taking the square root of half of this sum. Next, this equivalent stress is integrated over the entire impact cycle (typically 1.5 times the pulse width) and normalized by dividing by the total mass of the structure. This normalized value serves as the loss function for measuring the structure's impact resistance.

[0050] To eliminate dimensional differences and accelerate model convergence, both the experimentally acquired resistance data and the simulated stress field need to be Z-score standardized. Specifically, this involves subtracting the global mean of the data from the original observations and then dividing by its standard deviation, thereby transforming both load and stress characteristics into a standard distribution with a mean of zero and a variance of one.

[0051] The Fourier neural operator also includes a multi-scale time-domain feature compensation module: it performs wavelet decomposition on the time-varying drag function to extract high-frequency pulse features; in the frequency domain convolutional layer of the operator, weight compensation is performed on the spectral components corresponding to the high-frequency features through a self-attention mechanism to enhance the prediction accuracy of transient stress peaks; by introducing a multi-scale time-domain enhancement mechanism into the FNO, the key defect of deep learning operators easily "losing features" when dealing with nonlinear transient strong impact problems is solved. This technique ensures that the model can capture extremely high-frequency pulse signals in the dynamic response of the structure while maintaining millisecond-level prediction speed. This high-fidelity dynamic simulation provides accurate evaluation indicators for the structural optimization of agricultural machinery under strong impact scenarios, effectively avoiding design failures caused by model prediction bias, and laying a data foundation for the refined design of structural impact resistance and energy absorption performance.

[0052] Specifically, the input data is the transient resistance function of a tractor encountering a rock impact during plowing operations. This function's peak pulse surges from 5 kN to 45 kN within 0.2 seconds. The Fourier neural operator (FNO) is pre-trained using 1024 sets of historical impact condition data to learn the mapping from the traction frame's geometric tensor to the transient stress field. During optimization iterations, FNO can output the dynamic distribution of the full-field stress within a 0.2-second time window within 5 milliseconds. The impact energy loss index is calculated, and by continuously adjusting the cross-sectional distribution of the frame branches, the maximum transient stress is reduced from 320 MPa to 185 MPa (below the material's yield strength of 235 MPa), while increasing the structure's energy absorption rate by 24%. Compared to the traditional Newmark-β numerical integration method, FNO's inference speed is increased by 1500 times, making it possible to introduce transient dynamic constraints in real-time during each round of training of the generative adversarial network, ensuring that the traction frame does not experience instantaneous failure or cracking under severe impact conditions.

[0053] This invention utilizes a transient impact surrogate model constructed using Fourier neural operators (FNOs), successfully integrating extremely time-consuming time-domain dynamic analysis into a real-time topology optimization loop. The convolution operation performed by FNOs in the frequency domain captures the deep nonlinear mapping between structural geometry and its dynamic response, completely avoiding the cumbersome numerical integration calculations required by traditional finite element methods when dealing with nonlinear transient problems. By introducing impact energy loss as an evaluation index, the optimization process can accurately locate the weak points of the structure under impact and guide the material to accumulate in high-energy-dissipation regions. This significantly improves the dynamic load-bearing capacity of mechanical structures when facing sudden loads in agricultural operations, enhances the structure's impact robustness, and provides crucial technical support for extending the operational life of equipment in harsh environments.

[0054] Furthermore, the calculation of the frequency bandgap loss specifically involves constructing a frequency domain feature prediction neural operator using a three-dimensional encoder-decoder architecture. The input is the overall structure voxel field, and the output is a tensor with six channels, each channel representing the displacement field of the first six modal modes of the structure. The operator is trained under supervision using historical modal analysis data to learn the nonlinear mapping relationship from geometric topology to modal modes. For each predicted modal displacement field, the corresponding global modal kinetic energy and modal potential energy are calculated using the voxel integration method, and the natural frequency value of the corresponding order is approximately solved by substituting it into the Rayleigh quotient formula. The frequency bandgap range is set to the idling excitation frequency range of an agricultural machinery diesel engine. A potential energy penalty function is constructed, which generates an exponentially increasing loss value when the estimated frequency falls within the frequency bandgap range, and zero otherwise. The idle speed excitation frequency range (i.e., the preset frequency band gap) of the agricultural machinery diesel engine is set to 18Hz to 22Hz. This range is determined based on the measured idle speed data of a specific model of agricultural machinery engine, and aims to completely avoid this range by optimizing the first and higher natural frequencies of the structure to prevent fatigue damage caused by resonance.

[0055] The frequency domain feature prediction neural operator adopts a three-dimensional symmetric encoder-decoder architecture. Specifically, the encoder consists of four consecutive three-dimensional convolutional layers, each with a kernel size of 3×3×3 and a stride of 2. This kernel extracts multi-scale spatial topological features of the overall structure voxel field layer by layer through downsampling operations and compresses the feature dimension. The intermediate bottleneck layer captures global geometric correlations through global average pooling and fully connected layers. The decoder consists of four corresponding three-dimensional transposed convolutional layers. It gradually restores spatial resolution through upsampling operations and establishes skip connections between the decoder and encoder layers of the same dimension to preserve local geometric details of the structure. The final output layer uses a six-channel three-dimensional convolutional kernel, corresponding to the first six modal displacement fields of the structure. During training, normalized mean square error is used as the loss function. By comparing the displacement field predicted by the neural operator with historical high-fidelity modal analysis data, the network weights are updated using backpropagation until the prediction accuracy reaches a preset correlation requirement of over 95%.

[0056] The core of the voxel integration method lies in discretizing continuous structural dynamics problems into algebraic operations based on voxel elements. First, a mapping is established between voxel elements and physical properties: the mass of each voxel is determined by the product of the predicted density at that location, the material's intrinsic density, and the voxel volume (the cube of the side length). For kinetic energy calculation, the displacement vector field predicted by the neural operator is extracted, and the product of the square of the displacement modulus of each voxel element and the element mass is calculated, then globally summed to obtain the total modal kinetic energy of that order. This method logically corresponds to the mass matrix lumping scheme in the finite element method, but achieves rapid characterization of complex topologies through voxel representation.

[0057] The process of calculating the natural frequency value is as follows: obtain the density value of each voxel in the current overall structure voxel field, calculate the equivalent mass and equivalent stiffness matrix of each voxel according to the material properties; combine the frequency domain characteristics to predict the modal displacement field output by the neural operator, sum and aggregate the unit kinetic energy and unit potential energy of each voxel in the voxel space to obtain the global modal kinetic energy and global modal potential energy, and finally substitute them into the Rayleigh quotient formula for approximate solution.

[0058] The natural frequencies were ultimately determined using the Rayleigh quotient formula. This formula states that the natural frequency of a certain order is equal to the square root of the quotient of the total potential energy and total kinetic energy of that mode (in radians per second), which is then converted to Hertz by dividing by twice pi. The theoretical basis of this calculation method lies in the energy conservation characteristics of linear elastic systems. To ensure the accuracy of higher-order mode calculations, high-fidelity finite element simulation data (such as 512 sets of samples calculated using the Lanczos algorithm) were introduced as monitoring signals. The neural operator was forced to learn the nonlinear mapping between complex geometric topology and mode displacements by using a normalized mean square error loss function, thereby achieving extremely high correlation on the validation set.

[0059] The Pareto dynamic weighting employs a multi-objective gradient descent algorithm: during backpropagation, the angle between the impact energy loss gradient and the frequency bandgap loss gradient is monitored in real time. When a gradient conflict is detected, a common descent direction is found by solving a quadratic programming problem, and the weights of the two are dynamically adjusted to achieve collaborative optimization of multi-physics objectives.

[0060] The solution to the quadratic programming problem is as follows: The impact energy loss gradient is set as the first gradient, and the frequency bandgap loss gradient is set as the second gradient. An optimization objective is constructed, namely, by finding a weight coefficient with a value between zero and one, the norm square of the weighted vector sum of the first and second gradients is minimized. The optimal weight allocation is determined by solving this convex optimization problem, thereby synthesizing the common descent direction of the two objectives. If the angle between the first and second gradients is detected to be greater than 90 degrees (i.e., there is a directional conflict), the synthesized gradient vector with the smallest norm is found using the aforementioned weight coefficient to effectively alleviate the gradient conflict between different physical field objectives.

[0061] Specifically, the main excitation frequency range of the tractor engine at idle is 18Hz to 22Hz. A frequency-domain neural operator predicts the first six modes of the drawbar, with the initial predicted first-order bending frequency at 20.5Hz, within the bandgap. The potential energy penalty function then generates an exponentially increasing loss value (Loss jumps from 0 to 150). During optimization, Pareto dynamic weighting detects a 135-degree angle between the impact energy gradient and the frequency bandgap gradient (a conflict exists). By solving a quadratic programming problem, the frequency penalty weight is automatically increased by 1.2 times, and a common descent direction is sought. After 50 parameter updates, the first-order frequency of the drawbar is successfully pushed out of the bandgap, moving to 28.6Hz. Multiphysics co-optimization results show that the structure perfectly avoids the engine excitation zone while meeting impact resistance requirements. The vibration amplitude caused by resonance is reduced by more than 70%, significantly improving structural fatigue performance and driving comfort during operation.

[0062] This invention achieves automatic trade-off optimization between shock resistance and vibration damping performance by constructing a frequency domain feature prediction operator and a Pareto dynamic weighting mechanism. The Pareto dynamic weighting technology effectively solves the gradient conflict problem commonly encountered in multiphysics optimization, ensuring that the optimization direction always lies on the Pareto frontier of multi-objective optimality. This time-frequency collaborative evaluation system enables the generated agricultural machinery structure to exhibit excellent vibration and noise performance under complex dynamic conditions, effectively avoiding early fatigue fracture caused by resonance and improving the overall dynamic quality of the product.

[0063] Furthermore, the specific implementation of the global casting draft projection layer is as follows: the casting draft direction is defined as the positive Z-axis in the geometric space; this projection layer is constructed as a differentiable geometric morphological operator: performing a cumulative max-pooling operation along the Z-axis on the global structure voxel field; that is, for any coordinate (x, y, z) in space, its corrected density value is forcibly set to be no less than all coordinates (x, y, z). The maximum density value at point () is where Less than z; This operator utilizes the monotonicity constraint of mathematical morphology to ensure that the generated solid geometry has a non-decreasing cross section along the demolding direction, thereby eliminating undercuts in geometric principle. Moreover, this process is entirely based on tensor operations, maintaining the differentiability of the entire process.

[0064] The global casting draft projection layer includes a thermal shrinkage compensation module: it uses a morphological expansion operator to identify the local sphere core voxel density in the structure; it calculates the ratio of the sphere core volume to the average wall thickness of the neighborhood as a thermal limit index; when the index exceeds the thermal limit index threshold, it generates a geometric contrast penalty term, prompting the generation network to eliminate locally thick regions by thinning or setting weight reduction holes.

[0065] The thermal index threshold is set to 1.8. This threshold is determined based on an empirical formula for cooling uniformity in the casting process. When the ratio of the sphere's core volume to the average wall thickness of its neighborhood exceeds this threshold, it is determined that there is a quality risk of shrinkage cavities or cracks, and geometric evolution is triggered to perform thinning treatment.

[0066] As the core load-bearing component of the agricultural machinery transmission system, the rear axle housing not only has a complex geometry but also requires extremely high casting quality. During the optimization process, the design space was discretized into a voxel grid with dimensions of 256×128×128, where each voxel represents a side length of 4mm in actual space.

[0067] First, the casting draft direction is defined as the positive Z-axis direction in geometric space. The global casting draft projection layer performs cumulative max pooling operations along the Z-axis to correct the generated structure in real time. In actual calculations, if the voxel density at the height coordinate z is less than the density value at the corresponding coordinate z-1 below it, this layer will force it to be raised to a level no lower than the density of the lower layer. For example, in the optimization evolution of the shell sidewall, the initial network tends to generate reinforcing ribs with concave shapes to pursue extreme weight reduction, but the projection layer fills these geometric gaps that would cause "overturning" in real time in each iteration, ensuring that the cross-section of the generated solid geometry along the draft direction exhibits monotonically non-decreasing characteristics. Experimental data shows that this projection layer can process more than 4 million voxel Boolean operations per second and fully maintains the differentiability of the entire process, allowing the optimization algorithm to directly perceive the impact of casting constraints on structural stiffness. The thermal shrinkage compensation module intervenes simultaneously to solve the shrinkage caused by casting hot spots. Potential hole hazards were identified. A spherical morphological expansion operator with a radius of 20 mm was used to scan the voxel field and identify the local voxel density at the structural intersection. The ratio of the volume of the sphere center to the average wall thickness of the neighborhood (set as a benchmark of 25 mm) was calculated and defined as the thermal index. In the connection area between the rear axle housing bearing seat and the main housing, a solid, thick area with a diameter of 95 mm was detected, with a thermal index as high as 2.4, far exceeding the set thermal index threshold of 1.8. This resulted in an exponentially increasing geometric contrast penalty term, prompting the generation network to automatically "develop" a non-through-hole weight reduction space with a diameter of 45 mm in the center of the thick area, which shortened the solidification cooling time of this area by 35%. The final generated solution was tested by engineering software, and its draft angle qualification rate reached 100%. It also completely eliminated the risk of internal shrinkage cavities caused by uneven cooling, achieving a closed-loop design with high performance and high manufacturability.

[0068] This invention achieves a native unity of structural optimization and casting feasibility through deep coupling of the global casting draft projection layer and the thermal shrinkage compensation module. Utilizing a differentiable cumulative max-pooling operator, monotonicity constraints are enforced in real-time during the generation process, ensuring that the topology geometrically eliminates undercuts, achieving 100% demolding compliance and eliminating tedious post-processing manual repairs. More importantly, the thermal shrinkage compensation module, through dynamic monitoring and penalty of the thermal expansion index, forces the generated network to automatically evolve into weight-reducing holes or thin-walled structures in thick areas, fundamentally solving the problems of shrinkage cavities and cracks caused by uneven cooling in casting production.

[0069] The specific steps for generating the welding assembly penalty include: defining the rigid space occupancy of the welding torch and its connecting rod as a three-dimensional geometric convolution kernel; identifying the set of voxels at the interface between the skeleton field and the shell field as the area to be welded; performing a binary cross-correlation operation on the overall structural voxel field using the three-dimensional geometric convolution kernel: traversing each voxel position in space, calculating the cumulative sum of the product of the welding torch envelope voxel value and the structural density voxel value within the coverage area of ​​the convolution kernel; when the cumulative sum is non-zero, determining that geometric interference has occurred; calculating the total cumulative sum at all areas to be welded as the welding assembly penalty term, characterizing the geometric interference volume when the welding torch touches the welding point; and by minimizing the welding assembly penalty term, forcing the generation network to automatically reserve free space around the welding point that conforms to the welding torch's movement trajectory by adjusting its geometric shape.

[0070] The generated welding assembly penalty includes trajectory connectivity evaluation: based on the fast traversal algorithm, the distance gradient field is calculated from the weld point as the source point to the outside of the design domain; connected obstacles in the gradient field are identified; the volume of the obstacles is statistically analyzed as a welding trajectory occlusion penalty, forcing the generated network to retain the geometrically connected space that conforms to the welding torch cutting trajectory.

[0071] In the lightweight topology optimization design of the chassis frame of a large grain combine harvester, the chassis frame, as the load-bearing core, is welded from a complex skeleton stiffener and an envelope shell. Due to its compact structure, the topology results generated by traditional optimization methods often result in internal weld points being located in physically inaccessible areas, leading to failures in subsequent manufacturing process verification. This embodiment introduces a welding assembly penalty term. First, the rigid space occupation of the welding torch and its connecting rod of the industrial welding robot is defined as an L-shaped three-dimensional geometric convolution kernel with a diameter of 45mm and a length of 200mm. By identifying the voxel set at the interface between the skeleton field and the shell field, 32 critical areas to be welded are determined. During the optimization iteration process, the three-dimensional convolution kernel is used to perform binary cross-correlation operations on the overall structural voxel field of 128×128×128. By traversing the spatial position of each weld point, the interference within the coverage area of ​​the convolution kernel is calculated. Initial experimental data show that due to the randomness of structural evolution, a total of 8 weld points produce severe geometric interference, with a cumulative interference volume of 8500mm³. To further ensure the dynamic reachability of the welding torch, this embodiment simultaneously initiates trajectory connectivity assessment: based on a fast traversal algorithm, using each welding point voxel as the source point, a distance gradient field is calculated towards the outside of the design domain, and two connectivity obstacles formed by the closed area of ​​the shell are successfully identified. By introducing interference volume and occlusion penalty terms into the loss function of the generative adversarial network, the generative network is forced to adjust its geometry while maintaining its load-bearing capacity. After 200 rounds of parameter updates, the generative network automatically evolved four 120mm diameter process operation holes in the shell area with severe interference and fine-tuned the curvature of the adjacent skeleton, reserving free space that conforms to the welding torch's movement trajectory. The final virtual assembly verification results show that the welding robot's welding head reach rate increased from the initial 62% to 100%, completely eliminating welding dead zones and achieving seamless integration of topology optimization and automated assembly processes.

[0072] This invention effectively solves the manufacturing bottleneck problem of "visible but unweldable" complex topologies by constructing a welding assembly penalty and trajectory connectivity evaluation mechanism based on geometric convolution kernels. This technique upgrades traditional static interference checks to dynamic path reachability constraints, using a differentiable fast traversal algorithm to guide the generator network to proactively reserve process holes in the shell or skeleton, ensuring that the generated lightweight solution possesses inherently high assembly feasibility. This manufacturing-oriented design pattern not only fundamentally avoids manual secondary repairs and design iterations caused by overly complex topologies, greatly shortening the process conversion cycle from design to production, but also lays the foundation for the large-scale adoption of automated welding robots in agricultural machinery, significantly improving the production efficiency and manufacturing cost control capabilities of large structural components.

[0073] In the specific process of updating the parameters of the generative adversarial network, this embodiment constructs a total loss function composed of a weighted combination of multiple sub-objectives. The specific steps are as follows: The co-dynamic loss calculated by the Fourier neural operator, the welding assembly penalty term obtained by the binarized cross-correlation operation, and the adversarial loss of the discriminator built into the generative adversarial network are all normalized to keep their numerical magnitudes in the same dimension, thus avoiding gradient explosion caused by differences in dimensions.

[0074] The total loss function is defined as the weighted sum of the three losses mentioned above. The weight coefficient of the adversarial loss is set to one to ensure the geometric topological continuity of the generated structure; the weight coefficient of the cooperative dynamics loss is dynamically adjusted between 0.5 and 2.0 according to mechanical performance requirements to force the structure to meet impact resistance and vibration damping requirements; the weight coefficient of the welding assembly penalty term is set between 3.0 and 5.0. By setting a higher penalty weight, it ensures that the generated network prioritizes avoiding geometric interference points in the early stages of optimization.

[0075] Using a stochastic gradient descent algorithm (such as the Adam optimizer), the gradient of the network parameters is calculated based on the total loss function, and the weights of the generator are updated layer by layer. When the decrease in the total loss function is less than one ten-thousandth within one hundred consecutive training batches, or when the welding interference volume drops to zero and the natural frequency completely avoids the frequency bandgap, it is determined that the network parameters have reached steady-state convergence, the update is stopped, and the final topology optimization structure is output.

[0076] Convergence is defined as the fluctuation range of the total loss function of the generative adversarial network being less than 3% over 50 consecutive iterations, or the L2 norm of the physical mechanism residual decreasing to below 0.05. At this point, the model is determined to have captured stable topological features, and parameter updates are stopped.

[0077] This invention addresses the model convergence challenge of tractor traction frames in small-sample scenarios by introducing physical mechanism loss and cross-domain feature transfer mechanisms, reducing data acquisition costs and improving design reliability. A time-frequency co-dynamic evaluation system constructed using Fourier neural operators enables millisecond-level prediction and trade-off optimization of the transient shock resistance and steady-state vibration damping performance of the traction frame, significantly enhancing the fatigue life and dynamic robustness of the structure under harsh operating environments. Furthermore, a heterogeneous dual-flow generation architecture combined with global process projection technology ensures that the generated complex topology directly meets the stringent requirements of casting draft and automated welding, achieving a high degree of synergy between structural performance and manufacturing process, and significantly shortening the product development cycle.

[0078] Example 2: This embodiment selects the chassis frame of a large grain combine harvester as the optimization object, aiming to verify the performance of the present invention in handling ultra-large heterogeneous components and extreme working conditions. As the core load-bearing component of the entire machine, the harvester chassis frame not only needs to withstand transient random impact loads from uneven road surfaces during field operations, but also needs to support the static torque generated by heavy components such as the engine, grain bin, and header. Due to the harsh operating environment of agricultural machinery, the chassis frame often suffers fatigue cracking due to high-frequency vibration. Furthermore, due to its complex structure and enormous size, traditional welding processes are prone to problems such as weld heads failing to reach the target area or excessive thermal deformation. This embodiment achieves a deep integration of performance and process in a "small sample" scenario lacking large-scale historical chassis frame data through a physical perception transfer and global collaborative optimization method using heterogeneous geometric fields.

[0079] As one embodiment of the present invention, refer to Figure 1 Flowchart of a lightweight topology optimization method for mechanical structures based on generative adversarial networks, referencing Figure 2 Heterogeneous dual-stream generation network architecture diagram, refer to Figure 3 Flowchart for time-frequency coordination and process constraint evaluation.

[0080] In the initialization phase, this embodiment acquired 80,000 sets of topological data on heavy truck beams in the source domain. For the target domain, the harvester chassis frame, only 30 sets of preliminary design CAD samples were available, representing a typical sparse simulation sample scenario. By introducing physical mechanism loss as a regularization term and utilizing a meshless physical information neural network strategy, 20,000 configuration point coordinates were randomly sampled within the design domain. The residual L2 norm of the continuum mechanics equilibrium equations was calculated using automatic differentiation technology. Experiments show that even with extremely scarce data in the target domain, relying on the force flow transmission laws of general mechanical structures in the source domain for pre-training and combining the maximum mean difference algorithm to align feature distributions, the model can still converge rapidly within 150 iterations. The generated initial topology structure exhibits a high degree of consistency with the heavy truck beam in terms of load-bearing logic.

[0081] Furthermore, a heterogeneous dual-stream generation architecture for the chassis frame was constructed. The main longitudinal beams and crossbeams of the chassis frame were defined as sets of hard points of the skeleton branches. A topological skeleton graph generated by a geometric graph neural network was used to map 48 key connection nodes into a skeleton voxel field through a differentiable skeleton materialization layer. Simultaneously, the shell branches utilized a U-Net 3D convolutional network containing skip connections to generate an envelope shell field, and morphological convolutional layers were concatenated to ensure a minimum wall thickness of no less than 10 mm. Through learnable weighted masks, high-strength skeleton features were automatically preserved in the complex stress-bearing reducer mounting area of ​​the chassis frame, while uniform shell features were preserved in areas such as the fuel tank cover. This dual-stream fusion architecture resulted in a 15.8% weight reduction and a 21.4% increase in torsional stiffness compared to the original design.

[0082] Regarding dynamic performance, this embodiment utilizes a Fourier neural operator to construct a transient impact surrogate model in the time domain. The time-varying resistance data generated by the harvester as it traverses field furrows is processed as a continuous function input. The neural operator learns the mapping from geometric parameters to transient stress across the entire field in the frequency domain, avoiding the time-consuming solution process of traditional numerical integration. The calculated impact energy loss effectively evaluates the structure's impact resistance efficiency. Simultaneously, for the harvester's diesel engine idling excitation frequency (18Hz–22Hz), the frequency domain characteristics predict the first six mode shapes output by the neural operator, and the natural frequency values ​​are solved using the Rayleigh quotient formula. When the estimated frequency falls within the bandgap, the resulting exponential penalty forces the model to adjust its geometric distribution, ultimately shifting the first-order bending frequency of the chassis frame from 19.5Hz to 27.2Hz, successfully avoiding the resonance zone.

[0083] Regarding manufacturing constraints, this embodiment introduces a global casting draft projection layer, defining the positive Z-axis direction as the demolding direction. By performing cumulative max pooling along the Z-axis, this projection layer forces the generation network to eliminate all geometric undercuts, ensuring smooth demolding of large-sized chassis castings. For the numerous welding points on the chassis frame, this embodiment defines the spatial occupancy of the welding torch and its connecting rods as a three-dimensional geometric convolution kernel; the interface between the longitudinal beam and the support plate is identified as the area to be welded, and binary cross-correlation is performed using the convolution kernel. When geometric interference is detected, the resulting welding assembly penalty term forces the generation network to reserve free space around the welding point that conforms to the welding torch's movement trajectory. By minimizing this penalty term, the final generated chassis frame structure requires no post-construction manual repairs and can directly meet the construction requirements of automated welding robots, shortening the development cycle by more than 30%.

[0084] This invention significantly overcomes the bottleneck of existing deep learning topology optimization methods' reliance on massive training data through the aforementioned technical means. When dealing with agricultural machinery components such as combine harvester chassis frames—which have "small sample" characteristics and complex dynamic impact requirements—this embodiment not only ensures high-quality generation of the structure in terms of physical logic but also achieves time-frequency coordinated dynamic balance. By deeply integrating heterogeneous dual-stream architecture with global process projection technology, this invention ensures that the generated lightweight topology structure has extremely high manufacturing feasibility, truly realizing integrated collaborative design of performance and process.

[0085] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A lightweight topology optimization method for mechanical structures based on generative adversarial networks, characterized in that, include: Acquire source domain mechanical structure data and target domain agricultural machinery data, and construct a generative adversarial network; During the pre-training phase, physical mechanism loss is introduced as a regularization term; Align the feature distributions of the source and target domains to obtain a shared feature vector; The shared feature vectors are input into the skeleton branch and the shell branch respectively; the skeleton branch uses a geometric graph neural network to generate a topological skeleton graph and maps it to a skeleton voxel field through a differentiable skeleton materialization layer; the shell branch uses three-dimensional convolution to generate a shell voxel field; the skeleton voxel field and the shell voxel field are weighted and superimposed using a learnable weighted mask to output the overall structure voxel field. In the time domain, a transient impact surrogate model is constructed using Fourier neural operators to calculate impact energy loss; in the frequency domain, the frequency bandgap loss is calculated; and a co-dynamic loss is generated by combining impact energy loss and frequency bandgap loss through Pareto dynamic weighting. By forcing the overall structure's voxel field to exhibit a monotonically non-decreasing distribution along the demolding direction through a global casting draft projection layer, welding assembly penalties are generated using the welding torch envelope convolution kernel. The parameters of the generative adversarial network are then updated until convergence by combining the cooperative dynamics loss, the welding assembly penalty term, and the adversarial loss of the generative adversarial network.

2. The lightweight topology optimization method for mechanical structures based on generative adversarial networks according to claim 1, characterized in that, The generative adversarial network includes a shared feature extractor, a domain discriminator, and a physical residual module; the source domain data is selected from a three-dimensional voxel model of a general mechanical load-bearing structure and its corresponding stress field data, and the target domain data is selected from sparse simulation geometric samples of agricultural machinery structures. The physical mechanism loss is constructed using a meshless physical information neural network strategy. Specifically, the coordinates of configuration points are randomly sampled in the continuous design domain space. The partial derivatives of the density field output by the network with respect to the spatial coordinates are calculated using automatic differentiation technology. These derivatives are then substituted into the partial differential equations of equilibrium in continuous medium mechanics, and the L2 norm of the equation residuals is calculated as the physical mechanism loss. Align the feature distributions of the source and target domains and use the maximum mean difference algorithm; in the regenerating kernel Hilbert space, minimize the distance between the feature distributions of the source and target domains, and force the shared feature extractor to ignore the differences in geometric scale between agricultural machinery and automobiles, retaining only the topological features of force flow transmission.

3. The lightweight topology optimization method for mechanical structures based on generative adversarial networks according to claim 1, characterized in that, The skeleton branch employs a geometric graph neural network, with the input being an initial graph constructed from hard points within the design domain, and the output being updated node coordinates and edge connectivity attributes. The differentiable skeleton materialization layer uses an implicit function mapping method based on a distance field: each edge output by the graph network is modeled as a cylindrical segment with a preset radius, and each node is modeled as a sphere; the minimum geometric distance from any voxel center point in space to the skeleton centerline is calculated, and a density decay distribution is constructed using a smooth sigmoid function to convert the geometric distance into a voxel density value between 0 and 1; when multiple skeleton segments overlap at a certain point in space, a soft maximization operator is used to aggregate the local voxel density, maintaining the continuity of gradient backpropagation.

4. The lightweight topology optimization method for mechanical structures based on generative adversarial networks according to claim 1, characterized in that, The shell branch uses a U-Net 3D convolutional network with skip connections to generate an initial shell field; after the initial shell field, a morphological convolutional layer is connected in series, and erosion and dilation operations are performed sequentially using spherical structural elements with a diameter equal to the minimum wall thickness of the casting to filter out geometric features smaller than the minimum wall thickness. The learnable weighted mask is generated by a convolutional attention module connected in parallel; the convolutional attention module simultaneously receives the skeleton voxel field and the shell voxel field as input channels and outputs a spatial weight matrix with the same size as the voxel field. The weighted superposition operation is as follows: at each voxel position in space, the values ​​of the weight matrix are used as coefficients to linearly interpolate the skeleton voxel density and the shell voxel density. The weight distribution is automatically adjusted through training to preserve skeleton features in stress concentration areas and shell features in boundary areas.

5. The lightweight topology optimization method for mechanical structures based on generative adversarial networks according to claim 1, characterized in that, The specific steps for constructing a transient impact surrogate model in the time domain include: processing the time-varying resistance data of agricultural machinery operation into a continuous time function input; constructing a Fourier neural operator as an impact response predictor: the Fourier neural operator performs a convolution operation on the input geometric field and load function in the frequency domain space, learning the nonlinear operator mapping from structural geometric parameters to the transient stress distribution across the entire field, avoiding the numerical integration process; using historical experimental data to supervise the training of the Fourier neural operator, learning real-time inference capabilities; the calculated impact energy loss is defined as the ratio of the integral of the predicted transient stress field modulus within the impact time window to the total mass of the structure, serving as a meshless index for evaluating the structure's impact resistance efficiency.

6. The lightweight topology optimization method for mechanical structures based on generative adversarial networks according to claim 1, characterized in that, The calculation of the frequency bandgap loss specifically involves constructing a frequency domain feature prediction neural operator using a three-dimensional encoder-decoder architecture. The input is the overall structure voxel field, and the output is a tensor with six channels, each channel representing the displacement field of the first six modal modes of the structure. The operator is then trained under supervised supervision using historical modal analysis data to learn the nonlinear mapping relationship from geometric topology to modal modes. For each predicted modal displacement field, the corresponding global modal kinetic energy and modal potential energy are calculated using the voxel integration method, and the natural frequency value of the corresponding order is approximated by substituting it into the Rayleigh quotient formula. The frequency bandgap range is set to the idling excitation frequency range of an agricultural machinery diesel engine. A potential energy penalty function is constructed, which generates an exponentially increasing loss value when the estimated frequency falls within the frequency bandgap range, and zero otherwise. The Pareto dynamic weighting employs a multi-objective gradient descent algorithm: during backpropagation, the angle between the impact energy loss gradient and the frequency bandgap loss gradient is monitored in real time. When a gradient conflict is detected, a common descent direction is found by solving a quadratic programming problem, and the weights of the two are dynamically adjusted to achieve collaborative optimization of multi-physics objectives.

7. The lightweight topology optimization method for mechanical structures based on generative adversarial networks according to claim 1, characterized in that, The specific implementation of the global casting draft projection layer includes: defining the demolding direction of the casting process as the positive Z-axis direction; the global casting draft projection layer is constructed as a differentiable geometric morphology operator: performing a cumulative max pooling operation along the Z-axis direction on the overall structure voxel field, forcing the generation network to actively generate a structure shape that is easy to demold; The specific steps for generating the welding assembly penalty include: defining the rigid space occupancy of the welding torch and its connecting rod as a three-dimensional geometric convolution kernel; identifying the set of voxels at the interface between the skeleton field and the shell field as the area to be welded; performing a binary cross-correlation operation on the overall structural voxel field using the three-dimensional geometric convolution kernel: traversing each voxel position in space, calculating the cumulative sum of the product of the welding torch envelope voxel value and the structural density voxel value within the coverage area of ​​the convolution kernel; when the cumulative sum is non-zero, determining that geometric interference has occurred; calculating the total cumulative sum at all areas to be welded as the welding assembly penalty term, characterizing the geometric interference volume when the welding torch touches the welding point; and by minimizing the welding assembly penalty term, forcing the generation network to automatically reserve free space around the welding point that conforms to the welding torch's movement trajectory by adjusting its geometric shape.

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