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CN-121279067-B - Product structure intelligent integrated design method based on neural network re-parameterization

CN121279067BCN 121279067 BCN121279067 BCN 121279067BCN-121279067-B

Abstract

The invention belongs to the field of structural optimization design, and discloses a product structure intelligent integrated design method based on neural network heavy parameterization, which comprises the steps of constructing a feedforward neural network fused with multi-scale Fourier features, re-parameterizing Gaussian point density into weights and offsets related to the neural network, taking product structure flexibility as an optimization target, taking neural network model parameters as design variables, establishing an intelligent integrated design model, solving structural displacement and unit flexibility through isogeometric analysis, processing constraint by adopting an augmented Lagrangian method, calculating loss of the neural network based on linear weighting of an objective function under each volume fraction, dynamically balancing weight coefficients based on learning speed and loss values, realizing solving of the optimization model through a built-in optimizer, and calculating global density function under expected volume fraction by adopting trained network parameters so as to obtain an optimal product structure. The invention can obtain the product structure meeting the design requirement with high efficiency and intelligence.

Inventors

  • CHENG JIN
  • YAN MING
  • LIU HUI
  • LIU DAXIN
  • LIU ZHENYU
  • TAN JIANRONG

Assignees

  • 浙江大学

Dates

Publication Date
20260508
Application Date
20250829

Claims (6)

  1. 1. The intelligent integrated design method for the product structure based on the neural network re-parameterization is characterized by comprising the following steps: 1) Constructing a NURBS and other geometric analysis grid model according to the design domain, determining the parameter space, the basis function and the coordinates of control points and Gaussian points, and applying boundary conditions and geometric constraints to the discretized structure; 2) Building a neural network model, and obtaining the density of corresponding points by designing the parameter coordinates and the volume fraction of Gaussian points in the domain; 3) Taking the flexibility of the structure as an optimization target, taking the neural network model parameters as design variables, and establishing an intelligent integrated design model of the product structure based on the re-parameterization of the neural network; 4) Calculating structural displacement and unit flexibility based on Gaussian point density obtained by the neural network model; 5) Adopting an augmented Lagrangian method to process constraint, and calculating a loss function of the neural network model based on an objective function linear weighting under each volume fraction; 6) Checking whether the relative change value of the total loss in the iteration is smaller than a set threshold value, dynamically balancing the weight coefficient based on the loss value if the condition is met, otherwise dynamically balancing the weight coefficient based on the learning speed; 7) The trained neural network model parameters are adopted, the density of each Gaussian point under the expected volume fraction is output, the global density function is calculated, and the optimized structure is obtained; the step 4) comprises the following sub-steps: 4.1 Calculating cell stiffness matrix : Wherein D represents an elastic matrix, Representing a geometric matrix, p representing a first penalty factor, Representing cell stiffness matrix At the Gaussian point An integral term at the location of the point, Representing the corresponding integral weights; Representing a jacobian mapping NURBS parameter space to physical space, A jacobian matrix representing a mapping of gaussian integral space to NURBS parameter space; 4.2 Assembling a global stiffness matrix K and solving a global displacement vector U; 4.3 Calculating the volume of the gaussian integral unit by Compliance with : Wherein, the Representing the geometric unit displacement.
  2. 2. The intelligent integrated design method of the product structure based on the neural network reparameterization of claim 1, wherein in the step 2), the neural network model adopts a feedforward neural network model fused with multi-scale Fourier features, and is input as coordinates of Gaussian points in a parameter space And volume fraction The output is the density of Gaussian points Re-parameterizing design variables in topology optimization into neural network-related weights and biases And for the input coordinate parameters And volume fraction The following random fourier feature map is made: , wherein the parameter sequence Randomly sampled from a standard normal distribution with standard deviation sigma.
  3. 3. The intelligent integrated design method for the product structure based on the neural network re-parameterization of claim 1, wherein in the step 3), the intelligent integrated design model for the product structure based on the neural network re-parameterization is as follows: Wherein, the A set of preset volume fractions is indicated, 、 And (3) with Representing structural flexibility, global displacement vector and Gaussian point density field under the corresponding volume fraction; representing a global stiffness matrix of the vehicle, Indicating the load of the external force applied thereto, Representing parameters related to the neural network model, including weights and biases; Representing the set of all gaussian points within the structural design domain, Representing the coordinates of the gaussian point in NURBS parameter space, Representing the density of the Gaussian points output by the neural network, and re-parameterizing the density by Characterization of the related functions; Representing an isogeometric unit Is provided with a gaussian integral unit volume, Representing the structural volume.
  4. 4. The method for intelligent integrated design of product structure based on neural network reparameterization according to claim 1, wherein in the step 5), the following loss functions are constructed and calculated based on the objective functions under each volume fraction and the corresponding constraints linear weights thereof: Wherein, the Wherein, the The weight coefficient is represented by a number of weight coefficients, Representing the lagrangian multiplier and, A second penalty factor is indicated and is indicated, Representing the initial compliance of the structure.
  5. 5. The intelligent integrated design method for the product structure based on the neural network reparameterization according to claim 4, wherein in the step 6), the Lagrangian multiplier and the penalty factor are updated according to the following rules: wherein t represents the number of iterations, Representing step size, weight coefficient at t-th iteration The expression is as follows: Wherein, the Represent the learning speed of the t-th iteration, consisting of The loss ratio of the first two iterations is defined.
  6. 6. The intelligent integrated design method for the product structure based on the neural network reparameterization of claim 1, wherein in the step 7), the global density function Calculated from the following formula: wherein, the Representing the matrix of NURBS basis functions, Representing a matrix of values of NURBS basis functions at various gaussian points, And the Gaussian point density vector which is output by the neural network after training is represented.

Description

Product structure intelligent integrated design method based on neural network re-parameterization Technical Field The invention belongs to the field of structural optimization design, and particularly relates to an intelligent integrated design method for a product structure based on neural network reparameterization. Background The product structure integrated design method driven by the isogeometric analysis accurately characterizes complex high-curvature geometric boundaries by adopting spline basis functions with high-order continuous characteristics such as non-uniform rational B-splines (NURBS) and the like as a shape function, unifies a CAD geometric model, a CAE analysis model and a topology optimization model of the product structure, and shows remarkable advantages in analysis precision and geometric continuity. However, this advantage is accompanied by a more complex numerical calculation process, resulting in a significant increase in the computational cost of topology optimization. With the rapid development of machine learning technologies such as neural networks, many researches are beginning to be conducted to apply the technologies in the field to improve the efficiency of product structure integrated design based on isogeometric analysis. The existing product structure integrated design based on the data-driven neural network aims at training a proxy model with optimization capability, when some problem description characteristics are given, the optimal product structure is obtained in a non-iterative mode, huge calculation cost is often required to be spent to generate a large number of topological structures as training samples, and the problem of structure fracture exists in the optimization result. Furthermore, existing neural networks have a lack of expression capability for fine features in topology. Disclosure of Invention In order to solve the defects of the existing product structure integrated design technology based on the isogeometric analysis, reduce the calculation cost, improve the optimization accuracy and avoid structural fracture, the invention adopts the following technical scheme: a product structure intelligent integrated design method based on neural network reparameterization comprises the following steps: 1) Constructing a NURBS and other geometric analysis grid model according to the design domain, determining the parameter space, the basis function and the coordinates of control points and Gaussian points, and applying boundary conditions and geometric constraints to the discretized structure; 2) Building a neural network model, and obtaining the density of corresponding points by designing the parameter coordinates and the volume fraction of Gaussian points in the domain; 3) Taking the flexibility of the structure as an optimization target, taking the neural network model parameters as design variables, and establishing an intelligent integrated design model of the product structure based on the re-parameterization of the neural network; 4) Calculating structural displacement and unit flexibility based on Gaussian point density obtained by the neural network model; 5) Adopting an augmented Lagrangian method to process constraint, and calculating a loss function of the neural network model based on an objective function linear weighting under each volume fraction; 6) Checking whether the relative change value of the total loss in the iteration is smaller than a set threshold value, dynamically balancing the weight coefficient based on the loss value if the condition is met, otherwise dynamically balancing the weight coefficient based on the learning speed; 7) And outputting the density of each Gaussian point under the expected volume fraction by adopting the trained neural network model parameters, and calculating a global density function to obtain an optimized structure. Further, in the step 2), a feedforward neural network model fused with multi-scale fourier features is adopted, and the input is coordinates (ζ, η) of a gaussian point in a parameter space, and the volume fraction v is output as the density of the gaussian pointRe-parameterizing design variables in topology optimization into weights and offsets w related to a neural network, and carrying out the following random Fourier feature mapping on input coordinate parameters (ζ, η) and volume fraction v: γ(v)=[sin(2πv)cos(2πv)] Wherein the parameter sequence { a 1,a2,...,an}{b1,b2,...,bn } is randomly sampled from a standard normal distribution with standard deviation sigma. Further, in the step 3), the intelligent integrated design model of the product structure based on the neural network re-parameterization is as follows: i=1,2...,Nv Wherein, the Representing a set of predetermined volume fractions, c i、Ui andRepresenting structural flexibility, global displacement vector and Gaussian point density field under the corresponding volume fraction; Representing a global stiffness matrix, F representing