CN113191007A - Diversified metamaterial reverse topology optimization design method and system - Google Patents
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Abstract
The invention belongs to the technical field related to structural optimization, and discloses a diversified metamaterial reverse topology optimization design method and a diversified metamaterial reverse topology optimization design system, wherein the method comprises the following steps: carrying out finite element analysis by changing the values of the volume fraction, the penalty index, the filtering radius and the filtering mode of the metamaterial structure to obtain a plurality of groups of topological configurations and corresponding elasticity tensor matrixes of the metamaterial structure; selecting eigenvalues in the elasticity tensor matrix and averaging the eigenvalues of which the difference value is within a preset range to be used as attribute values; encoding the attribute values into single-channel tensor information, and encoding multiple topological configurations into multi-channel tensor information; training the neural network by adopting the attribute values and the corresponding various topological configurations to obtain the trained neural network; and obtaining attribute values to be designed, inputting the attribute values to be designed into the trained neural network, and obtaining a plurality of corresponding topology configurations. The reverse design mode of this application need not to debug repeatedly and verify, can realize diversified customized demand, very big promotion design efficiency.
Description
Technical Field
The invention belongs to the technical field related to structural optimization, and particularly relates to a diversified metamaterial reverse topology optimization design method and system.
Background
Obtaining a metamaterial structure with specific properties is a hot problem in the academic and industrial fields at present, and theoretically, there are two feasible methods for analyzing, wherein one method is to change a material, and replace a material with poor properties by finding a material with more superior properties, and the method is expensive in cost and very poor in economy, and the other method is to change a design, generally change the structural properties by changing the micro-structure unit cell configuration of a porous structure, is a relatively cheap way, and is popular with engineering designers. The structural topology optimization design method can find the most reasonable distribution mode for the materials in a given design domain, so that the structure obtains the best mechanical property under a given constraint condition, and the material utilization rate is highest. On one hand, however, in the existing topology optimization design methods, the attribute value of the structure can only be obtained after the structure optimization is completed, and the design can only be performed first, and then whether the attribute value of the designed structure meets the requirement is determined, if the attribute value does not meet the requirement, the structure design is performed again, and the parameter debugging is required to be performed for many times to obtain the structure meeting the requirement; on the other hand, the traditional structural topology optimization design method is based on finite element analysis, which results in long time consumption, so that the structural topology optimization design method is low in efficiency and difficult to be applied to the design of an actual engineering material structure, diversified customized design is always the target pursued by engineering designers, the existing design method is debugged one by one based on finite element analysis, a large amount of manpower and material resources are consumed, and the economy is very poor. Chinese patent CN111723420A discloses a structural topology optimization method based on deep learning, which includes generating training data, preprocessing the training data, constructing a deep learning model for training, and optimizing by using the trained deep learning model to obtain an output result, i.e. a topology optimization structure. The adopted deep learning model is a U-Net network, the input is the input tensor of 6 channels, the discontinuous structure is easy to appear when the input parameters are improperly selected, the discontinuous structure is unavailable in engineering, particularly, the attribute value of the metamaterial with diversified requirements is limited and simple, and the overfitting phenomenon can be caused in network training if the U-Net is used, namely, the accuracy of predicting the new material structure is greatly reduced; meanwhile, the input of the method is that the multi-channel output is a single channel, and the requirement of diversified topological structures with the same attribute value cannot be met. Therefore, it is desirable to design a method for efficiently designing diversified topologies.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a diversified metamaterial reverse topology optimization design method and system, based on a neural network, the corresponding diversified topology configuration can be directly obtained by taking an attribute value as input, the reverse design mode does not need repeated debugging and verification, the diversified customization requirements can be realized, and the design efficiency is greatly improved.
To achieve the above object, according to an aspect of the present invention, there is provided a method for designing a reverse topology optimization of a diversified metamaterial, the method including: s1: carrying out finite element analysis by changing the values of the volume fraction, the penalty index, the filtering radius and the filtering mode of the metamaterial structure to obtain a plurality of groups of topological configurations of the metamaterial structure and an elasticity tensor matrix corresponding to the topological configurations; s2, selecting eigenvalues representing specific attributes of the topological structure in the elastic tensor matrix, comparing the multiple groups of eigenvalues, averaging the eigenvalues of which the difference values are within a preset range, taking the average value of the eigenvalues as attribute values corresponding to the multiple groups of topological structures, and further obtaining the attribute values and multiple topological structures corresponding to the attribute values; s3: encoding each group of attribute values into single-channel tensor information, encoding a plurality of topological configurations into a corresponding number of multi-channel tensor information, and forming a data set by a plurality of groups of attribute values and the corresponding plurality of topological configurations; s4: training a neural network by taking the attribute values as input and taking various topological configurations as output to obtain a trained neural network, wherein the neural network is a SegNet convolutional neural network or a Mobile-SegNet convolutional neural network, and the Mobile-SegNet convolutional neural network is obtained by modifying an encoder of the SegNet convolutional neural network into a MobileNet network; s5: and obtaining attribute values of the topology configuration to be designed, coding the attribute values, and inputting the coded attribute values into the trained neural network to obtain a plurality of corresponding topology configurations.
Preferably, in step S1, multiple sets of topological configurations of the metamaterial structure and the corresponding elasticity tensor matrix of the topological configurations are obtained by using a homogenization method.
Preferably, the characteristic value comprises a shear modulus value and/or a volume modulus value.
Preferably, in step S3, the size of the shape of the single-channel tensor information is the same as the size of the shape of each of the multi-channel tensor information.
Preferably, step S4 includes: and dividing the data set into two parts, wherein one part is used for training the neural network, and the other part is used for carrying out cross validation on the hyperparametric regulation decision of the neural network.
Preferably, the Adam algorithm is adopted in the training process to adaptively modify the actual learning rate in the training process of the SegNet convolutional neural network until the loss function value is smaller than the preset value or converges.
Preferably, the loss function of the neural network is:
wherein the content of the first and second substances,
is the topological configuration of the metamaterial structure in the kth channel tensor;
n and M are respectively the length and width of the metamaterial topological structure as the prediction result of the k-th layer configuration output by the neural network in the training process,
the true value of the cell in row i and column j in the kth channel tensor,
the output value of the unit at the ith row and the jth column in the kth channel tensor predicted by the neural network.
According to another aspect of the present invention, there is provided a diversified metamaterial reverse topology optimization design system, comprising: a first obtaining module: the method comprises the steps of carrying out finite element analysis by changing values of volume fraction, penalty index, filtering radius and filtering mode of the metamaterial structure to obtain multiple groups of topological configurations of the metamaterial structure and an elasticity tensor matrix corresponding to the topological configurations; the second acquisition module is used for selecting eigenvalues representing specific attributes of the topological structure in the elastic tensor matrix, comparing the multiple groups of eigenvalues, averaging the eigenvalues of which the difference values are within a preset range, and taking the average value of the eigenvalues as attribute values corresponding to the multiple groups of topological structures, so as to obtain the attribute values and multiple topological structures corresponding to the attribute values; the coding module: the data set is composed of a plurality of groups of attribute values and a plurality of corresponding topological configurations; a training module: the neural network is trained by taking the attribute values as input and taking various topological configurations as output to obtain a trained neural network, wherein the neural network is a SegNet convolutional neural network or a Mobile-SegNet convolutional neural network, and the Mobile-SegNet convolutional neural network is obtained by modifying an encoder of the SegNet convolutional neural network into a MobileNet network; an input module: the method is used for obtaining the attribute value of the topological configuration to be designed, encoding the attribute value and inputting the encoded attribute value into the trained neural network to obtain a plurality of corresponding topological configurations.
In general, compared with the prior art, through the technical scheme of the invention, the diversified metamaterial reverse topology optimization design method provided by the invention has the following beneficial effects:
1. according to the method, various metamaterial structure topological configurations can be generated for the designated attribute values by adopting a reverse design method, so that the design of the various metamaterial configurations can be realized.
2. Due to the fact that the attribute values needed in the process of the diversified design of the metamaterial are simple, the traditional network is easy to generate an overfitting phenomenon, the accuracy rate of structure prediction is greatly reduced, reasonable input parameters need to be selected, otherwise, discontinuous structures are easy to generate, the SegNet convolutional neural network is adopted in the method, the diversified design of the metamaterial can be achieved, the input parameters are simple, and one-to-many output can be achieved.
3. According to the method, the topological structure can be output in real time by performing topological optimization design on the metamaterial structure based on the deep learning technology, so that the time is obviously shortened, and the design efficiency is improved.
4. The method comprises the steps of obtaining an attribute value and a topological configuration of a metamaterial structure by taking a volume fraction, a penalty index, a filtering radius and a filtering mode as variables by adopting a homogenization method, wherein multiple factors are considered, the volume fraction is used for representing the volume of the optimized metamaterial topological configuration, the penalty index is used for representing the penalty of the optimized metamaterial topological configuration on the intermediate density of a material in the optimization process, the filtering radius is used for representing the checkerboard phenomenon in the optimization process, and the filtering mode is used for representing which strategy is adopted in the optimization process to inhibit the numerical instability phenomenon, so that the accurate attribute value and topological configuration can be obtained.
Drawings
FIG. 1 is a schematic diagram illustrating steps of a method for designing a reverse topology optimization of a diversified metamaterial according to an embodiment;
FIG. 2 is a flow chart schematically illustrating a method for designing a reverse topology optimization of a diversified metamaterial according to the embodiment;
fig. 3 schematically shows an encoding strategy of input information of the present embodiment;
fig. 4 schematically shows an encoding strategy of tag information of the present embodiment;
fig. 5 schematically illustrates a SegNet convolutional neural network of the present embodiment;
FIG. 6 is a diagram schematically illustrating a network training process for training a SegNet convolutional neural network to predict a first metamaterial topology configuration according to the present embodiment;
FIGS. 7A-7I schematically illustrate nine metamaterial topologies with bulk modulus values equal to-0.583 obtained in this example;
FIGS. 8A-8I schematically illustrate nine metamaterial topologies with shear modulus values equal to-0.101 obtained in this example.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to fig. 1 and 2, the present invention provides a method for designing a reverse topology optimization of a diversified metamaterial, which includes the following steps S1-S5.
S1: and carrying out finite element analysis by changing the values of the volume fraction, the penalty index, the filtering radius and the filtering mode of the metamaterial structure to obtain a plurality of groups of topological configurations of the metamaterial structure and an elasticity tensor matrix corresponding to the topological configurations.
For example, in the design domain of the metamaterial, the volume fraction is increased from 0.4 to 0.001 in a gradient manner to 201 in total from 0.6, the penalty index is increased from 2 to 1 in a gradient manner to 19 in total from 20, the filtering radius is increased from 1.5 to 0.5 in a gradient manner to 10 in total from 6, and the filtering manner is sensitivity filtering or density filtering in two manners, wherein one variable is selected from the four variables respectively, namely according to the selection of the four variables
The combined arrangement mode selects a variable value from four variable terms of volume fraction, penalty index, filtering radius and filtering mode, and integrates the selected variable value and the values of other variable terms on an average elementary domain to obtain a plurality of groups of topological configurations of the metamaterial structure and an elastic tensor matrix corresponding to the topological configurations.
Obtaining a plurality of groups of topological structures and elastic tensor matrixes corresponding to the topological structures by the following formulas:
wherein the content of the first and second substances,
is the elasticity tensor matrix, Y is the average elementary field, N is the finite element number of the dispersion of the average elementary field Y, e is the e-th unit in the design field, A (ij) is the ij direction,
is a unit displacement vector of the load working condition in the ij direction, T is a matrix transposition, keIs the stiffness matrix of the e-th material element,
for the solution of the cell displacement corresponding to the cell test strain field, A (kl) is the kl direction, where
Are functions of volume fraction, penalty index, filter radius and filter mode.
S2: and selecting eigenvalues representing the topological structure structures in the elasticity tensor matrix, comparing the multiple groups of eigenvalues, averaging the eigenvalues of the difference values of the eigenvalues within a preset range, and taking the average value of the eigenvalues as attribute values corresponding to the multiple groups of topological structures, thereby obtaining the attribute values and multiple topological structures corresponding to the attribute values.
The eigenvalue that can most characterize the topological structure is selected from the elasticity tensor matrix, and in this embodiment, the eigenvalue is preferably a shear modulus value and/or a volume modulus value, and may also be a parameter such as poisson ratio. Therefore, the plurality of groups of topological structures correspond to a plurality of groups of characteristic values, the plurality of groups of characteristic values are compared, then the characteristic values of which the difference values are within a preset range, such as a range of +/-0.002, are classified into one group for averaging, the average value is used as an attribute value for representing the plurality of groups of topological structures, and then the attribute values and the plurality of topological structures corresponding to the attribute values are obtained.
S3: encoding each group of attribute values into single-channel tensor information, encoding a plurality of topological configurations into a corresponding number of multi-channel tensor information, and forming a data set by a plurality of groups of attribute values and the corresponding plurality of topological configurations;
the method comprises the steps of encoding attribute values of the metamaterial into single-channel tensor information, encoding multiple topological configurations into multi-channel tensor information of corresponding quantity, wherein the shape size of the single-channel tensor information and the shape size of each piece of channel tensor information in the multi-channel tensor information are the same as the size of a design domain. For example, if the size of the design domain is 48 × 48, the size of the single-channel tensor information and the per-channel tensor information are also 48 × 48.
The attribute values of the metamaterial structure are encoded into single-channel tensor information as input information of a training neural network, as shown in fig. 3, the topological configuration of the metamaterial structure is encoded into multi-channel tensor information as label information of the training neural network, as shown in fig. 4, wherein each channel represents one topological configuration.
S3: and training the neural network by taking the attribute values as input and taking various topological configurations as output to obtain the trained neural network, wherein the neural network is a SegNet convolutional neural network or a Mobile-SegNet convolutional neural network, and the Mobile-SegNet convolutional neural network is obtained by modifying an encoder of the SegNet convolutional neural network into a MobileNet network.
And dividing the data set into two parts, wherein one part is used for training the neural network, and the other part is used for performing cross validation on the hyper-parameter adjustment decision of the neural network.
In this embodiment, the label information in all channels is divided into a training set and a verification set according to a ratio of 9: 1, in each complete training process, information of only one channel is selected at a time according to the sequence of multi-channel tensor information in the label information, and input information is combined and simultaneously input into the neural network to train the neural network until the number of iterations reaches a preset value or a loss function value converges, as shown in fig. 6. In this embodiment, the neural network is preferably a SegNet convolutional neural network, and as shown in fig. 5, in order to reduce the network computation amount and reduce the network training time, the encoder may be changed to a Mobile-SegNet convolutional neural network. In the training process, the Adam algorithm is adopted to adaptively modify the actual learning rate in the SegNet network training process. The loss function is preferably a MSE loss function calculated:
wherein the content of the first and second substances,
is the topological configuration of the metamaterial structure in the kth channel tensor;
n and M are respectively the length and width of the metamaterial topological structure as the prediction result of the k-th layer configuration output by the neural network in the training process,
the true value of the cell in row i and column j in the kth channel tensor,
the output value of the unit at the ith row and the jth column in the kth channel tensor predicted by the neural network.
S4: and obtaining an attribute value of the topology to be designed, coding the attribute value, and inputting the coded attribute value into the trained neural network to obtain the corresponding topology.
The attribute values of the topological structure to be designed are encoded into a single-channel tensor, the encoded attribute values are input into a trained neural network, and diversified metamaterial structure topological structures with the same attribute values and different configurations can be obtained as shown in fig. 7A to 7I and fig. 8A to 8I.
This application another aspect provides a reverse topological optimization design system of diversified metamaterial, the system includes first acquisition module, second acquisition module, coding module, training module and input module, wherein:
a first obtaining module: the method comprises the steps of carrying out finite element analysis by changing values of volume fraction, penalty index, filtering radius and filtering mode of the metamaterial structure to obtain multiple groups of topological configurations of the metamaterial structure and an elasticity tensor matrix corresponding to the topological configurations;
the second acquisition module is used for selecting eigenvalues representing specific attributes of the topological structure in the elastic tensor matrix, comparing the multiple groups of eigenvalues, averaging the eigenvalues of which the difference values are within a preset range, and taking the average value of the eigenvalues as attribute values corresponding to the multiple groups of topological structures, so as to obtain the attribute values and multiple topological structures corresponding to the attribute values;
the coding module: the data set is composed of a plurality of groups of attribute values and a plurality of corresponding topological configurations;
a training module: the neural network is trained by taking the attribute values as input and taking various topological configurations as output to obtain a trained neural network, wherein the neural network is a SegNet convolutional neural network or a Mobile-SegNet convolutional neural network, and the Mobile-SegNet convolutional neural network is obtained by modifying an encoder of the SegNet convolutional neural network into a MobileNet network;
an input module: the method is used for obtaining the attribute value of the topological configuration to be designed, encoding the attribute value and inputting the encoded attribute value into the trained neural network to obtain a plurality of corresponding topological configurations.
To sum up, this application is based on neural network to attribute value can directly obtain corresponding topological structure as the input, and the demand of diversified customization can be realized to the mode of this kind of reverse design, need not to debug repeatedly and verify, very big promotion design efficiency.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A reverse topological optimization design method for diversified metamaterials is characterized by comprising the following steps:
s1: carrying out finite element analysis by changing the values of the volume fraction, the penalty index, the filtering radius and the filtering mode of the metamaterial structure to obtain a plurality of groups of topological configurations of the metamaterial structure and an elasticity tensor matrix corresponding to the topological configurations;
s2, selecting eigenvalues representing specific attributes of the topological structure in the elastic tensor matrix, comparing the multiple groups of eigenvalues, averaging the eigenvalues of which the difference values are within a preset range, taking the average value of the eigenvalues as attribute values corresponding to the multiple groups of topological structures, and further obtaining the attribute values and multiple topological structures corresponding to the attribute values;
s3: encoding each group of attribute values into single-channel tensor information, encoding a plurality of topological configurations into a corresponding number of multi-channel tensor information, and forming a data set by a plurality of groups of attribute values and the corresponding plurality of topological configurations;
s4: training a neural network by taking the attribute values as input and taking various topological configurations as output to obtain a trained neural network, wherein the neural network is a SegNet convolutional neural network or a Mobile-SegNet convolutional neural network, and the Mobile-SegNet convolutional neural network is obtained by modifying an encoder of the SegNet convolutional neural network into a MobileNet network;
s5: and obtaining attribute values of the topology configuration to be designed, coding the attribute values, and inputting the coded attribute values into the trained neural network to obtain a plurality of corresponding topology configurations.
2. The optimization design method according to claim 1, wherein in step S1, a homogenization method is used to obtain multiple sets of topological configurations of the metamaterial structure and the corresponding elasticity tensor matrices of the topological configurations.
3. The method of claim 1, wherein the characteristic values comprise shear modulus values and/or volume modulus values.
4. The optimal design method according to claim 1, wherein in step S3, the shape size of the single-channel tensor information and the shape size of each of the multi-channel tensor information are both the same as the size of the design domain.
5. The optimal design method according to claim 4, wherein step S4 includes:
the data set is divided into two parts, wherein one part is used for training the neural network, and the other part is used for cross-verifying the hyper-parameter adjustment decision of the neural network.
6. The optimal design method according to claim 5, wherein an Adam algorithm is adopted in the training process to adaptively modify the actual learning rate in the SegNet convolutional neural network training process until the loss function value is smaller than a preset value or converges.
7. The optimal design method of claim 6, wherein the loss function of the neural network is:
wherein the content of the first and second substances,
is the topological configuration of the metamaterial structure in the kth channel tensor;
n and M are respectively the length and width of the metamaterial topological structure as the prediction result of the k-th layer configuration output by the neural network in the training process,
the true value of the cell in row i and column j in the kth channel tensor,
the output value of the unit at the ith row and the jth column in the kth channel tensor predicted by the neural network.
8. A diversified metamaterial reverse topology optimization design system, comprising:
a first obtaining module: the method comprises the steps of carrying out finite element analysis by changing values of volume fraction, penalty index, filtering radius and filtering mode of the metamaterial structure to obtain multiple groups of topological configurations of the metamaterial structure and an elasticity tensor matrix corresponding to the topological configurations;
the second obtaining module is used for selecting eigenvalues representing the topological structure structures in the elastic tensor matrix, comparing the multiple groups of eigenvalues, averaging the eigenvalues of which the difference values are within a preset range, taking the average value of the eigenvalues as attribute values corresponding to the multiple groups of topological structures, and further obtaining the attribute values and multiple topological structures corresponding to the attribute values;
the coding module: the data set is composed of a plurality of groups of attribute values and a plurality of corresponding topological configurations;
a training module: the neural network is trained by taking the attribute values as input and taking various topological configurations as output to obtain a trained neural network, wherein the neural network is a SegNet convolutional neural network or a Mobile-SegNet convolutional neural network, and the Mobile-SegNet convolutional neural network is obtained by modifying an encoder of the SegNet convolutional neural network into a MobileNet network;
an input module: the method is used for obtaining the attribute value of the topological configuration to be designed, encoding the attribute value and inputting the encoded attribute value into the trained neural network to obtain a plurality of corresponding topological configurations.
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| CN116432330B (en) * | 2022-12-23 | 2024-03-19 | 华中科技大学 | Multi-scale shell design method and equipment filled with functionally gradient auxetic metamaterial |
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