A product structure intelligent integrated design method based on neural network reparameterization

Abstract

The application belongs to the field of structure optimization design, and discloses a product structure intelligent integrated design method based on neural network reparameterization, constructs a feedforward neural network fusing multi-scale Fourier features, reparameterizes Gaussian point density into weights and biases related to the neural network, takes product structure flexibility as an optimization target, takes neural network model parameters as design variables, and establishes an intelligent integrated design model; solves structure displacement and element flexibility through isogeometric analysis, processes constraints by using the augmented Lagrange method, calculates neural network loss based on linear weighting of the objective function under each volume fraction, dynamically balances weight coefficients based on learning speed and loss value, and realizes solving of the optimization model through an embedded optimizer; calculates a global density function under an expected volume fraction by using trained network parameters, so that an optimal product structure is obtained. The application can efficiently and intelligently obtain a product structure meeting design requirements.

Description

Technical Field

[0001] This invention belongs to the field of structural optimization design, specifically relating to an intelligent integrated design method for product structures based on neural network reparameterization. Background Technology

[0002] The integrated product structure design method driven by geometric analysis employs spline basis functions with high-order continuity properties, such as non-uniform rational B-splines (NURBS), as shape functions. This accurately characterizes complex high-curvature geometric boundaries and unifies the CAD geometric model, CAE analysis model, and topology optimization model of the product structure, demonstrating significant advantages in analysis accuracy and geometric continuity. However, this advantage is accompanied by a more complex numerical calculation process, leading to a significant increase in the computational cost of topology optimization.

[0003] With the rapid development of machine learning technologies such as neural networks, many studies have begun to focus on using these technologies to improve the efficiency of integrated product structure design based on isogeometric analysis. Existing integrated product structure design based on data-driven neural networks aims to train a surrogate model with optimization capabilities. Given some problem-descriptive features, it obtains the optimal product structure in a non-iterative manner, often requiring huge computational costs to generate a large number of topological structures as training samples, and the optimization results suffer from structural fragmentation. Furthermore, existing neural networks lack the ability to represent fine-grained features within the topological structure. Summary of the Invention

[0004] To address the shortcomings of existing integrated product structure design technologies based on isogeometric analysis, reduce computational costs, improve optimization accuracy, and prevent structural fractures, this invention adopts the following technical solution:

[0005] A product structure intelligent integrated design method based on neural network reparameterization includes the following steps:

[0006] 1) Construct a geometric analysis mesh model such as NURBS based on the design domain, determine the parameter space, basis functions, control points, and coordinates of Gaussian points, and apply boundary conditions and geometric constraints to the discretized structure;

[0007] 2) Build a neural network model and obtain the density of the corresponding points by designing the parameter coordinates and volume fraction of Gaussian points in the domain;

[0008] 3) Using structural flexibility as the optimization objective and neural network model parameters as design variables, a product structure intelligent integrated design model based on neural network reparameterization is established.

[0009] 4) Calculate structural displacement and element compliance based on the Gaussian point density obtained from the neural network model;

[0010] 5) The augmented Lagrangian method is used to handle the constraints, and the loss function of the neural network model is calculated by linear weighting of the objective function under each volume fraction;

[0011] 6) Optimize and update the neural network model parameters; check whether the relative change value of the total loss in this iteration is less than the set threshold. If the condition is met, dynamically balance the weight coefficients based on the loss value; otherwise, dynamically balance the weight coefficients based on the learning speed. Check whether the proportion of gray units is less than the set threshold. If the condition is met, exit the iteration and end the training; otherwise, update the Lagrange multipliers and penalty parameters, and repeat steps 4) to 6).

[0012] 7) Using the parameters of the trained neural network model, output the density of each Gaussian point under the expected volume fraction, calculate the global density function, and obtain the optimized structure.

[0013] Furthermore, in step 2), a feedforward neural network model fusing multi-scale Fourier features is adopted, with the input being the coordinates (ξ, η) of the Gaussian point in the parameter space and the volume fraction v, and the output being the density of the Gaussian point. The design variables in topology optimization are reparameterized into neural network-related weights and biases w; and the input coordinate parameters (ξ,η) are mapped to the volume fraction v using the following stochastic Fourier feature mapping:

[0014]

[0015] γ(v)=[sin(2πv)cos(2πv)]

[0016] Where the parameter sequence {a1, a2, ..., a n}{b1,b2,...,b n Random sampling is performed from a standard normal distribution with a standard deviation of σ.

[0017] Furthermore, in step 3), the intelligent integrated design model for product structure based on neural network reparameterization is as follows:

[0018]

[0019] i = 1, 2, ..., N v

[0020] in, c represents a set of preset volume fractions. i U i and This represents the structural compliance, global displacement vector, and Gaussian point density field at the corresponding volume fraction. Let represent the global stiffness matrix, F represent the applied external force load, w represent the parameters related to the neural network model, including weights and biases; Ω represent the set of all Gaussian points within the structural design domain, and (ξ,η) represent the coordinates of the Gaussian points in the NURBS parameter space. This represents the density at the Gaussian point output by the neural network, which is characterized by a w-related function after reparameterization; V represents the volume of a Gaussian integral element in an isogeometric element e. i Indicates the volume of the structure.

[0021] Furthermore, step 4) includes the following sub-steps:

[0022] 4.1) Calculate the element stiffness matrix k e :

[0023]

[0024] Where D represents the elasticity matrix, B represents the geometric matrix, and p represents the first penalty factor. Represents the element stiffness matrix k e The integral term at the Gaussian point (ξ,η), ω ξ ω η J1 represents the corresponding integral weight; J2 represents the Jacobian matrix that maps the NURBS parameter space to the physical space; J3 represents the Jacobian matrix that maps the Gaussian integral space to the NURBS parameter space.

[0025] 4.2) Assemble the global stiffness matrix K and solve for the global displacement vector U;

[0026] 4.3) Calculate the volume of the Gaussian integral unit using the following formula. With softness

[0027]

[0028] Among them, u e This indicates the displacement of equal geometric elements.

[0029] Further, in step 5), the following loss function is constructed and calculated based on the objective function and its corresponding constraints for each volume fraction using linear weighting:

[0030]

[0031] in,

[0032]

[0033] Where, α i λ represents the weighting coefficient. iLet μ denote the Lagrange multiplier, and μ denote the second penalty factor. This indicates the initial flexibility of the structure.

[0034] Furthermore, in step 6), the Lagrange multiplier and penalty factor are updated according to the following rules:

[0035]

[0036] μ (t+1) =βμ (t)

[0037] Where t represents the iteration number and β represents the step size; in the t-th iteration, the weight coefficient α i The expression is as follows:

[0038]

[0039] in, Let f represent the learning speed in the t-th iteration. i (w) Definition of the loss ratio for the first two iterations;

[0040] Further, in step 7), the global density function X(ξ,η) is calculated by the following formula:

[0041] X(ξ,η)=N(ξ,η)R -1 G

[0042] Where N(ξ,η) represents the NURBS basis function matrix, R represents the matrix composed of the values ​​of the NURBS basis functions at each Gaussian point, and G represents the Gaussian point density vector output by the trained neural network.

[0043] The advantages and beneficial effects of this invention are as follows:

[0044] This invention fully utilizes the neural network reparameterization method, eliminating the need to construct a large-scale dataset. It optimizes the product structure density field by updating the neural network parameters. It establishes a continuous mapping relationship between structural volume, coordinates, and density, enabling the direct acquisition of optimized structures under arbitrary volumes after the network model is trained, thereby reducing time costs. It achieves accurate geometric description and structural response analysis of the product structure through isogeometric methods, embedding the objective function in topology optimization into the loss function to guide model training, thus overcoming the structural breakage problem. Furthermore, it performs random Fourier feature mapping on the input, enhancing the neural network's ability to learn high-frequency details. Attached Figure Description

[0045] Figure 1 This is a flowchart illustrating the intelligent integrated design process of product structure based on neural network reparameterization, as described in this invention.

[0046] Figure 2 This is a schematic diagram showing the design domain and boundary conditions of the arc-shaped structural component in an embodiment of the present invention;

[0047] Figure 3 This is a schematic diagram of the neural network reparameterization process in an embodiment of the present invention;

[0048] Figure 4 This is a diagram showing the topology optimization results of the arc-shaped structural component in an embodiment of the present invention. Detailed Implementation

[0049] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0050] like Figure 1 As shown, this invention presents an intelligent integrated design method for product structures based on neural network reparameterization. It reparameterizes the Gaussian point density into weights and biases related to the neural network by constructing a feedforward neural network that integrates multi-scale Fourier features. Structural flexibility is used as the optimization objective, and weights and biases are used as design variables to establish an intelligent integrated design model for product structures based on neural network reparameterization. Structural displacement and element flexibility are solved through isogeometric analysis, and constraints are handled using the augmented Lagrangian method. The loss of the neural network is calculated using a linear weighted average of the objective function under each volume fraction, and the weight coefficients are dynamically balanced based on the learning speed or loss value. The optimization model is solved using a built-in optimizer. The global density function under the expected volume fraction is calculated using the trained network parameters, thereby obtaining the final optimized structure. This achieves intelligent integrated design of product structures based on neural network reparameterization, specifically including the following steps:

[0051] 1) such as Figure 2 As shown, an arc-shaped structural component is used as the research object. A NURBS geometric analysis mesh model is constructed based on the design domain. The relationship between the major and minor diameters is L = 2R, and the NURBS node vectors in the two directions are {ξ1, ξ2, ..., ξ}. 102+2+1} and {η1,η2,...,η 51+1+1}, introduce control points

[0052] P i,j (i=1,2,...,102,j=1,2,...,51), the orders of the NURBS basis functions are p=2 and q=1 respectively, and 3×3 Gaussian points are set in each geometric unit; boundary conditions and geometric constraints are applied to the discretized structure, including the vertically downward load at the top and the fixed support at the bottom of the structure;

[0053] 2) Build a neural network model, and obtain the density of the corresponding points by designing the coordinates and volume fraction of Gaussian points within the domain; in this embodiment, the neural network reparameterization process is as follows: Figure 3 As shown, specifically:

[0054] A feedforward neural network model incorporating multi-scale Fourier features is adopted, consisting of 20 sequentially connected hidden layers, each with 50 neurons. LeakyReLU is used as the unified activation function, and the last layer is a classifier layer with a SoftMax activation function. The design variables in topology optimization are reparameterized into neural network-related weights and biases. The input coordinate parameters (ξ,η) are mapped to the volume fraction v using the following stochastic Fourier feature mapping:

[0055]

[0056] γ(v)=[sin(2πv)cos(2πv)]

[0057] Where the parameter sequence {a1, a2, ..., a 10}{b1,b2,...,b 10 Random sampling is performed from a standard normal distribution with a standard deviation of σ = 0.5.

[0058] 3) Using structural flexibility as the optimization objective and neural network model parameters as design variables, a product structure intelligent integrated design model based on neural network reparameterization is established; specifically:

[0059]

[0060] i = 1, 2, ..., 5

[0061] in, c represents a set of preset volume fractions. i U i and This represents the structural compliance, global displacement vector, and Gaussian point density field at the corresponding volume fraction. Let represent the global stiffness matrix, F represent the applied external force load, w represent the parameters related to the neural network model, including weights and biases; Ω represent the set of all Gaussian points within the structural design domain, and (ξ,η) represent the coordinates of the Gaussian points in the NURBS parameter space. This represents the density at the Gaussian point output by the neural network, which is characterized by a w-related function after reparameterization; V represents the volume of a Gaussian integral element in an isogeometric element e. i =(L 2 -R 2 )πv i / 4 represents the structural volume.

[0062] 4) Calculate structural displacement and element compliance based on the Gaussian point density obtained from the neural network model; specifically:

[0063] 4.1) Calculate the element stiffness matrix k e :

[0064]

[0065] Where D represents the elasticity matrix, B represents the geometric matrix, and p = 3 represents the first penalty factor. Represents the element stiffness matrix k e The integral term at the Gaussian point (ξ,η), ω ξ ω η J1 represents the corresponding integral weight; J2 represents the Jacobian matrix that maps the NURBS parameter space to the physical space; J3 represents the Jacobian matrix that maps the Gaussian integral space to the NURBS parameter space.

[0066] 4.2) Assemble the global stiffness matrix K and solve for the global displacement vector U;

[0067] 4.3) Calculate the volume of the Gaussian integral unit using the following formula. With softness

[0068]

[0069] Among them, u e This indicates the displacement of equal geometric elements.

[0070] 5) The augmented Lagrangian method is used to handle constraints, and the loss function of the neural network model is calculated based on the linear weighted sum of the objective function under each volume fraction:

[0071]

[0072] in,

[0073]

[0074] Where, α i λ represents the weighting coefficient, initialized to 1 / 5. i represents the Lagrange multiplier, initialized to 0; μ represents the second penalty factor, initialized to 0.1; This indicates the initial flexibility of the structure.

[0075] 6) Update the neural network model parameters using the Adam optimizer, setting the learning rate to 0.01 and the gradient clipping threshold to 0.1; in the t-th iteration, the weight coefficient α... i The expression is as follows:

[0076]

[0077] in, Let f represent the learning speed in the t-th iteration. i (w) Definition of the loss ratio for the first two iterations;

[0078] Check if the proportion of grayscale units is less than the set threshold ε = 3%. If the condition is met, exit the iteration and end the training. Otherwise, repeat steps 4) to 6) and update the Lagrange multiplier. Penalty parameter μ (t+1) =βμ (t) , where step size β = 1.1.

[0079] 7) After 126 training rounds, using the trained neural network model parameters, output the global Gaussian point density vectors at the expected volume fractions of 30%, 45%, and 60%, and calculate the global density function X(ξ,η)=N(ξ,η)R. -1 G and N(ξ,η) represent the NURBS basis function matrices, R represents the matrix composed of the values ​​of the NURBS basis functions at each Gaussian point, and G represents the Gaussian point density vector output by the trained neural network; the final optimization result of the obtained arc-shaped structural component is as follows: Figure 4 As shown, this verifies the effectiveness of the proposed method.

[0080] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A product structure intelligent integrated design method based on neural network reparameterization, characterized in that... Includes the following steps: 1) Construct a geometric analysis mesh model such as NURBS based on the design domain, determine the parameter space, basis functions, control points, and coordinates of Gaussian points, and apply boundary conditions and geometric constraints to the discretized structure; 2) Build a neural network model and obtain the density of the corresponding points by designing the parameter coordinates and volume fraction of Gaussian points in the domain; 3) Using structural flexibility as the optimization objective and neural network model parameters as design variables, establish an intelligent integrated design model for product structure based on neural network reparameterization; 4) Calculate structural displacement and element compliance based on the Gaussian point density obtained from the neural network model; 5) The augmented Lagrangian method is used to handle the constraints, and the loss function of the neural network model is calculated by linear weighting of the objective function under each volume fraction; 6) Optimize and update the neural network model parameters; check if the relative change in total loss in this iteration is less than a set threshold. If the condition is met, dynamically balance the weight coefficients based on the loss value; otherwise, dynamically balance the weight coefficients based on the learning speed. Check if the proportion of grayscale units is less than a set threshold. If the condition is met, exit the iteration and end the training; otherwise, update the Lagrange multipliers and penalty parameters, and repeat steps 4) to 6). 7) Using the trained neural network model parameters, output the density of each Gaussian point under the expected volume fraction, calculate the global density function, and obtain the optimized structure; Step 4) includes the following sub-steps: 4.1) Calculate the element stiffness matrix : Where D represents the elasticity matrix, Let p denote the geometric matrix, and p denote the first penalty factor. Represents the element stiffness matrix At Gauss point The integral term at the point, This indicates the corresponding integral weight; This represents the Jacobian matrix that maps the NURBS parameter space to the physical space. This represents the Jacobian matrix that maps the Gaussian integral space to the NURBS parameter space; 4.2) Assemble the global stiffness matrix K and solve for the global displacement vector U; 4.3) Calculate the volume of the Gaussian integral unit using the following formula. With softness : in, This indicates the displacement of equal geometric elements.

2. The intelligent integrated design method for product structure based on neural network reparameterization according to claim 1, characterized in that: In step 2), the neural network model adopts a feedforward neural network model that integrates multi-scale Fourier features, and the input is the coordinates of the Gaussian point in the parameter space. and volume fraction The output is the density of Gaussian points. The design variables in topology optimization are reparameterized into neural network-related weights and biases. And the input coordinate parameters With volume fraction Perform the following random Fourier feature mapping: , Among them, parameter sequence Random sampling is performed from a standard normal distribution with a standard deviation of σ.

3. The intelligent integrated design method for product structure based on neural network reparameterization according to claim 1, characterized in that: In step 3), the intelligent integrated design model for product structure based on neural network reparameterization is as follows: in, This represents a set of preset volume fractions. , and This represents the structural compliance, global displacement vector, and Gaussian point density field at the corresponding volume fraction. Represents the global stiffness matrix. Indicates the applied external force load. These represent parameters related to the neural network model, including weights and biases. This represents the set of all Gaussian points within the structural design domain. This represents the coordinates of the Gaussian point in the NURBS parameter space. This represents the density at that Gaussian point output by the neural network, after reparameterization... Related functional representations; Representing equal geometric units Gaussian integral unit volume in Indicates the volume of the structure.

4. The intelligent integrated design method for product structure based on neural network reparameterization according to claim 1, characterized in that: In step 5), the following loss function is constructed and calculated based on the linear weighted sum of the objective function and its corresponding constraints for each volume fraction: in, in, Indicates the weighting coefficient. Represents the Lagrange multiplier. Indicates the second penalty factor. This indicates the initial flexibility of the structure.

5. The intelligent integrated design method for product structure based on neural network reparameterization according to claim 4, characterized in that: In step 6), the Lagrange multiplier and penalty factor are updated according to the following rules: Where t represents the number of iterations. Indicates the step size; in the t-th iteration, the weight coefficients... The expression is as follows: in, The learning speed in the t-th iteration is represented by... The loss ratio of the first two iterations is defined.

6. The intelligent integrated design method for product structure based on neural network reparameterization according to claim 1, characterized in that: In step 7), the global density function Calculated by the following formula: in, Represents the NURBS basis function matrix. This represents a matrix composed of the values ​​of the NURBS basis functions at each Gaussian point. This represents the Gaussian point density vector output by the trained neural network.

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