A three-period minimal surface spatial positioning fusion structure design method based on inverse distance weighting method

Abstract

The present application relates to the technical field of fusion design, in particular to a three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method, in the present application, by setting the implicit function equation of the three-period minimal surface and screening the control points according to the spatial distribution and geometric constraints, the accurate selection and positioning of the structure unit in the design target area are realized, the accuracy of geometric mapping is improved, the inverse distance weighting calculation is carried out through the convolutional neural network, the difference of the geometric region in the space can be effectively identified, the response ability of structure fusion is improved, the weight is calculated combined with the spatial distribution of the control points, and the weight distribution mechanism is formed by using the actual geometric distance between the control points, the continuity and smoothness of the geometric response in the interpolation region are guaranteed, the graph neural network is introduced to process the surface continuity problem, the local geometric mutation area is identified and corrected through the edge weight and topological structure between nodes, and the geometric smoothness and boundary consistency of the whole structure are improved.

Description

Technical Field

[0001] This invention relates to the field of fusion design technology, and in particular to a three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method. Background Technology

[0002] The field of integrated design technology generally refers to the integration and optimization of multiple design objectives and computational methods to achieve the design scheme with optimal overall performance. It is particularly common in structural design, mechanical optimization, and multi-physics coupling problems, involving the coordination and integration of multiple factors.

[0003] The purpose of this paper is to propose a three-period minimum surface spatial positioning fusion structural design method based on the inverse distance weighting method. This method aims to improve the accuracy and stability of structural design by optimizing the application of the three-period minimum surface in spatial positioning. The goal is to achieve optimal structural performance through precise positioning and optimization of the design model, and to enable effective design fusion in complex environments, thus providing more accurate and optimized solutions.

[0004] In existing technologies, fusion design based on direct parameter control or simplified interpolation models often ignores the distribution correlation of control points in space and the nonlinear response relationship of parameters within the region. This results in insufficient adaptability of the model in the design of highly complex structures. Furthermore, the lack of a fine weight relationship between control points makes it easy for them to become over-concentrated or discretely distributed in the interpolation region, leading to problems such as geometric instability and local abrupt changes in the fusion results, which affect the continuity of the structure and the feasibility of manufacturing. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method, comprising the following steps:

[0007] S1: Based on the design requirements of the three-period minimal surface, define the TPMS implicit function equation, set control points, determine the spatial distribution and geometric constraints, select control points that meet the requirements, calculate the geometric position, and generate the TPMS implicit function equation and control point definition results.

[0008] S2: Based on the implicit function equation of TPMS and the definition of control points, select multiple TPMS surfaces, define interpolation center points, calculate the spatial distance of control points, determine the geometric distribution, calculate the weighted weights, select suitable control points, and generate the geometric weight calculation results of control points.

[0009] S3: Based on the geometric weight calculation results of the control points, a convolutional neural network is used to perform inverse distance weighting calculation, adjust the control point weights, determine whether they meet the design requirements, adjust unqualified areas, and generate a weighted fusion structure generation result;

[0010] S4: Perform geometric optimization on the weighted fusion structure generation result, using a graph neural network to determine whether there are abrupt changes in the connection region, perform correction and smoothing, optimize the surface, and generate the geometrically optimized fusion surface result;

[0011] S5: Based on the results of the fused surface geometry optimization, optimize the stiffness-to-mass ratio, analyze the region stiffness-to-mass ratio, adjust the geometric properties, export the STL file, and obtain the STL format optimized design file.

[0012] As a further aspect of the present invention, the specific steps for generating the TPMS implicit function equation and control point definition results are as follows:

[0013] Based on the design requirements of the three-period minimal surface, the initial position of the control points is selected, and geometric dimensions and morphology analysis are performed. The spatial position of the control points is determined through geometric analysis, the initial layout is executed, and the layout conditions are set to generate the initial layout of the control points.

[0014] Based on the initial layout of the control points, spatial distribution and geometric constraint analysis are performed, the distance and distribution between the control points are adjusted to meet the preset geometric conditions, the geometric constraints and relative positions of each control point are checked, and a control point layout that meets the requirements is generated.

[0015] Based on the control point layout that meets the requirements, the geometric position of each control point is calculated, position correction is performed, the matching between the spatial distribution and the surface requirements is verified, and the TPMS implicit function equation and control point definition results are generated.

[0016] As a further aspect of the present invention, the specific steps for generating the geometric weight calculation results of the control points are as follows:

[0017] Based on the implicit function equations and control point definitions of the TPMS, multiple TPMS surfaces are selected, the interpolation center point positions are defined, the spatial distance from the control points to each interpolation center point is calculated, the distance between the control points is measured one by one, the spatial distance value of each pair of control points is obtained, and the spatial distance calculation result of the control points is generated.

[0018] Based on the spatial distance calculation results of the control points, check the geometric distribution of the control points in space, perform geometric relationship calculation between the control points, compare the distance between the control points with the preset geometric requirements, adjust the distribution position of the control points, and generate geometric distribution adjustment results.

[0019] Based on the geometric distribution adjustment results, the geometric weight of each control point is calculated, the weighting ratio of the control points is adjusted, control points that meet the conditions are selected, and the geometric weight calculation results of the control points are generated.

[0020] As a further aspect of the present invention, the specific steps for generating the weighted fusion structure generation result are as follows:

[0021] Based on the geometric weight calculation results of the control points, a convolutional neural network is used to perform inverse distance weighting calculation, measure the spatial distance between control points, calculate the weight value of each control point, and adjust the weight of the control points according to the calculation results to generate the inverse distance weighting calculation results.

[0022] Based on the inverse distance weighted calculation results, the weight of each control point is adjusted, and it is checked whether the design requirements are met. Weight adjustment is performed on areas that do not meet the requirements. During the adjustment process, the area is optimized point by point to generate the adjusted control point weights.

[0023] Based on the adjusted control point weights, the control point positions and weights are fused together, and a fused structure is generated by combining the optimized control points. The control point fusion process is then executed to generate the weighted fused structure result.

[0024] As a further aspect of the present invention, the convolutional neural network is configured according to the formula:

[0025] ;

[0026] in: Indicate control points The weighted value, Indicate control points Geometric weights, Indicate control points Environmental sensitivity coefficient Indicate control points semantic association coefficient, Indicate control points With control points Spatial distance between them Indicate control points The perturbation suppression term, Indicates the basic inverse distance weighted index. Indicate control points The nonlinear response adjustment coefficient, This indicates the number of control points involved in the calculation.

[0027] As a further aspect of the present invention, the weighted fusion structure generation result includes the adjusted control point weight distribution, fused surface lattice data, and structural integrity marker set.

[0028] As a further aspect of the present invention, the specific steps for generating the fused surface geometry optimization result are as follows:

[0029] Based on the weighted fusion structure generation result, a graph neural network is used to perform geometric abrupt checks on the connection region. A spatial scanning method is used to measure the geometry of the connection region point by point, calculate the curvature change of the connection region, determine whether there are unsmooth or discontinuous regions, and generate the geometric abrupt check result of the connection region.

[0030] Based on the results of the geometric abrupt change check of the connection region, the regions with geometric abrupt changes are corrected. The abrupt change regions are smoothly adjusted point by point. During the adjustment process, the transition of the surface is optimized to ensure continuity and generate the corrected geometric region.

[0031] Based on the corrected geometric region, the entire surface is optimized by performing a surface smoothing operation, adjusting the connection between surface nodes and boundaries, gradually optimizing the overall geometric shape, and generating a fused surface geometric optimization result.

[0032] As a further aspect of the present invention, the graph neural network is configured according to the formula:

[0033] ;

[0034] in: This indicates the curvature change in the connected region. Represents a node The structural propagation weights, Represents a node The density adjustment coefficient, Represents a node To the reference point Euclidean distance, This represents the disturbance suppression term. Represents a node In spatial coordinates The elevation value below, Represents a node In space coordinate, Represents a node In space coordinate, This represents the number of neighboring nodes used for curvature calculation.

[0035] As a further aspect of the present invention, the fused surface geometry optimization result includes a surface smoothness evaluation value, a set of abrupt change correction node indices, and optimized surface mesh data.

[0036] As a further aspect of the present invention, the specific steps for generating the STL format optimized design file are as follows:

[0037] Based on the optimized results of the fused surface geometry, the stiffness-mass ratio is optimized, the stiffness-mass ratio of each region is measured, and the ratio of each region is checked one by one to analyze whether it meets the design specifications. The region stiffness-mass ratio is calculated, and the region stiffness-mass ratio analysis results are generated.

[0038] Based on the analysis results of the region stiffness and mass ratio, the geometric properties of each region are adjusted. By modifying the region shape, thickness or structural distribution, the stiffness and mass ratio are optimized point by point, and the geometric property adjustment results are generated.

[0039] Based on the results of the geometric characteristic adjustment, the optimized geometric structure is exported as an STL file, the file format is converted, the output precision is adjusted, and an optimized design file in STL format is generated.

[0040] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0041] 1. In this invention, by setting the implicit function equation of the three-period minimal surface and selecting control points based on spatial distribution and geometric constraints, the precise selection and positioning of structural units within the design target area is achieved, thereby improving the accuracy of geometric mapping;

[0042] 2. In this invention, inverse distance weighted calculation is performed by convolutional neural network, which can effectively identify the differences in geometric regions in space, make local adjustments to regions that do not meet the structural requirements, improve the response capability of structural fusion, calculate weights by combining the spatial distribution of control points, and form a weight distribution mechanism by using the actual geometric distance between control points to ensure the continuity and stability of geometric response within the interpolation region.

[0043] 3. In this invention, a graph neural network is introduced to handle the problem of surface continuity. By using the edge weights between nodes and the topological structure, local geometric abrupt regions are identified and corrected, thereby improving the overall geometric smoothness and boundary consistency of the structure. Combined with the calculation results of regional stiffness and mass ratio, the geometric shape is adjusted to balance the load-bearing capacity and lightweight requirements, thus realizing an integrated collaborative design process from parameter definition, weight allocation, spatial interpolation, fusion generation to performance optimization. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the main steps of the present invention;

[0045] Figure 2 This is a detailed schematic diagram of S1 of the present invention;

[0046] Figure 3 This is a detailed schematic diagram of S2 of the present invention;

[0047] Figure 4This is a detailed schematic diagram of S3 of the present invention;

[0048] Figure 5 This is a detailed schematic diagram of S4 of the present invention;

[0049] Figure 6 This is a detailed schematic diagram of S5 of the present invention. Detailed Implementation

[0050] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0051] Please see Figure 1 This invention provides a technical solution: a three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method, comprising the following steps:

[0052] To achieve the above objectives, the present invention adopts the following technical solution: a three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method, comprising the following steps:

[0053] S1: Based on the design requirements of the three-period minimal surface, define the TPMS implicit function equation, set control points, determine the spatial distribution and geometric constraints, select control points that meet the requirements, calculate the geometric position, and generate the TPMS implicit function equation and control point definition results.

[0054] S2: Based on the implicit function equations of TPMS and the definition results of control points, select multiple TPMS surfaces, define interpolation center points, calculate the spatial distance of control points, determine the geometric distribution, calculate the weighted weights, select suitable control points, and generate the geometric weight calculation results of control points.

[0055] S3: Based on the calculation results of the geometric weights of the control points, a convolutional neural network is used to perform inverse distance weighting calculation, adjust the control point weights, determine whether they meet the design requirements, adjust unqualified areas, and generate a weighted fusion structure.

[0056] S4: Perform geometric optimization on the weighted fusion structure generation result. Use a graph neural network to determine whether there are abrupt changes in the connection region, perform correction and smoothing, optimize the surface, and generate the geometrically optimized fusion surface result.

[0057] S5: Based on the results of the fused surface geometry optimization, optimize the stiffness-to-mass ratio, analyze the region stiffness-to-mass ratio, adjust the geometric properties, export the STL file, and obtain the STL format optimization design file.

[0058] Please see Figure 2The specific steps for generating the implicit function equations and control point definitions for TPMS are as follows:

[0059] Based on the design requirements of the three-period minimal surface, the initial position of the control points is selected, and geometric dimensions and morphology analysis are performed. The spatial position of the control points is determined through geometric analysis, the initial layout is executed, and the layout conditions are set to generate the initial layout of the control points.

[0060] Based on the initial layout of control points, spatial distribution and geometric constraint analysis are performed. The distance and distribution between control points are adjusted to meet the preset geometric conditions. The geometric constraints and relative positions of each control point are checked to generate a control point layout that meets the requirements.

[0061] Based on the control point layout that meets the requirements, the geometric position of each control point is calculated, the position is corrected, the matching between the spatial distribution and the surface requirements is verified, and the TPMS implicit function equation and control point definition results are generated.

[0062] Based on the design requirements of a three-period minimal surface, the initial positions of control points are selected, and geometric dimensions and morphology are analyzed. The least squares method is used for geometric analysis, specifically using the scipy.optimize.leastsq function. The error function is set as the difference between the point and the fitted surface, and the initial coordinates of the control points are set as initial values. The Jacobian matrix is ​​calculated, and the partial derivative of the control point coordinates is set as the matrix. Numerical differentiation is performed using numpy.gradient. The initial layout is executed, and the layout conditions are set. The B-spline interpolation method is used, and the initial coordinate set of the control points is set as the basis to generate a smooth curve and generate the initial layout of the control points.

[0063] Based on the initial layout of control points, spatial distribution and geometric constraint analysis are performed. The Voronoi diagram algorithm is adopted, specifically using the scipy.spatial.Voronoi function. The coordinate set of the control points is input to divide the spatial distribution. The distance and distribution between control points are adjusted by calculating the centroid and boundary of each region. The k-means clustering algorithm is used, specifically using sklearn.cluster.KMeans. The number of clusters is set to the preset number of control points. Iterative clustering analysis is performed to update the position of the control points and to verify the geometric constraints. The Euclidean distance between control points is calculated using geopy.distance.distance to ensure that each pair of control points meets the set distance constraints and to generate a control point layout that meets the requirements.

[0064] Based on the control point layout that meets the requirements, an interpolation method is adopted, specifically using the `scipy.interpolate.griddata` function. An appropriate interpolation method, such as linear interpolation, is selected to map the spatial coordinates of the control points onto the target surface. The geometric position of each control point is calculated, position correction is performed, and the match between the spatial distribution and the surface requirements is verified. The RANSAC algorithm is used for outlier removal, and `sklearn.linear_model.RANSACRegressor` is used for interior point optimization. The maximum number of iterations is set to 100, and the tolerance for fit is 0.1. The TPMS implicit function equations and control point definitions are generated. The implicit function equations are then solved using `scipy.optimize.fsolve` to generate the final control point definitions and equation results.

[0065] Please see Figure 3 The specific steps for generating the geometric weight calculation results of control points are as follows:

[0066] Based on the implicit function equations and control point definitions of TPMS, multiple TPMS surfaces are selected, the positions of interpolation center points are defined, the spatial distance from each control point to each interpolation center point is calculated, the distance between control points is measured one by one, the spatial distance value of each pair of control points is obtained, and the spatial distance calculation results of control points are generated.

[0067] Based on the spatial distance calculation results of control points, check the geometric distribution of control points in space, perform geometric relationship calculation between control points, compare the distance between control points with the preset geometric requirements, adjust the distribution position of control points, and generate geometric distribution adjustment results;

[0068] Based on the geometric distribution adjustment results, the geometric weight of each control point is calculated, the weighting ratio of the control points is adjusted, the control points that meet the conditions are selected, and the geometric weight calculation results of the control points are generated.

[0069] Based on the implicit function equations and control point definitions of TPMS, multiple TPMS surfaces are selected, the interpolation center point positions are defined, and the Euclidean distance algorithm is adopted. By using the scipy.spatial.distance.euclidean function, the spatial distance between each control point and each interpolation center point is calculated. The distance between control points is measured one by one, and the spatial distance value of each pair of control points is obtained by calculating point by point, generating the control point spatial distance calculation result.

[0070] Based on the spatial distance calculation results of the control points, the geometric distribution of the control points in space is checked. A geometric relationship calculation algorithm is adopted. By using the scipy.spatial.distance.cdist function, all pairwise distances between control points are calculated. By setting preset geometric requirements (such as distance range or distance ratio), the geometric relationship calculation between control points is performed. The distances between control points are compared with the preset geometric requirements, the distribution position of control points is adjusted, and the geometric distribution adjustment result is generated.

[0071] Based on the geometric distribution adjustment results, the geometric weight of each control point is calculated using an inverse distance weighting algorithm. The distance between each pair of control points is calculated using the scipy.spatial.distance.pdist function, and the distance is exponentially weighted using the numpy.exp function. The weighting ratio is calculated, and control points that meet the conditions are selected to generate the geometric weight calculation results of the control points.

[0072] Please see Figure 4 The specific steps for generating the weighted fusion structure are as follows:

[0073] Based on the geometric weight calculation results of the control points, a convolutional neural network is used to perform inverse distance weighting calculation, measure the spatial distance between control points, calculate the weight value of each control point, and adjust the weight of the control points according to the calculation results to generate the inverse distance weighting calculation results.

[0074] Based on the inverse distance weighted calculation results, the weight of each control point is adjusted to check whether the design requirements are met. Weight adjustment is performed on areas that do not meet the requirements. During the adjustment process, the area is optimized point by point to generate the adjusted control point weights.

[0075] Based on the adjusted control point weights, the control point positions and weights are fused together, and the optimized control points are combined to generate a fused structure. The control point fusion process is then executed to generate the weighted fused structure result.

[0076] Based on the geometric weight calculation results of the control points, a convolutional neural network is used to perform inverse distance weighting calculation to measure the spatial distance between control points. The Euclidean distance between all control point pairs is calculated using the scipy.spatial.distance.cdist function, and the weight value of each control point is calculated. The convolution kernel is set using tensorflow.keras.layers.Conv2D to perform inverse distance weighting convolution operation, and the weighting weights of the control points are adjusted according to the calculation results to generate the inverse distance weighting calculation result.

[0077] Based on the inverse distance weighted calculation results, the weights of each control point are adjusted to check whether they meet the design requirements. Gradient descent is used, and the tensorflow.keras.optimizers.Adam optimizer is used with a learning rate of 0.01 to adjust the weights of regions that do not meet the requirements. During the adjustment process, the regions are optimized point by point. Specifically, tensorflow.keras.layers.Dense layers are used to iteratively optimize the control point weights and make fine adjustments to generate the adjusted control point weights.

[0078] Based on the adjusted control point weights, the control point positions and weights are fused together. The optimized control points are then combined to generate a fused structure. The control point fusion process is executed using a three-dimensional interpolation algorithm. By using the scipy.interpolate.griddata function and selecting the linear interpolation method, the adjusted control point coordinates and weights are combined to generate the weighted fused structure.

[0079] Convolutional neural networks are based on the formula:

[0080] ;

[0081] in: Indicate control points The weighted value, Indicate control points Geometric weights, Indicate control points Environmental sensitivity coefficient Indicate control points semantic association coefficient, Indicate control points With control points Spatial distance between them Indicate control points The perturbation suppression term, Indicates the basic inverse distance weighted index. Indicate control points The nonlinear response adjustment coefficient, Indicates the number of control points involved in the calculation;

[0082] Execution process: First, calculate the geometric weight of each control point. Then utilize spatial distance Calculate control points With all other control points To more accurately reflect the relationship between control points, an environmental sensitivity coefficient was introduced to determine their relative positions. Used to measure control points The response to characteristic density changes within a local space is represented by the set of distances between statistical control points in the local neighborhood. Calculate, then calculate the control points. With target control point semantic association coefficient Based on the cosine similarity between convolutional feature vectors, the similarity between control points in the feature space is characterized. To prevent computational anomalies caused by zero spatial distance, a perturbation suppression term is added. The value is a constant to ensure the stability of the formula. Finally, a nonlinear response adjustment coefficient is introduced. By calculating control points The sensitivity to distance changes is adjusted by varying the response in the feature space, and the control points are calculated using the sigmoidal function. weighted value This allows for more precise adjustment of the control point weights, thereby optimizing the fusion structure design of the three-cycle minimal surface spatial positioning and achieving higher accuracy and stability.

[0083] The weighted fusion structure generation result includes the adjusted control point weight distribution, fused surface lattice data, and structural integrity marker set.

[0084] Please see Figure 5 The specific steps for generating the geometric optimization results of the fused surface are as follows:

[0085] Based on the weighted fusion structure generation results, a graph neural network is used to perform geometric abrupt checks on the connection region. A spatial scanning method is used to measure the geometry of the connection region point by point, calculate the curvature change of the connection region, determine whether there are non-smooth or discontinuous regions, and generate the geometric abrupt check results of the connection region.

[0086] Based on the results of geometric abrupt change checks in the connected regions, regions with geometric abrupt changes are corrected. The abrupt change regions are smoothly adjusted point by point. During the adjustment process, the transition of the surface is optimized to ensure continuity and generate the corrected geometric region.

[0087] Based on the corrected geometric region, the entire surface is optimized, a surface smoothing operation is performed, the connection between surface nodes and boundaries is adjusted, the overall geometric shape is gradually optimized, and the fused surface geometric optimization result is generated.

[0088] Based on the weighted fusion structure generation results, a graph neural network is used to perform geometric abrupt changes in the connection regions. A spatial scanning method is used to measure the geometry of the connection regions point by point. The distance matrix between points in the connection regions is calculated using the scipy.spatial.distance.pdist function. Temporal data processing is performed using tensorflow.keras.layers.GRU layers. The geometric curvature of each point is calculated through the network's feedback mechanism, and the curvature change is calculated using numpy.diff to determine whether there are non-smooth or discontinuous regions, thus generating geometric abrupt change detection results for the connection regions.

[0089] Based on the results of the geometric abrupt change check in the connected region, the regions with geometric abrupt changes are corrected. The abrupt change regions are smoothed point by point. The B-spline interpolation method is used. The surface interpolation is performed by using the scipy.interpolate.BSpline function. The smoothness of the curve is adjusted by setting control points and curve smoothness to optimize the transition of the surface. The scipy.optimize.minimize function is used for minimization to ensure the continuity of the transition region and generate the corrected geometric region.

[0090] Based on the corrected geometric region, the entire surface is optimized by performing a surface smoothing operation using the Laplacian smoothing algorithm. The Laplacian matrix of the surface nodes is calculated using scipy.sparse.csgraph.laplacian, and the connection between the surface nodes and the boundary is adjusted to gradually optimize the overall geometric shape and generate the fused surface geometric optimization result.

[0091] Graph neural networks, according to the formula:

[0092] ;

[0093] in: This indicates the curvature change in the connected region. Represents a node The structural propagation weights, Represents a node The density adjustment coefficient, Represents a node To the reference point Euclidean distance, This represents the disturbance suppression term. Represents a node In spatial coordinates The elevation value below, Represents a node In space coordinate, Represents a node In space coordinate, This represents the number of neighboring nodes used for curvature calculation;

[0094] Execution process: First, for each node within the connected region... Process the data to determine the structural propagation weights of the nodes. The feature aggregation of adjacent edges in the graph is used to learn and represent the importance of a node in the graph. Next, the importance of each node is calculated. Density adjustment coefficient This is achieved by adjusting the node distribution density within a local area, enhancing sensitivity to curvature changes in dense regions, and then calculating the nodes. To the reference point Euclidean distance Used to describe the relative position of nodes in space, with perturbation suppression terms added. To ensure that numerical anomalies are avoided when the distance is zero during the calculation process, the next step is to calculate the node. In its spatial coordinates and Elevation value below Furthermore, the second-order partial derivatives of the curves are calculated to obtain the curvature change of each node. Then, the local curvature changes of each node are weighted according to their respective weights, and the overall curvature change of the connected region is obtained by accumulating the weighted curvature changes of all neighboring nodes. This allows for geometric mutation checks to determine if there are any unsmooth or discontinuous regions, effectively identifying and optimizing potential geometric problems in three-period minimal surface structures.

[0095] The results of the fused surface geometry optimization include surface smoothness evaluation values, abrupt change correction node index set, and optimized surface mesh data.

[0096] Please see Figure 6 The specific steps for generating an optimized design file in STL format are as follows:

[0097] Based on the results of the fused surface geometry optimization, the stiffness-mass ratio is optimized. The stiffness-mass ratio of each region is measured. By checking the ratio of each region one by one, it is analyzed whether it meets the design specifications. The region stiffness-mass ratio is calculated, and the region stiffness-mass ratio analysis results are generated.

[0098] Based on the analysis results of regional stiffness and mass ratio, the geometric properties of each region are adjusted. By modifying the region shape, thickness or structural distribution, the stiffness and mass ratio are optimized point by point, and the geometric property adjustment results are generated.

[0099] Based on the results of the geometric property adjustment, the optimized geometric structure is exported as an STL file, the file format is converted, the output precision is adjusted, and an optimized design file in STL format is generated.

[0100] Based on the results of the integrated surface geometry optimization, the stiffness-mass ratio is optimized. The stiffness-mass ratio of each region is measured. The volume and mass of each region are calculated by using the scipy.integrate.quad function. The stiffness matrix of each region is calculated by using the scipy.linalg.eigh function. The ratio of each region is checked one by one. A ratio threshold is set and the ratio is calculated to generate the region stiffness-mass ratio analysis results.

[0101] Based on the analysis results of regional stiffness and mass ratio, the geometric properties of each region are adjusted. By modifying the region shape, thickness or structural distribution, the finite element analysis method is used. By using the pycalculix library, the geometric constraints and material properties of each region are set, and the stiffness and mass ratio are optimized point by point to generate the geometric property adjustment results.

[0102] Based on the results of the geometric property adjustments, the optimized geometric structure is exported as an STL file. The file format is converted, and the mesh.Mesh object in the numpy-stl library is used to read the optimized geometric data, adjust the output precision, and use the stl.mesh.Mesh.save function to save the STL file, generating an STL format optimized design file.

[0103] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for designing a spatial positioning fusion structure of a three-period minimal surface based on the inverse distance weighting method, characterized in that, Includes the following steps: S1: Based on the design requirements of the three-period minimal surface, define the TPMS implicit function equation, set control points, determine the spatial distribution and geometric constraints, select control points that meet the requirements, calculate the geometric position, and generate the TPMS implicit function equation and control point definition results. S2: Based on the implicit function equation of TPMS and the definition results of control points, select multiple TPMS surfaces, define interpolation center points, calculate the spatial distance from control points to each interpolation center point, determine the geometric distribution, calculate the geometric weights, select suitable control points, and generate the geometric weight calculation results of control points. S3: Based on the geometric weight calculation results of the control points, a convolutional neural network is used to perform inverse distance weighting calculation, adjust the control point weights, determine whether they meet the design requirements, adjust unqualified areas, and generate a weighted fusion structure generation result; S4: Perform geometric optimization on the weighted fusion structure generation result, using a graph neural network to determine whether there are abrupt changes in the connection region, perform correction and smoothing, optimize the surface, and generate the geometrically optimized fusion surface result; S5: Based on the results of the fused surface geometry optimization, optimize the stiffness-mass ratio, analyze the region stiffness-mass ratio, adjust the geometric properties, export the STL file, and obtain the STL format optimization design file; The specific steps for generating the geometric weight calculation results of the control points are as follows: Based on the implicit function equations and control point definitions of the TPMS, multiple TPMS surfaces are selected, the interpolation center point positions are defined, the spatial distance from the control points to each interpolation center point is calculated, the distance between the control points is measured one by one, the spatial distance value of each pair of control points is obtained, and the spatial distance calculation result of the control points is generated. Based on the spatial distance calculation results of the control points, check the geometric distribution of the control points in space, perform geometric relationship calculation between the control points, compare the distance between the control points with the preset geometric requirements, adjust the distribution position of the control points, and generate geometric distribution adjustment results. Based on the geometric distribution adjustment results, the geometric weight of each control point is calculated using a weighted average. The weighting ratio of the control points is adjusted, and control points meeting the criteria are selected to generate the geometric weight calculation results. Alternatively, based on the geometric distribution adjustment results, the geometric weight of each control point is calculated using an inverse distance weighting algorithm. This involves calculating the distance between each pair of control points using the `scipy.spatial.distance.pdist` function, exponentially weighting the distances using the `numpy.exp` function, calculating the weighting ratio, selecting control points meeting the criteria, and generating the geometric weight calculation results. The specific steps for generating the weighted fusion structure are as follows: Based on the geometric weight calculation results of the control points, a convolutional neural network is used to perform inverse distance weighting calculation, measure the spatial distance between control points, calculate the weight value of each control point, and adjust the weight of the control points according to the calculation results to generate the inverse distance weighting calculation results. Based on the inverse distance weighted calculation results, the weight of each control point is adjusted, and it is checked whether the design requirements are met. Weight adjustment is performed on areas that do not meet the requirements. During the adjustment process, the area is optimized point by point to generate the adjusted control point weights. Based on the adjusted control point weights, the control point positions and weights are fused together, and the optimized control points are combined to generate a fused structure. The control point fusion process is then executed to generate the weighted fusion structure result. Based on the geometric weight calculation results of the control points, a convolutional neural network is used to perform inverse distance weighting calculation to measure the spatial distance between control points. The Euclidean distance between all control point pairs is calculated using the scipy.spatial.distance.cdist function, and the weight value of each control point is calculated. The convolution kernel is set using tensorflow.keras.layers.Conv2D to perform inverse distance weighting convolution operation, and the weighting weights of the control points are adjusted according to the calculation results to generate the inverse distance weighting calculation result. The convolutional neural network is configured according to the formula: ； in: Indicate control points The weighted value, Indicate control points Geometric weights, Indicate control points Environmental sensitivity coefficient Indicate control points semantic association coefficient, Indicate control points With control points Spatial distance between them Indicate control points The perturbation suppression term, Indicates the basic inverse distance weighted index. Indicate control points The nonlinear response adjustment coefficient, Indicates the number of control points involved in the calculation; Execution process: First, calculate the geometric weight of each control point. Then utilize spatial distance Calculate control points With all other control points To more accurately reflect the relationship between control points, an environmental sensitivity coefficient was introduced to determine their relative positions. Used to measure control points The response to characteristic density changes within a local space is represented by the set of distances between statistical control points in the local neighborhood. Calculate, then calculate the control points. With target control point semantic association coefficient Based on the cosine similarity between convolutional feature vectors, the similarity between control points in the feature space is characterized. To prevent computational anomalies caused by zero spatial distance, a perturbation suppression term is added. The value is a constant to ensure the stability of the formula. Finally, a nonlinear response adjustment coefficient is introduced. By calculating control points The sensitivity to distance changes is adjusted by varying the response in the feature space, and the control points are calculated using the sigmoidal function. weighted value This allows for more precise adjustment of the control point weights, thereby optimizing the fusion structure design of the three-cycle minimal surface spatial positioning and achieving higher accuracy and stability.

2. The three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method according to claim 1, characterized in that, The specific steps for generating the TPMS implicit function equations and control point definitions are as follows: Based on the design requirements of the three-period minimal surface, the initial position of the control points is selected, and geometric dimensions and morphology analysis are performed. The spatial position of the control points is determined through geometric analysis, the initial layout is executed, and the layout conditions are set to generate the initial layout of the control points. Based on the initial layout of the control points, spatial distribution and geometric constraint analysis are performed, the distance and distribution between the control points are adjusted to meet the preset geometric conditions, the geometric constraints and relative positions of each control point are checked, and a control point layout that meets the requirements is generated. Based on the control point layout that meets the requirements, the geometric position of each control point is calculated, position correction is performed, the matching between the spatial distribution and the surface requirements is verified, and the TPMS implicit function equation and control point definition results are generated.

3. The three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method according to claim 1, characterized in that, The weighted fusion structure generation result includes the adjusted control point weight distribution, fused surface lattice data, and structural integrity marker set.

4. The three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method according to claim 1, characterized in that, The specific steps for generating the fused surface geometry optimization result are as follows: Based on the weighted fusion structure generation result, a graph neural network is used to perform geometric abrupt checks on the connection region. A spatial scanning method is used to measure the geometry of the connection region point by point, calculate the curvature change of the connection region, determine whether there are unsmooth or discontinuous regions, and generate the geometric abrupt check result of the connection region. Based on the results of the geometric abrupt change check of the connection region, the regions with geometric abrupt changes are corrected. The abrupt change regions are smoothly adjusted point by point. During the adjustment process, the transition of the surface is optimized to ensure continuity and generate the corrected geometric region. Based on the corrected geometric region, the entire surface is optimized by performing a surface smoothing operation, adjusting the connection between surface nodes and boundaries, gradually optimizing the overall geometric shape, and generating a fused surface geometric optimization result.

5. The three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method according to claim 4, characterized in that, The graph neural network is defined according to the formula: ； in: This indicates the curvature change in the connected region. Represents a node The structural propagation weights, Represents a node The density adjustment coefficient, Represents a node To the reference point Euclidean distance, This represents the disturbance suppression term. Represents a node In spatial coordinates The elevation value below, Represents a node In space coordinate, Represents a node In space coordinate, This represents the number of neighboring nodes used for curvature calculation; Execution process: First, for each node within the connected region... Process the data to determine the structural propagation weights of the nodes. The feature aggregation of adjacent edges in the graph is used to learn and represent the importance of a node in the graph. Next, the importance of each node is calculated. Density adjustment coefficient This is achieved by adjusting the node distribution density within a local area, enhancing sensitivity to curvature changes in dense regions, and then calculating the nodes. To the reference point Euclidean distance Used to describe the relative position of nodes in space, with perturbation suppression terms added. To ensure that numerical anomalies are avoided when the distance is zero during the calculation process, the next step is to calculate the node. In its spatial coordinates and Elevation value below Furthermore, the second-order partial derivatives of the curves are calculated to obtain the curvature change of each node. Then, the local curvature changes of each node are weighted according to their respective weights, and the overall curvature change of the connected region is obtained by accumulating the weighted curvature changes of all neighboring nodes. This allows for geometric mutation checks to determine if there are any unsmooth or discontinuous regions, effectively identifying and optimizing potential geometric problems in three-period minimal surface structures.

6. The three-period minimum surface spatial positioning fusion structure design method based on the inverse distance weighting method according to claim 4, characterized in that, The fused surface geometry optimization results include surface smoothness evaluation values, a set of abrupt change correction node indices, and optimized surface mesh data.

7. The three-period minimal surface spatial positioning fusion structure design method based on the inverse distance weighting method according to claim 1, characterized in that, The specific steps for generating the STL format optimized design file are as follows: Based on the optimized results of the fused surface geometry, the stiffness-mass ratio is optimized, the stiffness-mass ratio of each region is measured, and the ratio of each region is checked one by one to analyze whether it meets the design specifications. The region stiffness-mass ratio is calculated, and the region stiffness-mass ratio analysis results are generated. Based on the analysis results of the region stiffness and mass ratio, the geometric properties of each region are adjusted. By modifying the region shape, thickness or structural distribution, the stiffness and mass ratio are optimized point by point, and the geometric property adjustment results are generated. Based on the results of the geometric characteristic adjustment, the optimized geometric structure is exported as an STL file, the file format is converted, the output precision is adjusted, and an optimized design file in STL format is generated.

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