Microstructure rapid design and filling method and system based on macroscopic strain

Abstract

The invention belongs to the technical field of microstructure and multi-scale structure design, and particularly relates to a microstructure rapid design and filling method and system based on macroscopic strain. Constructing a microstructure topological optimization model based on the macroscopic strain, sampling the macroscopic strain and the volume fraction to generate a corresponding optimized microstructure, and establishing a microstructure training data sample library with labels; carrying out equivalence analysis on a strain energy expression, solving the problem of variable inconsistency by utilizing an intermediate variable, and converting the strain in the training sample into the intermediate variable; establishing a deep neural network with an intermediate variable and a volume fraction as input and a microstructure topological configuration as output, and training the deep neural network by using a data sample to obtain a microstructure fast reverse design network; and carrying out staged multi-scale structure filling design by using the microstructure fast reverse design network. According to the method, the online calculation cost of microstructure and multi-scale structure design can be reduced, and the design efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of microstructure and multi-scale structure design, and particularly relates to a microstructure rapid design and filling method and system based on macroscopic strain. BACKGROUND

[0002] In the field of mechanical structure design, microstructure generally refers to microstructure with obvious length scale difference from macrostructure. Microstructure with the same or similar configuration arranged in an array in space can exhibit physical properties that natural materials do not have or have less, so microstructure is also considered as an artificial material. Multi-scale structure design considers macro material distribution and microstructure topology at the same time, fully utilizes the diversity and natural scarcity of equivalent physical properties of microstructure, and has higher design freedom compared to traditional single-scale design, so that the performance potential of structure design can be fully tapped. Multi-scale structure has excellent performance characteristics such as high stiffness, high strength and light weight, and has extremely high research value and application prospect for important equipment that needs to consider range and fuel economy and is in an extraordinary service environment.

[0003] Computational cost and time is one of the pain points restricting the wide application of multi-scale structure design. On the one hand, the introduction of micro design scale requires the use of homogenization and other numerical calculation methods to solve the equivalent physical properties of microstructure to establish the connection between macro and micro analysis; on the other hand, the number of microstructure types is proportional to the size of micro design variables, and it is inevitable to repeatedly call optimization algorithm subprograms when designing multiple types of microstructure. The above reasons cause the multi-scale structure design to have heavy computational cost, long time consumption and low optimization design efficiency. And the problem becomes more and more serious with the increase of grid refinement degree and the number of microstructure types, so that a choice between structure performance and design efficiency has to be made.

[0004] Overall, microstructure and multi-scale structure design have excellent performance and wide application prospect, but the design solving based on numerical calculation analysis method and optimization algorithm has problems such as high computational cost and low optimization efficiency, which limits its wide application to practical engineering problems. SUMMARY

[0005] The purpose of the present application is to provide a microstructure rapid design and filling method and system based on macroscopic strain, which generates microstructure samples with macroscopic strain as given input conditions, and constructs a deep neural network model for microstructure rapid design and filling, which can significantly reduce the online computational cost of microstructure and multi-scale structure design and improve the design efficiency.

[0006] To achieve the above purpose, the present application provides a construction method of a deep neural network model for microstructure rapid design and filling, comprising the following steps:

[0007] S1, construct a microstructure topology optimization model based on a parameterized level set method, a given parameter of the microstructure topology optimization model is a macroscopic strain to which the microstructure is subjected, constraint conditions include a microstructure volume fraction constraint; sample the macroscopic strain and the volume fraction of the microstructure, then input the microstructure topology optimization model, generate a corresponding optimized microstructure, and finally establish a labeled microstructure training data sample library;

[0008] S2, analyze the equivalence of a strain energy expression with a macroscopic strain as a variable and a strain energy expression with a macrostructure macroscopic displacement as a variable, to establish a connection between the macroscopic strain and the macroscopic displacement through an intermediate variable; then convert the macroscopic strain in the labeled microstructure training data sample library into the intermediate variable to obtain a new labeled microstructure training data sample library;

[0009] S3, build a deep neural network model with an input of the intermediate variable and the volume fraction of the microstructure and an output of a microstructure topology configuration, and train the deep neural network model using the new labeled microstructure training data sample library to obtain a deep neural network model for rapid design and filling of microstructures.

[0010] Further, in step S1, the microstructure topology optimization model takes a microstructure macroscopic compliance as a minimization objective function, takes an extension coefficient of a radial basis function in the parameterized level set method as a design variable, and updates the design variable through an optimization criterion method;

[0011] The microstructure macroscopic compliance is calculated by calculating an equivalent elastic matrix of the microstructure through a homogenization method, and then calculating the microstructure macroscopic compliance through the macroscopic strain and the equivalent elastic matrix;

[0012] The sampling of the macroscopic strain and the volume fraction of the microstructure is Latin hypercube sampling and uniform random sampling, respectively.

[0013] Further, the design variable is updated through a sensitivity analysis-based optimization criterion method, a linear penalty strategy is adopted for the volume fraction constraint to gradually reduce the volume fraction, and finally the microstructure is optimized. The exact optimization result obtained in step S1 is used as a training sample to further construct a prediction model, which can directly output a target microstructure topology configuration in subsequent applications, and if the microstructure topology optimization model is directly used for design each time, the efficiency is relatively low.

[0014] Further, the microstructure topology optimization model has the following structure:

[0015] Given: ε

[0016] Find: α=[α1α2...α N ] T

[0017]

[0018] where ε is the given macroscopic strain input parameter, the strain vector is three-dimensional and six-dimensional in two and three dimensional cases, respectively; α is the dilation coefficient of the radial basis function in the parametric level set method and determines the level set function Φ(α); minimizing the optimization objective function C(α) is the macroscopic compliance of the microstructure; D H (Φ(α)) is the equivalent elastic matrix of the microstructure; denotes the i-th row and j-th column component of the equivalent elastic matrix, which is obtained by the homogenization method, i.e. the constraint condition first formula; Ω denotes the design domain of the microstructure; D kl denotes the local material property inside the microstructure, which is generally considered to be composed of a base phase and a void phase; H(Φ) denotes the Heaviside function; denotes the unit test strain, which is obtained by the equilibrium equation of the constraint condition second formula; v denotes the virtual displacement field on the microstructure; ρ denotes the upper limit of the volume fraction; V0 denotes the volume of the design domain of the microstructure; the constraint condition third formula is the volume fraction constraint of the microstructure.

[0019] In step S1, the macroscopic strain is taken as the given input condition instead of the macroscopic displacement as the given input in the traditional multi-scale structure topology optimization, which can avoid the problems of too high data dimension, sparse effective information and program accidental interruption. However, the training data generated by the microstructure topology optimization model based on the macroscopic strain in step S1 has input labels of macroscopic strain and volume fraction, and the mechanical information obtained from the macroscopic finite element analysis is still the unit node displacement. The inconsistency between the variables of strain and displacement leads to the inability to construct a directly usable deep neural network model to realize the rapid reverse design of the microstructure. Therefore, the present application establishes the relationship between the macroscopic strain and the macroscopic displacement through an intermediate variable.

[0020] Further, in step S2, the two strain energy expressions are expanded first, the Gauss quadrature method is used to realize numerical calculation for the integral in the formula, then the multipliers of the same elastic matrix components are taken as equivalent and denoted as an intermediate variable, so as to establish the relationship between the macroscopic strain and the macroscopic displacement through a set of intermediate variables containing six components. Specifically:

[0021] The strain energy expression for generating the microstructure with the macroscopic strain as the variable is expanded as:

[0022]

[0023] where ε k (k=1,2,3) denotes the k-th component of the strain vector, D ij(i,j=1,2,3) represents the component on the i-th row and j-th column of the elastic matrix;

[0024] The strain energy expression of the macroscopic finite element analysis with the microstructure macroscopic displacement as the variable is expanded as:

[0025]

[0026] wherein u represents a displacement vector, (x i ,y j (i,j=1,2,...,G) represents the coordinates of the Gauss integral point, E mn represents a matrix with the component on the m-th row and n-th column being 1 and the remaining components being 0, m,n=1,2,3; and B represents a strain-displacement matrix.

[0027] The multipliers of the same elastic matrix components are taken as equivalents and denoted as intermediate variables, and the following variable equivalence relationship is obtained:

[0028]

[0029] Finally, a set of intermediate variables iv a (a=1,2,...,6) containing 6 components are obtained.

[0030] Further, in step S3, the deep neural network model is built based on an SE-ResNeXt module, including a residual network, a grouped convolution, and an SE block; specifically, the grouped convolution and the SE block are introduced based on the residual network: the residual network introduces a skip connection representing an identity mapping between a plurality of convolution layers, and converts learning a mapping function into learning a residual between an input and an output; the grouped convolution groups input and output channels, and each group independently performs convolution operation, and groups are independent of each other; the SE block introduces a fully connected network with an output dimension equal to the number of feature map channels, and the output of the fully connected network is used as a scaling factor acting on feature map data to realize a channel attention mechanism. After the deep neural network model is trained by using the new labeled microstructure training data sample library, the rapid reverse design of the microstructure can be realized to improve the design efficiency.

[0031] The application also provides a deep neural network model for microstructure rapid design and filling obtained by the construction method.

[0032] The application further provides a microstructure rapid design and filling method based on macroscopic strain, comprising: first, optimizing the distribution of macroscopic materials according to given design conditions of macroscopic structure to obtain unit density distribution and macroscopic displacement, then converting the macroscopic displacement into an intermediate variable, and splicing the unit density as the volume fraction of the microstructure and the intermediate variable as the input of a deep neural network model for microstructure rapid design and filling, and then outputting the microstructure topology configuration, and filling the microstructure topology configuration to obtain a multi-scale structure.

[0033] Further, the optimization of the distribution of macroscopic materials comprises: taking the unit density distribution as a design variable, minimizing the compliance as an optimization target, solving the unit density distribution based on the density method according to the given design conditions, and outputting the macroscopic displacement; the given design conditions comprise the design domain, boundary conditions and volume fraction constraints of the macroscopic structure.

[0034] The design variable is updated by using the optimization criterion method based on sensitivity analysis to obtain the unit density distribution result, and the unit node displacement obtained by macroscopic finite element analysis is outputted.

[0035] Further, the deep neural network model for microstructure rapid design and filling outputs specific microstructure level set function values on the macroscopic unit, and then draws an overall structure image according to the position relationship of the level set function values of each microstructure, that is, obtains a multi-scale structure composed of microstructure topology configurations.

[0036] The application further provides a microstructure rapid design and filling system based on macroscopic strain, comprising an executor configured to execute the microstructure rapid design and filling method based on macroscopic strain.

[0037] Overall, compared with the prior art, the above technical solutions conceived by the application mainly have the following technical advantages:

[0038] 1. The microstructure topology optimization model based on macroscopic strain ensures scale correlation, fully considers the mechanical information of macroscopic finite element analysis, guarantees the consistency of microstructure design and multi-scale structure design targets, realizes the decoupling of microstructure design from the multi-scale design process, and provides a basis for generating training data samples for subsequent construction and training of a deep neural network.

[0039] 2. The application generates microstructure samples with macroscopic strain as a given input condition, which can avoid the following problems compared with directly taking macroscopic displacement as a given input in reference to traditional multi-scale structure topology optimization: (1) high data dimension: the unit strain is a 3-dimensional vector, and the unit node displacement is an 8-dimensional vector, considering that if n values are sampled for each component, the sample numbers of the two methods are n 3 and n 8Therefore, the method can reduce the dimension and quantity of sample data; (2) effective information sparsity: different unit node displacements may correspond to the same strain form and obtain the same microstructure, so that the unit node displacement is given as input, which will cause more same microstructures in the data set, resulting in unnecessary additional calculation overhead; (3) program unexpected interruption: sampling of unit node displacement may appear rigid body displacement, at this time the strain energy is always zero, and the optimization program cannot proceed normally, while sampling of strain does not have this problem.

[0040] 3. The microstructure rapid reverse design model is constructed by adopting the SE-ResNeXt neural network module, and the latest research results in the field of computer vision and image recognition are used to realize implicit mapping of design information to microstructure. Among them, the residual network can solve the problems of gradient disappearance and gradient explosion in the training of deep neural network; the grouped convolution can reduce the density of channel connection while maintaining the feature extraction ability, and reduce the calculation overhead; the SE block introduces the channel attention mechanism, and further improves the expression ability of the model.

[0041] 4. The microstructure design is decoupled from the overall process of traditional multi-scale structure topology optimization design, and the neural network is used to realize the iteration-free and efficient reverse design of microstructure, reduce the online calculation overhead, and improve the design efficiency. The constructed microstructure reverse design model can be used for any microstructure design domain, and has sufficient applicability and reusability. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is a specific process schematic diagram of a microstructure rapid design and filling method based on macroscopic strain provided by the application.

[0043] Figure 2 is a composition schematic diagram of the SE-ResNeXt neural network module of the application.

[0044] Figure 3 is a composition schematic diagram of the microstructure rapid reverse design neural network of the application.

[0045] Figure 4 is the convergence curve of the objective function and volume fraction of the microstructure topology optimization design in the implementation example of the application, wherein the upper graph is the macroscopic strain

[110] T , and the volume fraction is 0.5; the lower graph is the macroscopic strain

[001] T , and the volume fraction is 0.5.

[0046] Figure 5 is the microstructure topology optimization design result of the same macroscopic strain and different volume fractions in the implementation example of the application.

[0047] Figure 6is the loss function convergence curve of the microstructure rapid reverse design network in the implementation example of the present application.

[0048] Figure 7 is the accuracy rate of the microstructure in the test set predicted by the trained microstructure rapid reverse design network in the implementation example of the present application.

[0049] Figure 8 is the time consumption comparison of the microstructure predicted by the trained microstructure rapid reverse design network and the calculation of the topological optimization method in the implementation example of the present application.

[0050] Figure 9 is the design domain and boundary condition diagram of the half MBB beam design problem in the implementation example of the present application.

[0051] Figure 10 is the macroscopic material distribution optimization design result diagram of the half MBB beam design problem in the implementation example of the present application.

[0052] Figure 11 is the result diagram of the microstructure design and filling of the half MBB beam design problem by using the microstructure rapid reverse design network in the implementation example of the present application.

[0053] Figure 12 is the topological configuration and equivalent elastic matrix of part of the typical microstructure in the result of the half MBB beam design problem in the implementation example of the present application. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described in detail below in combination with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0055] The present application first provides a construction method of a deep neural network model for microstructure rapid design and filling, comprising the following steps:

[0056] S1, constructing a microstructure topological optimization model based on a parameterized level set method, the given parameter of the microstructure topological optimization model is the macroscopic strain suffered by the microstructure, and the constraint conditions include the microstructure volume fraction constraint; sampling the macroscopic strain and the volume fraction of the microstructure, then inputting the microstructure topological optimization model to generate the corresponding optimized microstructure, and finally establishing a labeled microstructure training data sample library;

[0057] S2, equivalence analysis is performed on the strain energy expression taking macroscopic strain as a variable and the strain energy expression taking microstructure macroscopic displacement as a variable, to establish the relationship between the macroscopic strain and the macroscopic displacement through an intermediate variable; then the macroscopic strain in the labeled microstructure training data sample library is converted into the intermediate variable, to obtain a new labeled microstructure training data sample library;

[0058] S3, a deep neural network model with input of the intermediate variable and the microstructure volume fraction and output of the microstructure topological configuration is built, and the new labeled microstructure training data sample library is used to train the deep neural network model, to obtain a deep neural network model for microstructure rapid design and filling.

[0059] The exact optimization result obtained in step S1 is used as a training sample to provide a reliable basis for the construction and training of the deep neural network model, and the model can be directly used to quickly output the target microstructure topological configuration in subsequent applications, so that the design efficiency is significantly improved.

[0060] Specifically, referring to Figure 1 The microstructure rapid design and filling method based on macroscopic strain provided by the application comprises the following steps:

[0061] Step 1. Microstructure topological optimization model based on macroscopic strain

[0062] On the microscale, the macroscopic strain of the microstructure unit is taken as a given parameter, the equivalent elastic matrix of the microstructure is calculated through the homogenization method, the microstructure macroscopic compliance (i.e. strain energy) calculated by the macroscopic strain and the equivalent elastic matrix is taken as a minimum objective function, and the microstructure is described and optimized based on the parameterized level set method. The optimization model is constructed as follows:

[0063]

[0064] In the formula, ε is a given macroscopic strain input parameter, the macroscopic strain vector is three-dimensional and six-dimensional in the two-dimensional and three-dimensional cases respectively; the design variable α is the expansion coefficient of the radial basis function in the parameterized level set method, and determines the level set function Φ(α); the minimum optimization objective function C(α) is the macroscopic compliance; D H (Φ(α)) indicates the equivalent elastic matrix of the microstructure, represents the component on the i-th row and the j-th column, which is obtained by the homogenization method, i.e. the constraint condition of the first formula. Ω represents the microstructure design domain; D kl represents the local material property inside the microstructure, and it is generally considered that the microstructure is composed of a base phase and a void phase; H(Φ) represents the Heaviside function; represents the unit test strain, The equilibrium equation of the second constraint condition is obtained by the second formula; v represents the virtual displacement field on the microstructure; p represents the upper limit of the volume fraction; V0 represents the volume of the microstructure design domain; the third constraint condition is the microstructure volume fraction constraint. Sensitivity analysis is performed on the optimization model, and the relevant derivation details are omitted. The sensitivity expression of the objective function to the design variable is as follows:

[0065]

[0066] The derivative of the equivalent elastic matrix component to the design variable is as follows:

[0067]

[0068] The nth radial basis function is represented by δ (Φ) ) ; and the Dirac delta function is represented by δ (Φ) ).

[0069] The sensitivity expression of the volume fraction constraint to the design variable is as follows:

[0070]

[0071] Further, the design variable is updated by using the optimization criterion method, and in order to improve the iteration stability, a linear penalty strategy is adopted for the volume fraction constraint to gradually reduce the volume fraction, and finally the microstructure optimization design is realized.

[0072] Further, the macroscopic strain and the volume fraction are subjected to Latin hypercube sampling and uniform random sampling, and then the above microstructure topology optimization model is used to generate the corresponding microstructure, and a labeled training data sample set is established, that is, each group of data contains the macroscopic strain and the volume fraction and the corresponding optimal microstructure.

[0073] In order to facilitate related analysis and discussion, the comparative scheme of the present application is simply explained as follows. In the traditional multi-scale topology optimization method, the macroscopic mechanical information is presented in the form of macroscopic displacement and is used as a given parameter for microstructure design. The microstructure topology optimization model established accordingly changes the given parameter and the optimization target to the following form:

[0074]

[0075] u represents the macroscopic displacement vector; and B represents the strain-displacement matrix.

[0076] However, input sampling and microstructure generation of the optimization model are faced with problems of too high data dimension, sparse effective information and unexpected program interruption.

[0077] Step 2. Strain energy equivalence analysis and intermediate variable method

[0078] In the traditional multi-scale topology optimization framework, the solution of macro finite element analysis is given in the form of element node displacement, which is used to calculate the flexibility of microstructure on the element and as the minimization objective function of microstructure optimization design. However, the present application uses macro strain as an input parameter for microstructure design and sample generation, which will cause the inconsistency of variables between strain and displacement, resulting in the inability to build a directly usable deep neural network model to realize the rapid reverse design of microstructure. Therefore, the present application establishes the relationship between macro strain and displacement through intermediate variables.

[0079] The strain energy equivalence analysis is carried out, and the intermediate variable is used to solve the variable inconsistency problem. The two strain energy expressions are expanded, the symmetry of the elastic matrix is considered, and the Gaussian quadrature method is used to process the integral expression. The objective function of the strain energy expression for generating microstructure with macro strain as the variable, i.e. formula (1), is expanded as:

[0080]

[0081] Wherein, ε k (i = 1, 2, 3) represents the kth component of the strain vector, D ij (i, j = 1, 2, 3) represents the component of the elastic matrix on the i row and j column.

[0082] The strain energy expression of macro finite element analysis with macro displacement as the variable, i.e. formula (5), is expanded as:

[0083]

[0084] Wherein, u represents the displacement vector, (x i ,y j )(i, j = 1, 2,..., G) represents the coordinates of the Gaussian integral point, E mn represents the matrix with the component on the m row and n column being 1 and the rest of the components being 0, m, n = 1, 2, 3.

[0085] The multipliers of the same elastic matrix components are taken as equivalent and recorded as intermediate variables, and the following variable equivalence relationship is obtained:

[0086]

[0087] Finally, a set of intermediate variables iv a (a = 1, 2,..., 6) containing 6 components are obtained, which establishes the connection between microstructure generation and multi-scale design application.

[0088] Further, before using the data samples generated by the microstructure topology optimization model described in step 1 to train the deep neural network, the macro strain should be mapped to the intermediate variable according to formula (8).

[0089] Further, considering that the microstructure topology optimization model is only related to the direction of the input information, and is not related to the numerical size, that is, after arbitrary linear scaling of the input, the microstructure topology configuration obtained is unchanged, therefore, the intermediate variable data is normalized by the maximum absolute value:

[0090]

[0091] Step 3. Rapid reverse design of microstructure based on deep neural network

[0092] A neural network model is constructed with intermediate variables and volume fraction as input and optimal microstructure as output. The present application establishes this network based on SE-ResNeXt block, mainly including residual network, grouped convolution and SE block (as shown in Figure 2 ).

[0093] The residual network block introduces a skip connection representing an identity mapping between several convolution layers, converts the learning mapping function into learning the residual between input and output, and can solve the gradient disappearance and gradient explosion problems in the training of deep neural network.

[0094] Grouped convolution groups the input and output channels, and each group performs convolution operation independently. The groups are independent of each other, which can reduce the density of channel connection and reduce the computational overhead while maintaining the feature extraction capability.

[0095] The SE block introduces a fully connected network with an output dimension equal to the number of channels, and the output of the fully connected network is used as a scaling factor to act on the feature map data, realizing the channel attention mechanism and further improving the model expression ability.

[0096] Further, in order to convert vector data into feature map data and realize feature information extraction and data dimensionality lifting, the deep neural network should also include fully connected layers, convolution layers, transpose convolution layers, etc. (as shown in Figure 3 ).

[0097] Further, the deep neural network described above is trained using the labeled data set generated in step 1 and processed in step 2, thereby realizing rapid reverse design of microstructure.

[0098] Step 4. Stage-based multi-scale structure filling design

[0099] The stage-based strategy is used for multi-scale structure filling design, which is divided into macro material distribution optimization and microstructure design filling, and the two are connected in stages.

[0100] In the macro material distribution optimization stage, the minimum compliance is taken as the optimization objective, and the element density distribution is solved based on the density method according to the given design domain, boundary conditions and volume fraction constraints, and the element node displacement is output. The macro topology optimization model is established as follows:

[0101]

[0102] where x represents the cell density vector and is taken as the design variable, whose components x i denotes the density of the i-th cell. F represents the external load vector, K represents the global stiffness matrix of the structure, and U represents the global displacement vector of the structure. u i denotes the cell node displacement vector, k i denotes the cell stiffness matrix. V0 represents the cell volume, V max denotes the material volume constraint. x min and x max respectively represent the minimum and maximum values of the cell density.

[0103] A material interpolation model is introduced to establish a functional relationship between the cell stiffness matrix and the density:

[0104]

[0105] k solid denotes the solid cell, i.e., the cell stiffness matrix when the density is 1; k min takes the minimum value to avoid the singularity of the stiffness matrix; and p represents the penalty factor.

[0106] Sensitivity analysis is performed on the macroscopic optimization model, and the sensitivity expression of the objective function with respect to the design variable is as follows:

[0107]

[0108] The sensitivity expression of the volume fraction constraint with respect to the design variable is as follows:

[0109]

[0110] Further, the design variable is updated using the optimization criterion method, the cell density distribution result is obtained, and the cell node displacement u i (i = 1, 2,..., M) obtained by finite element analysis is output.

[0111] In the microstructure design filling stage, the cell node displacement data obtained by macroscopic finite element analysis is converted into intermediate variables according to formulas (8) and (9), and the cell density is taken as the microstructure volume fraction and is spliced with the intermediate variable data to obtain the input of the neural network. The microstructure fast reverse design neural network constructed in step 3 is used to output the specific microstructure level set function value on each macroscopic cell. Finally, the level set function values of the microstructures are plotted into an overall structure image according to the positional relationship.

[0112] Implementation Example

[0113] 1. Numerical example of microstructure topology optimization design

[0114] Referring to Figure 4 , the microstructure topology optimization model based on macroscopic strain is used to design the microstructure, and the design domain is discretized into a 60x60 grid cell. The macroscopic strain of the cell is taken as

[110] T and

[001] T , and the volume fraction is 0.5. It can be seen from Figure 4 that the objective function is stably decreased without obvious oscillation, and the microstructure configuration is basically unchanged in the later iteration, indicating the iteration stability of the method. The equivalent elastic matrix of the microstructure is obtained as

[0115]

[0116] Comparing the two, it can be seen that has a larger bulk modulus, especially D 11 and D 22 , which enhances the load-carrying capacity of the x and y direction normal strain and reduces the macroscopic flexibility; and has a larger shear modulus, which enhances the load-carrying capacity of the shear strain. In summary, the proposed design method is effective and stable, and the design result and its equivalent elastic matrix meet the expectations.

[0117] Referring to Figure 5 , the volume fraction is taken as 0.5 and 0.35 for the same macroscopic strain, the microstructure topology configuration and the equivalent elastic matrix are obtained, and the 3x3 array image is output. Overall, when the macroscopic strain is mainly in the x direction normal strain, the material is concentrated along the horizontal direction; similarly, when the macroscopic strain is mainly in the y direction normal strain, the material is concentrated along the vertical direction; when there is shear strain, the microstructure material distribution rotates to some extent, and part of the material is distributed along the diagonal direction.

[0118] 2. Training and prediction of microstructure rapid reverse design network

[0119] Referring to Figure 6 , Figure 7 , Figure 8 , the network is trained using the training data set, and the iteration number is set to n=300. The microstructure in the test set is predicted, and the average accuracy is 96.959%. It can be seen from Figure 7 that the predicted structure output by the trained neural network is very close to the topology of the real structure, with only slight shape errors at the edges of the structure. It can be seen from Figure 8 that the use of neural networks for microstructure reverse design has an order of magnitude improvement in speed compared to traditional topology optimization methods, and considering that the number of filled microstructures in the design domain is generally large, the proposed method can significantly improve the efficiency of multi-scale structure design.

[0120] 3. Stage multi-scale structure filling optimization design

[0121] Referring to Figure 9 , Figure 10 , Figure 11 , Figure 12 , based on the constructed microstructure rapid reverse design network to carry out stage multi-scale structure filling optimization design. Figure 9 As shown in a long L = 0.6m, high H = 0.35m half MBB beam design domain, the upper left corner has a concentrated load F = 50N, the left boundary horizontal degree of freedom is constrained, the right lower corner vertical degree of freedom is constrained. The design domain is discretized into 60x35 grid elements, the material volume fraction is set to 0.6, the penalty factor p = 1 is taken to obtain more intermediate density units, the unit density is limited between 0.2 and 0.8, and the unit density result obtained by macroscopic material distribution optimization is shown in Figure 10 .

[0122] In the displacement vector obtained by macroscopic finite element analysis, the node displacement of each unit is taken, which is converted into intermediate variable according to formula (8) and formula (9), and it is spliced with the unit density. Input the data into the microstructure reverse design network, and output the specific microstructure level set function value on each macroscopic unit. Finally, the level set function values of each microstructure are drawn according to the position relationship to obtain the overall structure image as shown in Figure 11 , Figure 12 As shown in the topological configuration and equivalent elastic matrix of part of the typical microstructure in the result, Figure 11 It can be seen that the high volume fraction of the frame beam part, the orientation of the microstructure conforms to the trend of the main frame beam; the low volume fraction of the filling part, the rod microstructure is interlaced to support the main frame beam. Overall, the overall trend and trend of macro-microstructure are reasonable.

[0123] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for constructing a deep neural network model for microstructure rapid design and filling, characterized in that, The method comprises the following steps: S1, constructing a microstructure topology optimization model based on a parameterized level set method, wherein a given parameter of the microstructure topology optimization model is a macroscopic strain to which the microstructure is subjected, and a constraint condition comprises a microstructure volume fraction constraint; sampling the macroscopic strain and the microstructure volume fraction, and then inputting the microstructure topology optimization model to generate a corresponding optimized microstructure, and finally establishing a labeled microstructure training data sample library; S2, performing equivalence analysis on a strain energy expression with the macroscopic strain as a variable and a strain energy expression with a microstructure macroscopic displacement as a variable to establish a relationship between the macroscopic strain and the macroscopic displacement through an intermediate variable; then converting the macroscopic strain in the labeled microstructure training data sample library into the intermediate variable to obtain a new labeled microstructure training data sample library; S3, building a deep neural network model with an input of the intermediate variable and the microstructure volume fraction and an output of a microstructure topology configuration, and training the deep neural network model using the new labeled microstructure training data sample library to obtain a deep neural network model for microstructure rapid design and filling.

2. The construction method of claim 1, wherein, In step S1, the microstructure topology optimization model takes a microstructure macroscopic compliance as a minimum objective function, takes an extension coefficient of a radial basis function in the parameterized level set method as a design variable, and updates the design variable through an optimization criterion method; The microstructure macroscopic compliance is calculated by an equivalent elastic matrix of the microstructure through a homogenization method, and then the microstructure macroscopic compliance is calculated through the macroscopic strain and the equivalent elastic matrix; The sampling of the macroscopic strain and the microstructure volume fraction is Latin hypercube sampling and uniform random sampling, respectively.

3. The construction method of claim 2, wherein, The microstructure topology optimization model has the following structure: Given: ε Find: a = [a1 a2... a N ] T where ε is a given macroscopic strain input parameter, the strain vector is three-dimensional and six-dimensional in two and three dimensions, respectively; α is the dilation coefficient of the radial basis function in the parametric level set method and determines the level set function Φ(α); minimizing the optimization objective function C(α) is the macroscopic compliance of the microstructure; D H denotes the i-th row and j-th column component of the equivalent elastic matrix of the microstructure, which is obtained by the homogenization method, i.e., the constraint condition first formula; Ω denotes the microstructure design domain; D denotes the i-th row and j-th column component of the equivalent elastic matrix of the microstructure, which is obtained by the homogenization method, i.e., the constraint condition first formula; Ω denotes the microstructure design domain; D kl denotes the local material property inside the microstructure; H(Φ) denotes the Heaviside function; denotes the unit test strain, which is obtained by the equilibrium equation of the constraint condition second formula; v denotes the virtual displacement field on the microstructure; ρ denotes the volume fraction upper limit; V0 denotes the volume of the microstructure design domain; the constraint condition third formula is the volume fraction constraint of the microstructure.

4. The construction method of claim 1, wherein, In step S2, the two strain energy expressions are first expanded, and the integrals in the expressions are numerically calculated using the Gauss quadrature method. Then, the multipliers of the same elastic matrix components are taken as equivalent and recorded as intermediate variables, to obtain the following variable equivalence relationship, so that the macroscopic strain and the macroscopic displacement are related through a set of six-component intermediate variables iv a (a = 1, 2,..., 6) ε k (k = 1,2,3) denotes the k-th component of the macroscopic strain vector; u denotes the macroscopic displacement vector; B denotes the strain-displacement matrix; (x i ,y j )(i,j = 1,2,...,G) denotes the coordinates of the Gauss integration points; E mn denotes the matrix with the component in the m-th row and n-th column equal to 1 and the remaining components equal to 0, m,n = 1,2,3.

5. The construction method of claim 1, wherein, In step S3, the deep neural network model is built based on an SE-ResNeXt module, and comprises a residual network, a grouped convolution, and an SE block; specifically, the grouped convolution and the SE block are introduced based on the residual network: the residual network introduces a skip connection representing an identity mapping between a plurality of convolution layers, and converts learning a mapping function into learning a residual between an input and an output; the grouped convolution groups input and output channels, and each group independently performs convolution operation without being associated with other groups; the SE block introduces a fully connected network with an output dimension equal to a feature map channel number, and outputs of the fully connected network are used as scaling factors acting on feature map data to realize a channel attention mechanism.

6. A deep neural network model for microstructure rapid design and filling obtained by the construction method of any one of claims 1-5.

7. A macro-strain based microstructure rapid design and fill method, characterized in that, The method comprises the following steps: First, the distribution of the macroscopic material is optimized according to the given design conditions of the macroscopic structure to obtain a unit density distribution and a macroscopic displacement, and then the macroscopic displacement is converted into an intermediate variable, and the unit density is taken as the microstructure volume fraction and spliced with the intermediate variable to be used as an input of the deep neural network model for microstructure rapid design and filling of claim 6, and then a microstructure topology configuration is output, and the microstructure topology configuration is filled in space to obtain a multi-scale structure.

8. The macro-strain based microstructure rapid design and fill method of claim 7, wherein, The optimization of the distribution of the macroscopic material comprises: solving the unit density distribution based on the density method and outputting the macroscopic displacement according to the given design condition, with minimization of the compliance as the optimization target; The given design condition comprises a design domain, a boundary condition and a volume fraction constraint of the macroscopic structure.

9. The macro-strain based microstructure rapid design and fill method of claim 7, wherein, The deep neural network model for the microstructure rapid design and filling outputs specific microstructure level set function values on the macroscopic unit, and then draws an overall structure image according to the positional relationship of the level set function values of each microstructure, that is, a multi-scale structure image composed of microstructure topological configurations.

10. A macro-strain based microstructure rapid design and fill system, comprising: An executor is included, and the executor is used to execute the macroscopic strain-based microstructure rapid design and filling method according to any one of claims 7-9.

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