A compensation control method and system for a composite material forming tool

Abstract

The application provides a kind of compensation control method and system of composite material forming tool, comprising obtaining tool initial three-dimensional grid model, constructing node contains initial geometric feature tensor of principal curvature unit vector and curvature value;Input process parameters to parameter coding sub-network to obtain multi-objective modulation vector;Lightweight network hierarchical extraction geometry features, shallow asymmetric convolution kernel is aligned with local principal curvature, deep mapping three-dimensional coordinates to two-dimensional space, by the first part of modulation vector Adjustment B-spline control point generates interpolation kernel aggregation features to obtain geometry feature map;Then use modulation vector second, third part to obtain affine scale, translation factor transformation features, linear combination coefficient is output by regression head;With the fourth part to generate modal adjustment weight and adjust orthogonal basis, obtain modal displacement base, weighted sum of both and scale transformation reconstruction three-dimensional displacement field, according to field calculation compensation displacement correction grid model, output compensation tool control model.

Description

Technical Field

[0001] This application belongs to the field of composite materials, and in particular relates to a compensation control method and system for composite material molding tooling. Background Technology

[0002] Composite materials, due to their high specific strength, high specific stiffness, and strong designability, have been widely used in aerospace, automotive manufacturing, and high-end equipment industries. However, during the molding process of composite materials, the coupling of multiple factors, such as the chemical curing shrinkage of the resin matrix, the anisotropic thermal expansion of the material, and the interaction between the molding tooling and the component, can easily generate residual stress within the component and cause irreversible curing deformation. Such geometric deviations not only affect the assembly accuracy and aerodynamic shape of the product but also increase manufacturing rework costs and material waste. To ensure the dimensional accuracy of composite material components, it is usually necessary to perform reverse compensation design on the tooling mold surface before molding. Traditional tooling compensation methods mainly rely on manual trial and error or finite element numerical simulation. Among them, the trial and error method is time-consuming, costly, and difficult to adapt to complex curved surface components; although finite element simulation has high prediction accuracy, when dealing with large structures, the modeling process is cumbersome, the nonlinear calculation is complex, and it requires a lot of computing resources and time, which is difficult to meet the needs of modern industry for rapid iteration and efficient design of composite material molding tooling.

[0003] The deformation of composite material molding is typically formed by the combined effects of three-dimensional spatial geometric features and multi-dimensional molding process parameters. Existing network models, when dealing with such problems, often suffer from large parameter scales and high computational loads due to conventional 3D neural networks, hindering lightweight deployment. Furthermore, when faced with variable 3D mesh models, the models lack the ability to recognize key geometric features such as local surface curvature changes, resulting in insufficient feature extraction. Current deep learning methods often simply linearly concatenate spatial geometric information with process parameters, lacking deeper fusion and modulation mechanisms. In the 3D displacement field reconstruction stage, it is also difficult to combine spatial orthogonal basis functions and scale transformations to achieve continuous and smooth displacement representation. These shortcomings cause existing prediction models to suffer from insufficient generalization ability, poor smoothness of displacement field reconstruction, and limited compensation accuracy when facing tooling models with different process conditions and mesh divisions. Therefore, there is an urgent need for a 3D deformation compensation control method that balances lightweight network structure with multi-scale feature fusion capabilities to achieve efficient reverse compensation for composite material molding tooling. Summary of the Invention

[0004] According to a first aspect of the present invention, a compensation control method for a composite material molding tooling is proposed for realizing reverse compensation of the composite material molding tooling, comprising the following steps:

[0005] An initial 3D mesh model of the composite material molding tooling is obtained. The unit vectors and curvature values ​​of the mesh model nodes along the principal curvature direction are calculated to form the initial geometric feature tensor of the nodes. Molding process parameters are obtained and input into the parameter encoding sub-network to generate a multi-objective modulation vector. A lightweight network structure is used to extract geometric feature maps from the initial geometric feature tensor of the nodes at multiple scales. The shallow layer of the network structure uses an asymmetric convolution kernel with the calculation direction aligned with the local principal curvature direction of the nodes. The deep layer maps the 3D coordinates of the nodes to a 2D parameter space and then uses an interpolation kernel function to perform feature aggregation. The interpolation kernel function is generated by adjusting the first part of the multi-objective modulation vector through the reference B-spline kernel weight control points. The scaling and translation factors of the affine transformation are calculated using the second and third parts of the multi-objective modulation vector, and the geometric feature map is transformed element-wise to obtain the process-modulated geometric features. The process-modulated geometric features are input into the regression prediction head, which outputs a set of linear combination coefficients. The fourth part of the multi-objective modulation vector is used to adjust the weights of the orthogonal basis function set to generate a modal displacement basis. The linear combination coefficients and the modal displacement basis are weighted and summed, and the three-dimensional displacement prediction field is reconstructed by combining the scaling transformation parameters. The compensation displacement vector of the calculation node based on the three-dimensional displacement prediction field is applied to the initial three-dimensional mesh model to generate the compensated tooling control model.

[0006] According to a second aspect of the present invention, a compensation control system for a composite material molding tooling is provided, comprising the following modules: The computation module is used to acquire the initial three-dimensional mesh model of the composite material molding tooling, and to calculate the unit vector and curvature value of the mesh model nodes along the principal curvature direction to form the initial geometric feature tensor of the nodes; to acquire molding process parameters and input them into the parameter encoding sub-network to generate a multi-objective modulation vector; and to use a lightweight network structure to perform multi-scale feature extraction on the initial geometric feature tensor of the nodes to generate a geometric feature map. The shallow layer of the network structure uses an asymmetric convolution kernel, and the calculation direction is aligned with the local principal curvature direction of the nodes. The deep layer maps the three-dimensional coordinates of the nodes to a two-dimensional parameter space and then uses an interpolation kernel function to perform feature aggregation. The interpolation kernel function is generated by adjusting the first part of the multi-objective modulation vector through the reference B-spline kernel weight control points. The generation module is used to calculate the scaling factor and translation factor of the affine transformation using the second and third parts of the multi-objective modulation vector, and perform element-wise transformation on the geometric feature map to obtain process-modulated geometric features; input the process-modulated geometric features into the regression prediction head to output a set of linear combination coefficients, and use the fourth part of the multi-objective modulation vector to adjust the weights of the orthogonal basis function set to generate a modal displacement basis; perform a weighted summation of the linear combination coefficients and the modal displacement basis, and reconstruct a three-dimensional displacement prediction field by combining the scaling transformation parameters; apply the compensation displacement vector of the calculation node based on the three-dimensional displacement prediction field to the initial three-dimensional mesh model to generate a compensated tooling control model.

[0007] This invention constructs initial geometric features by extracting unit vectors and curvature values ​​along the principal curvature directions. It then combines these with asymmetric convolution kernels aligned with the local principal curvature directions and two-dimensional parametric space interpolation kernels for feature aggregation, enhancing the tooling geometric feature extraction capability while maintaining a lightweight network. A multi-objective modulation vector is generated through a parametric encoding network and used for kernel function adjustment, feature map affine transformation, and orthogonal basis function adjustment, respectively, achieving deep integration of molding process parameters and geometric features, and improving the model's adaptability and predictive stability under different process conditions. Furthermore, a three-dimensional displacement prediction field is reconstructed using linear combination coefficients and modulated modal displacement basis weights to characterize the spatial distribution of surface deviations under current process conditions, thereby improving the accuracy of compensation displacement prediction and obtaining a tooling control model with high compensation accuracy. Attached Figure Description

[0008] Figure 1 A flowchart of the first embodiment; Figure 2 A histogram showing the distribution of linear combination coefficients of the modal basis; Figure 3 Line plot of the modal basis weight distribution. Detailed Implementation

[0009] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0010] In the first embodiment, the present invention proposes a compensation control method for composite material molding tooling, such as... Figure 1 It includes the following steps: S1. Obtain the initial three-dimensional mesh model of the composite material molding tooling, calculate the unit vector and curvature value of the mesh model nodes along the principal curvature direction to form the initial geometric feature tensor of the nodes; obtain the molding process parameters and input them into the parameter encoding sub-network to generate a multi-objective modulation vector; use a lightweight network structure to perform multi-scale feature extraction on the initial geometric feature tensor of the nodes to generate a geometric feature map, wherein the shallow layer of the network structure uses an asymmetric convolution kernel, and the calculation direction is aligned with the local principal curvature direction of the node; the deep layer maps the three-dimensional coordinates of the nodes to the two-dimensional parameter space and then uses an interpolation kernel function to perform feature aggregation. The interpolation kernel function is generated by adjusting the first part of the multi-objective modulation vector through the reference B-spline kernel weight control points.

[0011] The tooling 3D mesh model file is read from the Standard Trigonometric Language (STL) or 3D Object (OBJ) format. Node coordinates and patch connectivity are loaded, and a half-edge data structure is constructed to obtain the normal vector for each node. For each node, a first-order or 2-Ring neighborhood of vertices is selected as the local neighborhood point set. Principal component analysis (PCA) is performed using the coordinate covariance matrix of the local neighborhood point set to obtain the local tangent plane and two orthogonal reference directions within the tangent plane. Then, quadratic surface fitting or Taubin discrete curvature estimation is performed on the changes in the coordinates and normal vectors of the neighborhood vertices within the local tangent plane to obtain the local curvature tensor. Eigenvalue decomposition is performed on the local curvature tensor, extracting two eigenvectors as the unit vectors for the first and second principal curvature directions, respectively. The corresponding eigenvalues ​​are used as the maximum and minimum principal curvature values. The above PCA steps are used to establish the local tangent plane and local reference datum. The principal curvature directions and curvature values ​​are uniformly determined by the same local curvature tensor. The coordinate vector, normal vector, first principal curvature direction unit vector, second principal curvature direction unit vector, maximum principal curvature value, and minimum principal curvature value of each node are concatenated along the channel dimension to construct the initial geometric feature tensor of the node. Before concatenation, the node coordinates and principal curvature values ​​are dimensionless. The node coordinates are normalized according to the diagonal length of the tooling bounding box or a preset feature length. The principal curvature values ​​are scaled by dividing the reciprocal of the feature length, or equivalently by multiplying the principal curvature values ​​by the feature length. The normal vector and principal curvature direction unit vector remain in a normalized state, thus obtaining the dimensionless initial geometric feature tensor of the node.

[0012] The highest heating temperature, longest holding time, and curing environmental pressure of the composite material molding process are collected by sensors or a process formulation database to form a process parameter vector. This process parameter vector is then input into a parameter encoding subnetwork. This network consists of three fully connected layers connected in series. Each fully connected layer is followed by a LayerNorm and a Gaussian error linear unit (GELU) activation function. The last layer outputs a dense vector. To avoid inconsistencies between the unconstrained output range and the subsequent modulation range, the original vector output by the last layer is constrained by a hyperbolic tangent function or a preset truncation function, preferably falling within the range of -1.5 to 1.5, serving as a multi-objective modulation vector. The multi-objective modulation vector is divided into multiple sub-vectors according to a preset channel interval. Different sub-vectors are used to adjust the interpolation kernel function, generate affine transformation parameters, and adjust the orthogonal basis function set, respectively. In this embodiment, the multi-objective modulation vector is divided into four sub-vectors in the channel dimension, serving as the first part, the second part, the third part, and the fourth part, respectively.

[0013] A lightweight geometric feature extraction network is constructed by inputting the initial geometric feature tensors of the nodes for multi-scale feature extraction. In the first three shallow layers of the network, 1×3 and 3×1 dimensional asymmetric convolution kernels are used for local convolution calculations. Before computation, a node-specific two-dimensional rotation matrix is ​​generated based on the orientation angle of the node's first principal curvature direction in the local tangent plane reference coordinate system. The local tangent plane reference coordinate system is composed of the node's normal vector and two orthogonal reference directions within the tangent plane, independent of the UV parameters carried by the STL or OBJ files themselves. The receptive field direction of the asymmetric convolution kernel is rotated and aligned to the node's local principal curvature direction using bilinear interpolation to extract anisotropic geometric features.

[0014] In the last three deep stages of the network, the local patches of the 3D mesh are parameterized and unfolded into a 2D parameter space. This 2D parameter space is a local parameter space generated in real-time based on the connectivity of the local patches, generating 2D parameter coordinates for each node within its local neighborhood. It is not required that the initial STL or OBJ model pre-include the overall UV parameters. After generating the 2D parameter coordinates for each node, a 4×4 baseline B-spline kernel weight control point matrix is ​​initialized using a B-spline surface interpolation algorithm. This B-spline surface preferably uses a cubic tensor product B-spline, with a preset order of 3 for both the U and V directions. The node vectors are all open uniform node vectors [0,0,0,0,1,1,1,1]. When using a rational form, the initial weight coefficients of each control point are set to 1 or obtained from the training process. Thus, the kernel weight control point matrix, order, node vectors, and weight coefficients together define the interpolation kernel function. A multilayer perceptron is used to map the first part of the multi-target modulation vector into a bias matrix with the same dimension as the kernel weight control point matrix. The bias matrix is ​​then element-wise added to the baseline B-spline kernel weight control point matrix to obtain the updated kernel weight control point matrix. A Cox-De Boor recursive basis function is calculated based on a preset order, node vectors, and two-dimensional parametric coordinates. This recursive basis function is then weighted and combined with the updated kernel weight control point matrix and weight coefficients to obtain continuous interpolation kernel function weights. These weights are used to weighted aggregate the features of neighboring nodes to generate a geometric feature map.

[0015] In an optional embodiment, the step of acquiring molding process parameters and inputting them into a parameter encoding subnetwork to generate a multi-target modulation vector includes: Extract the highest heating temperature, longest holding time, and curing environment pressure in the current molding process, and combine them to form an initial process parameter vector; Calculate the deviation of each value in the initial process parameter vector from its respective preset minimum extreme value, and normalize the deviation by dividing it by the maximum span of the parameter interval corresponding to the deviation to obtain a standardized feature vector. The standardized feature vector is input into a multilayer perceptron containing a two-layer hidden layer structure; The feature dimension is increased by the fully connected mapping of the multilayer perceptron, and the output feature vector consisting of 128 real numbers is used as the multi-target modulation vector.

[0016] In the step of obtaining molding process parameters, three core parameters that determine the curing deformation of the composite material are extracted in real time through sensors or process formula databases: maximum heating temperature, longest holding time, and curing environment pressure. These parameters are then constructed in sequence into an initial process parameter vector, which contains... , and In actual aerospace carbon fiber or epoxy resin composite molding processes, the preferred values ​​for the above parameters are typically set as follows: a maximum heating temperature between 160°C and 200°C, a maximum holding time between 100 minutes and 140 minutes, and a curing environmental pressure between 0.4 MPa and 0.8 MPa. For example, if a specific process formulation has parameters of a maximum heating temperature of 180°C, a holding time of 120 minutes, and a curing pressure of 0.6 MPa, then the initial process parameter vector includes 180, 120, and 0.6. To remove the influence of different dimensions on the neural network gradient, the corresponding minimum extrema are preset to include... =150、 =90、 =0.3 and the maximum span of the parameter range includes =60、 =60、 =0.6.

[0017] Calculate the deviation of each value and divide it by the range. For example, the difference between 180 and 150 in the normalized temperature calculation, divided by 60, equals 0.5; the difference between 120 and 90 in the time calculation, divided by 60, equals 0.5; and the difference between 0.6 and 0.3 in the pressure calculation, divided by 0.6, equals 0.5. This generates a normalized feature vector containing three values ​​of 0.5. The standardized feature vector The input data to the parameter encoding sub-network is fed into the multilayer perceptron parameter encoding sub-network for high-dimensional mapping. This network structure is designed with two hidden layers. The input layer contains three neurons, and the first hidden layer has 32 neurons, employing the GELU activation function to introduce non-linear features. The second hidden layer expands to 64 neurons, also using the GELU activation function and a Dropout layer with a 0.1 inactivation rate to prevent overfitting. This is connected to a fully connected linear output layer with 128 neurons for feature upscaling. After forward propagation, the fully connected output layer first outputs a 1×128 original real-valued vector, then multiplies it by a preset amplitude upper limit of 1.5 using a hyperbolic tangent function, or limits its range using a preset truncation function, to obtain a multi-target modulation vector preferably distributed within the range of -1.5 to 1.5. This multi-level upscaling mechanism allows process parameters to be mapped into feature vectors for multi-stage modulation.

[0018] In an optional embodiment, the step of using a lightweight network structure to perform multi-scale feature extraction on the initial geometric feature tensor of the node to generate a geometric feature map, wherein the shallow layers of the network structure use asymmetric convolution kernels and the computation direction is aligned with the local principal curvature direction of the node, including: The local principal curvature direction angle of each node in the initial three-dimensional mesh model is obtained, and a local rotation matrix specific to each node is constructed accordingly. Each node and its local neighborhood are projected onto a local tangent plane for two-dimensional parametric flattening, and then converted into regular two-dimensional raster data through mesh interpolation. Using the local rotation matrix, the preset asymmetric convolution kernels of size 1×3 and 3×1 are rotated to be geometrically aligned with the local principal curvature direction of the corresponding node; The two-dimensional raster data is convolved and multiplied using aligned asymmetric convolution kernels. The convolutional multiplication results of the same node are summed and the output is stored in the feature channel of the corresponding node to form a shallow geometric feature map.

[0019] In the shallow geometric feature extraction network processing, the input to the network is the local geometric morphology data of each node. For the anisotropic deformation characteristics of composite material molding fixtures caused by abrupt changes in hyperbola, the initial 3D mesh model is traversed, for example, a triangular mesh containing 50,000 nodes. For each node, 15 to 25 neighboring nodes in a local 2-Ring neighborhood are selected. A local tangent plane is established based on the vertex coordinates and normal vectors of this neighborhood, and the first and second principal curvature directions are obtained using the same local curvature tensor solution method as the initial geometric feature tensor of the aforementioned nodes. The direction vector corresponding to the first principal curvature is extracted as the local principal curvature direction. In the local tangent plane of this node, the global coordinate axis is projected onto the tangent plane to form the first reference direction; if the projection length is lower than a preset threshold, another global coordinate axis is used to project to form the first reference direction, and the second reference direction is obtained by cross product of the normal vectors. The angle θ between the local principal curvature direction and the first reference direction is calculated, for example, θ = 45°. The included angle θ is used to construct a node-specific local rotation matrix, no longer relying on the overall UV parameterized coordinate system of the tooling. Based on this angle, a 2×2 local rotation matrix R is constructed, with the first row containing cosθ and -sinθ, and the second row containing sinθ and cosθ. A local tangent plane is established centered on this node. The local spatial neighborhood with a radius of 5mm is projected onto this tangent plane along the normal direction. The irregularly distributed scattered points are resampled into 5×5 regular two-dimensional raster data with a spatial resolution of 1mm, resulting in local image patches with multi-channel geometric properties such as height and curvature, which serve as the actual input features of the network.

[0020] In the feature extraction network structure, the network pre-defines a lateral asymmetric convolutional kernel with a spatial receptive field of 1×3, primarily extracting the deformation gradient in the direction of maximum curvature; and a longitudinal asymmetric convolutional kernel with a spatial receptive field of 3×1, primarily extracting the deformation gradient in the direction of minimum curvature. The weights of the convolutional kernels are initially initialized randomly using a Kaiming normal distribution. The aforementioned local rotation matrix R is applied inversely to the weight grid coordinates of these two convolutional kernels, causing a corresponding θ-angle rotation in the computational space, achieving spatial geometric alignment between the receptive field direction and the direction of maximum principal curvature of the node. The network uses the aligned asymmetric convolutional kernels to perform sliding dot product calculations with a stride of 1 and zero padding on the 5×5 two-dimensional raster data input, respectively, to obtain feature response maps of two independent dimensions. Each asymmetric convolutional branch has a preset number of output channels, such as 64 output channels; the convolutional responses of the two asymmetric branches are summed element-wise on the corresponding channels, and then integrated through a ReLU activation function and a 1×1 linear mapping layer, ultimately resulting in each node outputting a 1×64 feature vector, rather than just a single scalar. The 1×64 feature vector is stored in the feature channel cache pool of the corresponding node, and the aggregated output size is... A shallow geometric feature map of ×64, in which This represents the total number of nodes.

[0021] S2, using the second and third parts of the multi-objective modulation vector to calculate the scaling factor and translation factor of the affine transformation, the geometric feature map is transformed element-wise to obtain the process-modulated geometric features; the process-modulated geometric features are input into the regression prediction head to output a set of linear combination coefficients; the fourth part of the multi-objective modulation vector is used to adjust the weights of the orthogonal basis function set to generate a modal displacement basis; the linear combination coefficients and the modal displacement basis are weighted and summed, and combined with the scaling transformation parameters to reconstruct a three-dimensional displacement prediction field; the compensation displacement vector of the calculation node based on the three-dimensional displacement prediction field is applied to the initial three-dimensional mesh model to generate a compensated tooling control model.

[0022] Two single-layer linear mapping networks trained using the Adam optimizer with adaptive moment estimation receive the second and third parts of the multi-target modulation vector as input, respectively. After linear mapping, the second part is first processed by a Sigmoid activation function to obtain intermediate variables between 0 and 1, and then mapped to a scale factor vector through linear scaling and translation operations; for example, multiplying the intermediate variable by 1.5 and adding 0.5 ensures the scale factor falls within the range of 0.5 to 2.0. After linear mapping, the third part is mapped to a translation factor vector through a hyperbolic tangent function or a preset truncation function, ensuring it falls within the range of -1.0 to 1.0. The geometric feature map is then multiplied sequentially along the channel dimension by the scale factor vector and added with the translation factor vector to achieve instance-normalized affine modulation transformation, resulting in a process-modulated geometric feature tensor that incorporates the influence of process parameters.

[0023] The geometric feature tensor, modulated by the process, is input into a regression prediction head composed of an average pooling layer and a multilayer perceptron. The last layer of the regression prediction head does not have a Softmax normalization function; it directly outputs a vector of continuous floating-point numbers that can be positive, negative, or greater than 1, serving as linear combination coefficients. These linear combination coefficients represent the response amplitude of each modal displacement basis; they are not required to be non-negative, nor are they required to sum to 1. Before establishing the historical deformation sample matrix, the historical tooling deformation samples and the current initial 3D mesh model are unified to the same template mesh node set, ensuring consistent node count, node index order, and coordinate correspondence. When the input mesh is inconsistent with the template mesh, node correspondence is established through surface projection, nearest-point matching, or non-rigid registration. A deformation sample matrix is ​​established based on historical tooling deformation data. The mean parameter μ and scale parameter σ of the historical displacement samples are calculated, and the historical displacement samples are standardized by subtracting μ and then dividing by σ. Principal component analysis (PCA) or singular value decomposition (SVD) is performed on the standardized historical deformation sample matrix to extract a predetermined number M of dimensionless orthogonal basis functions as an orthogonal basis function set. The orthogonal basis function set represents the basic three-dimensional deformation space point field data of the tooling during the historical forming process. The fourth part of the multi-objective modulation vector is received using a weighted generation network to generate a mode adjustment weight table equal to the number of orthogonal basis functions. This mode adjustment weight table is multiplied by attribute points of the corresponding order of orthogonal basis function point field data to amplify or reduce the amplitude of each order of deformation modes under different process conditions without changing the spatial direction of the orthogonal basis functions by matrix rotation.

[0024] The normalized displacement field is obtained by performing a multiplication-addition calculation on the linear combination coefficients and the modal displacement basis containing multiple basis vectors. The scale transformation parameters saved during the historical deformation data preprocessing stage are read. These parameters include the displacement data mean parameter μ and the scale parameter σ, where the scale parameter σ can be determined based on the standard deviation of historical displacement samples, statistical values ​​of finite element simulation samples, or a preset engineering scale. For scenarios lacking sufficient measured historical deformation data, a substitute deformation sample library can be constructed using multiple sets of tooling deformation samples obtained from finite element simulation. An orthogonal basis function set is extracted based on this substitute deformation sample library. Simultaneously, the maximum thermal deformation extremum extracted from the finite element simulation is used as the initial estimate or upper limit constraint of the scale parameter σ. However, in the inverse normalization calculation, a unified recovery method of "multiplying by σ and adding μ" is adopted. All elements in the normalized displacement field are inversely normalized according to their corresponding coordinate directions to restore the true engineering scale, reconstructing a three-dimensional displacement prediction field containing the offsets of all nodes in the mesh model in the X, Y, and Z axes. This three-dimensional displacement prediction field represents the predicted deviation field of the formed component surface relative to the target surface under the current forming process parameters.

[0025] The 3D displacement of each node in the 3D displacement prediction field is extracted. This prediction deviation is multiplied by a negative one and inverted to obtain the compensated displacement vector. This compensated displacement vector is then element-wise accumulated onto the original 3D coordinates of the corresponding node in the initial 3D mesh model to update the position information of all nodes. Local high-frequency spikes generated after coordinate updates are smoothed, and potential local folding regions are corrected using patch normal consistency checks or mesh quality constraints. While maintaining the topology, the smoothed coordinate update data is output. This smoothed data is exported as a 3D model file as the compensated tooling control model for subsequent CNC machining model input.

[0026] In an optional embodiment, the step of calculating the scaling factor and translation factor of the affine transformation using the second and third parts of the multi-target modulation vector and performing an element-wise transformation on the geometric feature map to obtain the process-modulated geometric features includes: The 128-dimensional multi-target modulation vector is divided into four 32-dimensional sub-vectors, which are respectively called the first part, the second part, the third part, and the fourth part. The second part is input into the first single-layer fully connected network and mapped into a vector of the same length as the number of feature channels, which serves as the scaling factor for the affine transformation. The third part is input into the second single-layer fully connected network and mapped as a vector of the same length as the number of feature channels, which serves as the translation factor for the affine transformation. Traverse all node feature bits of the geometric feature map, multiply the feature value of each node in the corresponding channel by the scaling factor and add the translation factor to generate the process-modulated geometric feature.

[0027] To inject process parameters and modulate the 3D geometric features of the tooling, a tensor slicing operation is used in memory to evenly divide the 128-length multi-target modulation vector output by the multilayer perceptron along the feature dimension. The slicing operation divides the vector into four parts: index 0-31 as the first part, 32-63 as the second part, 64-95 as the third part, and 96-127 as the fourth part, with each sub-vector having a dimension of 1×32. Taking a geometric feature map with a channel dimension of 64 as an example, the second part is extracted as input data and fed into a first single-layer fully connected network. This first single-layer fully connected network consists of 32 input neurons and 64 output neurons, and intermediate variables are obtained through matrix multiplication. .Will After inputting the Sigmoid activation function, an intermediate result between 0 and 1 is obtained. Then, according to γ=0.5+1.5× The linear scaling method yields a scale factor vector γ of dimension 1×64, thus ensuring the scale factor preferably falls within the range of 0.5 to 2.0. Similarly, the system inputs the third part as input data into the second single-layer fully connected network. This second single-layer fully connected network has the same network topology as the first single-layer fully connected network but its weights are initialized independently, containing 32 input neurons and 64 output neurons. The second single-layer fully connected network outputs intermediate variables. Then, through β= ×tanh( Alternatively, a translation factor vector β of dimension 1×64 can be obtained using a preset truncation method, where... It can be set to 1.0. During this process, the weights of both fully connected networks are collaboratively optimized during backpropagation.

[0028] During the element-wise feature transformation phase, the traversal size is... ×64, of which For example, consider a shallow geometric feature map matrix with 50,000 grid nodes. For any 1×64 eigenvector corresponding to the i-th node in the matrix, an instance-normalized affine transformation operation is performed via a broadcast mechanism. At the same j-th channel dimension, the original eigenvalues... Multiply by the corresponding scaling factor And add a translation factor For example, the original feature value of channel 0 of a certain node is 0.8, and the network calculates... It is 1.2. If the value is -0.1, the modulated eigenvalue is updated to 0.8 × 1.2 - 0.1 = 0.86. This operation achieves nonlinear amplification / scaling or bias shifting of the local geometric response characteristic intensity by process parameters at the feature channel level, and generates fused process information with the same size in parallel. ×64 process-modulated geometric feature map.

[0029] In an optional embodiment, the step of inputting the process-modulated geometric features into the regression prediction head and outputting a set of linear combination coefficients includes: The process-modulated geometric features are input into a global average pooling layer, and the average calculation is performed on each channel of the feature map in the node dimension to compress and generate a global one-dimensional feature vector. The global one-dimensional feature vector is input into a fully connected dimension reduction mapping layer for feature extraction. The output dimension of the fully connected dimensionality reduction mapping layer is set to be equal to the total number of basis functions in the orthogonal basis function set, and the output generates a corresponding fixed-length vector as the set of linear combination coefficients.

[0030] In the regression analysis phase for predicting the coefficients of a linear combination, the acceptor dimension is... ×C, for example A process-modulated geometric feature matrix with 50,000 nodes and C=64 feature channels is used. To extract globally representative features that are stable to local mesh topology changes, this feature matrix is ​​input into a spatially global average pooling layer. This pooling layer, for each independent feature channel j, where j belongs to 0 to 63, pools all... The feature response values ​​of each node on this channel are arithmetically summed and then divided by the total number of nodes. The process involves averaging the node dimensions. This reduces the impact of node arrangement differences on global features, compressing and reducing the dimensionality of the original high-dimensional matrix, and concatenating them to generate a global one-dimensional feature vector with a constant length of 1×64. For example, for the 0th feature channel, if the sum of the feature values ​​of 50,000 nodes is 25,000, then the pooling output of this channel has an average value of 0.5, constructing a global feature description. The generated global one-dimensional feature vector is then input into the regression prediction head network for final feature mapping extraction. The main structure of this regression prediction head network is a linear fully connected dimensionality reduction mapping layer with no softmax function and no non-negativity constraint in the last layer.

[0031] In the preprocessing stage, based on principal component analysis, the total number M of orthogonal basis functions that can explain more than 95% of the tooling deformation variance has been set. For example, M=20 order basis functions are retained to balance computational efficiency and reconstruction accuracy. Therefore, the output neuron dimension of the fully connected mapping layer is set to be equal to the number of basis functions M=20. During the forward propagation of the network, the 1×64 global one-dimensional feature vector input is multiplied by a 64×20 weight matrix and a 1×20 bias vector is added to perform a dimensionality reduction mapping from high to low dimensions. The regression prediction head network outputs a fixed-length vector containing 20 consecutive floating-point numbers. The linear combination coefficient distributions corresponding to each order of orthogonal basis are as follows: Figure 2 As shown, this set of floating-point numbers constitutes the aforementioned set of linear combination coefficients, representing the response amplitude and projection weight of the global process geometry fusion feature on each independent deformation mode basis. Since this set of linear combination coefficients is used to express the modal response amplitude, it can be positive, negative, or a value greater than 1, and the sum of the coefficients is not required to be 1.

[0032] In an optional embodiment, the step of using the fourth part of the multi-target modulation vector to weight the orthogonal basis function set to generate a modal shift basis includes: The fourth part of the multi-target modulation vector is input into the weight generation network to generate a set of mode adjustment weight tables equal to the number of orthogonal basis functions. A predetermined number of orthogonal basis functions are retrieved by performing principal component analysis on historical tooling deformation data. The orthogonal basis functions represent the basic three-dimensional deformation space point field data of the tooling. Each weight value in the modal adjustment weight table is subjected to a node-by-node, coordinate-by-coordinate scalar multiplication modulation operation with the corresponding order of orthogonal basis function point field data to generate a corrected modal displacement data group. Perform uniform amplitude clipping or uniform scale normalization on all corrected modal displacement data sets, and construct the modal displacement basis that is adjusted by process parameters while preserving the relative amplitude relationships of each mode.

[0033] During the transformation of the modal shift basis, the fourth part of the 1×32 multi-target modulation vector is extracted as input data and fed into the weight generation network. This weight generation network consists of two multilayer perceptrons. The input layer receives 32-dimensional features, the hidden layer performs feature transformation, and the output layer dimension is equal to the preset retention quantity of the orthogonal basis functions, for example, M=20. The output layer first generates a set of original weight variables, and then obtains a modal adjustment weight table through the Sigmoid activation function and linear scaling. For example, the Sigmoid output is multiplied by 0.4 and then added by 0.8, so that each modal adjustment weight preferably falls within the range of 0.8 to 1.2. The output of this weight generation network maps to generate a set of modal adjustment weight tables consisting of 20 floating-point numbers. The distribution of modal basis adjustment weights corresponding to orthogonal bases of orders 1 to 20 is as follows: Figure 3 As shown, the preferred range of each weight value is normalized and limited to between 0.8 and 1.2 to represent the local sensitivity of a specific deformation mode under different process conditions. For example, for a certain high forming pressure parameter, the weight increase of the first principal mode, i.e., the overall bending deformation, is predicted to be 1.15, while the weight decrease of the twentieth higher-order mode, i.e., the local undulation, is predicted to be 0.95.

[0034] In parallel, a set of 20 orthogonal basis functions pre-extracted from a historical database of measured deformations of forming tooling using Principal Component Analysis (PCA) or Singular Value Decomposition (SVD) is retrieved. Each orthogonal basis function has a size equal to... A discrete spatial point field matrix of ×3, where The total number of tooling nodes is represented by 3, where 3 represents the X, Y, and Z axes, indicating an inherent, mutually independent, basic three-dimensional deformation space shape of the tooling. M represents the number of orthogonal basis functions. This indicates the total number of nodes in the initial 3D mesh model; the two are no longer represented by the same symbol.

[0035] A matrix-dot-multiplication-level correction is performed. The modal sequences from 1 to 20 are traversed, and the scalar values ​​in the modal adjustment weight table are broadcast and multiplied into the X, Y, and Z displacement attribute values ​​of each node in the orthogonal basis function matrix of the corresponding order. This attribute-point-by-attribute scalar multiplication amplification or reduction operation generates an updated matrix set, i.e., the corrected modal displacement data set. Since the orthogonal basis functions have already undergone orthogonal normalization in the preprocessing stage, and multiplying a single basis function by a positive scalar does not destroy the mutual orthogonality between different basis functions, after multiplying into the modal adjustment weights, unit L2 norm normalization is not performed individually on each corrected basis function to avoid offsetting the amplitude modulation effect of the modal adjustment weights. To prevent overall amplitude anomalies caused by parameter adjustment, group-level normalization or amplitude pruning is performed only on the modal adjustment weight table, or group-level normalization is performed on all corrected modal displacement data sets using the same global scale factor, thereby preserving the relative adjustment amplitudes between modes of different orders. After the above processing, the reconstructed 20th-order modified basis function matrix has a size of 20× The ×3 modal displacement basis preserves the topological deformation characteristics of the tooling and can be adjusted according to current process variables such as temperature and pressure.

[0036] In an optional embodiment, the step of weighting and summing the linear combination coefficients with the modal displacement basis, and reconstructing the three-dimensional displacement prediction field by combining the scaling parameters, includes: Extract each coefficient value from the set of linear combination coefficients in sequence as a modal control scalar; Based on the sequence index, retrieve the three-dimensional node position adjustment amount in the modal displacement basis corresponding to each modal control scalar from the data table; Each modal control scalar is multiplied by the coordinate variation values ​​of all nodes in the X, Y, and Z axes of its corresponding modal displacement basis to establish a weighted modal displacement numerical field for each mode. The displacement numerical fields of the same node in all modes in the corresponding directions of the X, Y, and Z axes are vector summed and summarized. Then, the magnitude is restored by inverse normalization in combination with the scaling parameters. The resulting output is a three-dimensional displacement prediction field that matches the corresponding node of the initial three-dimensional mesh model.

[0037] In the step of reconstructing the 3D displacement prediction field of the tooling, an increasing sequence of M=20 orthogonal basis functions, assuming 0 to M-1, is retained from the memory array. Each independent floating-point value is then extracted from the 20 linear combination coefficient vectors output by the regression prediction head network, and this value is set as the modal control scalar for the corresponding mode. Based on the same sequence index k, where k belongs to 1 to 20, the 3D node position adjustment matrix corresponding to the k-th mode is located and extracted from the loaded modal displacement basis data table. The size of this matrix is... ×3, where For example, with 50,000 mesh nodes, the basic displacement components along the X, Y, and Z axes of all nodes in this specific mode are stored. Using a low-level parallel tensor computation framework, the extracted single-mode control scalar, for example, with a scalar value of 3.5, is uniformly multiplied into the coordinate variations along the X, Y, and Z axes of all 50,000 nodes in the matrix corresponding to that scalar value through a broadcast mechanism. This matrix scaling operation quantizes the geometric deformation components under a single mode, independently constructing 20 weighted modal displacement numerical fields in video memory, representing global bending, torsion, or local contraction modes, respectively.

[0038] For all tooling mesh nodes, along the X, Y, and Z spatial coordinate directions, the numerical values ​​of the aforementioned 20 weighted modal displacement fields at the same node index and the same coordinate axis are cumulatively summed element-wise. A dimensionless composite displacement tensor containing 50,000 node coordinate changes is then calculated by performing a dimensionless basis space expansion operation. To ensure the prediction results have engineering processing guidance significance, scale transformation parameters pre-stored during the historical deformation data preprocessing stage are retrieved. These scale transformation parameters are uniformly defined as the historical mean parameter μ and scale parameter σ used in the standardization process of the training set displacement data, where μ can be a 1×3 coordinate direction mean vector or... A ×3 node-level mean matrix, σ can be a scalar, a 1×3 coordinate direction scale vector, or... A ×3 node-level scale matrix is ​​used. Inverse normalization is performed by multiplying the dimensionless synthesized displacement tensor by σ and then adding μ to restore the data magnitude. The maximum thermal deformation extremum extracted from finite element simulation can be used as an initial estimate or upper bound constraint value for σ. When measured training data is missing, μ and σ are obtained statistically from the deformation sample library obtained by finite element simulation, and are no longer considered as different calculation paths alongside the mean-standard-deviation inverse normalization method. This operation restores the displacement magnitude compressed by the normalization process before network training and reconstructs a set of outputs containing... The displacement matrix, which is a three-dimensional real coordinate increment value, i.e., the three-dimensional displacement prediction field, can be imported into the CNC machining system to guide the reverse deformation machining compensation of the downstream tooling surface.

[0039] In the second embodiment, the present invention also proposes a compensation control system for composite material molding tooling, comprising the following modules: The computation module is used to acquire the initial three-dimensional mesh model of the composite material molding tooling, and to calculate the unit vector and curvature value of the mesh model nodes along the principal curvature direction to form the initial geometric feature tensor of the nodes; to acquire molding process parameters and input them into the parameter encoding sub-network to generate a multi-objective modulation vector; and to use a lightweight network structure to perform multi-scale feature extraction on the initial geometric feature tensor of the nodes to generate a geometric feature map. The shallow layer of the network structure uses an asymmetric convolution kernel, and the calculation direction is aligned with the local principal curvature direction of the nodes. The deep layer maps the three-dimensional coordinates of the nodes to a two-dimensional parameter space and then uses an interpolation kernel function to perform feature aggregation. The interpolation kernel function is generated by adjusting the first part of the multi-objective modulation vector through the reference B-spline kernel weight control points. The generation module is used to calculate the scaling factor and translation factor of the affine transformation using the second and third parts of the multi-objective modulation vector, and perform element-wise transformation on the geometric feature map to obtain process-modulated geometric features; input the process-modulated geometric features into the regression prediction head to output a set of linear combination coefficients, and use the fourth part of the multi-objective modulation vector to adjust the weights of the orthogonal basis function set to generate a modal displacement basis; perform a weighted summation of the linear combination coefficients and the modal displacement basis, and reconstruct a three-dimensional displacement prediction field by combining the scaling transformation parameters; apply the compensation displacement vector of the calculation node based on the three-dimensional displacement prediction field to the initial three-dimensional mesh model to generate a compensated tooling control model.

[0040] The above description represents the preferred embodiments of the present invention. It should be noted that, for those skilled in the art, various improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A compensation control method for a composite material molding tooling, characterized in that, Includes the following steps: Obtain the initial three-dimensional mesh model of the composite material molding tooling, and calculate the initial geometric feature tensor of the mesh model nodes by the unit vector and curvature value along the principal curvature direction. The molding process parameters are obtained and input into the parameter encoding sub-network to generate a multi-target modulation vector. A lightweight network structure is used to extract multi-scale features from the initial geometric feature tensor of the nodes to generate a geometric feature map. The shallow layer of the network structure uses an asymmetric convolution kernel with the calculation direction aligned with the local principal curvature direction of the node. The deep layer maps the three-dimensional coordinates of the nodes to a two-dimensional parameter space and then uses an interpolation kernel function to perform feature aggregation. The interpolation kernel function is generated by adjusting the reference B-spline kernel weight control points through the first part of the multi-target modulation vector. The geometric feature map is transformed element-wise using the second and third parts of the multi-target modulation vector to calculate the scaling factor and translation factor of the affine transformation, thereby obtaining the process-modulated geometric feature. The geometric features modulated by the process are input into the regression prediction head, which outputs a set of linear combination coefficients. The fourth part of the multi-objective modulation vector is used to adjust the weights of the orthogonal basis function set to generate a modal displacement basis. The linear combination coefficients and the modal displacement basis are weighted and summed, and the three-dimensional displacement prediction field is reconstructed by combining the scale transformation parameters. The compensation displacement vector of the calculation node based on the three-dimensional displacement prediction field is applied to the initial three-dimensional mesh model to generate the compensated tooling control model.

2. The method according to claim 1, characterized in that, The process of acquiring molding process parameters and inputting them into the parameter encoding sub-network to generate multi-target modulation vectors includes: Extract the highest heating temperature, longest holding time, and curing environment pressure in the current molding process, and combine them to form an initial process parameter vector; Calculate the deviation of each value in the initial process parameter vector from its respective preset minimum extreme value, and normalize the deviation by dividing it by the maximum span of the parameter interval corresponding to the deviation to obtain a standardized feature vector. The standardized feature vector is input into a multilayer perceptron containing a two-layer hidden layer structure; The feature dimension is increased by the fully connected mapping of the multilayer perceptron, and the output feature vector consisting of 128 real numbers is used as the multi-target modulation vector.

3. The method according to claim 2, characterized in that, The process of using a lightweight network structure to perform multi-scale feature extraction on the initial geometric feature tensor of the node to generate a geometric feature map, wherein the shallow layers of the network structure use asymmetric convolution kernels and the computation direction is aligned with the local principal curvature direction of the node, including: The local principal curvature direction angle of each node in the initial three-dimensional mesh model is obtained, and a local rotation matrix specific to each node is constructed accordingly. Each node and its local neighborhood are projected onto a local tangent plane for two-dimensional parametric flattening, and then converted into regular two-dimensional raster data through mesh interpolation. Using the local rotation matrix, the preset asymmetric convolution kernels of size 1×3 and 3×1 are rotated to be geometrically aligned with the local principal curvature direction of the corresponding node; The two-dimensional raster data is convolved and multiplied using aligned asymmetric convolution kernels. The convolutional multiplication results of the same node are summed and the output is stored in the feature channel of the corresponding node to form a shallow geometric feature map.

4. The method according to claim 1, characterized in that, The step of calculating the scaling factor and translation factor of the affine transformation using the second and third parts of the multi-target modulation vector, and then performing an element-wise transformation on the geometric feature map to obtain the process-modulated geometric features includes: The 128-dimensional multi-target modulation vector is divided into four 32-dimensional sub-vectors, which are respectively called the first part, the second part, the third part, and the fourth part. The second part is input into the first single-layer fully connected network and mapped into a vector of the same length as the number of feature channels, which serves as the scaling factor for the affine transformation. The third part is input into the second single-layer fully connected network and mapped as a vector of the same length as the number of feature channels, which serves as the translation factor for the affine transformation. Traverse all node feature bits of the geometric feature map, multiply the feature value of each node in the corresponding channel by the scale factor and add the translation factor to generate the process-modulated geometric feature.

5. The method according to claim 1 or 4, characterized in that, The step of inputting the process-modulated geometric features into the regression prediction head and outputting a set of linear combination coefficients includes: The process-modulated geometric features are input into a global average pooling layer, and the average calculation is performed on each channel of the feature map in the node dimension to compress and generate a global one-dimensional feature vector. The global one-dimensional feature vector is input into a fully connected dimension reduction mapping layer for feature extraction. The output dimension of the fully connected dimensionality reduction mapping layer is set to be equal to the total number of basis functions in the orthogonal basis function set, and the output generates a corresponding fixed-length vector as the set of linear combination coefficients.

6. The method according to claim 1, characterized in that, The step of using the fourth part of the multi-objective modulation vector to adjust the weights of the orthogonal basis function set to generate a modal shift basis includes: The fourth part of the multi-target modulation vector is input into the weight generation network to generate a set of mode adjustment weight tables equal to the number of orthogonal basis functions. A predetermined number of orthogonal basis functions are retrieved by performing principal component analysis on historical tooling deformation data. The orthogonal basis functions represent the basic three-dimensional deformation space point field data of the tooling. Each weight value in the modal adjustment weight table is subjected to a node-by-node, coordinate-by-coordinate scalar multiplication modulation operation with the corresponding order of orthogonal basis function point field data to generate a corrected modal displacement data group. Perform uniform amplitude clipping or uniform scale normalization on all corrected modal displacement data sets, and construct the modal displacement basis that is adjusted by process parameters while preserving the relative amplitude relationships of each mode.

7. The method according to claim 1, characterized in that, The step of weighted summing of the linear combination coefficients and the modal displacement basis, combined with scaling transformation parameters, to reconstruct the three-dimensional displacement prediction field includes: Extract each coefficient value from the set of linear combination coefficients in sequence as a modal control scalar; Based on the sequence index, retrieve the three-dimensional node position adjustment amount in the modal displacement basis corresponding to each modal control scalar from the data table; Each modal control scalar is multiplied by the coordinate variation values ​​of all nodes in the X, Y, and Z axes of its corresponding modal displacement basis to establish a weighted modal displacement numerical field for each mode. The displacement numerical fields of the same node in all modes in the corresponding directions of the X, Y, and Z axes are vector summed and summarized. Then, the magnitude is restored by inverse normalization in combination with the scaling parameters. The resulting output is a three-dimensional displacement prediction field that matches the corresponding node of the initial three-dimensional mesh model.

8. A compensation control system for a composite material molding fixture, characterized in that, Includes the following modules: The calculation module is used to obtain the initial three-dimensional mesh model of the composite material molding tooling, and calculate the unit vector and curvature value of the mesh model node along the principal curvature direction to form the node's initial geometric feature tensor. The molding process parameters are obtained and input into the parameter encoding sub-network to generate a multi-target modulation vector. A lightweight network structure is used to extract multi-scale features from the initial geometric feature tensor of the nodes to generate a geometric feature map. The shallow layer of the network structure uses an asymmetric convolution kernel with the calculation direction aligned with the local principal curvature direction of the node. The deep layer maps the three-dimensional coordinates of the nodes to a two-dimensional parameter space and then uses an interpolation kernel function to perform feature aggregation. The interpolation kernel function is generated by adjusting the reference B-spline kernel weight control points through the first part of the multi-target modulation vector. The generation module is used to calculate the scaling factor and translation factor of the affine transformation using the second and third parts of the multi-target modulation vector, and then perform an element-wise transformation on the geometric feature map to obtain the process-modulated geometric features. The geometric features modulated by the process are input into the regression prediction head, which outputs a set of linear combination coefficients. The fourth part of the multi-objective modulation vector is used to adjust the weights of the orthogonal basis function set to generate a modal displacement basis. The linear combination coefficients and the modal displacement basis are weighted and summed, and the three-dimensional displacement prediction field is reconstructed by combining the scale transformation parameters. The compensation displacement vector of the calculation node based on the three-dimensional displacement prediction field is applied to the initial three-dimensional mesh model to generate the compensated tooling control model.

9. The system according to claim 8, characterized in that, The process of acquiring molding process parameters and inputting them into the parameter encoding sub-network to generate multi-target modulation vectors includes: Extract the highest heating temperature, longest holding time, and curing environment pressure in the current molding process, and combine them to form an initial process parameter vector; Calculate the deviation of each value in the initial process parameter vector from its respective preset minimum extreme value, and normalize the deviation by dividing it by the maximum span of the parameter interval corresponding to the deviation to obtain a standardized feature vector. The standardized feature vector is input into a multilayer perceptron containing a two-layer hidden layer structure; The feature dimension is increased by the fully connected mapping of the multilayer perceptron, and the output feature vector consisting of 128 real numbers is used as the multi-target modulation vector.

10. The system according to claim 8, characterized in that, The process of using a lightweight network structure to perform multi-scale feature extraction on the initial geometric feature tensor of the node to generate a geometric feature map, wherein the shallow layers of the network structure use asymmetric convolution kernels and the computation direction is aligned with the local principal curvature direction of the node, including: The local principal curvature direction angle of each node in the initial three-dimensional mesh model is obtained, and a local rotation matrix specific to each node is constructed accordingly. Each node and its local neighborhood are projected onto a local tangent plane for two-dimensional parametric flattening, and then converted into regular two-dimensional raster data through mesh interpolation. Using the local rotation matrix, the preset asymmetric convolution kernels of size 1×3 and 3×1 are rotated to be geometrically aligned with the local principal curvature direction of the corresponding node; The two-dimensional raster data is convolved and multiplied using aligned asymmetric convolution kernels. The convolutional multiplication results of the same node are summed and the output is stored in the feature channel of the corresponding node to form a shallow geometric feature map.

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