Isogeometric topology optimization method and device based on neural network model

Abstract

The invention provides an isogeometric topology optimization method and device based on a neural network model, and relates to the field of isogeometric topology optimization. The method comprises the steps that an initial isogeometric topological optimization design model corresponding to a to-be-optimized structure is constructed, unit division operation is conducted on the initial isogeometric topological optimization design model, and the unit division operation is used for dividing an isogeometric grid model into a plurality of isogeometric units; obtaining a preset neural network size, and constructing a first neural network model according to the preset neural network size; obtaining the center coordinates of the isogeometric units, and obtaining the center density of the isogeometric units through a first neural network model according to the center coordinates; constructing a loss function according to the center density of the isogeometric unit, and updating the first neural network model by minimizing the loss function to obtain an updated second neural network model; and performing isogeometric topology optimization operation on the to-be-optimized structure through the second neural network model. According to the method, the problem that when the performance of the material is remarkably changed in the optimization process, the sensitivity analysis in a common isogeometric topology optimization method becomes very complicated, so that the analysis result of the optimal material distribution is not accurate enough is solved.

Description

Technical Field

[0001] The present application relates to the field of isogeometric topology optimization, and in particular to an isogeometric topology optimization method and device based on a neural network model. Background Art

[0002] Topology Optimization (TO) is a mathematical method to find the optimal material distribution in a given area under certain constraints. Representative methods include homogenization method, solid isotropic material penalty method, level set method and mobile deformable component method. Among them, isogeometric topology optimization (ITO) is an advanced method that combines isogeometric analysis and topology optimization. Isogeometric analysis is used in topology optimization with its advantages of high precision and high-order continuity, so as to achieve more accurate analysis and optimization.

[0003] The usual isogeometric topology optimization method requires sensitivity analysis during the design process, and has problems such as high computational cost and numerical instability. In actual engineering, complex constraints and nonlinear problems greatly increase the difficulty of sensitivity analysis. The reason is that when the optimization problem involves nonlinear material properties or responses, nonlinear behavior may lead to the unavailability of analytical solutions, especially when the performance of the material changes significantly during the optimization process. At this time, the sensitivity analysis becomes very complicated, resulting in inaccurate analysis results of the optimal material distribution.

[0004] Therefore, there is an urgent need for an isogeometric topology optimization method and device based on a neural network model. Summary of the invention

[0005] The present application provides an isogeometric topology optimization method and device based on a neural network model, which solves the problem that when the performance of the material changes significantly during the optimization process, the sensitivity analysis in the conventional isogeometric topology optimization method becomes very complicated, resulting in inaccurate analysis results of the optimal material distribution.

[0006] In the first aspect of the present application, a method for isogeometric topology optimization based on a neural network model is provided, the method comprising: constructing an initial isogeometric topology optimization design model corresponding to the structure to be optimized, and performing a unit division operation on the initial isogeometric topology optimization design model, the unit division operation being used to divide the isogeometric body mesh model into a plurality of isogeometric units; obtaining a preset neural network size, and constructing a first neural network model according to the preset neural network size; obtaining the center coordinates of the isogeometric units, and obtaining the center density of the isogeometric units through the first neural network model based on the center coordinates; constructing a loss function based on the center density of the isogeometric units, and updating the first neural network model by minimizing the loss function to obtain an updated second neural network model; and performing an isogeometric topology optimization operation on the structure to be optimized through the second neural network model.

[0007] Optionally, construct an initial isogeometric topology optimization design model corresponding to the structure to be optimized, specifically including: obtaining a first corresponding relationship, the first corresponding relationship being the corresponding relationship between the isogeometric unit and the unit Young's modulus; according to the first corresponding relationship, with flexibility minimization as the goal and the structural volume as the constraint, constructing an initial isogeometric topology optimization design model.

[0008] Optionally, the first corresponding relationship is represented by the following functional relationship:

[0009]

[0010] Among them, ρ e is the density of the isogeometric unit, E e (ρ e ) is the unit Young's elastic modulus, E min is the Young's modulus of the void unit, E 0 is the Young's modulus of the standard solid material, p is the first penalty factor, and p∈[3,4];

[0011] The expression of the initial isogeometric topology optimization design model is:

[0012]

[0013] in, Indicates search The target solution ρ in is n, which is the number of equal geometry units. It represents the cell center density corresponding to the geometric cell number i. represents the flexibility minimization according to the target solution ρ, where K is the global stiffness matrix, U is the global displacement vector of each isogeometric unit, T is the transposed matrix, and u eis the unit displacement vector, subject to:K(ρ)U=F means the constraint condition is K(ρ)U=F, F is the global force vector, V(ρ) is the material volume of the structure to be optimized, V f is the design domain volume corresponding to the structure to be optimized.

[0014] Optionally, constructing a first neural network model specifically includes: obtaining a neural network model to be trained, and setting the depth and height of the neural network model to be trained in a preset manner, the depth being the number of hidden layers of the neural network, and the height being the number of neurons in each layer of the neural network; initializing the weights and biases of the neural network model to be trained; performing model training on the neural network model to be trained through a first activation function, a preset normalization function, and a second activation function, the first activation function being used to perform nonlinear mapping of the weights and biases corresponding to each layer of neurons in the neural network model to be trained, the preset normalization function being used to normalize the neural network model to be trained, and the second activation function being used to adjust the output of the hidden layer to within a preset range; and using the neural network model to be trained after model training as the first neural network model.

[0015] Optionally, before the neural network model to be trained is trained by using the first activation function, the preset normalization function and the second activation function, the method further includes: obtaining a preset pre-activation value, and obtaining the first activation function, the preset normalization function and the second activation function according to the preset pre-activation value; the preset pre-activation value is obtained by the following formula:

[0016]

[0017] in, is the preset value before activation, x and y are the center coordinates of the equal geometric unit, represents the weight associated with the i-th neuron in the k-1th layer and the i-th neuron in the kth layer; Represents the weight associated with the j-th neuron in the k-1th layer and the i-th neuron in the k-th layer.

[0018] Optionally, a loss function is constructed according to the center density of the isogeometric unit, specifically comprising: constructing the loss function by the following formula:

[0019]

[0020] Among them, L(λ) is the loss function, λ is the set of neural network weights and biases, C 0 is the initial flexibility of the structure to be optimized, ρ e is the cell center density corresponding to the isogeometric cell, ν e is the volume of the isogeometric unit, α is the second penalty factor, and α∈(0,100].

[0021] Optionally, isogeometric topology optimization is performed on the structure to be optimized through the second neural network model, specifically including: obtaining the optimization result corresponding to the structure to be optimized through the second neural network model; judging whether the optimization result meets the preset convergence condition; if the optimization result meets the preset convergence condition, completing the isogeometric topology optimization operation.

[0022] In a second aspect of the present application, a isogeometric topology optimization device based on a neural network model is provided, the device comprising a unit division module, a neural network construction module and an isogeometric topology optimization module, wherein:

[0023] The unit division module is used to construct an initial isogeometric topology optimization design model corresponding to the structure to be optimized, and to perform unit division operations on the initial isogeometric topology optimization design model. The unit division operation is used to divide the isogeometric mesh model into multiple isogeometric units.

[0024] A neural network construction module is used to obtain a preset neural network size and construct a first neural network model based on the preset neural network size; obtain the center coordinates of the isogeometric units, and obtain the center density of the isogeometric units through the first neural network model based on the center coordinates; construct a loss function based on the center density of the isogeometric units, and update the first neural network model by minimizing the loss function to obtain an updated second neural network model.

[0025] The isogeometric topology optimization module is used to perform isogeometric topology optimization operations on the structure to be optimized through a second neural network model.

[0026] In the third aspect of the present application, an electronic device is provided, including a processor, a memory, a user interface and a network interface, the memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory so that the electronic device executes any one of the methods described above.

[0027] In a fourth aspect of the present application, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and the computer program is executed by a processor to perform any of the above methods.

[0028] One or more technical solutions provided in the embodiments of the present application have at least the following technical effects or advantages:

[0029] 1. Construct an initial isogeometric topology optimization design model corresponding to the structure to be optimized, and perform unit division operation on the initial isogeometric topology optimization design model to divide the isogeometric body mesh model into multiple isogeometric units; obtain a preset neural network size, and construct a first neural network model according to the preset neural network size; obtain the center coordinates of the isogeometric unit, and obtain the center density of the isogeometric unit through the first neural network model based on the center coordinates, construct a loss function based on the center density of the isogeometric unit, and update the first neural network model by minimizing the loss function to obtain an updated second neural network model, so as to perform isogeometric topology optimization operation on the structure to be optimized through the second neural network model, without the need to derive the sensitivity analysis formula, reducing the complexity of the sensitivity analysis, and making the analysis result of the optimal material distribution more accurate.

[0030] 2. Obtain the neural network model to be trained, and set the depth and height of the neural network model to be trained in a preset manner, where the depth is the number of hidden layers of the neural network, and the height is the number of neurons in each layer of the neural network. Initialize the weights and biases of the neural network model to be trained, and perform model training on the neural network model to be trained through a first activation function, a preset normalization function, and a second activation function, so that the neural network model to be trained after the model training is used as the first neural network model, thereby enhancing the ability of the first neural network to handle complex problems and better adapt to complex design problems in topology optimization.

[0031] 3. Obtain the optimization result corresponding to the structure to be optimized through the second neural network model, and judge whether the optimization result meets the preset convergence condition. Only when the optimization result meets the preset convergence condition, complete the geometric topology optimization operation, so that the best optimization result corresponding to the structure to be optimized can be obtained effectively and accurately through the second neural network model. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of an isogeometric topology optimization method based on a neural network model provided in an embodiment of the present application;

[0033] Figure 2 It is a schematic diagram of the correspondence between a two-dimensional isogeometric unit and its control points provided in an embodiment of the present application;

[0034] Figure 3 It is a schematic diagram of a neural network model setting provided in an embodiment of the present application;

[0035] Figure 4 It is a schematic diagram of the design domain and boundary condition settings of a cantilever beam example provided in an embodiment of the present application;

[0036] Figure 5It is a schematic diagram of a topological structure obtained by using a standard isogeometric topological optimization method provided in an embodiment of the present application;

[0037] Figure 6 It is a schematic diagram of a topological structure obtained by an isogeometric topological optimization method based on a neural network model provided in an embodiment of the present application;

[0038] Figure 7 It is a module schematic diagram of an isogeometric topology optimization device based on a neural network model provided in an embodiment of the present application;

[0039] Figure 8 It is a structural schematic diagram of an electronic device provided in an embodiment of the present application.

[0040] Explanation of the reference numerals: 21, isogeometric unit; 22, control point; 71, unit division module; 72, neural network construction module; 73, isogeometric topology optimization module; 801, processor; 802, communication bus; 803, user interface; 804, network interface; 805, memory. DETAILED DESCRIPTION

[0041] In order to enable technicians in this field to better understand the technical solutions in this specification, the technical solutions in the embodiments of this specification will be clearly and completely described below in conjunction with the drawings in the embodiments of this specification. Obviously, the described embodiments are only part of the embodiments of this application, not all of the embodiments.

[0042] The terms used in the following embodiments of the present application are only for the purpose of describing specific embodiments, and are not intended to be used as limitations to the present application. As used in the specification of the present application, the singular expressions "one", "a kind of", "said", "above", "the" and "this" are intended to also include plural expressions, unless there is a clear indication to the contrary in the context. It should also be understood that the term "and / or" used in the present application refers to and includes any or all possible combinations of one or more listed items.

[0043] In the following, the terms "first" and "second" are used for descriptive purposes only and are not to be understood as suggesting or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of the features, and in the description of the embodiments of the present application, unless otherwise specified, "plurality" means two or more.

[0044] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings.

[0045] Topology Optimization (TO) is a mathematical method to find the optimal material distribution in a given area under certain constraints. Representative methods include homogenization method, solid isotropic material penalty method, level set method and mobile deformable component method. Among them, isogeometric topology optimization (ITO) is an advanced method that combines isogeometric analysis and topology optimization. Isogeometric analysis is used in topology optimization with its advantages of high precision and high-order continuity, so as to achieve more accurate analysis and optimization.

[0046] The usual isogeometric topology optimization method requires sensitivity analysis during the design process, and has problems such as high computational cost and numerical instability. In actual engineering, complex constraints and nonlinear problems greatly increase the difficulty of sensitivity analysis. The reason is that when the optimization problem involves nonlinear material properties or responses, nonlinear behavior may lead to the unavailability of analytical solutions, especially when the performance of the material changes significantly during the optimization process. At this time, the sensitivity analysis becomes very complicated, resulting in inaccurate analysis results of the optimal material distribution.

[0047] Therefore, there is an urgent need for an isogeometric topology optimization method and device based on a neural network model.

[0048] Please refer to Figure 1 , which shows a flow chart of an isogeometric topology optimization method based on a neural network model provided in an embodiment of the present application, and the flow chart mainly includes the following steps: S101 to S105.

[0049] Step S101, constructing an initial isogeometric topology optimization design model corresponding to the structure to be optimized, and performing a unit division operation on the initial isogeometric topology optimization design model, wherein the unit division operation is used to divide the isogeometric mesh model into a plurality of isogeometric units.

[0050] Specifically, based on the first correspondence, with flexibility minimization as the goal and structural volume as the constraint, an initial isogeometric topology optimization design model is constructed. The first correspondence is the correspondence between the isogeometric unit and the unit Young's elastic modulus:

[0051]

[0052] Among them, ρ e is the density of the isogeometric unit, E e (ρ e ) is the unit Young's elastic modulus, E min is the Young's modulus of the void unit, E 0is the Young's modulus of the standard solid material, p is the first penalty factor, and p∈[3,4]. The expression of the initial isogeometric topology optimization design model is:

[0053]

[0054] in, Indicates search The target solution ρ in is n, which is the number of equal geometry units. It represents the cell center density corresponding to the geometric cell number i. represents the flexibility minimization according to the target solution ρ, where K is the global stiffness matrix, U is the global displacement vector of each isogeometric unit, T is the transposed matrix, and u e is the unit displacement vector, subject to:K(ρ)U=F means the constraint condition is K(ρ)U=F, F is the global force vector, V(ρ) is the material volume of the structure to be optimized, V f is the design domain volume corresponding to the structure to be optimized. After that, the structure to be optimized is meshed to obtain an isogeometric mesh model to obtain multiple isogeometric units and the control points and Gaussian points corresponding to each isogeometric unit. Please refer to Figure 2 , which shows a schematic diagram of the corresponding relationship between a two-dimensional isogeometric unit and its control points provided in an embodiment of the present application, Figure 2 In the figure, the relationship between the two-dimensional isogeometric unit of NURBS order 2 and its control points, where 21 is the isogeometric unit and 22 is the control point. Finally, the volume unit, control point and Gauss point are numbered respectively to determine the volume constraint, and the isogeometric analysis force loading, boundary and displacement conditions of the design domain are determined.

[0055] Step S102, obtaining a preset neural network size, and constructing a first neural network model according to the preset neural network size.

[0056] Specifically, the first neural network model is composed of several hidden layers related to activation functions. The complexity and functionality of the first neural network model are related to the number of hidden layers and neurons. The specific setting method of the first neural network model is as follows: obtain the neural network model to be trained, set the depth and height of the neural network model to be trained according to the preset method, and initialize the penalty factor, weight and bias of the neural network model to be trained. Please refer to Figure 3, which shows a schematic diagram of a neural network model setting provided by an embodiment of the present application, solves the minimization problem with flexibility as the goal in structural isogeometric topology optimization through a neural network; the neural network model to be trained is trained through a first activation function, a preset normalization function and a second activation function, the first activation function is used to nonlinearly map the weights and biases corresponding to each layer of neurons in the neural network model to be trained, the preset normalization function is used to normalize the neural network model to be trained, and the second activation function is used to adjust the output of the hidden layer to within a preset range. In order to convert the two-dimensional (x, y) coordinates of the center of the input isogeometric unit of the neural network into the center density of the output isogeometric unit and link it with the neural network, first calculate the preset activation value Preset activation value Obtained through the following formula:

[0057]

[0058] in, is the preset value before activation, x and y are the center coordinates of the equal geometric unit, represents the weight associated with the i-th neuron in the k-1th layer and the i-th neuron in the kth layer; represents the weight associated with the jth neuron in the k-1th layer and the i-th neuron in the kth layer. Then the output of the neuron is for:

[0059]

[0060] Among them, σ represents the first activation function selected, and the first activation function is the LeakyReLU activation function:

[0061]

[0062] Among them, (ε~10 -2 ). A preset normalization function is used for normalization processing to speed up the training process of the neural network and improve the convergence and stability of the model. The preset normalization function is the BatchNorm function. The output layer uses the second activation function to adjust the output of the hidden layer within a preset range. The preset range is between 0 and 1. The second activation function is the softMax function. The neural network model to be trained after model training is used as the first neural network model, and the model is optimized according to the initial isogeometric topology. The expression of the first neural network model is obtained as follows:

[0063]

[0064] Among them, λ is the set of neural network weights w and bias b.

[0065] Step S103, obtaining the center coordinates of the isogeometric units, and obtaining the center density of the isogeometric units through the first neural network model according to the center coordinates.

[0066] Specifically, according to the center coordinates, the center density of the isogeometric unit is obtained through the first neural network model for:

[0067]

[0068] Since in step S102, the second activation function is used to control the output of the hidden layer within a preset range, then

[0069] Step S104, constructing a loss function according to the center density of the isogeometric unit, and updating the first neural network model by minimizing the loss function to obtain an updated second neural network model.

[0070] Specifically, a loss function is constructed, and the flexibility optimization problem is replaced by the problem of minimizing the loss function. The loss function is constructed by the following formula:

[0071]

[0072] Among them, L(λ) is the loss function, λ is the set of neural network weights w and bias b, C 0 is the initial flexibility of the structure to be optimized, v e is the cell center density corresponding to the isogeometric cell, υ e is the volume of the isogeometric unit, and α is the second penalty factor. In this embodiment, flexibility is incorporated into the loss function. The reduction of the loss function reduces the flexibility of the structure to be optimized. The first neural network model is optimized and updated by minimizing the loss function through the Adam optimizer, thereby converting the flexibility minimization problem into the loss function minimization problem, and then obtaining the expression of the updated second neural network model as follows:

[0073]

[0074] The isogeometric analysis is performed through the second neural network model to obtain the structural response and solve the unit stiffness matrix to assemble the global stiffness matrix. The isogeometric analysis equilibrium equation of the design problem is established, the displacement at the isogeometric analysis control point is solved, and the flexibility of the structure to be optimized is calculated.

[0075] Step S105, performing isogeometric topology optimization operation on the structure to be optimized through the second neural network model.

[0076] Specifically, the optimization result corresponding to the structure to be optimized is obtained through the second neural network model; it is determined whether the optimization result meets the preset convergence condition; if the optimization result meets the preset convergence condition, the isogeometric topology optimization operation is completed. If the optimization result does not meet the preset convergence condition, the loss function is calculated, and the neural network back propagation is performed to implement the iterative update of the design variables until the optimization result meets the preset convergence condition. Among them, the sensitivity of the loss function to the design variables is designed as follows:

[0077]

[0078] Among them, λ i is the i-th design variable, the design variables are the weights and biases of the neural network, when When the second neural network model passes through back propagation, It is expressed as:

[0079]

[0080] Among them, ρ k is the density of the kth isogeometric unit, v k is the volume of the kth isogeometric unit, then the loss function is about the design variable λ i The sensitivity expression of can finally be expressed as:

[0081]

[0082] Among them, C e Represents the element flexibility.

[0083] In order to prove the validity of the application, the second neural network model in this application will be verified through a specific example: please refer to Figure 4 , which shows a schematic diagram of the design domain and boundary condition settings of a cantilever beam example provided in the embodiment of this application. The left boundary of the cantilever beam is fully constrained, and a load of force F = 1N acts on the lower end of its right boundary, where L = 1.5. In this example, the order of the selected NURBS basis function is 2, the cantilever beam is divided into 2048 span units, a total of 2244 control points, the material Young's modulus is 1MPa, and the Poisson's ratio is 0.4. Please refer to Figure 5 , which shows a schematic diagram of a topological structure obtained by using a standard isogeometric topological optimization method provided in an embodiment of the present application, wherein the volume constraint is set to 50% and the structural flexibility value is 159.51. Please refer to Figure 6 The schematic diagram of the topological structure obtained by an isogeometric topology optimization method based on a neural network model provided in the embodiment of the present application has a structural flexibility value of 102.19, which is about 36% less flexible than the standard method, achieving a better design for structural performance.

[0084] The present application constructs an initial isogeometric topology optimization design model corresponding to the structure to be optimized by adopting the above method, and performs a unit division operation on the initial isogeometric topology optimization design model, wherein the unit division operation is used to divide the isogeometric body mesh model into multiple isogeometric units; obtains a preset neural network size, and constructs a first neural network model according to the preset neural network size; obtains the center coordinates of the isogeometric units, and obtains the center density of the isogeometric units through the first neural network model based on the center coordinates; constructs a loss function based on the center density of the isogeometric units, and updates the first neural network model by minimizing the loss function to obtain an updated second neural network model; performs an isogeometric topology optimization operation on the structure to be optimized through the second neural network model, thereby eliminating the need to derive a sensitivity analysis formula, reducing the complexity of the sensitivity analysis, and making the analysis result of the optimal material distribution more accurate.

[0085] Please refer to Figure 7 , which shows a module schematic diagram of an isogeometric topology optimization device based on a neural network model provided in an embodiment of the present application, the device includes a unit division module 71, a neural network construction module 72 and an isogeometric topology optimization module 73, wherein,

[0086] The unit division module 71 is used to construct an initial isogeometric topology optimization design model corresponding to the structure to be optimized, and perform unit division operation on the initial isogeometric topology optimization design model. The unit division operation is used to divide the isogeometric mesh model into multiple isogeometric units.

[0087] The neural network construction module 72 is used to obtain a preset neural network size and construct a first neural network model according to the preset neural network size; obtain the center coordinates of the isogeometric units, and obtain the center density of the isogeometric units through the first neural network model based on the center coordinates; construct a loss function based on the center density of the isogeometric units, and update the first neural network model by minimizing the loss function to obtain an updated second neural network model.

[0088] The isogeometric topology optimization module 73 is used to perform isogeometric topology optimization operations on the structure to be optimized through the second neural network model.

[0089] In a possible implementation, the unit division module 71 is used to construct an initial isogeometric topology optimization design model corresponding to the structure to be optimized, specifically including: obtaining a first corresponding relationship, which is the corresponding relationship between the isogeometric unit and the unit Young's modulus; based on the first corresponding relationship, with flexibility minimization as the goal and the structural volume as a constraint, constructing an initial isogeometric topology optimization design model.

[0090] In a possible implementation manner, the unit division module 71 is used to express the first corresponding relationship through the following functional relationship:

[0091]

[0092] Among them, ρ e is the density of the isogeometric unit, E e (ρ e ) is the unit Young's elastic modulus, E min is the Young's modulus of the void unit, E 0 is the Young's modulus of the standard solid material, p is the first penalty factor, and p∈[3,4];

[0093] The expression of the initial isogeometric topology optimization design model is:

[0094]

[0095] in, Indicates search The target solution ρ in is n, which is the number of equal geometry units. It represents the cell center density corresponding to the geometric cell number i. represents the flexibility minimization according to the target solution ρ, where K is the global stiffness matrix, U is the global displacement vector of each isogeometric unit, T is the transposed matrix, and u e is the unit displacement vector, subject to:K(ρ)U=F means the constraint condition is K(ρ)U=F, F is the global force vector, V(ρ) is the material volume of the structure to be optimized, V f is the design domain volume corresponding to the structure to be optimized.

[0096] In one possible implementation, the neural network construction module 72 is used to construct a first neural network model, specifically including: obtaining a neural network model to be trained, and setting the depth and height of the neural network model to be trained in a preset manner, wherein the depth is the number of hidden layers of the neural network, and the height is the number of neurons in each layer of the neural network; initializing the weights and biases of the neural network model to be trained; performing model training on the neural network model to be trained through a first activation function, a preset normalization function, and a second activation function, wherein the first activation function is used to perform nonlinear mapping of the weights and biases corresponding to each layer of neurons in the neural network model to be trained, the preset normalization function is used to normalize the neural network model to be trained, and the second activation function is used to adjust the output of the hidden layer to within a preset range; and using the neural network model to be trained after model training as the first neural network model.

[0097] In a possible implementation, the neural network construction module 72 is used to perform model training on the neural network model to be trained by using the first activation function, the preset normalization function and the second activation function. The method also includes: obtaining a preset pre-activation value, and obtaining the first activation function, the preset normalization function and the second activation function according to the preset pre-activation value; the preset pre-activation value is obtained by the following formula:

[0098]

[0099] in, is the preset value before activation, x and y are the center coordinates of the equal geometric unit, represents the weight associated with the i-th neuron in the k-1th layer and the i-th neuron in the kth layer; Represents the weight associated with the j-th neuron in the k-1th layer and the i-th neuron in the k-th layer.

[0100] In a possible implementation, the neural network construction module 72 is used to construct a loss function according to the center density of the isogeometric unit, specifically including: constructing the loss function by the following formula:

[0101]

[0102] Among them, L(λ) is the loss function, λ is the set of neural network weights and biases, C 0 is the initial flexibility of the structure to be optimized, ρ e is the cell center density corresponding to the isogeometric cell, v e is the volume of the isogeometric unit, α is the second penalty factor, and α∈(0,100].

[0103] In one possible implementation, the isogeometric topology optimization module 73 is used to perform isogeometric topology optimization on the structure to be optimized through the second neural network model, specifically including: obtaining the optimization result corresponding to the structure to be optimized through the second neural network model; judging whether the optimization result meets the preset convergence condition; if the optimization result meets the preset convergence condition, completing the isogeometric topology optimization operation.

[0104] It should be noted that: when the device provided in the above embodiment realizes its function, only the division of the above functional modules is used as an example. In actual application, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. In addition, the device and method embodiments provided in the above embodiment belong to the same concept, and the specific implementation process is detailed in the method embodiment, which will not be repeated here.

[0105] The present application also provides an electronic device. Figure 8 , Figure 8 801 , at least one communication bus 802 , a user interface 803 , at least one network interface 804 , and a memory 805 .

[0106] The communication bus 802 is used to realize the connection and communication between these components.

[0107] The user interface 803 may include a display screen (Display) and a camera (Camera), and the optional user interface 803 may also include a standard wired interface and a wireless interface.

[0108] The network interface 804 may optionally include a standard wired interface or a wireless interface (such as a WI-FI interface).

[0109] Among them, the processor 801 may include one or more processing cores. The processor 801 uses various interfaces and lines to connect various parts in the entire server, and executes various functions of the server and processes data by running or executing instructions, programs, code sets or instruction sets stored in the memory 805, and calling data stored in the memory 805. Optionally, the processor 801 can be implemented in at least one hardware form of digital signal processing (Digital Signal Processing, DSP), field programmable gate array (Field-Programmable Gate Array, FPGA), and programmable logic array (Programmable Logic Array, PLA). The processor 801 can integrate one or more combinations of a central processing unit (Central Processing Unit, CPU), a graphics processing unit (Graphics Processing Unit, GPU) and a modem. Among them, the CPU mainly processes the operating system, user interface and application programs; the GPU is responsible for rendering and drawing the content to be displayed on the display screen; the modem is used to process wireless communications. It can be understood that the above-mentioned modem may not be integrated into the processor 801, and it can be implemented separately through a chip.

[0110] Among them, the memory 805 may include a random access memory (Random Access Memory, RAM) and may also include a read-only memory (Read-Only Memory). Optionally, the memory 805 includes a non-transitory computer-readable storage medium. The memory 805 can be used to store instructions, programs, codes, code sets or instruction sets. The memory 805 may include a program storage area and a data storage area, wherein the program storage area may store instructions for implementing an operating system, instructions for at least one function (such as a touch function, a sound playback function, an image playback function, etc.), instructions for implementing the above-mentioned various method embodiments, etc.; the data storage area may store data involved in the above-mentioned various method embodiments, etc. The memory 805 may optionally also be at least one storage device located away from the aforementioned processor 801. Refer to Figure 8 , as a computer storage medium, the memory 805 may include an operating system, a network communication module, a user interface module, and a geometric topology optimization application based on a neural network model.

[0111] exist Figure 8 In the electronic device shown, the user interface 803 is mainly used to provide an input interface for the user and obtain the data input by the user; and the processor 801 can be used to call the isogeometric topology optimization application based on the neural network model stored in the memory 805. When executed by one or more processors 801, the electronic device executes one or more of the methods described in the above embodiments. It should be noted that for the aforementioned method embodiments, for the sake of simple description, they are all expressed as a series of action combinations, but those skilled in the art should know that the present application is not limited to the described order of actions, because according to the present application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also know that the embodiments described in the specification are all preferred embodiments, and the actions and modules involved are not necessarily required for the present application.

[0112] The present application also provides a computer-readable storage medium, which stores instructions. When executed by one or more processors, the electronic device executes one or more of the methods described in the above embodiments.

[0113] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0114] In the several embodiments provided in this application, it should be understood that the disclosed devices can be implemented in other ways. For example, the device embodiments described above are only schematic, such as the division of units, which is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some service interfaces, and the indirect coupling or communication connection of devices or units can be electrical or other forms.

[0115] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0116] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0117] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable memory. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, which is stored in a memory and includes several instructions for a computer device (which can be a personal computer, server or network device, etc.) to perform all or part of the steps of the various embodiments of the present application. The aforementioned memory includes: various media that can store program codes, such as USB flash drives, mobile hard drives, magnetic disks or optical disks.

[0118] The above are only exemplary embodiments disclosed in this application, and the scope of the disclosure of this application cannot be limited by this. That is, any equivalent changes and modifications made according to the teachings disclosed in this application are still within the scope of the disclosure of this application. After considering the disclosure of the specification and the truth of practice, those skilled in the art will easily think of other implementation schemes disclosed in this application.

[0119] This application is intended to cover any modifications, uses or adaptive changes disclosed in this application, which follow the general principles disclosed in this application and include common knowledge or customary technical means in the technical field not recorded in this application.

Claims

1. An isogeometric topology optimization method based on a neural network model, characterized in that: The method comprises: Constructing an initial isogeometric topology optimization design model corresponding to the structure to be optimized, and performing a unit division operation on the initial isogeometric topology optimization design model, wherein the unit division operation is used to divide the isogeometric body mesh model into a plurality of isogeometric units; Obtaining a preset neural network size, and constructing a first neural network model according to the preset neural network size; Acquire the center coordinates of the isogeometric units, and acquire the center density of the isogeometric units through the first neural network model according to the center coordinates; Constructing a loss function according to the center density of the isogeometric unit, and updating the first neural network model by minimizing the loss function to obtain an updated second neural network model; The isogeometric topology optimization operation is performed on the structure to be optimized through the second neural network model.

2. The method according to claim 1, characterized in that The constructing of an initial isogeometric topology optimization design model corresponding to the structure to be optimized specifically includes: Acquire a first corresponding relationship, where the first corresponding relationship is a corresponding relationship between the isogeometric unit and the unit Young's modulus of elasticity; According to the first corresponding relationship, the initial isogeometric topology optimization design model is constructed with flexibility minimization as the goal and structural volume as the constraint.

3. The method according to claim 2, characterized in that The method further comprises: The first corresponding relationship is expressed by the following functional relationship: Among them, ρ e is the density of the isogeometric unit, E e (ρ e ) is the unit Young's elastic modulus, E mi is the Young's modulus of the void element, E0 is the Young's modulus of the standard solid material, p is the first penalty factor, and p∈[3,4]; The expression of the initial isogeometric topology optimization design model is: in, Indicates search The target solution ρ in is n, which is the number of isogeometric units. represents the cell center density corresponding to the isogeometric cell described in number i, represents the minimization of the flexibility according to the target solution ρ, and K is the global stiffness matrix, U is the global displacement vector of each of the isogeometric units, T is the transposed matrix, u e is the unit displacement vector, subject to:K(ρ)U=F means the constraint condition is K(ρ)U=F, F is the global force vector, V(ρ) is the material volume of the structure to be optimized, V f is the design domain volume corresponding to the structure to be optimized.

4. The method according to claim 1, characterized in that: The constructing of the first neural network model specifically includes: Obtain a neural network model to be trained, and set the depth and height of the neural network model to be trained in a preset manner, wherein the depth is the number of hidden layers of the neural network, and the height is the number of neurons in each layer of the neural network; Initializing the weights and biases of the neural network model to be trained; The neural network model to be trained is trained by a first activation function, a preset normalization function and a second activation function, wherein the first activation function is used to perform nonlinear mapping on the weights and biases corresponding to each layer of neurons in the neural network model to be trained, the preset normalization function is used to normalize the neural network model to be trained, and the second activation function is used to adjust the output of the hidden layer to within a preset range; The neural network model to be trained after model training is used as the first neural network model.

5. The method according to claim 4, characterized in that Before performing model training on the neural network model to be trained by using the first activation function, the preset normalization function and the second activation function, the method further includes: Obtaining a preset pre-activation value, and obtaining the first activation function, the preset normalization function, and the second activation function according to the preset pre-activation value; The preset pre-activation value is obtained by the following formula: in, is the preset value before activation, x and y are the center coordinates of the isogeometric unit, represents the weight associated with the i-th neuron in the k-1-th layer and the i-th neuron in the k-th layer; Represents the weight associated with the j-th neuron in the k-1-th layer and the i-th neuron in the k-th layer.

6. The method according to claim 4, characterized in that The step of constructing a loss function according to the center density of the isogeometric unit specifically includes: The loss function is constructed by the following formula: Wherein, L(λ) is the loss function, λ is the set of the neural network weights and the neural network bias, C 0 is the initial flexibility of the structure to be optimized, ρ e is the unit center density corresponding to the isogeometric unit, υ e is the volume of the isogeometric unit, α is the second penalty factor, and α∈(0,100].

7. The method according to claim 1, characterized in that The performing isogeometric topology optimization on the structure to be optimized by the second neural network model specifically includes: Obtaining an optimization result corresponding to the structure to be optimized through the second neural network model; Determining whether the optimization result meets a preset convergence condition; If the optimization result satisfies the preset convergence condition, the isogeometric topology optimization operation is completed.

8. An isogeometric topology optimization device based on a neural network model, characterized in that: The device includes a unit partitioning module, a neural network construction module and an isogeometric topology optimization module, wherein: The unit division module is used to construct an initial isogeometric topology optimization design model corresponding to the structure to be optimized, and perform a unit division operation on the initial isogeometric topology optimization design model, wherein the unit division operation is used to divide the isogeometric body mesh model into a plurality of isogeometric units; The neural network construction module is used to obtain a preset neural network size and construct a first neural network model according to the preset neural network size; obtain the center coordinates of the isogeometric units, and obtain the center density of the isogeometric units through the first neural network model according to the center coordinates; construct a loss function according to the center density of the isogeometric units, and update the first neural network model by minimizing the loss function to obtain an updated second neural network model; The isogeometric topology optimization module is used to perform isogeometric topology optimization operations on the structure to be optimized through the second neural network model.

9. An electronic device, characterized in that: It includes a processor, a communication bus, a user interface, a network interface and a memory, wherein the memory is used to store instructions, the user interface and the network interface are used to communicate with other devices, and the processor is used to execute the instructions stored in the memory so that the electronic device executes the method according to any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores instructions, and when the instructions are executed, the method according to any one of claims 1 to 7 is performed.

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