A deep learning-based reverse design method for periodic super-barrier

Abstract

The present invention relates to a method for reverse design of a periodic super-barrier based on deep learning, comprising the following steps: determining the type of the periodic super-barrier; determining the material composition of the scatterer; forming a data set A according to the type and material composition of the periodic super-barrier; randomly selecting enough topological configurations from the data set A, and obtaining a data set B containing topological configurations, material parameters and band gaps through numerical simulation. The variational autoencoder is trained and tested using the data set A to obtain a trained inference model and a generative model; a tandem neural network is constructed; the target band gap and site conditions are input into the tandem neural network, and the trained generative model and two expressions are combined to obtain the final design result. The present invention does not require experience, and can quickly and accurately give the topological configuration and periodic constant of a periodic super-barrier composed of multiple materials that meets the vibration isolation requirements under different site conditions, making the design of the periodic super-barrier more intelligent and efficient.

Description

Technical Field

[0001] The present invention relates to a periodic super-barrier inverse design method based on deep learning. Background Art

[0002] The periodic superbarrier can effectively block low-frequency vibrations caused by environmental factors or earthquakes, and is of great significance for building safety, protection of ancient cultural relics, people's life and work, and the use of precision instruments. The periodic superbarrier is a composite structure whose materials and shapes are periodically distributed in space. The periodic superbarrier relies on the resonance characteristics of the scatterer to produce a low-frequency band gap, attenuating elastic waves with wavelengths much larger than the size of its own basic unit, thereby achieving low-frequency vibration blocking. For different vibration sources or the natural vibration period of the protected structure, the frequency range required to block the vibration is often different. Therefore, it is necessary to design the periodic constant of the periodic superbarrier and the topological configuration of the basic unit so that the band gap can match the target frequency range, thereby achieving an effective vibration isolation effect. Therefore, the reasonable design of the periodic superbarrier is an important part of achieving precise vibration isolation.

[0003] At present, the research on periodic superbarriers is mainly forward mechanism analysis. When designing on demand, experienced researchers need to spend a lot of time, energy and resources to try repeatedly to get the results, and the accuracy is difficult to guarantee; traditional intelligent design algorithms, such as genetic algorithms and simulated annealing algorithms, need to run for a long time and consume a lot of computing resources for each design; for periodic structures composed of two materials, although the reverse topological design based on deep learning has made initial progress, the deep learning model used cannot realize the topological design of periodic superbarriers composed of more than two materials and cannot give the periodic constant at the same time. Therefore, a new method is needed to realize the experience-free, efficient and multifunctional design of periodic superbarriers, which is also one of the difficulties in the current research in this field. Summary of the invention

[0004] In order to solve the above-mentioned deficiencies in the prior art, the present invention provides a design method for periodic super-barrier topological configurations and periodic constants that can quickly and accurately provide vibration isolation requirements under different site conditions without requiring experience. The intelligent and efficient design of periodic super-barrier topological configurations and periodic constants is achieved under different vibration isolation requirements and site conditions, overcoming the deficiencies of the existing methods, such as high time cost, large amount of calculation, and single design capability.

[0005] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0006] A periodic super-barrier inverse design method based on deep learning, comprising the following steps:

[0007] Step 1: Determine the type of periodic super barrier;

[0008] Step 2: Determine the material composition of the scatterer; determine the site conditions to be considered;

[0009] Step 3: Formulate topological generation rules according to the type and material composition of the periodic super-barrier, randomly generate topological configurations, and form data set A;

[0010] Step 4: Randomly select enough topological configurations from data set A, assign material parameters, set the unit period constant a, and then calculate the corresponding band gap by numerical simulation method, and finally obtain data set B including topological configuration, material parameters and band gap;

[0011] Step 5: Use dataset A to train and test the variational autoencoder to obtain the trained inference model and generation model;

[0012] Step 6: Use the trained inference model to convert the topological configuration in dataset B into a latent vector, then train and test the forward simulation network with the latent vector and the corresponding material parameters as input and the band gap as output.

[0013] Step 7: Connect a design network, a forward simulation network and the expression F=f / a in series to form a series neural network, where f is the bandgap frequency output by the forward simulation network and F is the predicted bandgap frequency when the period constant is a;

[0014] Step 8: Input the target band gap into the design network and the site conditions into the forward simulation network. The tandem neural network performs self-learning through the back propagation method; when the tandem neural network is self-learning, the internal parameters of the forward simulation network remain unchanged, and only the internal parameters of the design network are updated to adjust the periodic constant and the value of the latent vector outputted by it.

[0015] Step 9: After the loss function L of the cascaded neural network converges, the latent vector output by the design network is input into the trained generative model to obtain the basic unit topology configuration of the design, and then combined with the periodic constant output by the design network to obtain the final design result.

[0016] After step 7 is completed, only steps 8 and 9 need to be repeated for each design.

[0017] The types described in step 1 include body waves or surface waves, one-dimensional periodic or two-dimensional periodic structures, and the two-dimensional periodic structure is arranged in a triangular lattice, a square lattice or a rectangular lattice.

[0018] In step 2, the material composition is rubber and any one or a combination of two or more of steel, lead, aluminum, and concrete; the site condition parameters considered include the elastic modulus, mass density, and Poisson's ratio of the soil.

[0019] In step 3, the basic unit area is divided into equal grids, where each grid is assigned a material and each material is represented by a different vector.

[0020] In step 5, a variational autoencoder is constructed, in which each convolution, deconvolution and pooling operation and the fully connected layer contain a batch normalization operation, the activation function of the last hidden layer is the Softmax activation function, and the activation functions of the remaining hidden layers are all ReLU activation functions. The inference model is DenseNet, the generation model is a 3D deconvolutional neural network, and the Adam optimizer is used.

[0021] In step 7, one output of the design network is connected to a in the expression F=f / a, the remaining output parts of the design network are connected to the latent vectors of the input parts in the forward simulation network, the output of the forward simulation network is connected to f in F=f / a, and the material parameters are conditional variables of the series neural network.

[0022] In step 9, the loss function of the cascaded neural network is L = (T1-F1) 2 +(T2-F2) 2 , where T1 and T2 are the lower and upper limits of the target band gap, respectively, and F1 and F2 are the lower and upper limits of the predicted band gap, respectively.

[0023] Beneficial effects of the invention: The invention does not require experience and can quickly and accurately give the topological configuration and period constant of a periodic super-barrier composed of various materials that meets the vibration isolation requirements under different site conditions, making the design of the periodic super-barrier more intelligent and efficient. The cost is low and the calculation amount is small. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] The present invention has the following accompanying drawings:

[0025] Figure 1 : Flowchart of cycle super-barrier reverse design based on deep learning;

[0026] Figure 2 : Schematic diagram of periodic super barrier;

[0027] Figure 3 : Schematic diagram of variational autoencoder;

[0028] Figure 4 :Schematic diagram of tandem neural network;

[0029] Figure 5 : Schematic diagram of the training process;

[0030] Figure 6 :Schematic diagram of the design process;

[0031] Figure 7 : Schematic diagram of the design results of the embodiment. DETAILED DESCRIPTION

[0032] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0033] A periodic super-barrier inverse design method based on deep learning, comprising the following steps:

[0034] Step 1: Determine the type of periodic super-barrier, such as for body waves or surface waves, one-dimensional periodic or two-dimensional periodic structure, triangular lattice, square lattice or rectangular lattice, etc.

[0035] Step 2: Determine the material composition of the scatterer, which can be a combination of rubber and one or more of the commonly used engineering materials such as steel, lead, aluminum, concrete, etc.; determine the site conditions to be considered, such as the elastic modulus, mass density, Poisson's ratio, etc. of the soil.

[0036] Step 3: According to the type and material composition of the periodic superbarrier, a topological generation rule is formulated to randomly generate a large number of topological configurations to form data set A. The basic unit area is divided into equal grids, each grid is assigned a material, and each material is represented by a different vector. For example, [1, 0, 0], [0, 1, 0] and [0, 0, 1] represent three different materials respectively, [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0] and [0, 0, 0, 1] represent four different materials respectively, and so on.

[0037] Step 4: Randomly select enough topological configurations from data set A, assign material parameters, set the unit period constant a, and then calculate the corresponding band gap through numerical simulation methods, and finally obtain data set B containing topological configuration, material parameters and band gap.

[0038] Step 5: Use dataset A to train and test the variational autoencoder to obtain the trained inference model and generation model.

[0039] Step 6: Use the trained inference model to convert the topological configuration in dataset B into a latent vector, then train and test the forward simulation network with the latent vector and the corresponding material parameters as input and the band gap as output.

[0040] Step 7: Connect a design network, a forward simulation network and the expression F=f / a (f is the band gap frequency output by the forward simulation network, and F is the predicted band gap frequency when the periodic constant is a) in series to form a series neural network, wherein an output of the design network is connected to a in the expression F=f / a, the remaining output parts of the design network are connected to the latent vectors of the input parts in the forward simulation network, the output of the forward simulation network is connected to f in F=f / a, and the material parameters are conditional variables of the series neural network.

[0041] Step 8: Input the target bandgap into the design network and the site conditions into the forward simulation network. The tandem neural network is self-learned by back propagation, and its loss function L = (T1-F1) 2 +(T2-F2) 2 , where T1 and T2 are the lower and upper limits of the target band gap, respectively, and F1 and F2 are the lower and upper limits of the predicted band gap, respectively; when the tandem neural network is self-learning, the internal parameters of the forward simulation network remain unchanged, and only the internal parameters of the design network are updated to adjust the value of the periodic constant and latent vector of its output.

[0042] Step 9: After the loss function L converges, the latent vector output by the design network is input into the trained generative model to obtain the basic unit topology configuration of the design, and then combined with the periodic constant output by the design network to obtain the final design result.

[0043] After step 7 is completed, only steps 8 and 9 need to be repeated for each design.

[0044] In step 5, a variational autoencoder is constructed, in which each convolution, deconvolution, pooling operation and fully connected layer contains a batch normalization operation, the activation function of the last hidden layer is the Softmax activation function, and the activation functions of the remaining hidden layers are all ReLU activation functions. The inference model is DenseNet, the generation model is a 3D deconvolutional neural network, and the Adam optimizer is used.

[0045] The designed network and forward simulation network are multi-layer perceptrons.

[0046] Example:

[0047] Consider a two-dimensional periodic super-barrier for out-of-plane body waves, with a square lattice arrangement. The scatterers are composed of steel and rubber, and the matrix is ​​soil. The material parameters are shown in Table 1, among which the only variable material parameter is the mass density of the soil (since the shear modulus of the soil has little effect on the band gap, its change is not considered), and the other material parameters are fixed values.

[0048] Table 1

[0049]

[0050] The generation rules of the topological configuration are as follows: the basic unit area is divided into 20×20 equal square grids; the outermost grid of the basic unit is soil; the distribution of steel materials forms a simply connected domain, each steel material grid is connected to other steel material grids by at least two edges, and the height difference between the two outermost adjacent grids in the steel material area does not exceed the distance of one grid; the distribution of rubber materials forms a doubly connected domain, the inner boundary of the rubber material area coincides with the outer boundary of the steel material area, each rubber material grid is connected to other rubber material grids by at least two edges, and the height difference between the two outermost adjacent grids in the rubber material area does not exceed the distance of one grid; the remaining grids are allocated as soil materials; the shape of the basic unit is considered to be one-eighth symmetrical; the filling ratio of steel is greater than or equal to 0.15 and less than or equal to 0.3, and the total filling ratio of steel and rubber is less than or equal to 0.5.

[0051] Based on the above rules, 600,000 topological configurations were generated to form data set A, in which the ratio of training set, validation set and test set was 8:1:1.

[0052] A variational autoencoder is constructed, in which each convolution, deconvolution, pooling operation and fully connected layer contains a batch normalization operation. The activation function of the last hidden layer is the Softmax activation function, and the activation functions of the remaining hidden layers are all ReLU activation functions. The inference model is DenseNet, the generation model is a 3D deconvolutional neural network, the latent space dimension is 2, and the Adam optimizer is used. The variational autoencoder is trained and tested with dataset A.

[0053] 150,000 topological configurations were randomly selected from data set A and the corresponding material parameters were randomly assigned. The band gap was calculated using the finite element method. 150,000 sets of topological configurations, soil mass density and band gap constitute data set B.

[0054] The trained inference model is used to transform the topological configuration in data set B into latent vectors. The forward simulation network is then trained and tested with the transformed latent vectors, the corresponding soil mass density and the band gap. The ratio of the training set, the validation set and the test set is 8:1:1, and then a tandem neural network is constructed.

[0055] The main frequency range of vibration caused by subway trains (13.5-21.2 Hz) and site conditions (soil mass density of 1900 kg / m 3 ) is input into the cascade neural network to obtain the latent vector and periodic constant; the latent vector is input into the trained generative model to obtain the designed topological configuration; the design takes a total of 8 seconds.

[0056] Figure 7The design results of the deep learning model are given. The white area is steel, the gray area is rubber, and the black area is soil. The band gap range calculated by the finite element method is 13.5-21.2Hz, which is exactly the same as the target band gap.

[0057] Terminology explanation:

[0058] Periodic superbarrier: A structure that can block elastic waves with wavelengths much larger than the size of its own basic units and whose basic units are periodically arranged in space is called a periodic superbarrier.

[0059] Deep learning: An algorithm that uses artificial neural networks as a framework to learn how to represent data.

[0060] Topological design: Designing the distribution of materials in a given area.

[0061] Band gap: The periodic wave barrier has a band gap characteristic, that is, when elastic waves propagate in the periodic wave barrier, elastic waves within a certain frequency range cannot pass through, and this frequency range is called a band gap.

[0062] Matrix and scatterers: When a periodic superbarrier is composed of two or more materials, the interconnected materials are called matrix, and the unconnected materials are called scatterers.

[0063] Period constant: The size of a basic unit in the periodic superbarrier.

[0064] The above implementation modes are only used to illustrate the present invention, but not to limit the present invention. Ordinary technicians in the relevant technical field can make various changes and modifications without departing from the essence and scope of the present invention. Therefore, all equivalent technical solutions also belong to the protection scope of the present invention.

[0065] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

Claims

1. A periodic super-barrier inverse design method based on deep learning, characterized in that: The steps include: Step 1: Determine the type of periodic super barrier; Step 2: Determine the material composition of the scatterer; determine the site conditions to be considered; Step 3: Formulate topological generation rules according to the type and material composition of the periodic super-barrier, randomly generate topological configurations, and form data set A; Step 4: Randomly select enough topological configurations from data set A, assign material parameters, set the unit period constant a, and then calculate the corresponding band gap by numerical simulation method, and finally obtain data set B including topological configuration, material parameters and band gap; Step 5: Use dataset A to train and test the variational autoencoder to obtain the trained inference model and generation model; Step 6: Use the trained inference model to convert the topological configuration in dataset B into latent vectors, then train and test the forward simulation network with the latent vectors and corresponding material parameters as inputs and band gaps as outputs; Step 7: Connect a design network, a forward simulation network and the expression F=f / a in series to form a series neural network, where f is the bandgap frequency output by the forward simulation network and F is the predicted bandgap frequency when the period constant is a; Step 8: Input the target band gap into the design network and the site conditions into the forward simulation network; the tandem neural network performs self-learning through the back propagation method; when the tandem neural network is self-learning, the internal parameters of the forward simulation network remain unchanged, and only the internal parameters of the design network are updated to adjust the periodic constant and the value of the latent vector outputted by it; Step 9: After the loss function L of the cascaded neural network converges, the latent vector output by the design network is input into the trained generative model to obtain the basic unit topology configuration of the design, and then combined with the periodic constant output by the design network to obtain the final design result.

2. The periodic super-barrier inverse design method based on deep learning as claimed in claim 1, characterized in that: After step 7 is completed, only steps 8 and 9 need to be repeated for each design.

3. The periodic super-barrier inverse design method based on deep learning as claimed in claim 1, characterized in that: The types described in step 1 include body waves or surface waves, one-dimensional periodic or two-dimensional periodic structures, and the two-dimensional periodic structure is arranged in a triangular lattice, a square lattice or a rectangular lattice.

4. The periodic super-barrier inverse design method based on deep learning as claimed in claim 1, characterized in that: In step 2, the material composition is rubber and any one or a combination of two or more of steel, lead, aluminum, and concrete; the site condition parameters considered include the elastic modulus, mass density, and Poisson's ratio of the soil.

5. The periodic super-barrier inverse design method based on deep learning as claimed in claim 1, characterized in that: In step 3, the basic unit area is divided into equal grids, where each grid is assigned a material and each material is represented by a different vector.

6. The periodic super-barrier inverse design method based on deep learning as claimed in claim 1, characterized in that: In step 5, a variational autoencoder is constructed, in which each convolution, deconvolution, pooling operation and fully connected layer contains a Batchnormalization operation, the activation function of the last hidden layer is the Softmax activation function, and the activation functions of the remaining hidden layers are all ReLU activation functions. The inference model is DenseNet, the generation model is a 3D deconvolutional neural network, and the Adam optimizer is used.

7. The periodic super-barrier inverse design method based on deep learning as claimed in claim 1, characterized in that: In step 7, one output of the design network is connected to a in the expression F=f / a, the remaining output parts of the design network are connected to the latent vectors of the input parts in the forward simulation network, the output of the forward simulation network is connected to f in F=f / a, and the material parameters are conditional variables of the series neural network.

8. The periodic super-barrier inverse design method based on deep learning as claimed in claim 1, characterized in that: In step 9, the loss function of the cascaded neural network is L = (T1-F1) 2 +(T2-F2) 2 , where T1 and T2 are the lower and upper limits of the target band gap, respectively, and F1 and F2 are the lower and upper limits of the predicted band gap, respectively.

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