CN-121302856-B - Product structure and other geometric topology optimization method and system based on neural network

CN121302856BCN 121302856 BCN121302856 BCN 121302856BCN-121302856-B

Abstract

The invention discloses a geometric topological optimization method and a geometric topological optimization system for a product structure and the like based on a neural network, which belong to the field of structural optimization, and comprise the steps of firstly constructing a geometric topological optimization model for the product structure and the like, adopting an geometric topological optimization algorithm, taking the space coordinates and the relative density of fine grid control points and the displacement and the sensitivity of coarse grid control points as inputs, taking the sensitivity of the fine grid control points as outputs to generate a training data set, then training a graph convolution neural network model with multi-resolution information extraction capability by utilizing the data set, integrating the trained neural network model into an geometric topological optimization solving process, and finally directly predicting the sensitivity of the fine grid control points through the neural network, thereby avoiding the geometric analysis of high calculation cost on the fine grid layer surface and remarkably improving the calculation efficiency of geometric optimization for the product structure and the like.

Inventors

CHENG JIN
Peng Deshang
HU XINTING
LIU ZHENYU
LIU DAXIN
LIU HUI
TAN JIANRONG

Assignees

浙江大学

Dates

Publication Date: 20260512
Application Date: 20250917

Claims (9)

1. The product structure and other geometric topology optimization method based on the neural network is characterized by comprising the following steps: S1, taking the flexibility of a product structure as a target, the material consumption as constraint, and the relative density of control points of an isogeometric unit as a design variable, and constructing a geometric topological optimization model of the product structure and the like; S2, discrete product structure design domain is used for obtaining coarse grid of product structure, coarse grid is refined, geometric topological optimization is carried out on the coarse grid and the fine grid, and a group of offline data sets are obtained, wherein the offline data sets are formed by taking space coordinates and relative density of fine grid control points, displacement and sensitivity of the coarse grid control points as input data and sensitivity of the fine grid control points as output data; Step S3, training a neural network model by using an offline data set, wherein the neural network model comprises a global stiffness information extraction neural network module and a local information fusion neural network module; The system comprises a global stiffness information extraction neural network module, a aggregation layer and a feature dimension aggregation layer, wherein the global stiffness information extraction neural network module comprises a graph roll input layer, a graph roll hiding layer and a graph roll aggregation layer, the outputs of the input layer and the hiding layer are connected to the aggregation layer through knowledge jump, the input layer receives global fine grid control point information; The local information fusion neural network module specifically comprises a full-connection neural network model, wherein the full-connection neural network model comprises a full-connection input layer, a full-connection hidden layer and a full-connection output layer, the input layer acquires displacement and sensitivity on a local coarse unit control point, and extracts characteristic information extracted by the neural network module through global stiffness information on a local fine unit control point, the local coarse unit refers to a single NURBS basis function unit under a coarse grid, the local fine unit refers to a plurality of fine units which are obtained by subdivision of a node insertion strategy in the single coarse unit, and the full-connection output layer is used for outputting the sensitivity on the local fine unit control point; and S4, online applying the trained neural network model to the isogeometric topological optimization of the product structure so as to obtain a topological optimization density distribution result of the product structure.
2. The neural network-based product structure isogeometric topology optimization method according to claim 1, wherein the step S2 specifically comprises the following steps: s2.1, adopting an isogeometric basis function as a design domain of a discrete product structure of a shape function to obtain a coarse grid of the product structure; S2.2, refining a coarse grid of a product structure by adopting an isogeometric node insertion strategy to obtain a fine grid and a mapping matrix of the fine grid and coarse grid control points; s2.3, respectively performing geometric analysis on the coarse grid and the fine grid to obtain displacement of two control points of the coarse grid and the fine grid; s2.4, calculating the sensitivity of the coarse grid control points and the fine grid control points; S2.5, taking the space coordinates and the relative density of the fine grid control points and the displacement and the sensitivity of the coarse grid control points as input data, and taking the sensitivity of the fine grid control points as output data to construct a group of offline training data sets; s2.6, according to the sensitivity information of the fine grid control points, updating the relative density on the fine grid control points by using a moving asymptote algorithm, and calculating the relative density of the coarse grid control points according to the mapping matrix; and S2.7, judging whether convergence conditions of the isogeometric topological optimization are met, if not, jumping to the step S2.3, and if so, stopping the isogeometric topological optimization iteration.
3. The neural network-based product structure isogeometric topology optimization method is characterized in that isogeometric node insertion strategies refine NURBS coarse grids of the product structure, the nodes are inserted into coarse grid node vectors to obtain refined node vectors, control points of fine grids are formed by linearly combining the coarse grid control points, the coarse grid control points are mapped to the fine grid control points through a difference matrix, the control points of each fine grid are the result of weighted average of a plurality of coarse grid control points around the fine grid control points, each row in an interpolation matrix corresponds to a weighting coefficient needed by one fine grid control point, the weighting coefficient is obtained through multiple recursion calculation through the ratio of fine grid node vector values to coarse grid node vector values, and a mapping relation between the coarse grid and the fine grid control points is established based on the difference matrix.
4. The neural network-based product structure isogeometric topology optimization method of claim 3, wherein the coarse grid node vector is N represents the number of coarse grid control points in the parameter domain, p represents the NURBS basis function order, and the refined node vector , , Control point matrix representing degree of refinement, fine grid Control of dot matrix by coarse grid Is formed by linear combination of the components, and the specific mapping relation is as follows: Wherein, the Representing coarse grid control points Mapping to fine mesh control points Is used for the interpolation matrix of (a), Representing coarse mesh node vectors The value of the j-th node in the list, Representing fine-grid node vectors Is a value of the i-th node in the list, Representing the element values at the j-th column of the i-th row in the interpolation matrix of the q-th order, Represents fine grid control points based on coarse grid refinement, Representing coarse grid control points.
5. The neural network-based product structure isogeometric topology optimization method according to claim 1, wherein the step S4 specifically comprises the following steps: S4.1, utilizing an isogeometric basis function as a shape function discrete product structure design domain, and combining an isogeometric node insertion strategy to obtain coarse grid and fine grid control points of a product structure and a mapping matrix of the coarse grid and the fine grid control points; S4.2, performing isogeometric analysis on the product structure on the coarse grid, and calculating the sensitivity corresponding to the control points of the coarse grid; s4.3, inputting the coordinates and the relative density of control points of the fine grid of the product structure, the displacement and the sensitivity of control points of the coarse grid into a trained neural network model to obtain the sensitivity of the control points of the fine grid; S4.4, according to the sensitivity information of the fine grid control points, updating the relative density on the fine grid control points by adopting a moving asymptote algorithm, and calculating the relative density of the coarse grid control points according to the generalized inverse matrix of the coarse and fine grid control point mapping matrix; And S4.5, judging whether convergence conditions of the isogeometric topological optimization are met, if not, jumping to the step S4.2, and if so, stopping the isogeometric topological optimization iteration to obtain an isogeometric topological optimization density distribution result.
6. The neural network-based product structure isogeometric topology optimization method according to claim 1, wherein the product structure isogeometric topology optimization model expression in the step S1 is as follows: Wherein, the Indicating the structural flexibility of the product, And Representing the global displacement and the load vector respectively, Representing a global stiffness matrix of the vehicle, And Representing the cell displacement vector and stiffness matrix respectively, Representing the number of isogeometric units, The function of the volume of the structure is represented, And Respectively representing the total volume of the product structure and the utilization rate of materials, As a design variable to represent the relative density of the control points, And Respectively the number of control points in both directions of the parameter domain, The minimum of the design variables expressed as avoiding singular settings of the stiffness matrix.
7. The geometrical topological optimization system based on the neural network comprises a geometrical topological optimization model building module of the product structure, an offline data set generating module, a neural network module, a geometrical topological optimization generating module of the product structure, and the like, and is characterized in that the geometrical topological optimization method based on the neural network, which is disclosed in any one of claims 1 to 6, is adopted to sequentially build the geometrical topological optimization model of the product structure, generate the offline data set, build the neural network model, and generate the geometrical topological optimization result of the product structure, and the like.
8. The neural network-based product structure isogeometric topology optimization system of claim 7, wherein the offline data set generation module comprises a coarse grid generation unit, a mapping matrix generation unit, an isogeometric analysis unit, a sensitivity calculation unit, an offline training data set construction unit, a relative density generation unit and a judgment unit; the coarse grid generating unit adopts an isogeometric basis function as a design domain of a discrete product structure of the shape function to obtain a coarse grid of the product structure; the mapping matrix generation unit refines the coarse grid of the product structure by adopting an isogeometric node insertion strategy to obtain a fine grid and a mapping matrix of the fine grid and the coarse grid control points; The isogeometric analysis unit is used for respectively carrying out isogeometric analysis on the coarse grid and the fine grid to obtain the displacement of two control points of the coarse grid and the fine grid; The sensitivity calculation unit is used for calculating the sensitivities of the coarse grid control points and the fine grid control points; The off-line training data set construction unit takes the space coordinates and the relative density of the fine grid control points and the displacement and the sensitivity of the coarse grid control points as input data, and takes the sensitivity of the fine grid control points as output data to construct a group of off-line training data sets; The relative density generating unit is used for updating the relative density on the fine grid control points by using a moving asymptote algorithm according to the sensitivity information of the fine grid control points, and calculating the relative density of the coarse grid control points according to the mapping matrix; The judging unit is used for judging whether the convergence condition of the isogeometric topological optimization is met, if not, returning to the isogeometric analysis unit, and if so, stopping the isogeometric topological optimization iteration.
9. The neural network-based product structure isogeometric topological optimization system as set forth in claim 7, wherein the product structure isogeometric topological optimization generation module comprises a product structure discrete unit, a coarse grid isogeometric analysis unit, a fine grid sensitivity generation module, a relative density generation module and a density distribution generation module; The product structure discrete unit uses an isogeometric basis function as a shape function discrete product structure design domain, and obtains coarse grid and fine grid control points of a product structure and a mapping matrix of the coarse and fine grid control points by combining an isogeometric node insertion strategy; the geometric analysis unit of the coarse grid performs geometric analysis on the product structure on the coarse grid, and calculates the sensitivity corresponding to the control points of the coarse grid; The fine grid sensitivity generation module inputs the control point coordinates and relative density of the fine grid of the product structure, the control point displacement and sensitivity of the coarse grid into a trained neural network model to obtain the fine grid control point sensitivity; the relative density generation module is used for updating the relative density on the fine grid control points by adopting a moving asymptote algorithm according to the sensitivity information of the fine grid control points, and calculating the relative density of the coarse grid control points according to the generalized inverse matrix of the coarse and fine grid control point mapping matrix; and the density distribution generation module judges whether convergence conditions of the isogeometric topological optimization are met, if not, the isogeometric analysis unit of the coarse grid is returned, and if so, the isogeometric topological optimization iteration is stopped, and an isogeometric topological optimization density distribution result is obtained.

Description

Product structure and other geometric topology optimization method and system based on neural network Technical Field The invention belongs to the field of structural optimization, and particularly relates to a geometric topology optimization method and system for a product structure and the like based on a neural network. Background The geometric topological optimization adopts spline basis functions as a shape function, can characterize geometric boundaries with complex curvature with high precision, realizes the unification of CAD models, CAE models and topological optimization models, shows remarkable advantages in the aspects of geometric continuity and numerical analysis precision, but also leads to a more complex numerical calculation process, so that the calculation cost of topological optimization is greatly increased. With the rapid development of computer hardware technology and artificial intelligence, computing mechanics is gradually changing from traditional methods relying on strict mathematical derivation to heuristic intelligent methods of soft computing, and some of the prior art has begun to attempt to introduce techniques such as machine learning into the field of topology optimization. However, most of the existing researches focus on an end-to-end mapping method from a boundary condition to a topology optimization result, a large amount of training data is generally required, and the topology optimization result is highly sensitive to the boundary condition, so that generalization capability is poor when facing an optimization problem outside a training set, and the effect is often not ideal. In addition, the existing topology optimization research based on machine learning is mainly based on the traditional finite element analysis framework, so how to perform isogeometric topology optimization based on the product structure of the neural network has important significance and application value. Disclosure of Invention In order to solve the defects in the prior art and achieve the purposes of improving the structural design precision and efficiency of products and reducing the cost, the invention adopts the following technical scheme: the product structure and other geometric topology optimization method based on the neural network comprises the following steps: S1, taking the flexibility of a product structure as a target, the material consumption as constraint, and the relative density of control points of an isogeometric unit as a design variable, and constructing a geometric topological optimization model of the product structure and the like; S2, discrete product structure design domain is used for obtaining coarse grid of product structure, coarse grid is refined, geometric topological optimization is carried out on the coarse grid and the fine grid, and a group of offline data sets are obtained, wherein the offline data sets are formed by taking space coordinates and relative density of fine grid control points, displacement and sensitivity of the coarse grid control points as input data and sensitivity of the fine grid control points as output data; step S3, training a neural network model by using the offline data set; and S4, online applying the trained neural network model to the isogeometric topological optimization of the product structure so as to obtain a topological optimization density distribution result of the product structure. Further, the step S2 specifically includes the following steps: s2.1, adopting a double third-order NURBS basis function as a design domain of a discrete product structure of a shape function to obtain a NURBS coarse grid of the product structure; S2.2, refining NURBS coarse meshes of the product structure by adopting an isogeometric node insertion strategy to obtain NURBS fine meshes and a mapping matrix of the fine meshes and coarse mesh control points; s2.3, respectively performing geometric analysis on the coarse grid and the fine grid to obtain the displacement of the control points of the coarse grid and the fine grid; s2.4, calculating the sensitivity of the coarse grid control points and the fine grid control points; S2.5, taking the space coordinates and the relative density of the fine grid control points and the displacement and the sensitivity of the coarse grid control points as input data, and taking the sensitivity of the fine grid control points as output data to construct a group of offline training data sets; s2.6, according to the sensitivity information of the fine grid control points, updating the relative density on the fine grid control points by using a moving asymptote algorithm, and calculating the relative density of the coarse grid control points according to the mapping matrix; and S2.7, judging whether convergence conditions of the isogeometric topological optimization are met, if not, jumping to the step S2.3, and if so, stopping the isogeometric topological optimization iteration. Further, the equal geometry no