Method and system for automatically supplementing and generating process die surface of die based on deep learning

Abstract

The invention provides a deep learning-based die process die surface automatic supplement generation method and system, and relates to the technical field of deep learning, and the method comprises the steps: extracting the contour line and feature point information of a die surface as a training sample; feature learning is carried out based on a multi-scale image convolutional network and a double-flow network, and optimized local geometric features and global topological features are extracted; generating a supplementary modular surface through the generative adversarial network; and carrying out stress field constraint verification and then fusing with an original model. According to the method, intelligent supplementary generation of the mold surface is realized, and the mold design efficiency and quality are improved.

Description

Technical Field

[0001] The present invention relates to deep learning technology, and in particular to a method and system for automatically supplementing and generating mold process surfaces based on deep learning. Background Art

[0002] Automatic surface generation for mold production relies primarily on traditional geometric modeling and parametric design methods. These approaches typically utilize interpolation algorithms or spline surface fitting to achieve surface generation. Some researchers also employ rule-based expert systems to guide automatic surface generation. However, as industrial production demands increased precision and efficiency for molds, traditional methods are no longer able to meet the demands of modern manufacturing.

[0003] Existing automatic die surface generation methods lack comprehensive consideration of local geometric features and global topological features, resulting in defects in the geometric continuity and topological integrity of the generated die surfaces, especially cracks or unevenness at the junction of complex surfaces.

[0004] Existing supplementary methods based on mathematical models cannot effectively simulate the physical constraints in the actual molding process. Although the generated mold surface meets the requirements in terms of geometric shape, there may be problems such as stress concentration and excessive deformation during actual processing and use, which will affect the mold service life and product quality.

[0005] Existing die surface generation technology lacks an intelligent evaluation mechanism, making it difficult to automatically determine the processing feasibility and molding effect of the generated die surface. Designers are required to make repeated modifications and verifications, which greatly reduces design efficiency and increases development costs. Summary of the Invention

[0006] The embodiments of the present invention provide a method and system for automatically supplementing and generating mold process die surfaces based on deep learning, which can solve the problems in the prior art.

[0007] A first aspect of an embodiment of the present invention provides a method for automatically supplementing and generating a mold process die surface based on deep learning, comprising:

[0008] Extract the mold surface contour lines and feature point information of the mold to be processed as training samples;

[0009] Performing feature learning on the training samples based on a multi-scale graph convolutional network and a dual-stream network, and extracting and optimizing local geometric features and global topological features of the die surface by combining non-Euclidean space manifold learning, wherein the local geometric features include curvature, normal vectors, and tangent vectors, and the global topological features include connection relationships and boundary constraints of feature points;

[0010] Inputting the local geometric features and global topological features into a generative adversarial network to generate a supplementary die surface, wherein the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface;

[0011] The supplementary mold surface is subjected to stress field constraint verification, and the stress distribution of the mold surface during the forming process is calculated. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete three-dimensional mold model.

[0012] Based on the multi-scale graph convolutional network and the two-stream network, the training samples are subjected to feature learning. The local geometric features and global topological features of the die surface are extracted and optimized in combination with non-Euclidean space manifold learning. The local geometric features include curvature, normal vector and tangent vector. The global topological features include the connection relationship of feature points and boundary constraints, including:

[0013] Constructing a multi-scale graph structure modeling the training samples, including fine-grained graphs, medium-grained graphs, and coarse-grained graphs, and extracting a feature representation set through a multi-scale graph convolutional network with cross-scale information transfer;

[0014] A two-stream network architecture is used to separate feature representations. One branch extracts local geometric features including curvature, normal vectors, and tangent vectors, while the other branch extracts global topological features including connectivity and boundary constraints. A geometric constraint loss function is introduced to train the two-stream network. The geometric constraint loss function includes orthogonal constraints on normal and tangent vectors, unit length constraints on normal vectors, and curvature gradient constraints.

[0015] Based on the local geometric features, manifold learning is performed in a non-Euclidean space, a Riemannian metric tensor is constructed and geodesic distance is calculated, topological relationships are reconstructed using geodesic distance, global topological features are updated, and local geometric features are propagated and enhanced on the Riemannian manifold;

[0016] The enhanced local geometric features and updated global topological features are fused and normalized to obtain the final local geometric features and global topological features.

[0017] Based on the local geometric features, manifold learning is performed in a non-Euclidean space, a Riemannian metric tensor is constructed and geodesic distance is calculated, topological relationships are reconstructed using geodesic distance, global topological features are updated, and local geometric feature propagation and enhancement are performed on the Riemannian manifold, including:

[0018] A local tangent space is constructed using the normal vector and tangent vector at each feature point on the die surface to obtain a local coordinate transformation matrix. The local coordinate transformation matrix is multiplied by a diagonal matrix containing curvature information to construct a Riemannian metric tensor reflecting the local surface characteristics. The distance field is initialized and the fast marching equation is solved under the Riemannian metric to calculate the geodesic distance. A distance matrix is constructed based on the geodesic distance. The connection relationship of the feature points on the die surface is reconstructed based on the distance matrix to obtain a new topological adjacency matrix, and the global topological features are updated.

[0019] A heat kernel operator based on geodesic distance is constructed, and its parameters are determined by diffusion time and geodesic distance. The heat kernel operator is used to construct a feature propagation equation on a Riemannian manifold to propagate local geometric features. Local curvature difference is introduced to calculate feature propagation weights, and local geometric features are enhanced through heat kernel weighted summation. The feature propagation weights are jointly determined by local curvature difference and geodesic distance.

[0020] Inputting the local geometric features and the global topological features into a generative adversarial network to generate a supplementary die surface, wherein the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface, including:

[0021] Based on local geometric features and global topological features, a supplementary die surface boundary condition including boundary normal vector, transition angle and transition depth is constructed, and the generator of the generative adversarial network is input through feature space mapping;

[0022] The generative adversarial network includes a multi-scale generator and a discriminator based on geometric priors. The discriminator evaluation indicators include geometric continuity constraints, curvature constraints based on target curvature distribution, and processing feasibility constraints of minimum curvature radius and tilt angle. The multi-scale generator sequentially generates mold surfaces with different geometric detail levels, and introduces a deformation field based on a spatial weight function and a local deformation operator to perform smooth transition processing on the boundary transition area.

[0023] A multi-objective optimization function including geometric loss, topological loss, machinability loss and adversarial loss is constructed to train the generative adversarial network, and the supplemented mold surface is obtained through iterative optimization.

[0024] The design of the discriminator includes:

[0025] Construct a multi-channel discriminant network structure, including a feature extraction layer, a constraint evaluation layer, and a decision layer; the feature extraction layer extracts multi-scale features of the mold surface through three-dimensional convolution and residual connection; the constraint evaluation layer includes a geometric continuity evaluation module, a curvature constraint evaluation module, and a processing feasibility evaluation module; the decision layer synthesizes the outputs of each evaluation module to obtain a discrimination result;

[0026] The geometric continuity evaluation module calculates the continuity scores of the position continuity, tangent continuity and curvature continuity of the die surface based on the Sobolev norm, and measures the degree of jump of each order derivative of the die surface at the boundary; the curvature constraint evaluation module constructs the curvature distribution prior of the target surface through the Gaussian mixture model, calculates the Wasserstein distance between the generated die surface and the target distribution, and identifies the curvature mutation area; the processing feasibility evaluation module evaluates the minimum curvature radius constraint and tool accessibility constraint of the die surface through curvature tensor estimation and tool angle distribution.

[0027] The design of the multi-scale generator includes:

[0028] A hierarchical generative network structure is constructed, including a feature encoding layer, a geometric decoding layer, and a detail enhancement layer. The feature encoding layer converts local geometric features and global topological features into latent feature representations through nonlinear mapping. The geometric decoding layer uses upsampling and skip connections to gradually restore the geometric shape of the mold surface, and introduces a self-attention mechanism at different scale levels to enhance feature association.

[0029] The detail enhancement layer receives the output of the geometric decoding layer and constructs a deformation field based on a spatial weight function and a local deformation operator, wherein the spatial weight function is determined by the boundary distance and feature similarity, and the local deformation operator includes stretching, bending and torsion deformation basis functions; a smooth transition is achieved in the boundary transition area through the deformation field.

[0030] The supplementary mold surface is subjected to stress field constraint verification, and the stress distribution of the mold surface during the molding process is calculated. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete mold three-dimensional model including:

[0031] The supplementary die surface is used as a boundary condition to define the material parameters, temperature field, and pressure field of the molding process. Adaptive meshing technology is used for discretization. The stress distribution is obtained by solving the thermal-mechanical-fluid coupling control equations to obtain the stress field. The maximum equivalent stress value and stress concentration factor are evaluated based on the stress field. When stress violation areas exist, local deformation functions are used for optimization until the preset threshold is met.

[0032] For the supplementary die surface that meets the stress constraints, a sequence of feature points is extracted based on its boundary contour, and a radial basis function is constructed as the transition region mapping operator. The influence range is controlled by adjusting the support radius. The transition surface is constructed using piecewise Hermite spline interpolation to ensure positional continuity and tangential continuity. Multi-resolution B-spline parameterized representation is used for model fusion, in which the B-spline control points are determined by least squares fitting, and the control grid density is adaptively adjusted by the curvature distribution. Laplace smoothing based on curvature weight is applied to the fusion area to obtain a complete three-dimensional mold model.

[0033] A second aspect of an embodiment of the present invention provides a system for automatically supplementing and generating mold process surfaces based on deep learning, comprising:

[0034] The first unit is used to extract the mold surface contour line and feature point information of the mold to be processed as a training sample;

[0035] The second unit is used to perform feature learning on the training samples based on a multi-scale graph convolutional network and a two-stream network, and extract and optimize the local geometric features and global topological features of the mold surface in combination with non-Euclidean space manifold learning, wherein the local geometric features include curvature, normal vector and tangent vector, and the global topological features include the connection relationship and boundary constraints of feature points;

[0036] The third unit is used to input the local geometric features and global topological features into a generative adversarial network to generate a supplementary die surface, and the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface;

[0037] The fourth unit is used to verify the stress field constraints of the supplementary mold surface and calculate the stress distribution of the mold surface during the molding process. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete three-dimensional mold model.

[0038] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including:

[0039] processor;

[0040] a memory for storing processor-executable instructions;

[0041] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0042] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0043] The deep learning-based automatic supplementation and generation method for mold process mold surfaces provided by the present invention can effectively extract the local geometric features and global topological features of the mold surface through a multi-scale graph convolutional network and a dual-stream network combined with non-Euclidean geometric space manifold learning, thereby realizing the precise supplementation and generation of the mold surface and improving the geometric continuity and fitting accuracy of the supplemented mold surface.

[0044] The present invention adopts a generative adversarial network to generate mold surfaces and designs a special discriminator to evaluate geometric continuity and processing feasibility, so that the generated supplementary mold surfaces meet actual processing requirements, avoiding the common problems of geometric discontinuity and high processing difficulty in traditional methods, and reducing the complexity and time cost of mold design.

[0045] The present invention predicts and evaluates the stress distribution of the supplementary die surface during the forming process by introducing a stress field constraint verification mechanism, thereby ensuring the stability and reliability of the supplementary die surface during the actual forming process, reducing the risk of die failure, extending the service life of the die, and improving the comprehensive performance and economic benefits of the die. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 Schematic diagram of the process of automatically supplementing and generating a mold process surface based on deep learning according to an embodiment of the present invention;

[0047] Figure 2 A comparison chart of the connection accuracy of different methods in complex surface topology reconstruction;

[0048] Figure 3 This is a comparison chart of geometric continuity evaluation effects. DETAILED DESCRIPTION

[0049] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0050] The following specific embodiments are used to describe the technical solution of the present invention in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0051] Figure 1 FIG. 1 is a flow chart of a method for automatically supplementing and generating a mold process die surface based on deep learning according to an embodiment of the present invention. Figure 1 As shown, the method includes:

[0052] Extract the mold surface contour lines and feature point information of the mold to be processed as training samples;

[0053] Performing feature learning on the training samples based on a multi-scale graph convolutional network and a dual-stream network, and extracting and optimizing local geometric features and global topological features of the die surface by combining non-Euclidean space manifold learning, wherein the local geometric features include curvature, normal vectors, and tangent vectors, and the global topological features include connection relationships and boundary constraints of feature points;

[0054] Inputting the local geometric features and global topological features into a generative adversarial network to generate a supplementary die surface, wherein the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface;

[0055] The supplementary mold surface is subjected to stress field constraint verification, and the stress distribution of the mold surface during the forming process is calculated. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete three-dimensional mold model.

[0056] In an optional embodiment, feature learning is performed on the training samples based on a multi-scale graph convolutional network and a dual-stream network, and the local geometric features and global topological features of the mold surface are extracted and optimized in combination with non-Euclidean space manifold learning. The local geometric features include curvature, normal vectors, and tangent vectors, and the global topological features include the connection relationship of feature points and boundary constraints, including:

[0057] Constructing a multi-scale graph structure modeling the training samples, including fine-grained graphs, medium-grained graphs, and coarse-grained graphs, and extracting a feature representation set through a multi-scale graph convolutional network with cross-scale information transfer;

[0058] A two-stream network architecture is used to separate feature representations. One branch extracts local geometric features including curvature, normal vectors, and tangent vectors, while the other branch extracts global topological features including connectivity and boundary constraints. A geometric constraint loss function is introduced to train the two-stream network. The geometric constraint loss function includes orthogonal constraints on normal and tangent vectors, unit length constraints on normal vectors, and curvature gradient constraints.

[0059] Based on the local geometric features, manifold learning is performed in a non-Euclidean space, a Riemannian metric tensor is constructed and geodesic distance is calculated, topological relationships are reconstructed using geodesic distance, global topological features are updated, and local geometric features are propagated and enhanced on the Riemannian manifold;

[0060] The enhanced local geometric features and updated global topological features are fused and normalized to obtain the final local geometric features and global topological features.

[0061] For example, using the CAD data of the mold, equidistant sampling is used to obtain the mold surface boundary contour. Feature points are extracted based on extreme points and inflection points to form training samples. A hierarchical sampling strategy is then used to construct three graph structures of different granularities. In the fine-grained graph, all vertices of the original model are retained, and the edge weights between adjacent vertices are set to 1.0. In the medium-grained graph, voxel downsampling is performed using a voxel size of 0.02, merging points within the same voxel into a single point. Edge weights are calculated based on the Euclidean distance between points, and connections are established between points with a distance less than 0.05. In the coarse-grained graph, further downsampling is performed using a voxel size of 0.05, and the edge establishment condition is that the distance between point pairs is less than 0.1. For example, for an original model with 10,000 vertices, the fine-grained graph retains all 10,000 vertices, the medium-grained graph contains approximately 2,500 vertices, and the coarse-grained graph contains approximately 500 vertices.

[0062] A four-layer multi-scale graph convolutional network is designed, with each layer consisting of three parallel graph convolution operations, one for each graph structure at three different granularities. In the first layer, the kernel size used is 16; in the second layer, 32; in the third layer, 64; and in the fourth layer, 128. Graph convolution aggregates features over the local neighborhood of each vertex. Information transfer is achieved through cross-scale connections. After convolution, each granularity level transfers features to the adjacent granularity level. Coarse-grained features are upsampled using nearest neighbor interpolation and fused with fine-grained features. Fine-grained features are then downsampled using average pooling and fused with coarse-grained features. A ReLU activation function is applied after each cross-scale information transfer, with a feature transfer ratio of 0.3. The network outputs a 256-dimensional feature representation.

[0063] A two-stream network architecture is used to separate feature representations. The local geometric feature branch consists of three fully connected layers with 256-dimensional features as input, hidden layer dimensions of 128 and 64, and an output dimension of 9, corresponding to the curvature value (1-dimensional), unit normal vector (3-dimensional), and tangent vector (5-dimensional, containing two orthogonal unit vectors). The global topological feature branch also consists of three fully connected layers with 256-dimensional features as input, hidden layer dimensions of 128 and 64, and an output dimension of 32, representing the point connection relationship encoding (16-dimensional) and boundary constraint encoding (16-dimensional). A geometric constraint loss function is constructed, with the vector and tangent vector orthogonality constraint, requiring the absolute value of the dot product of the normal vector and the two tangent vectors to be less than 0.01; the normal vector unit length constraint, requiring the difference between the normal vector's Euclidean norm and 1 to be less than 0.005; and the curvature gradient constraint, requiring the curvature change gradient between adjacent vertices to not exceed 0.2. The Adam optimizer is used for training, with the initial learning rate set to 0.001, decaying to 0.8 times the original rate every 50 cycles, the batch size is 32, and the training cycle is 200.

[0064] Based on local geometric features, manifold learning is performed in non-Euclidean space. The Riemannian metric tensor is constructed and the geodesic distance is calculated. The topological relationship is reconstructed using the geodesic distance, the global topological features are updated, and local geometric features are propagated and enhanced on the Riemannian manifold.

[0065] Local geometric feature normalization involves re-orthogonalizing normal and tangent vectors to ensure orthogonality error less than 0.001, normalizing normal vector length to 1.0, and limiting curvature values to the range [0, 1]. Global topological feature normalization involves converting connectivity encoding into a binary adjacency matrix and normalizing boundary constraint encoding using a softmax function. Feature fusion is achieved through feature concatenation to obtain a complete feature representation for each vertex.

[0066] The present invention realizes hierarchical feature extraction through a multi-scale graph convolutional network, avoiding information loss at a single scale; the dual-stream network architecture can effectively separate and enhance local geometric features and global topological features, ensuring the integrity of feature representation; the manifold learning method based on non-Euclidean geometric space improves the expressive ability of complex surface features, and geometric constraints and standardized processing ensure the physical rationality of the features.

[0067] In an optional embodiment, performing manifold learning in a non-Euclidean space based on the local geometric features, constructing a Riemannian metric tensor and calculating geodesic distances, reconstructing topological relationships using geodesic distances, updating global topological features, and performing local geometric feature propagation and enhancement on a Riemannian manifold include:

[0068] A local tangent space is constructed using the normal vector and tangent vector at each feature point on the die surface to obtain a local coordinate transformation matrix. The local coordinate transformation matrix is multiplied by a diagonal matrix containing curvature information to construct a Riemannian metric tensor reflecting the local surface characteristics. The distance field is initialized and the fast marching equation is solved under the Riemannian metric to calculate the geodesic distance. A distance matrix is constructed based on the geodesic distance. The connection relationship of the feature points on the die surface is reconstructed based on the distance matrix to obtain a new topological adjacency matrix, and the global topological features are updated.

[0069] A heat kernel operator based on geodesic distance is constructed, and its parameters are determined by diffusion time and geodesic distance. The heat kernel operator is used to construct a feature propagation equation on a Riemannian manifold to propagate local geometric features. Local curvature difference is introduced to calculate feature propagation weights, and local geometric features are enhanced through heat kernel weighted summation. The feature propagation weights are jointly determined by local curvature difference and geodesic distance.

[0070] For example, for a given 3D model surface, its vertex coordinates and facet information are obtained, an initial mesh topology is constructed, and the normal vector and principal curvature information are calculated at each vertex. Specifically, for each vertex v on the model surface i , by analyzing the vertex distribution in its first-order neighborhood, calculate the normal vector n of the point i The normal vector is calculated by weighted average of the normal vectors of adjacent patches, with the weight proportional to the patch area. For example, for vertex v i The surrounding K adjacent patches {f1, f2, ..., f K}, whose areas are {A1, A2, ..., A K}, the normal vectors are {n f1 , n f2 ,...,n fK}, then vertex v i Normal vector n iThe calculation is: multiply each patch normal vector by the corresponding patch area, sum them up, and then normalize the result.

[0071] Construct a local tangent space at each vertex. For vertex v i , whose normal vector is n i , select two mutually orthogonal and normal vector n i The unit vectors t are all orthogonal to each other. i1 and t i2 As the basis of the tangent space. These three vectors together form a transformation matrix T from the global coordinate system to the local coordinate system. i In the specific implementation, you can first randomly select a i For non-parallel vectors, the first tangent vector is obtained by cross product, and then the second tangent vector is obtained by cross product. Finally, the two tangent vectors are normalized.

[0072] After constructing the local coordinate transformation matrix, the Riemann metric tensor G that reflects the local surface characteristics is calculated i First, according to the principal curvatures k1 and k2 of each vertex (which can be obtained by local quadratic surface fitting), a diagonal matrix D containing curvature information is constructed. i The first two elements of its diagonal are 1 plus α multiplied by the square of two principal curvatures, and the third element is 1, where α is a parameter that controls the degree of curvature influence and can be set to a value between 0.5 and 2.0 in practical applications. i By the local coordinate transformation matrix T i With the diagonal matrix D i Multiply and add T i Multiply by the transpose of .

[0073] After the Riemann metric tensor is constructed, the distance field is initialized and the geodesic distance is calculated. For the calculation of the geodesic distance between any two points on the module surface, the fast marching method is used. First, select the starting point v s , initialize the distance field d, and set v s The distance of v is set to 0 and the distance of other points is set to infinity. Then, s Mark as "visited", mark its first-order neighbors as "narrowband" and calculate their distance to v s Iteratively, each time select the point v with the smallest distance from the "narrow band" min, mark it as "visited" and update the distances of its neighbors. When updating the distance, a local quadratic equation is solved under the Riemannian metric. For example, for a point in a triangle, its distance update needs to consider the distance propagated along the geodesic from two adjacent points with known distances, and the minimum value is selected as the new distance of the point. Repeat the above steps until all points are marked as "visited" or there are no points in the "narrow band". Repeat this process for each pair of feature points on the surface to construct the complete geodesic distance matrix D geo .

[0074] Based on the geodesic distance matrix, the topological relationship of the feature points of the die surface is reconstructed. For each feature point v i , select K points with the smallest geodesic distance as their new neighbors, and the value of K is usually set between 8 and 12. The new topological adjacency matrix A constructed in this way new It can more accurately reflect the intrinsic geometric structure of the mold surface, especially for models with high curvature areas. The new topological adjacency matrix Anew is combined with the original boundary constraint encoding to update the global topological features.

[0075] The mold surface feature points are embedded into a Riemannian manifold in a non-Euclidean space via local coordinate mapping. This is achieved through the following steps: Local geometric features of each feature point, including the normal vector, tangent vector, and curvature value, are collected and organized into a high-dimensional feature vector. A manifold learning algorithm (such as locally linear embedding or Laplace eigenmapping) is used to map the high-dimensional feature vector into a low-dimensional manifold space, preserving the local geometric relationships between points. During the mapping process, a distance-preserving constraint based on the Riemannian metric is introduced to ensure that the distances in the embedded space reflect the geodesic distances on the original surface. Finally, the embedded result is optimized by minimizing the strain energy function to more accurately preserve the original geometric structure. On this manifold, the distances between points are defined by geodesic distances, and the geometric structure is described by the Riemannian metric tensor. This representation better preserves the intrinsic geometric properties of the mold surface. For each feature point, its local neighborhood can be viewed as a tangent space on the manifold, and feature propagation and enhancement are performed in this non-Euclidean space. By combining manifold learning with geometric feature representation, the essential geometric structure of the mold surface can be effectively captured, especially for areas with complex curvature changes. The embedding result can better maintain the intrinsic properties of the surface than the Euclidean space representation, providing a spatial basis for the subsequent propagation of heat kernel features.

[0076] Construct a heat kernel operator H based on geodesic distance, for feature point v i and v j , thermonuclear element H ij Defined as: Take the geodesic distance D geoThe square of (i, j) is divided by four times the diffusion time t (usually set to the square of the local feature scale), and the negative exponent is taken. The diffusion time t controls the range of feature propagation. Smaller values of t confine feature propagation to the immediate neighborhood, while larger values of t propagate the feature over a wider range.

[0077] Based on the heat kernel operator, the local curvature difference is introduced to calculate the feature propagation weight W ij , for point v i and v j , calculate the absolute value of their average curvature difference, multiply it by an attenuation factor (inversely proportional to the geodesic distance), and then normalize it to get W ij In practical applications, the mean curvature can be obtained by the average of the principal curvatures k1 and k2.

[0078] The local geometric features are enhanced by heat kernel weighted summation. For each point v i The original local geometric features F i , its enhanced feature F i It is obtained by taking a weighted sum of the features of all points, where the weights are determined by the heat kernel element and the curvature difference weight. This method allows features to be smoothly propagated within regions of similar curvature while maintaining sharp boundaries where curvature changes suddenly.

[0079] Figure 2 This is a comparison chart of the connection accuracy of different methods in complex surface topology reconstruction. As shown in the figure, the horizontal axis represents the surface sampling density (points / mm 2 ), the vertical axis represents the topological connection accuracy (%). The topological reconstruction method of the present invention (diamond dot line) performs well at all sampling densities, even at low sampling density (1.25 points / mm 2 ) can also achieve an accuracy of nearly 90%, and at high sampling density (10 points / mm 2 ) can reach 98.7% under low sampling density. The traditional k-nearest neighbor algorithm (circular point line) has an accuracy rate of less than 70% under low sampling density; although the performance of the algorithm based on Euclidean Delaunay triangulation (square point line) is close under high sampling density, the effect is obviously insufficient in medium and low density areas. The present invention accurately expresses the local surface characteristics by constructing the Riemann metric tensor, and the topological reconstruction based on the geodesic distance can better reflect the intrinsic geometric structure of the mold surface; the thermal kernel operator realizes the adaptive propagation of features, and its weight takes into account the geodesic distance and curvature difference at the same time, so that the features can be smoothly propagated in similar areas while maintaining the boundary features; it significantly improves the accuracy of complex surface feature extraction, and is particularly suitable for mold surface processing with high curvature change areas, providing a reliable feature basis for subsequent supplementary mold surface generation.

[0080] In an optional embodiment, the local geometric features and global topological features are input into a generative adversarial network to generate a supplementary die surface, and the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface, including:

[0081] Based on local geometric features and global topological features, a supplementary die surface boundary condition including boundary normal vector, transition angle and transition depth is constructed, and the generator of the generative adversarial network is input through feature space mapping;

[0082] The generative adversarial network includes a multi-scale generator and a discriminator based on geometric priors. The discriminator evaluation indicators include geometric continuity constraints, curvature constraints based on target curvature distribution, and processing feasibility constraints of minimum curvature radius and tilt angle. The multi-scale generator sequentially generates mold surfaces with different geometric detail levels, and introduces a deformation field based on a spatial weight function and a local deformation operator to perform smooth transition processing on the boundary transition area.

[0083] A multi-objective optimization function including geometric loss, topological loss, machinability loss and adversarial loss is constructed to train the generative adversarial network, and the supplemented mold surface is obtained through iterative optimization.

[0084] For example, based on the extraction of local geometric features and global topological features, the original model is preprocessed, the model surface is parameterized using the boundary representation method, and the normal vector distribution of the boundary area is extracted. For example, the normal vector at the boundary is sampled at intervals of 10 degrees to form a boundary normal vector sequence. At the same time, the angle variation range of the boundary transition area is measured, with a typical value of 45 degrees to 90 degrees, as a transition angle constraint. The transition depth is set according to the actual application scenario, usually 1.5 to 2 times the boundary feature size, specifically set to 8mm in the case of a certain automobile front cover mold. The extracted boundary normal vector sequence is converted into a 512-dimensional feature vector, the transition angle is encoded as an 8-dimensional control parameter, and the transition depth is encoded as a scalar value, which together constitute the input feature. In actual applications, the number of boundary sampling points is 248, each point contains 3-dimensional normal vector information, and after feature encoding, it is input into the generator of the generative adversarial network.

[0085] The generative adversarial network architecture utilizes a multi-scale generator and a discriminator based on geometric priors. The multi-scale generator consists of three cascaded modules, each generating a mold surface of varying precision. The first-stage module generates a coarse mold surface with a 16×16 resolution, primarily determining the overall shape; the second-stage module increases the resolution to 64×64, adding mid-scale geometric details; and the third-stage module further increases the resolution to 256×256, generating fine geometric features. Each module employs a residual connection structure. During the generation process, a deformation field based on a spatial weight function is introduced to address boundary transitions. The deformation field is defined as a function of distance from the boundary, with a weight of 1 within 2 mm and gradually transitioning to 0 at 10 mm, achieving a smooth transition. The local deformation operator is implemented by weighted averaging the positions of neighboring vertices, using a 5×5 neighborhood window to calculate the local surface deformation.

[0086] The discriminator design integrates geometric prior knowledge, and the evaluation indicators include geometric continuity constraints, curvature constraints and processing feasibility constraints.

[0087] The network is trained using a multi-objective optimization function consisting of four types of losses: geometric loss, topological loss, machinability loss, and adversarial loss. The geometric loss assesses continuity at the mold surface boundary, with a weight of 0.4; the topological loss ensures that the generated mold surface is topologically consistent with the original model, with a weight of 0.3; the machinability loss assesses the satisfaction of curvature and tilt angle constraints, with a weight of 0.2; and the adversarial loss, derived from discriminator feedback, with a weight of 0.1. Training is performed iteratively using a batch size of 32 data, with an initial learning rate of 0.0002 and a 10% learning rate decay every 50 epochs. Training is considered converged when the total loss change is less than 0.001 over 10 consecutive epochs, resulting in the obtained supplementary mold surface.

[0088] The present invention uses a multi-scale generator to gradually refine the mold surface's geometric features, combining a spatial weighting function with a local deformation operator to achieve smooth boundary transitions. A discriminator incorporates geometric prior knowledge to comprehensively assess the geometric continuity and machinability of the generated mold surface. A multi-objective optimization function comprehensively considers geometry, topology, machinability, and countermeasure loss to ensure the quality of the generated mold surface. This effectively generates supplementary mold surfaces that meet actual engineering needs, particularly with significant advantages in handling boundary transition areas, significantly improving the efficiency and quality of mold design.

[0089] In an optional embodiment, the design of the discriminator includes:

[0090] Construct a multi-channel discriminant network structure, including a feature extraction layer, a constraint evaluation layer, and a decision layer; the feature extraction layer extracts multi-scale features of the mold surface through three-dimensional convolution and residual connection; the constraint evaluation layer includes a geometric continuity evaluation module, a curvature constraint evaluation module, and a processing feasibility evaluation module; the decision layer synthesizes the outputs of each evaluation module to obtain a discrimination result;

[0091] The geometric continuity evaluation module calculates the continuity scores of the position continuity, tangent continuity and curvature continuity of the die surface based on the Sobolev norm, and measures the degree of jump of each order derivative of the die surface at the boundary; the curvature constraint evaluation module constructs the curvature distribution prior of the target surface through the Gaussian mixture model, calculates the Wasserstein distance between the generated die surface and the target distribution, and identifies the curvature mutation area; the processing feasibility evaluation module evaluates the minimum curvature radius constraint and tool accessibility constraint of the die surface through curvature tensor estimation and tool angle distribution.

[0092] For example, in the construction of the feature extraction layer, a three-dimensional convolutional network is used to extract multi-scale features of the mold surface. The input is the three-dimensional mold surface data to be evaluated, represented as a voxel grid of size 128×128×128. Feature extraction is performed by designing four convolutional blocks, each of which contains two 3×3×3 three-dimensional convolutional layers with 32, 64, 128, and 256 kernels, respectively. Each convolutional layer is followed by batch normalization and a Reluctant Unit (ReLU) activation function, and max pooling is used between each convolutional block to reduce spatial resolution. To enhance the network's feature extraction capabilities, a residual connection mechanism is introduced, adding the output of the first convolutional block to the output of the third convolutional block, and the output of the second convolutional block to the output of the fourth convolutional block, to form a multi-scale feature fusion. This structure enables the feature extraction layer to capture multi-level feature information of the mold surface, from local details to global morphology.

[0093] The constraint evaluation layer contains three parallel evaluation modules, which respectively evaluate geometric continuity, curvature constraints and processing feasibility.

[0094] The geometric continuity assessment module is implemented by performing boundary detection on the input die surface data, identifying the boundary area of the die surface, and sampling the boundary width in units of 1 mm, with sampling points taken every 0.5 mm along the boundary. For each sampling point, the position value, first-order derivative (tangent direction), and second-order derivative (curvature) of the die surface at that point are calculated. Based on the Sobolev norm concept, the degree of jump in the die surface's various derivatives at the boundary is measured: first, a parameterized representation of both sides of the boundary is constructed, and the third-order derivative value is calculated at uniformly distributed parameter points. Then, the weighted Sobolev norm formula is applied to calculate the jump metric. The weight coefficient increases with the order of the derivative, reflecting the importance of higher-order continuity. Specifically, for zero-order continuity (position), the Euclidean distance of the corresponding points on the boundary is calculated, and the jump threshold is set to 0.01 mm; for first-order continuity (tangent direction), the angle of the tangent vector is calculated, and the jump threshold is set to 3 degrees; for second-order continuity (curvature), the L2 norm of the principal curvature difference is calculated, and the jump threshold is set to 0.05 mm-1; for third-order continuity (curvature change rate), the difference of the curvature gradient vector is calculated, and the jump threshold is set to 0.08 mm-2. The ratio of the jump value at the boundary sampling point to the corresponding threshold is exponentially mapped to generate a continuity score in the interval [0, 1]. The closer the value is to 1, the better the continuity. The final geometric continuity evaluation score is the weighted sum of the four scores, with weights of 0.15, 0.25, 0.35 and 0.25 respectively, reflecting the greater impact of high-order continuity on quality.

[0095] The curvature constraint assessment module is implemented by extracting curvature distribution features from a pre-annotated database of high-quality die surfaces. For each sample surface, the principal curvature values are calculated. A mixture model with five Gaussian components is used to fit the curvature distribution, obtaining the mean vector [-0.15, -0.05, 0, 0.05, 0.15] and the variance vector [0.01, 0.02, 0.02, 0.02, 0.01] as prior knowledge. The curvature distribution of the generated die surface is similarly calculated, and the curvature values of 150 feature points are extracted to construct an empirical distribution. The Wasserstein distance between the generated die surface's curvature distribution and the prior distribution is then calculated using an optimal transfer algorithm iterated 40 times. The smaller the distance, the closer the curvature distribution of the die surface is to the design requirements. Furthermore, regions of sudden curvature changes (i.e., regions where the curvature value of adjacent regions varies by more than 0.2 mm⁻¹) are identified, and the proportion of these regions to the total area is calculated. This proportion should not exceed 5%.

[0096] The implementation method of the processing feasibility assessment module is as follows: evaluate the minimum curvature radius constraint, uniformly sample the die surface, take 2000 surface points, and calculate the principal curvature value of each point. According to industry standards, the minimum curvature radius threshold is set to 3 mm, and the proportion of points with a curvature radius less than the threshold is counted. This proportion should be less than 1% to meet the processing requirements. Secondly, evaluate the tool accessibility constraint, calculate the normal vector of each point on the die surface, and construct a spherical histogram to represent the tool direction distribution. The histogram resolution is 10 degrees. According to the working range of the standard five-axis machining equipment, set the allowable tool angle range to check whether there are surface areas that cannot be reached by existing machining equipment. Count the area ratio of the inaccessible area, which should be less than 0.5%.

[0097] The decision-making layer assigns weights of 0.35, 0.4, and 0.25 to the evaluation scores of the three modules, respectively, and calculates the weighted sum to obtain a comprehensive score. A scoring threshold of 0.75 is set, and mold surfaces above this threshold are judged to meet design and processing requirements.

[0098] Figure 3 This is a comparison chart of the geometric continuity evaluation effect. It can be seen from the figure that the method of the present invention (diamond dotted line) decreases the evaluation score significantly faster than the traditional method when the degree of boundary jump increases. In particular, when the jump exceeds 0.015mm, the evaluation score of the present invention has dropped below 0.72, indicating that it can keenly capture the discontinuity problem at the boundary, while the traditional CNN and GAN methods still maintain a score above 0.85 at the same jump degree, indicating that they cannot effectively identify these subtle continuity problems. This increase in sensitivity enables the present invention to accurately detect the first-order continuity (C1) and second-order continuity (C2) problems at the mold surface boundary, while traditional methods are prone to miss these problems. The results show that the geometric continuity evaluation method based on the Sobolev norm has a higher sensitivity to high-order derivative jumps and can more comprehensively evaluate the mold surface quality. The multi-channel discriminant network designed in the present invention comprehensively evaluates the quality of the die surface through a three-layer architecture. The feature extraction layer uses three-dimensional convolution and residual connection to accurately capture multi-scale features; the constraint evaluation layer conducts a comprehensive analysis from three aspects: geometric continuity, curvature constraint and processing feasibility. It accurately measures the degree of jump of each order derivative at the boundary based on the Sobolev norm, evaluates the rationality of the curvature distribution through the Gaussian mixture model, and ensures the processing feasibility by combining the curvature tensor and tool angle distribution. The design effectively identifies die surface defects, prevents unqualified die surfaces from entering the production process, significantly improves the quality and efficiency of mold manufacturing, and reduces the rework rate.

[0099] In an optional embodiment, the design of the multi-scale generator includes:

[0100] A hierarchical generative network structure is constructed, including a feature encoding layer, a geometric decoding layer, and a detail enhancement layer. The feature encoding layer converts local geometric features and global topological features into latent feature representations through nonlinear mapping. The geometric decoding layer uses upsampling and skip connections to gradually restore the geometric shape of the mold surface, and introduces a self-attention mechanism at different scale levels to enhance feature association.

[0101] The detail enhancement layer receives the output of the geometric decoding layer and constructs a deformation field based on a spatial weight function and a local deformation operator, wherein the spatial weight function is determined by the boundary distance and feature similarity, and the local deformation operator includes stretching, bending and torsion deformation basis functions; a smooth transition is achieved in the boundary transition area through the deformation field.

[0102] Exemplarily, the multi-scale generator consists of three cascaded modules, each of which consists of a feature encoding layer, a geometric decoding layer, and a detail enhancement layer. The feature encoding layer is responsible for converting the input local geometric features and global topological features into latent feature representations. The feature encoding layer uses a five-layer convolutional network structure, with each layer having a convolution kernel size of 3×3, a stride of 2, and the number of channels being 64, 128, 256, 512, and 512, respectively. Batch normalization and ReLU activation functions are applied after each convolution layer to improve nonlinear expression capabilities. For example, for an input mesh containing 10,000 vertices, after processing through the feature encoding layer, a 512-dimensional latent feature vector is generated, which contains the main geometric and topological information of the model.

[0103] The geometric decoding layer consists of five transposed convolutional networks. Each layer has a transposed convolution kernel size of 4×4, a stride of 2, and the number of channels is 512, 256, 128, 64, and 32, respectively. During the decoding process, a skip connection mechanism is introduced to concatenate the feature maps of the corresponding layers of the encoding layer with the feature maps of the decoding layer to enhance feature transfer. For example, the 64-channel feature map of the first encoding layer is concatenated with the 64-channel feature map of the second-to-last decoding layer. In addition, a self-attention mechanism is introduced in the second and fourth decoding layers to enhance the global correlation of features by calculating the correlation between each position within the feature map. The self-attention module first projects the input feature map into the query, key, and value feature spaces. It then calculates the similarity matrix between the query and the key, and performs weighted aggregation on the value features. In the actual implementation, for a 256×256 resolution feature map, the similarity matrix calculated by the self-attention is 65536×65536. Block processing is used to reduce computational complexity, with a block size of 32×32.

[0104] The detail enhancement layer is a key component of the multi-scale generator, responsible for enhancing local details based on the output of the geometric decoding layer. The detail enhancement layer receives the coarse grid output by the geometric decoding layer and constructs a deformation field based on the spatial weight function and the local deformation operator. In the specific implementation, the spatial weight function consists of two parts: boundary distance and feature similarity: In the boundary distance part, for each vertex on the grid, the shortest distance to the boundary is calculated. For example, for vertex P, its coordinates are (x, y, z), and its Euclidean distance to all boundary points is calculated, and the minimum value is taken as the boundary distance D(P). The distance is then mapped to the range of 0 to 1 through a normalization function to form a distance weight W d (P), calculated as 1 minus the natural logarithm base, the negative boundary distance divided by the parameter σ d is the exponential function value of the power, where σ d In order to control the decay rate parameter, the value is set to 2 times the average side length of the model in practice. The feature similarity part calculates the similarity weight based on the local geometric features of the vertex. For vertex P, its local feature vector F(P) is extracted, including the normal vector, mean curvature and Gaussian curvature, and compared with the reference feature F ref Calculate the similarity and get the similarity weight W s (P), calculated as the natural logarithm base, the square norm of the difference of negative eigenvectors divided by the parameter σ s The square of the exponential function is the power of s Controls the tolerance of feature differences, and the value is 0.3 in practice.

[0105] The final spatial weight function W(P) is the weighted sum of the boundary distance weight and the feature similarity weight, which is calculated as α multiplied by the distance weight plus (1-α) multiplied by the similarity weight, where α is a balance parameter that is adjusted according to actual application and is generally taken as 0.7.

[0106] The local deformation operator includes three basic deformation functions: stretching, bending and torsion. The stretching deformation is based on the radial displacement. For the vertex P, the stretching deformation is T stretch (P) = W(P)·S·(PC), where C is the center of deformation and S is the stretch coefficient matrix. Different stretch coefficients can be set for different directions. For example, [1.2, 0.8, 1.0] means 20% stretch in the x direction and 20% compression in the y direction. Bending deformation is based on curvature control, T bend (P) = W(P)·B·sin(θ·||PC|| / R)·N, where B is the bending strength, θ is the bending angle, R is the influence radius, and N is the bending direction vector. Torsional deformation is controlled based on the rotation angle, T twist (P) = W(P)·rot(PC, A, ω·||PC||), where rot represents rotation around axis A and ω is the torsion angle coefficient.

[0107] In the boundary transition region, the deformation field achieves a smooth transition. For the identified boundary transition region, defined as the area within a distance from the boundary less than a threshold δ (in practice, δ is set to 5 times the average edge length), a special transition function β(P) = (1-cos(π·D(P) / δ)) / 2 is applied to smoothly transition the deformation from 0 at the boundary to the full deformation in the interior region. The final deformation of each vertex is equal to the transition function value multiplied by the sum of the three deformations: tensile deformation, bending deformation, and torsional deformation.

[0108] Traditional mold patching technology is mainly based on geometric interpolation and surface fitting methods. It is often difficult to ensure geometric continuity and manufacturing feasibility when processing mold surfaces with complex topology and geometric features. Existing three-dimensional shape generation methods based on deep learning usually adopt a single encoding-decoding architecture, lack of effective utilization of features of different scales, and have obvious deficiencies in model detail expression and boundary transition processing. The present invention proposes a hierarchical generation network structure, which makes three innovative improvements in design: it introduces a three-layer cascaded feature processing architecture (feature encoding layer, geometric decoding layer and detail enhancement layer), which can more effectively process multi-scale feature information compared to the single encoding-decoding structure of the prior art. The feature encoding layer adopts a five-layer progressive convolutional structure, uses batch normalization and ReLU activation functions to enhance nonlinear expression capabilities, and can extract richer semantic information from the input geometric topological features; the geometric decoding layer innovatively introduces skip connections and self-attention mechanisms in the transposed convolutional network, and through cross-layer feature fusion and global correlation modeling, effectively solves the problems of insufficient feature transfer and difficulty in local-global information coordination in traditional methods; the detail enhancement layer is the core technological innovation of the present invention, which achieves precise control of mold surface details through a carefully designed spatial weight function and local deformation operator system. The present invention improves the processing method of the boundary transition area, innovatively proposes a dual weight function based on boundary distance and feature similarity, and combines the cosine transition function to achieve a smooth connection of the mold surface boundary, solving the problem of discontinuity and stress concentration at the boundary of the existing technology. The deformation field construction technology of the present invention takes into account both geometric feature preservation and manufacturing process requirements. Through the combination of three basic deformation functions of stretching, bending and torsion, it achieves precise control of complex surface morphology while ensuring the manufacturing feasibility of the generated mold surface. The present invention improves the geometric continuity and local detail fidelity of the generated die surface, solves the continuity and smoothness problems of traditional methods in complex surface boundary processing, and ensures the machinability of the die surface.

[0109] In an optional embodiment, stress field constraint verification is performed on the supplementary mold surface, and the stress distribution of the mold surface during the molding process is calculated. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete mold three-dimensional model, including:

[0110] The supplementary die surface is used as a boundary condition to define the material parameters, temperature field, and pressure field of the molding process. Adaptive meshing technology is used for discretization. The stress distribution is obtained by solving the thermal-mechanical-fluid coupling control equations to obtain the stress field. The maximum equivalent stress value and stress concentration factor are evaluated based on the stress field. When stress violation areas exist, local deformation functions are used for optimization until the preset threshold is met.

[0111] For the supplementary die surface that meets the stress constraints, a sequence of feature points is extracted based on its boundary contour, and a radial basis function is constructed as the transition region mapping operator. The influence range is controlled by adjusting the support radius. The transition surface is constructed using piecewise Hermite spline interpolation to ensure positional continuity and tangential continuity. Multi-resolution B-spline parameterized representation is used for model fusion, in which the B-spline control points are determined by least squares fitting, and the control grid density is adaptively adjusted by the curvature distribution. Laplace smoothing based on curvature weight is applied to the fusion area to obtain a complete three-dimensional mold model.

[0112] For example, the supplementary die surface is imported into the analysis system as a boundary condition to define the material parameters, temperature field, and pressure field of the molding process. Material parameters include elastic modulus, Poisson's ratio, yield strength, and thermal expansion coefficient. Taking mold steel SKD61 as an example, the elastic modulus is 210GPa, the Poisson's ratio is 0.3, the yield strength is 1200MPa, and the thermal expansion coefficient is 11.9×10 -6 The temperature field is set to an operating temperature of 450°C and an ambient temperature of 25°C, reflecting the actual molding process conditions. The pressure field is set to an injection pressure of 80 MPa, a holding pressure of 40 MPa, and a pressure application time of 10 seconds. These load conditions will be converted into nodal forces through subsequent mesh discretization.

[0113] Adaptive meshing technology is used for discretization. This technology serves as a bridge between the early physical parameter definition and the later solution calculation. The initial mesh unit size is set to 2mm. In the areas of large curvature changes and expected stress concentration areas of the previously defined supplementary mold surface, the mesh size is automatically optimized to 0.2mm. The adaptive meshing strategy is based on the geometric characteristics and estimated mechanical behavior of the early model, and ensures the accuracy of the areas of interest in subsequent analysis through iterative refinement. Taking a complex cavity mold as an example, the total number of mesh units reaches 150,000, of which the supplementary mold surface area accounts for approximately 30,000 units. The geometric accuracy of the model after meshing is controlled within 0.01mm.

[0114] Based on the high-quality mesh generated by adaptive meshing, the stress distribution is obtained by solving the coupled thermal-mechanical-fluid equations. These equations include the temperature field equation, the displacement field equation, and the fluid flow equation. The temperature field equation describes the conduction, convection, and radiation of heat in the mold, taking into account the interaction between the injection temperature of 450°C and the mold wall temperature. The displacement field equation describes the deformation behavior of the mold under the influence of temperature and pressure, accounting for thermal stresses caused by temperature gradients and mechanical stresses caused by injection pressure. The fluid flow equation describes the flow of the molten material in the mold, considering the filling process at an injection pressure of 80 MPa and the densification process at a holding pressure of 40 MPa. The solution process adopts a step-by-step coupling strategy: the first step solves the fluid flow and heat transfer to obtain the temperature distribution; the second step uses the temperature as a load input into the mechanical analysis to calculate the coupled thermal-mechanical stresses. The calculation uses the finite element method with a time step of 0.1 seconds, and the total calculation time is equivalent to one complete mold working cycle (approximately 60 seconds). During the calculation, the temperature, displacement, strain, and stress values of each mesh node are recorded at each time to generate complete stress field data. Taking the aforementioned mold as an example, the maximum temperature gradient occurs 2.5 seconds after the start of injection, reaching 85°C / mm. The maximum equivalent stress occurs during the holding phase, at the junction of the supplementary and original mold surfaces. Precise meshing enables the stress value in this critical area to be accurately calculated as 850 MPa. This data will serve as the basis for subsequent stress assessment and possible optimization of local deformation.

[0115] The mold material safety threshold is set at 75% of the yield strength, or 900 MPa. The stress concentration factor is calculated as the ratio of the local maximum stress to the nominal stress, with a threshold of 2.5. In the above example, the maximum equivalent stress is 850 MPa, which is less than the safety threshold of 900 MPa. The maximum stress concentration factor is 2.3, meeting the requirement of less than 2.5, thus satisfying the stress constraint for this supplementary mold surface. If stress violation areas exist, optimization is performed using a local deformation function. A local deformation algorithm based on radial basis functions is used to geometrically correct the stress-exceeding areas. For example, in the mold corner area, when the stress at the corner reaches 950 MPa, exceeding the threshold, the corner radius is increased from 0.5 mm to 1.2 mm, reducing the maximum stress to 870 MPa, meeting the preset threshold. The local deformation area is set as a spherical region with a radius of 10 mm centered at the stress violation point to ensure smooth deformation transitions. The optimization process is iterative until stress values in all areas meet the requirements.

[0116] For supplementary mold surfaces that meet stress constraints, they need to be fused with the original mold model to obtain a complete 3D mold model. The interface between the supplementary mold surface and the original mold must be precisely identified. This is achieved by executing a boundary detection algorithm. Based on geometric topology analysis, the algorithm locates the boundary contours of the two models and generates a closed boundary curve. The detection algorithm uses a gradient search method to locate surface discontinuities with an accuracy of 0.01 mm, ensuring that all boundary features are fully captured.

[0117] Based on the identified boundary contour, a sequence of feature points is extracted. The feature point extraction adopts an adaptive sampling strategy and dynamically adjusts the sampling density based on the change of local curvature. Specifically, the curvature value of each point on the boundary curve is calculated, and the sampling point density is dynamically allocated according to the curvature size: in areas where the curvature value is greater than 0.5 / mm (such as sharp corners and small radius areas), the feature point spacing is set to a minimum value of 0.2mm; in smooth areas where the curvature value is less than 0.1 / mm, the feature point spacing is set to a maximum value of 2.0mm; the sampling spacing in intermediate curvature areas is determined by linear interpolation. Taking a complex boundary with a length of 500mm as an example, the strategy extracts an average of about 500 feature points, of which about 40% are located in high curvature areas and 60% are distributed in flat areas, ensuring that key geometric features are not missed while keeping the data volume reasonable.

[0118] Constructing radial basis function as the transition region mapping operator is the core step to achieve smooth fusion of the supplementary mold surface and the original model. The construction of radial basis function uses multi-quadratic function as the basic form, which is defined as: φ(r)=(r 2 +c 2 ) (1 / 2) , where r is the distance from the spatial point to the feature point, and c is a shape parameter with a value between 0.1 and 1.0, which is adjusted according to the complexity of the boundary. Each feature point is associated with a radial basis function to form a function set, which is used to control spatial deformation. The influence range of each function is controlled by adjusting the support radius. The support radius is set to 1.5 times the distance from the feature boundary line to the nearest internal feature, usually 3-8mm. For example, in the mold parting surface area, if the distance from the feature boundary to the nearest internal feature is 3.3mm, the support radius is set to 5mm. If the support radius is too small, the transition will be uneven, and if it is too large, it may affect the area far away from the boundary. By setting it to 1.5 times the nearest feature distance, excessive influence can be avoided while ensuring smoothness.

[0119] The transition surface is constructed using piecewise Hermite spline interpolation, ensuring high-order continuity at the junction of the supplementary mold surface and the original mold. For each extracted feature point, its position coordinates and normal vector are calculated. Then, for the region between adjacent feature points, a cubic Hermite spline is constructed, which takes into account the position and tangential information of the endpoints. This construction method ensures positional and tangential continuity of the curve at the feature points. To obtain a complete transition surface, a uniform sampling grid is set in parameter space with a sampling point interval of 0.5 mm. The coordinates of each sampling point in three-dimensional space are calculated to form a detailed point cloud data.

[0120] A multi-resolution B-spline parametric representation is used for model fusion, and the point cloud data obtained in the previous step is converted into a parametric surface representation. To determine the position of the control points, the least squares fitting method is used to determine the optimal control point coordinates by solving the set of equations. The initial control point grid density is set to 10×10 control points in each direction (a total of 100), and the fitting accuracy is controlled within 0.005mm. The control grid density is adaptively adjusted by the curvature distribution: the curvature threshold is set to 0.3 / mm. When the local curvature exceeds the threshold, additional control points are inserted in the area to reduce the control point spacing to 1 / 3 of the original; areas with curvature less than 0.1 / mm maintain the original density. Taking a complex cavity mold as an example, after adaptive encryption processing, the total number of control points increased from the initial 100 to approximately 180, of which approximately 60% of the increase was concentrated in the high curvature area.

[0121] Curvature-weighted Laplace smoothing was applied to the fused region to further optimize surface quality. The weights were designed using an adaptive curvature-based weighting function: regions of high curvature had weights close to 0 to preserve geometric features, while regions of low curvature had weights close to 1 for a stronger smoothing effect. A smoothing strength coefficient of 0.3 was set to achieve a balance between smoothing and geometric feature preservation. The smoothing process was iterated five times, and the maximum surface deviation was calculated after each iteration to ensure it did not exceed 0.02 mm to avoid loss of geometric detail due to over-smoothing.

[0122] After the above steps, the final complete mold 3D model not only meets the stress field constraint conditions and ensures structural safety, but also achieves high-quality geometric fusion of the supplementary mold surface and the original mold, ensuring surface continuity and smoothness, laying the foundation for subsequent mold processing and manufacturing.

[0123] The present invention effectively solves the problems of stress safety and geometric continuity in the design of the supplementary die surface of the mold through stress analysis and geometric fusion processing; stress field constraint verification ensures that the mold will not fail due to excessive stress under actual working conditions, thereby extending the service life of the mold; geometric fusion technology based on radial basis functions and Hermite splines realizes high-quality connection between the supplementary die surface and the original mold, ensures the continuity and smoothness of the mold surface, and improves the quality of the molded product and the durability of the mold; the overall solution shortens the mold design and manufacturing cycle, reduces trial and error costs, and is particularly suitable for the rapid development and manufacturing of high-end precision molds.

[0124] A second aspect of an embodiment of the present invention provides a system for automatically supplementing and generating mold process surfaces based on deep learning, comprising:

[0125] The first unit is used to extract the mold surface contour line and feature point information of the mold to be processed as a training sample;

[0126] The second unit is used to perform feature learning on the training samples based on a multi-scale graph convolutional network and a two-stream network, and extract and optimize the local geometric features and global topological features of the mold surface in combination with non-Euclidean space manifold learning, wherein the local geometric features include curvature, normal vector and tangent vector, and the global topological features include the connection relationship and boundary constraints of feature points;

[0127] The third unit is used to input the local geometric features and global topological features into a generative adversarial network to generate a supplementary die surface, and the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface;

[0128] The fourth unit is used to verify the stress field constraints of the supplementary mold surface and calculate the stress distribution of the mold surface during the molding process. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete three-dimensional mold model.

[0129] According to a third aspect of an embodiment of the present invention, an electronic device is provided, including:

[0130] processor;

[0131] a memory for storing processor-executable instructions;

[0132] The processor is configured to call the instructions stored in the memory to execute the aforementioned method.

[0133] According to a fourth aspect of an embodiment of the present invention, a computer-readable storage medium is provided, on which computer program instructions are stored. When the computer program instructions are executed by a processor, the method described above is implemented.

[0134] The present invention may be a method, an apparatus, a system and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for executing various aspects of the present invention.

[0135] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for automatically supplementing and generating mold process surfaces based on deep learning, characterized in that: include: Extract the mold surface contour lines and feature point information of the mold to be processed as training samples; Performing feature learning on the training samples based on a multi-scale graph convolutional network and a dual-stream network, and extracting and optimizing local geometric features and global topological features of the die surface by combining non-Euclidean space manifold learning, wherein the local geometric features include curvature, normal vectors, and tangent vectors, and the global topological features include connection relationships and boundary constraints of feature points; Inputting the local geometric features and global topological features into a generative adversarial network to generate a supplementary die surface, wherein the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface; The supplementary mold surface is subjected to stress field constraint verification, and the stress distribution of the mold surface during the forming process is calculated. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete three-dimensional mold model.

2. The method according to claim 1, characterized in that Based on the multi-scale graph convolutional network and the two-stream network, the training samples are subjected to feature learning. The local geometric features and global topological features of the die surface are extracted and optimized in combination with non-Euclidean space manifold learning. The local geometric features include curvature, normal vector and tangent vector. The global topological features include the connection relationship of feature points and boundary constraints, including: Constructing a multi-scale graph structure modeling the training samples, including fine-grained graphs, medium-grained graphs, and coarse-grained graphs, and extracting a feature representation set through a multi-scale graph convolutional network with cross-scale information transfer; A two-stream network architecture is used to separate feature representations. One branch extracts local geometric features including curvature, normal vectors, and tangent vectors, while the other branch extracts global topological features including connectivity and boundary constraints. A geometric constraint loss function is introduced to train the two-stream network. The geometric constraint loss function includes orthogonal constraints on normal and tangent vectors, unit length constraints on normal vectors, and curvature gradient constraints. Based on the local geometric features, manifold learning is performed in a non-Euclidean space, a Riemannian metric tensor is constructed and geodesic distance is calculated, topological relationships are reconstructed using geodesic distance, global topological features are updated, and local geometric features are propagated and enhanced on the Riemannian manifold; The enhanced local geometric features and updated global topological features are fused and normalized to obtain the final local geometric features and global topological features.

3. The method according to claim 2, characterized in that Based on the local geometric features, manifold learning is performed in a non-Euclidean space, a Riemannian metric tensor is constructed and geodesic distance is calculated, topological relationships are reconstructed using geodesic distance, global topological features are updated, and local geometric feature propagation and enhancement are performed on the Riemannian manifold, including: A local tangent space is constructed using the normal vector and tangent vector at each feature point on the die surface to obtain a local coordinate transformation matrix. The local coordinate transformation matrix is multiplied by a diagonal matrix containing curvature information to construct a Riemannian metric tensor reflecting the local surface characteristics. The distance field is initialized and the fast marching equation is solved under the Riemannian metric to calculate the geodesic distance. A distance matrix is constructed based on the geodesic distance. The connection relationship of the feature points on the die surface is reconstructed based on the distance matrix to obtain a new topological adjacency matrix, and the global topological features are updated. A heat kernel operator based on geodesic distance is constructed, and its parameters are determined by diffusion time and geodesic distance. The heat kernel operator is used to construct a feature propagation equation on a Riemannian manifold to propagate local geometric features. Local curvature difference is introduced to calculate feature propagation weights, and local geometric features are enhanced through heat kernel weighted summation. The feature propagation weights are jointly determined by local curvature difference and geodesic distance.

4. The method according to claim 1, wherein Inputting the local geometric features and the global topological features into a generative adversarial network to generate a supplementary die surface, wherein the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface, including: Based on local geometric features and global topological features, a supplementary die surface boundary condition including boundary normal vector, transition angle and transition depth is constructed, and the generator of the generative adversarial network is input through feature space mapping; The generative adversarial network includes a multi-scale generator and a discriminator based on geometric priors. The discriminator evaluation indicators include geometric continuity constraints, curvature constraints based on target curvature distribution, and processing feasibility constraints of minimum curvature radius and tilt angle. The multi-scale generator sequentially generates mold surfaces with different geometric detail levels, and introduces a deformation field based on a spatial weight function and a local deformation operator to perform smooth transition processing on the boundary transition area. A multi-objective optimization function including geometric loss, topological loss, machinability loss and adversarial loss is constructed to train the generative adversarial network, and the supplemented mold surface is obtained through iterative optimization.

5. The method according to claim 4, characterized in that The design of the discriminator includes: Construct a multi-channel discriminant network structure, including a feature extraction layer, a constraint evaluation layer, and a decision layer; the feature extraction layer extracts multi-scale features of the mold surface through three-dimensional convolution and residual connection; the constraint evaluation layer includes a geometric continuity evaluation module, a curvature constraint evaluation module, and a processing feasibility evaluation module; the decision layer synthesizes the outputs of each evaluation module to obtain a discrimination result; The geometric continuity evaluation module calculates the continuity scores of the position continuity, tangent continuity and curvature continuity of the die surface based on the Sobolev norm, and measures the degree of jump of each order derivative of the die surface at the boundary; the curvature constraint evaluation module constructs the curvature distribution prior of the target surface through the Gaussian mixture model, calculates the Wasserstein distance between the generated die surface and the target distribution, and identifies the curvature mutation area; the processing feasibility evaluation module evaluates the minimum curvature radius constraint and tool accessibility constraint of the die surface through curvature tensor estimation and tool angle distribution.

6. The method according to claim 4, characterized in that The design of the multi-scale generator includes: A hierarchical generative network structure is constructed, including a feature encoding layer, a geometric decoding layer, and a detail enhancement layer. The feature encoding layer converts local geometric features and global topological features into latent feature representations through nonlinear mapping. The geometric decoding layer uses upsampling and skip connections to gradually restore the geometric shape of the mold surface, and introduces a self-attention mechanism at different scale levels to enhance feature association. The detail enhancement layer receives the output of the geometric decoding layer and constructs a deformation field based on a spatial weight function and a local deformation operator, wherein the spatial weight function is determined by the boundary distance and feature similarity, and the local deformation operator includes stretching, bending and torsion deformation basis functions; a smooth transition is achieved in the boundary transition area through the deformation field.

7. The method according to claim 1, characterized in that The supplementary mold surface is subjected to stress field constraint verification, and the stress distribution of the mold surface during the molding process is calculated. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete mold three-dimensional model including: The supplementary die surface is used as a boundary condition to define the material parameters, temperature field, and pressure field of the molding process. Adaptive meshing technology is used for discretization. The stress distribution is obtained by solving the thermal-mechanical-fluid coupling control equations to obtain the stress field. The maximum equivalent stress value and stress concentration factor are evaluated based on the stress field. When stress violation areas exist, local deformation functions are used for optimization until the preset threshold is met. For the supplementary die surface that meets the stress constraints, a sequence of feature points is extracted based on its boundary contour, and a radial basis function is constructed as the transition region mapping operator. The influence range is controlled by adjusting the support radius. The transition surface is constructed using piecewise Hermite spline interpolation to ensure positional continuity and tangential continuity. Multi-resolution B-spline parameterized representation is used for model fusion, in which the B-spline control points are determined by least squares fitting, and the control grid density is adaptively adjusted by the curvature distribution. Laplace smoothing based on curvature weight is applied to the fusion area to obtain a complete three-dimensional mold model.

8. A deep learning-based automatic supplementation and generation system for mold process die surfaces, used to implement the method described in any one of claims 1 to 7, characterized in that: include: The first unit is used to extract the mold surface contour line and feature point information of the mold to be processed as a training sample; The second unit is used to perform feature learning on the training samples based on a multi-scale graph convolutional network and a two-stream network, and extract and optimize the local geometric features and global topological features of the mold surface in combination with non-Euclidean space manifold learning, wherein the local geometric features include curvature, normal vector and tangent vector, and the global topological features include the connection relationship and boundary constraints of feature points; The third unit is used to input the local geometric features and global topological features into a generative adversarial network to generate a supplementary die surface, and the discriminator of the generative adversarial network is used to evaluate the geometric continuity and processing feasibility of the generated die surface; The fourth unit is used to verify the stress field constraints of the supplementary mold surface and calculate the stress distribution of the mold surface during the molding process. When the stress distribution meets the requirements, the supplementary mold surface is merged with the original mold model to obtain a complete three-dimensional mold model.

9. An electronic device, characterized in that: include: processor; a memory for storing processor-executable instructions; The processor is configured to call the instructions stored in the memory to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having computer program instructions stored thereon, characterized in that: When the computer program instructions are executed by a processor, the method according to any one of claims 1 to 7 is implemented.

Images