Topology optimization method and device based on neural network reparameterization

Abstract

The present disclosure provides a kind of topology optimization method and device based on neural network reparameterization, belong to topology optimization technical field.The scheme can be reparameterized based on microstructure cell in the topology optimization process, with central coordinates as input layer, with first geometric parameter as output layer, obtain neural network based on finite element discretization and microstructure cell filling in design domain and the environmental constraint condition of target three-dimensional structure setting;First loss function is constructed with compliance, the neural network is updated to minimize the first loss function, so that the design value of the first geometric parameter is obtained, driven.The method introduces neural network reparameterization in topology optimization, and topology design parameter variable is represented as network weight, does not depend on sensitivity analysis iteration, effectively reduces cost, improves the efficiency of topology optimization, can cope with the improvement of structure scale and complexity, is conducive to the widespread application in practical engineering.

Description

Technical Field

[0001] This disclosure relates to the field of topology optimization technology, and in particular to a topology optimization method and apparatus based on neural network reparameterization. Background Technology

[0002] In the aerospace field, lightweight design is commonly employed to improve aircraft performance. Traditional structural design methods and manufacturing processes have reached their limits for lightweight design and cannot meet the evolving needs of aircraft components. Currently, lightweight design methods that integrate lattice structure design with additive manufacturing processes are available. Lattice structures, a branch of artificial porous structures, possess high specific stiffness, high specific strength, and multifunctional characteristics. In applications such as aircraft skin, wing spars, or satellite supports, they can significantly reduce weight while maintaining mechanical performance.

[0003] For lattice structures, structural topology optimization methods are typically used in their design. This involves optimizing the material layout within a design domain under given constraints to achieve specific performance characteristics, such as material stiffness and strength. Traditional structural topology optimization methods include Solid Isotropic Material with Penalization (SIMP), two-way evolutionary structural optimization, and level set methods. These methods are usually implemented by combining finite element simulation and sensitivity analysis to minimize overall compliance. However, as the scale and complexity of structures increase, the cost of sensitivity iteration gradually rises, limiting the application of structural topology optimization methods in practical engineering.

[0004] Therefore, how to provide a low-cost structural topology optimization method to achieve high-efficiency lattice structure design is a technical problem that urgently needs to be solved in this field.

[0005] The information disclosed in the background section is only for enhancing the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this disclosure is to provide a topology optimization method and apparatus based on neural network reparameterization, which can achieve low-cost and high-efficiency topology optimization of target three-dimensional structures.

[0007] To achieve the above-mentioned objectives, the present disclosure adopts the following technical solution: According to a first aspect of this disclosure, a topology optimization method based on neural network reparameterization is provided. The method may include: setting environmental constraints for a target three-dimensional structure; performing finite element discretization in the design domain of the target three-dimensional structure and filling elements using microstructure unit cells; performing reparameterization based on the microstructure unit cells, using the center coordinates as the input layer and a first geometric parameter as the output layer to obtain a neural network; constructing a first loss function with compliance, driving the neural network to update so as to minimize the first loss function, and obtaining the design value of the first geometric parameter.

[0008] Optionally, constructing a first loss function based on compliance includes: setting a first penalty term based on compliance to obtain a first loss function; the first penalty term includes at least one of a volume fraction penalty term and a solid isotropic material penalty term.

[0009] Optionally, compliance is calculated from the global load vector and the global displacement vector; the global load vector includes the global displacement vector and the global stiffness matrix; the global stiffness matrix is ​​obtained by assembling the element stiffness matrix; the element stiffness matrix includes the strain matrix of the microstructure unit cell, the integral region, and the first equivalent elastic matrix; the first equivalent elastic matrix is ​​predicted by the multilayer perceptron model based on the first geometric parameters.

[0010] Optionally, the training steps of the multilayer perceptron model include: establishing a body-centered cubic lattice corresponding to the target three-dimensional structure; performing equivalent homogenization calculations on the microstructure unit cells in the body-centered cubic lattice under different second geometric parameters to obtain a second equivalent elastic matrix; constructing an input layer with the second geometric parameters, constructing an output layer with the second equivalent elastic matrix, and training the model on the multilayer perceptron architecture to obtain a multilayer perceptron model.

[0011] Optionally, constructing the output layer with the second equivalent elasticity matrix includes: merging the second equivalent elasticity matrix based on geometric symmetry to obtain three elastic independent constants, which serve as the output of the multilayer perceptron architecture.

[0012] Optionally, the input layer is constructed using the second geometric parameters, including: calculating the volume fraction of the microstructure unit cell based on the second geometric parameters; and using the second geometric parameters and the volume fraction as input to the multilayer perceptron architecture.

[0013] Optionally, model training on a multilayer perceptron architecture includes: setting a second penalty term based on the mean squared error to obtain a second loss function; setting the second penalty term based on mechanical constraints; and training the model on the multilayer perceptron architecture with the goal of minimizing the second loss function.

[0014] Optionally, the multilayer perceptron architecture also includes a hidden layer, the activation function of which is the SiLU function; the activation function of the output layer is implemented using the Softplus function combined with Tanh constraint mapping.

[0015] Optionally, the target three-dimensional structure is a simply supported beam structure; the environmental constraints include at least one of the following: applying a vertically downward and uniformly distributed load to a region of a predetermined width in the center of the upper surface of the simply supported beam structure; setting support regions at predetermined inward distances on both sides of the lower surface of the simply supported beam structure; and restricting the vertical displacement freedom of the simply supported beam structure.

[0016] According to a second aspect of this disclosure, a topology optimization device based on neural network reparameterization is provided. The device may include: a condition constraint module for setting environmental constraints for a target three-dimensional structure; a finite element module for performing finite element discretization in the design domain of the target three-dimensional structure and filling elements using microstructure unit cells; a reparameterization module for reparameterizing based on the microstructure unit cells, using the center coordinates as the input layer and a first geometric parameter as the output layer to obtain a neural network; and a topology optimization module for constructing a first loss function with compliance, driving the neural network to update to minimize the first loss function, and obtaining the design value of the first geometric parameter.

[0017] Optionally, the topology optimization module is specifically used to set a first penalty term based on compliance to obtain a first loss function; the first penalty term includes at least one of a volume fraction penalty term and a solid isotropic material penalty term.

[0018] Optionally, compliance is calculated from the global load vector and the global displacement vector; the global load vector includes the global displacement vector and the global stiffness matrix; the global stiffness matrix is ​​obtained by assembling the element stiffness matrix; the element stiffness matrix includes the strain matrix of the microstructure unit cell, the integral region, and the first equivalent elastic matrix; the first equivalent elastic matrix is ​​predicted by the multilayer perceptron model based on the first geometric parameters.

[0019] Optionally, the device may further include a multilayer perceptron model training module for establishing a body-centered cubic lattice corresponding to the target three-dimensional structure; performing equivalent homogenization calculations on the microstructure unit cells in the body-centered cubic lattice under different second geometric parameters to obtain a second equivalent elastic matrix; constructing an input layer with the second geometric parameters and an output layer with the second equivalent elastic matrix; and training the model on the multilayer perceptron architecture to obtain a multilayer perceptron model.

[0020] Optionally, the multilayer perceptron model training module is specifically used to merge the second equivalent elasticity matrix based on geometric symmetry to obtain three elastic independent constants, which serve as the output of the multilayer perceptron architecture.

[0021] Optionally, the multilayer perceptron model training module is specifically used to calculate the volume fraction of the microstructure unit cell based on the second geometric parameters; the second geometric parameters and the volume fraction are used as inputs to the multilayer perceptron architecture.

[0022] Optionally, the multilayer perceptron model training module is specifically used to set a second penalty term based on the mean square error to obtain a second loss function; the second penalty term is set based on mechanical constraints; and the model is trained on the multilayer perceptron architecture with the goal of minimizing the second loss function.

[0023] Optionally, the multilayer perceptron architecture also includes a hidden layer, the activation function of which is the SiLU function; the activation function of the output layer is implemented using the Softplus function combined with Tanh constraint mapping.

[0024] Optionally, the target three-dimensional structure is a simply supported beam structure; the environmental constraints include at least one of the following: applying a vertically downward and uniformly distributed load to a region of a predetermined width in the center of the upper surface of the simply supported beam structure; setting support regions at predetermined inward distances on both sides of the lower surface of the simply supported beam structure; and restricting the vertical displacement freedom of the simply supported beam structure.

[0025] This disclosure provides a topology optimization method and apparatus based on neural network reparameterization. In the topology optimization process, this scheme sets environmental constraints on the target 3D structure, performs finite element discretization in the design domain, and uses microstructured unit cells for element filling. It then performs reparameterization based on these microstructured unit cells, using the center coordinates as the input layer and the first geometric parameter as the output layer to obtain a neural network. A first loss function is constructed using compliance, driving the neural network to update and minimize the first loss function, thereby obtaining the design value of the first geometric parameter. This method introduces neural network reparameterization into topology optimization, representing topology design parameter variables as network weights. It does not rely on sensitivity analysis iterations, effectively reducing costs and improving the efficiency of topology optimization. It can handle increased structural scale and complexity, and is beneficial for widespread application in practical engineering. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 A flowchart illustrating the steps of a topology optimization method based on neural network reparameterization in an embodiment of this disclosure is shown.

[0028] Figure 2 A flowchart illustrating the steps of a multilayer perceptron model training method according to an embodiment of this disclosure is shown.

[0029] Figure 3 A schematic diagram of a microstructure unit cell in a body-centered cubic lattice according to an embodiment of the present disclosure is shown.

[0030] Figure 4 A schematic diagram of a microstructure unit cell and a corresponding equivalent homogeneous body is shown in the embodiments of this disclosure.

[0031] Figure 5 A schematic diagram of a multilayer perceptron architecture according to an embodiment of this disclosure is shown.

[0032] Figure 6 A schematic diagram of a neural network according to an embodiment of this disclosure is shown.

[0033] Figure 7 A schematic diagram of a simply supported beam structure according to an embodiment of this disclosure is shown.

[0034] Figure 8 A schematic diagram showing the results of topology optimization of a simply supported beam structure in the embodiments of this disclosure is provided.

[0035] Figure 9 A structural block diagram of a topology optimization device based on neural network reparameterization provided in this disclosure is shown.

[0036] Figure 10 A schematic diagram of an electronic device provided by an embodiment of the present disclosure is shown. Detailed Implementation

[0037] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are set forth to give a full understanding of embodiments of this disclosure.

[0038] The described features, structures, or characteristics can be combined in any suitable manner in one or more embodiments. Numerous specific details are provided in the following description to give a full understanding of embodiments of this disclosure. However, those skilled in the art will recognize that the technical solutions of this disclosure can be practiced without one or more of the specific details described, or other methods, components, materials, etc., can be employed. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring the main technical concept of this disclosure.

[0039] When a structure is "on" other structures, it may mean that the structure is integrally formed on other structures, or that the structure is "directly" set on other structures, or that the structure is "indirectly" set on other structures through another structure.

[0040] The terms “a,” “one,” and “the” are used to indicate the existence of one or more elements / components / etc.; the terms “including” and “having” are used to indicate an open-ended inclusion and that other elements / components / etc. may exist in addition to those listed. The terms “first” and “second” are used only as markers and are not a limitation on the number of objects.

[0041] Figure 1 A flowchart illustrating the steps of a topology optimization method based on neural network reparameterization in an embodiment of this disclosure is shown, as follows: Figure 1 As shown, the method may include steps 101 to 104. See below: Step 101: Set environmental constraints for the target 3D structure.

[0042] In this embodiment, the target three-dimensional structure can be an application structure corresponding to engineering requirements, such as a structure that requires topology optimization in applications like aircraft wing spars or satellite supports. During topology optimization, environmental constraints can be set for the target three-dimensional structure. These constraints can be obtained based on the geometric, performance, and manufacturing requirements of the target three-dimensional structure in actual engineering. For example, environmental constraints can include size, symmetrical configuration, stress distribution, and displacement amplitude to simulate engineering requirements.

[0043] Step 102: Perform finite element discretization in the design domain of the target three-dimensional structure, and fill the elements using microstructure unit cells.

[0044] In this embodiment of the disclosure, layout optimization can be performed in the design domain of the target three-dimensional structure. The design domain can be the entire target three-dimensional structure or it can be selected according to actual analysis conditions, engineering requirements, etc. For example, when the structural geometry and load distribution of the target three-dimensional structure are symmetrical, only a part on one side of the axis of symmetry can be selected as the design domain for topology optimization, thereby improving computational efficiency.

[0045] In this embodiment of the disclosure, during the topology optimization process, finite element discretization can be performed in the design domain of the target three-dimensional structure to disperse the design domain into different units. Then, microstructure unit cells are used to fill the different units respectively, so that the topology optimization of the design domain is decomposed into the geometric parameter design of the microstructure unit cells.

[0046] Step 103: Reparameterize based on microstructure unit cells, using the center coordinates as the input layer and the first geometric parameters as the output layer to obtain a neural network.

[0047] In this embodiment, the topology optimization problem can be implicitly represented using a neural network. When using micro-structured units for topology optimization design, the topology model can be reparameterized based on the micro-structured units to obtain the network weights of the neural network. For example, the center coordinates of the micro-structured units in the topology model can be set as the input layer of the neural network, and the first geometric parameter of the micro-structured units can be set as the output layer of the neural network. The neural network may also include hidden layers between the input and output layers to extract and transform features from the input center coordinates, thereby providing high-level features to the output layer. The neural network constructed based on this can receive the input of the center coordinates of the micro-structured units, perform inference and prediction, and output the predicted value corresponding to the first geometric parameter.

[0048] In this embodiment of the disclosure, the first geometric parameter can describe the size information of the microstructure unit cell. According to the design requirements of the actual engineering, the first geometric parameter can include different types, such as the length, width, and height of the microstructure unit cell. When there is a frame structure in the microstructure unit cell, it can also include the border width. When there is a column structure in the microstructure unit cell, it can also include the column diameter. This embodiment of the disclosure does not impose specific limitations on this.

[0049] Step 104: Construct a first loss function based on compliance, drive the neural network to update so as to minimize the first loss function, and obtain the design value of the first geometric parameter.

[0050] In this embodiment, based on the objective function design of minimizing compliance in topology optimization, the first loss function of the neural network can be constructed using compliance. In topology optimization, compliance typically represents the degree of deformation of a structure under external loads. Engineering design uses minimizing the compliance of the structure as the objective function to obtain a design value that maximizes stiffness. Based on this, the neural network is driven to update, and when the predicted value output by the neural network minimizes the first loss function, that predicted value is used as the design value, thus achieving topology optimization combined with deep learning.

[0051] Therefore, by leveraging the similarity between topology optimization and deep learning in high-dimensional variable optimization, forward propagation corresponds to the calculation of the objective function and backpropagation corresponds to sensitivity analysis within the logical framework of topology optimization. By employing a neural network reparameterization strategy to optimize the first geometric parameter using the automatic differentiation capability of the neural network, the solution of complex partial differential equations in sensitivity analysis can be avoided, and the manual and time costs of deriving sensitivity can be reduced, thereby improving the efficiency of topology optimization.

[0052] In an optional embodiment of the method disclosed herein, step 104 above, in which the first loss function is constructed based on compliance, may include the following step A.

[0053] Step A: Set a first penalty term based on compliance to obtain a first loss function; the first penalty term includes at least one of volume fraction penalty term and solid isotropic material penalty term.

[0054] In this embodiment of the disclosure, when a volume fraction constraint term exists in the topology optimization problem, the volume fraction constraint term can be converted into unconstrained optimization during the construction of the first loss function to adapt to the unconstrained optimization logic of the neural network. Therefore, when constructing the first loss function based on compliance, a first penalty term can be further set.

[0055] In this embodiment of the disclosure, the first penalty term may include a volume fraction penalty term. An initial value for the volume fraction deviation coefficient is set, and it can be dynamically adjusted based on the initial value during the topology optimization process based on the neural network, so as to strictly control the degree of constraint and avoid the volume fraction from deviating from the target.

[0056] In this embodiment of the disclosure, the first penalty term may include a solid isotropic material penalty (SIMP) term, which utilizes the concept of intermediate density penalty in the SIMP method to improve the physical feasibility and structural clarity of the topology optimization results.

[0057] For example, the first loss function Loss 1 It can be expressed as the following formula (1): (1) in, Indicates flexibility, The coefficient representing the volume fraction penalty term. For solid isotropic materials, the coefficient of the penalty term is given; and Indicates the first in the design domain i Volume fraction of each microstructure unit cell This represents the total volume fraction of the design domain. This indicates the upper limit of the volume fraction set for the design domain.

[0058] In the topology optimization process, the constraint on the volume fraction can be expressed as the following formula (2): (2) in, n This represents the total number of microstructure unit cells in the design domain. .

[0059] Thus, driven by the first loss function, the geometric parameters are updated through the automatic differentiation capability of the neural network, and the overall structural topology evolves accordingly, ultimately achieving efficient topology optimization of the lattice structure.

[0060] In an optional embodiment of the method disclosed herein, compliance is calculated from the overall load vector and the overall displacement vector; the overall load vector includes the overall displacement vector and the overall stiffness matrix; the overall stiffness matrix is ​​obtained by assembling the element stiffness matrix; the element stiffness matrix includes the strain matrix of the microstructure unit cell, the integral region, and the first equivalent elastic matrix.

[0061] Compliance is represented by a quadratic form of the displacement vector and the stiffness matrix, or by the dot product of the load vector and the displacement vector. In this embodiment, compliance may include the overall load vector and the overall displacement vector to characterize the degree of deformation of the entire design domain of the target three-dimensional structure under the applied load. Therefore, a smaller compliance indicates a greater structural stiffness.

[0062] For example, compliance can be expressed as the following formula (3): (3) in, Indicates flexibility, U represents the overall load vector, U represents the overall displacement vector, and T represents the transpose operation.

[0063] In online elastic statics, there exists the following formula (4): (4) in, K This represents the overall stiffness matrix.

[0064] Based on formula (4), and using linear elasticity, the above formula (2) can be derived as shown in formula (5): (5) Since K is symmetric positive definite, therefore K T Can be written K .

[0065] Furthermore, the overall stiffness matrix K It can be derived from the element stiffness matrix ki The assembly yields the following formula (6): (6) in, The strain matrix of a microstructure unit cell ， For the first The integral region of a microstructure unit cell For the first The first equivalent elastic matrix corresponding to each microstructure unit cell.

[0066] In addition, the overall displacement vector U It can also be determined by the element node displacement vector. u i The assembly process yields the following formula (7): (7) The above representation of compliance is for illustrative purposes only. Those skilled in the art can make adjustments according to engineering design requirements and data processing conditions. This disclosure does not impose any specific limitations on this aspect.

[0067] In an optional embodiment of the method disclosed herein, the first equivalent elasticity matrix is ​​predicted by a multilayer perceptron model based on the first geometric parameters.

[0068] In this embodiment, a pre-trained multilayer perceptron model can predict the corresponding first equivalent elasticity matrix based on the first geometric parameters. By introducing a multilayer perceptron (MLP) model, the finite element homogenization process can be replaced, thereby improving topology optimization efficiency while ensuring homogenization accuracy. The multilayer perceptron model can be trained on a multilayer perceptron architecture; for example, Figure 2 A flowchart illustrating the steps of a multilayer perceptron model training method according to an embodiment of this disclosure is shown, as follows: Figure 2 As shown, the method may include: Step 201: Establish the body-centered cubic lattice corresponding to the target three-dimensional structure.

[0069] In this embodiment of the disclosure, during the training of the multilayer perceptron model, a corresponding body-centered cubic (BCC) lattice can be first established for the target three-dimensional structure. In the BBC lattice, each microstructure unit cell can be composed of eight cylindrical rod structures and twelve fan-shaped rod structures, thereby assembling multiple microstructure unit cells into a BBC lattice, which represents the target three-dimensional structure.

[0070] For example, Figure 3A schematic diagram of a microstructure unit cell in a body-centered cubic lattice according to an embodiment of this disclosure is shown, such as... Figure 3 As shown, the blue area represents a structure with eight cylindrical rods, and the gray area represents a structure with twelve fan-shaped rods. The side length of each microstructure unit cell is represented as... L The internal cylindrical rod is represented as d And the radius of the outer frame sector column members is w .

[0071] Step 202: Perform equivalent homogenization calculations on the microstructure unit cells in the body-centered cubic lattice under different second geometric parameters to obtain the second equivalent elastic matrix.

[0072] In this embodiment, the equivalent homogenization calculation of the microstructure unit cell in the BBC lattice can be performed by first introducing strict periodic boundary conditions to ensure the continuity of relative edge, surface, and nodal displacements. Then, a linearly independent unit strain field is applied to the microstructure unit cell using the mean stress-strain theory, and the elastic modulus, shear modulus, and Poisson's ratio of the microstructure unit cell in each direction are calculated. Based on this, a second equivalent elastic matrix is ​​derived. The second equivalent elastic matrix can be calculated for different combinations of second geometric parameters. The values ​​of the second geometric parameters can be selected according to actual engineering and manufacturing requirements. For example, considering the conditions of actual additive manufacturing, the parameters can be set to... L= 2.5 mm and constrain the second geometric parameter of the microstructure unit cell in , The values ​​are selected from the data, and each group of second geometric parameters can have a corresponding second equivalent elasticity matrix.

[0073] For example, by applying nine sets of linearly independent unit strain fields to the microstructure unit cell, homogenization calculations can obtain the second equivalent elastic matrix. D H As shown in the following formula (8): (8) Within the aforementioned restricted parameter space, 177 different parameters can be uniformly sampled. d , w ) combinations, thereby obtaining each group ( d , w ) corresponding It can be used as a training sample set for multilayer perceptron models.

[0074] Figure 4 A schematic diagram of the microstructure unit cell and the corresponding equivalent homogeneous body in the embodiments of this disclosure is shown, such as... Figure 4 As shown, the microstructure unit cell 401 corresponds to the equivalent homogeneous body 402.

[0075] Step 203: Construct the input layer using the second geometric parameters, construct the output layer using the second equivalent elasticity matrix, train the model on the multilayer perceptron architecture, and obtain the multilayer perceptron model.

[0076] In this embodiment of the disclosure, based on obtaining a pair of second geometric parameters and a second equivalent elastic matrix as a training sample set, model training can be performed on a multilayer perceptron architecture. The second geometric parameters are used as the input layer and the second equivalent elastic matrix is ​​used as the output layer. The loss function between the predicted output of the multilayer perceptron architecture based on the second geometric parameters and the second equivalent elastic matrix is ​​calculated to update the parameters until the model converges to obtain the multilayer perceptron model.

[0077] For example, a multilayer perceptron architecture can be built using the PyTorch library for model training. The training sample set can be randomly split into 85% training, 10% test, and 5% validation sets. Normalization and denormalization can be performed before input and after output to improve the convergence efficiency of the multilayer perceptron model. The initial learning rate for model training can be set to... lr= The training batch size can be set to 8, the maximum number of epochs can be set to 2000, and the optimizer can be the Adam algorithm. The above example is for illustration only, and those skilled in the art can make selections according to actual engineering needs and data processing conditions. This disclosure does not impose specific limitations on these aspects.

[0078] In an optional embodiment of the method disclosed herein, step 203 above, which involves constructing the output layer using the second equivalent elasticity matrix, may include step B as follows.

[0079] Step B: The second equivalent elasticity matrix is ​​merged based on geometric symmetry to obtain three elastic independent constants, which are used as the output of the multilayer perceptron architecture.

[0080] In this embodiment, considering the geometric symmetry of the microstructure unit cell of the BBC-type lattice, the second equivalent elastic matrix can be approximated and merged accordingly to obtain three independent elastic constants. The independent elastic constants shown in the aforementioned formula (8) can be approximated and merged as follows: , as well as Using the three elastic independent constants obtained by merging as the output of the multilayer perceptron structure for model training can effectively reduce training costs and improve training efficiency.

[0081] In an optional embodiment of the method disclosed herein, step 203, which involves constructing the input layer using the second geometric parameters, may include steps C1 to C2.

[0082] Step C1: Calculate the volume fraction of the microstructure unit cell based on the second geometric parameter.

[0083] Step C2: Use the second geometric parameter and volume fraction as inputs to the multilayer perceptron architecture.

[0084] In this embodiment of the disclosure, the input to the multilayer perceptron architecture may include a second geometric parameter, and may also include a volume fraction calculated based on the second geometric parameter. .

[0085] In an optional embodiment of the method disclosed herein, step 203, which involves training the model on a multilayer perceptron architecture, may include steps D1 to D2.

[0086] Step D1: Set a second penalty term based on the mean square error to obtain the second loss function; the second penalty term is set based on mechanical constraints.

[0087] Step D2: Train the model on a multilayer perceptron architecture with the goal of minimizing the second loss function.

[0088] In this embodiment, the second loss function can use mean squared error (MSE) as the basic main loss term to measure the quadratic difference between the predicted value of the multilayer perceptron architecture and the true value provided by the second elasticity matrix. Furthermore, a second penalty term based on mechanical constraints can be introduced into the second loss function, such as... , Wait, through the second penalty item to ensure Positive definiteness of the predicted values.

[0089] In an optional embodiment of the method disclosed herein, the multilayer perceptron architecture further includes a hidden layer, the activation function of which is the SiLU function.

[0090] In this embodiment of the disclosure, the multilayer perceptron architecture may further include a hidden layer between the input layer and the output layer, used for feature extraction and transformation of the input information. The hidden layer may use the SiLU (Sigmoid Linear Unit) function as the activation function, which has good smoothness, can effectively alleviate gradient problems, and effectively improve training results.

[0091] In an optional embodiment of the method disclosed herein, the activation function of the output layer is implemented using the Softplus function combined with Tanh constraint mapping.

[0092] In this embodiment, the activation function of the output layer can be a Softplus function, which facilitates theoretical analysis and effectively avoids the zero gradient problem. Furthermore, Tanh constraints can be combined to map the output to the range (-1,1), ensuring that the predicted values ​​of the independent elastic constants conform to physical constraints.

[0093] It should be noted that the application of the above activation functions is only for illustrative purposes. Those skilled in the art can choose other activation functions according to actual needs, and this disclosure does not impose specific limitations on this.

[0094] Figure 5 A schematic diagram of a multilayer perceptron architecture according to an embodiment of this disclosure is shown, such as... Figure 5 As shown, the second geometric parameters d, w, and y are used as the input layer, and... , as well as It consists of an output layer and a hidden layer of 64×256×64 between the input and output layers.

[0095] Based on this, Figure 6 A schematic diagram of a neural network according to an embodiment of this disclosure is shown, such as... Figure 6 As shown, with the center coordinates ( x i , y i , z i ) as the input layer, with the first geometric parameter ( d i , w i The input layer consists of an output layer and a hidden layer of 32×64×32 between the input and output layers.

[0096] Among them, such as Figure 6 As shown, the activation function of the hidden layer can be the SiLU function to capture smooth, continuous transitions in geometric parameters; the activation function of the output layer can be the Sigmoid function, which transforms the first geometric parameter of the microstructure unit cell. and Limited to physical threshold range

[0097] In an optional embodiment of the method disclosed herein, the target three-dimensional structure can be a simply supported beam structure.

[0098] In this embodiment, the target three-dimensional structure may include various engineering component structures, such as a simply supported beam structure, which typically includes a beam resting on supports at both ends. These supports only constrain the vertical displacement of the beam, while allowing free rotation at the beam ends. One end of the simply supported beam may use a hinged support to constrain horizontal displacement, while the other end may use a rolling support to accommodate deformation. Simply supported beam structures have wide applications in bridge engineering and architectural design.

[0099] In an optional embodiment of the method disclosed herein, the environmental constraints include applying a vertically downward and uniformly distributed load to a region of a predetermined width at the center of the upper surface of the simply supported beam structure.

[0100] In this embodiment of the disclosure, environmental constraints may include load environment simulation of a simply supported beam structure, such as applying a vertically downward and uniformly distributed load to a region of a predetermined width in the center of the upper surface of the simply supported beam structure. The predetermined width, load, and other parameters can be set according to the dimensions of the simply supported beam structure, actual engineering requirements, data analysis conditions, etc., and this embodiment of the disclosure does not impose specific limitations in this regard.

[0101] In an optional embodiment of the method disclosed herein, the environmental constraints include setting support areas at predetermined inward distances on both sides of the lower surface of the simply supported beam structure.

[0102] In this embodiment, environmental constraints may include simulation of the support structure for a simply supported beam structure, such as setting support areas at preset distances inward from both sides of the lower surface of the simply supported beam structure. The preset distances and the sizes of the support areas can be set according to the dimensions of the simply supported beam structure, actual engineering requirements, data analysis conditions, etc., and this embodiment does not impose specific limitations in this regard.

[0103] In an optional embodiment of the method disclosed herein, environmental constraints include restricting the displacement degrees of freedom of the simply supported beam structure in the vertical direction.

[0104] In this embodiment of the disclosure, environmental constraints may include the allowable deformation range of the simply supported beam structure, such as the vertical displacement degree of freedom of the simply supported beam structure. The magnitude of the displacement degree of freedom can be set according to the dimensions of the simply supported beam structure, actual engineering requirements, data analysis conditions, etc., and this embodiment of the disclosure does not impose specific limitations on this.

[0105] Figure 7 A schematic diagram of a simply supported beam structure according to an embodiment of this disclosure is shown, such as... Figure 7 As shown, the geometric dimensions of the beam can be When setting environmental constraints, a vertically downward uniformly distributed load can be applied to a 5mm wide area in the center of the upper surface of the simply supported beam structure, with a total load of 60N; corresponding narrow support areas can be set at 15mm from each side edge on the lower surface to restrict the vertical displacement freedom of the simply supported beam structure.

[0106] Based on this, and considering the geometric and load distribution symmetry of the simply supported beam structure, its right half is selected as the design domain for topology optimization to improve optimization efficiency. The design domain can be discretized using eight-node hexahedral elements, divided into a 30×12×12 mesh, with each element in the mesh measuring 2.5mm×2.5mm×2.5mm, and filled with microstructured unit cells.

[0107] The objective function is to minimize the overall structural compliance. The volume fraction is set to not exceed 0.3. The mathematical expression of the topology optimization problem is then given by formula (9): (9) The above formula (9) can be referred to the relevant descriptions of the aforementioned formulas (3) to (7). To avoid repetition, it will not be repeated here.

[0108] Building upon this, the topology optimization problem will be implicitly represented using a neural network, with the geometric parameters reparameterized into network weights. The optimization problem can be represented by the following formulas (10-1) to (10-2): (10-1) (10-2) In the formula, These are the weights of the neural network.

[0109] Figure 8 A schematic diagram showing the topology optimization results of a simply supported beam structure according to an embodiment of this disclosure is shown, such as... Figure 8 As shown, the compliance of a simply supported beam structure The average iteration time during topology optimization is approximately 0.8 seconds, and the force transmission path of the structure is clear. Therefore, the topology optimization method based on neural network reparameterization provided in this disclosure achieves structural stiffness performance that meets practical engineering requirements while significantly improving topology optimization efficiency.

[0110] The topology optimization method based on neural network reparameterization provided in this disclosure, during the topology optimization process, sets environmental constraints on the target three-dimensional structure and obtains microstructure unit cells through finite element discretization in the design domain. It then reparameterizes these microstructure unit cells, using the center coordinates as the input layer and the first geometric parameter as the output layer to obtain a neural network. A first loss function is constructed using compliance, driving the neural network to update and minimize the first loss function, thereby obtaining the design value of the first geometric parameter. This method introduces neural network reparameterization into topology optimization, representing topology design parameter variables as network weights. It does not rely on sensitivity analysis iterations, effectively reducing costs and improving the efficiency of topology optimization. It can handle increased structural scale and complexity, and is beneficial for widespread application in practical engineering.

[0111] Based on this, the multilayer perceptron model established by the present invention can utilize the nonlinear representation capability of neural networks to efficiently predict the equivalent elasticity matrix of microstructure unit cells, providing support for topology optimization and further improving design efficiency.

[0112] Figure 9 This diagram illustrates a structural block diagram of a topology optimization device 900 based on neural network reparameterization, provided by an embodiment of this disclosure. This device is applied to the aforementioned topology optimization method based on neural network reparameterization. Figure 9 As shown, the device may include: a condition constraint module 901, used to set environmental constraints for the target three-dimensional structure; a finite element module 902, used to perform finite element discretization in the design domain of the target three-dimensional structure and to fill elements using microstructure unit cells; a reparameterization module 903, used to perform reparameterization based on microstructure unit cells, using the center coordinates as the input layer and the first geometric parameters as the output layer to obtain a neural network; and a topology optimization module 904, used to construct a first loss function with compliance, drive the neural network to update so as to minimize the first loss function, and obtain the design value of the first geometric parameters.

[0113] In an optional device embodiment of this disclosure, the topology optimization module 904 is specifically used to set a first penalty term based on compliance to obtain a first loss function; the first penalty term includes at least one of a volume fraction penalty term and a solid isotropic material penalty term.

[0114] In an optional embodiment of the device disclosed herein, compliance is calculated from the overall load vector and the overall displacement vector; the overall load vector includes the overall displacement vector and the overall stiffness matrix; the overall stiffness matrix is ​​obtained by assembling the element stiffness matrix; the element stiffness matrix includes the strain matrix of the microstructure unit cell, the integral region, and the first equivalent elastic matrix; the first equivalent elastic matrix is ​​predicted by the multilayer perceptron model based on the first geometric parameters.

[0115] In an optional embodiment of the present disclosure, the device may further include a multilayer perceptron model training module for establishing a body-centered cubic lattice corresponding to the target three-dimensional structure; performing equivalent homogenization calculations on the microstructure unit cells in the body-centered cubic lattice under different second geometric parameters to obtain a second equivalent elastic matrix; constructing an input layer with the second geometric parameters, constructing an output layer with the second equivalent elastic matrix, and performing model training on the multilayer perceptron architecture to obtain a multilayer perceptron model.

[0116] In an optional embodiment of the present disclosure, the multilayer perceptron model training module is specifically used to merge the second equivalent elasticity matrix based on geometric symmetry to obtain three elastic independent constants as the output of the multilayer perceptron architecture.

[0117] In an optional embodiment of the apparatus disclosed herein, the multilayer perceptron model training module is specifically used to calculate the volume fraction of the microstructure unit cell based on the second geometric parameters; the second geometric parameters and the volume fraction are used as inputs to the multilayer perceptron architecture.

[0118] In an optional device embodiment of this disclosure, the multilayer perceptron model training module is specifically used to set a second penalty term based on the mean square error to obtain a second loss function; the second penalty term is set based on mechanical constraints; and model training is performed on the multilayer perceptron architecture with the goal of minimizing the second loss function.

[0119] In an optional embodiment of the device disclosed herein, the multilayer perceptron architecture further includes a hidden layer, the activation function of which is the SiLU function; the activation function of the output layer is implemented using the Softplus function combined with Tanh constraint mapping.

[0120] In an optional embodiment of the device disclosed herein, the target three-dimensional structure is a simply supported beam structure; the environmental constraints include at least one of the following: applying a vertically downward and uniformly distributed load to a region of a predetermined width in the center of the upper surface of the simply supported beam structure; setting support regions at predetermined inward distances on both sides of the lower surface of the simply supported beam structure; and restricting the vertical displacement degree of freedom of the simply supported beam structure.

[0121] The topology optimization device based on neural network reparameterization provided in this disclosure, during the topology optimization process, sets environmental constraints on the target three-dimensional structure and obtains microstructure unit cells through finite element discretization in the design domain. It then reparameterizes these microstructure unit cells, using the center coordinates as the input layer and the first geometric parameter as the output layer to obtain a neural network. A first loss function is constructed based on compliance, driving the neural network to update and minimize the first loss function, thereby obtaining the design value of the first geometric parameter. This method introduces neural network reparameterization into topology optimization, representing topology design parameter variables as network weights. It does not rely on sensitivity analysis iterations, effectively reducing costs and improving the efficiency of topology optimization. It can handle increased structural scale and complexity, and is beneficial for widespread application in practical engineering.

[0122] Based on this, the multilayer perceptron model established by the present invention can utilize the nonlinear representation capability of neural networks to efficiently predict the equivalent elasticity matrix of microstructure unit cells, providing support for topology optimization and further improving design efficiency.

[0123] It should be noted that although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps, such as omitting certain steps, combining multiple steps into one step, and / or breaking down one step into multiple steps, should all be considered part of this disclosure.

[0124] It should be understood that this disclosure is not limited to the detailed structure and arrangement of the components presented in this specification. This disclosure can have other embodiments and can be implemented and performed in various ways. The foregoing variations and modifications fall within the scope of this disclosure. It should be understood that this disclosure, as disclosed and defined in this specification, extends to all alternative combinations of two or more individual features mentioned or apparent in the text and / or drawings. All these different combinations constitute multiple alternative aspects of this disclosure. The embodiments described in this specification illustrate the best known mode for implementing this disclosure and will enable those skilled in the art to utilize this disclosure.

[0125] The following reference Figure 10 To describe an electronic device 1000 according to such an embodiment of the present disclosure. Figure 10 The electronic device 1000 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0126] like Figure 10As shown, the electronic device 1000 is manifested in the form of a general-purpose computing device. The components of the electronic device 1000 may include, but are not limited to: at least one processing unit 1010, at least one storage unit 1020, a bus 1030 connecting different system components (including storage unit 1020 and processing unit 1010), and a display unit 1040.

[0127] The storage unit stores program code, which can be executed by the processing unit 1010, causing the processing unit 1010 to perform the steps described in the above-described method embodiment section of this specification according to various exemplary embodiments of this disclosure.

[0128] Storage unit 1020 may include readable media in the form of volatile storage units, such as random access memory (RAM) 1021 and / or cache memory 1022, and may further include read-only memory (ROM) 1023.

[0129] Storage unit 1020 may also include a program / utility 1024 having a set (at least one) program module 1025, such program module 1025 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0130] Bus 1030 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0131] Electronic device 1000 can also communicate with one or more external devices 1100 (e.g., keyboard, pointing device, Bluetooth device, etc.), one or more devices that enable a user to interact with electronic device 1000, and / or any device that enables electronic device 1000 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 1050. Furthermore, electronic device 1000 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 1060. As shown, network adapter 1060 communicates with other modules of electronic device 1000 via bus 1030. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 1000, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0132] Furthermore, exemplary embodiments of this disclosure also provide a computer-readable storage medium storing a program product capable of implementing the methods described above. In some possible embodiments, various aspects of this disclosure may also be implemented as a program product including program code that, when run on a terminal device, causes the terminal device to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of this disclosure.

[0133] It should be noted that the computer-readable medium disclosed herein may be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium may be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0134] In this disclosure, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in connection with an instruction execution system, apparatus, or device. In this disclosure, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A computer-readable signal medium can also be any computer-readable medium other than a computer-readable storage medium, which can transmit, propagate, or transfer a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wireline, optical fiber, RF, etc., or any suitable combination thereof.

[0135] Furthermore, program code for performing the operations of this disclosure can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0136] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the claims.

Claims

1. A topology optimization method based on neural network reparameterization, characterized in that, The method includes: Set environmental constraints for the target 3D structure; Finite element discretization is performed in the design domain of the target three-dimensional structure, and microstructure unit cells are used for element filling. Based on the microstructure unit cell, reparameterization is performed, with the center coordinates as the input layer and the first geometric parameters as the output layer to obtain a neural network; A first loss function is constructed based on compliance, which drives the neural network to be updated to minimize the first loss function, thereby obtaining the design value of the first geometric parameter.

2. The method according to claim 1, characterized in that, The construction of the first loss function based on compliance includes: A first penalty term is set based on compliance to obtain the first loss function; the first penalty term includes at least one of volume fraction penalty term and solid isotropic material penalty term.

3. The method according to claim 1, characterized in that, The compliance is calculated from the overall load vector and the overall displacement vector; The overall load vector includes the overall displacement vector and the overall stiffness matrix; The overall stiffness matrix is ​​obtained by assembling the element stiffness matrices; The element stiffness matrix includes the strain matrix of the microstructure unit cell, the integral region, and the first equivalent elastic matrix. The first equivalent elasticity matrix is ​​predicted by the multilayer perceptron model based on the first geometric parameters.

4. The method according to claim 3, characterized in that, The training steps of the multilayer perceptron model include: Establish a body-centered cubic lattice corresponding to the three-dimensional structure of the target; The microstructure unit cells in the body-centered cubic lattice are equivalently homogenized under different second geometric parameters to obtain the second equivalent elastic matrix. The input layer is constructed using the second geometric parameters, and the output layer is constructed using the second equivalent elasticity matrix. The model is trained on the multilayer perceptron architecture to obtain the multilayer perceptron model.

5. The method according to claim 4, characterized in that, The step of constructing the output layer using the second equivalent elasticity matrix includes: The second equivalent elasticity matrix is ​​merged based on geometric symmetry to obtain three elastic independent constants, which are used as the output of the multilayer perceptron architecture.

6. The method according to claim 4, characterized in that, The construction of the input layer using the second geometric parameters includes: The volume fraction of the microstructure unit cell is calculated based on the second geometric parameters; The second geometric parameter and the volume fraction are used as inputs to the multilayer perceptron architecture.

7. The method according to claim 4, characterized in that, The model training on the multilayer perceptron architecture includes: A second penalty term is set based on the mean square error to obtain the second loss function; the second penalty term is set based on mechanical constraints. The model is trained on the multilayer perceptron architecture with the goal of minimizing the second loss function.

8. The method according to claim 4, characterized in that, The multilayer perceptron architecture also includes a hidden layer, the activation function of which is the SiLU function; The activation function of the output layer is implemented using the Softplus function combined with Tanh constraint mapping.

9. The method according to claim 1, characterized in that, The target three-dimensional structure is a simply supported beam structure; The environmental constraints include at least one of the following: A vertically downward and uniformly distributed load is applied to a region of a predetermined width in the center of the upper surface of the simply supported beam structure; Support areas are provided at predetermined inward distances on both sides of the lower surface of the simply supported beam structure; The vertical displacement degree of freedom of the simply supported beam structure is restricted.

10. A topology optimization device based on neural network reparameterization, characterized in that, The device includes: The condition constraint module is used to set environmental constraints for the target 3D structure. The finite element module is used to perform finite element discretization in the design domain of the target three-dimensional structure and to fill elements using microstructure unit cells; The reparameterization module is used to reparameterize the microstructure unit cell, with the center coordinates as the input layer and the first geometric parameters as the output layer, to obtain a neural network. The topology optimization module is used to construct a first loss function with compliance, drive the neural network to update so as to minimize the first loss function, and obtain the design value of the first geometric parameter.

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