A method for designing acoustic metamaterials based on PGN model

Abstract

The application provides an acoustic metamaterial design method based on a PGN model, which not only overcomes the one-to-many mapping problem from spectral response to structural parameters in the traditional acoustic metamaterial design process, but also can significantly reduce the overall computing time and improve the design efficiency by predicting the solution immediately after the training phase. The design method first constructs a data set including the structural parameters of the acoustic metamaterial and the corresponding spectral response; then in a cascaded manner of a reverse GRU model in front and a forward DNN model pre-trained by the data set in back, a PGN model is constructed, and the PGN model is trained by the data set; wherein the candidate meta-structure obtained by Gaussian sampling of the output of the reverse GRU model is used as the input of the pre-trained forward DNN model; finally, the customized spectrum is input into the trained PGN model, and the Gaussian distribution predicted by the PGN model is probabilistically sampled to generate the structural parameters meeting the conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of acoustics, and particularly relates to a design method of acoustic metamaterials based on a PGN model. BACKGROUND

[0002] In the field of acoustics, it is a basic problem to design acoustic metamaterial structures to achieve efficient low-frequency broadband sound absorption. Designing low-frequency broadband acoustic structures usually relies on numerical methods such as finite element method, but due to its difficulty and complexity, it is often impossible to do so. In order to achieve certain desired performance and goals, researchers have proposed various design methods such as genetic algorithm, level set method and topological optimization, etc. These methods can achieve the design of acoustic structures, but due to the serious limitations of random search nature, they require a lot of time and cost, and occupy a large amount of computing resources, so they cannot efficiently design acoustic structures in practical applications. On the other hand, the inverse design based on deep learning has attracted more and more attention in the field of acoustic metamaterials, however, the corresponding relationship between the function and structure of acoustic metamaterials is usually not a deterministic injection or surjection, but a many-to-one mapping problem. Unfortunately, traditional artificial neural network models cannot solve the multi-value problem. SUMMARY

[0003] The purpose of the present application is to provide a design method of acoustic metamaterials based on a PGN model, which overcomes the shortcomings of the prior art in terms of time cost and computing resources, and solves the many-to-one mapping problem from spectral response to structure parameters in the traditional design process of acoustic metamaterials.

[0004] The technical scheme of the present application is as follows:

[0005] (1) Construct a data set including the structure parameters of acoustic metamaterials and the corresponding spectral response;

[0006] (2) Cascade a reverse GRU model in front of a forward DNN model pre-trained by the data set, and construct a PGN model, and train the PGN model by the data set; the candidate meta-structure obtained by Gaussian sampling of the output of the reverse GRU model is used as the input of the pre-trained forward DNN model;

[0007] (3) Input the customized spectrum into the trained PGN model, and perform probability sampling on the Gaussian distribution predicted by the PGN model to generate structure parameters that meet the conditions.

[0008] Further, the forward DNN model includes an input layer, a hidden layer and an output layer, and uses full connection between layers and uses the activation function ReLu and the optimizer Adam.

[0009] Further, the pre-training process of the forward DNN model takes the structural parameters as input and the frequency spectrum response as output to establish a forward mapping from the structural parameters to the frequency spectrum response.

[0010] Further, the inverse GRU model includes an input layer, a hidden layer and an output layer, the hidden layer adopts a GRU module and a full connection layer module, and uses an activation function ReLu and an optimizer Adam.

[0011] Further, the loss function of the PGN model is constructed by the difference between the input spectrum response into the PGN model and the predicted spectrum response output by the PGN model; the KL divergence and the regularization term are added in the loss function to ensure that the generated probability distribution is a Gaussian distribution.

[0012] Further, the loss function of the PGN model is:

[0013]

[0014] Wherein N is the total number of training samples, i is the sample serial number, and MAE represents a measurement index;

[0015] M represents the dimension of the structural parameters, μ j represents the jth component of the mean of the generated Gaussian distribution, σ j 2 represents the jth component of the variance vector of the generated Gaussian distribution, represents the reciprocal of the variance.

[0016] Further, the process of probability sampling on the Gaussian distribution predicted by the PGN model is: sampling an epsilon from the Gaussian distribution N(0, 1), and the generated meta-structure z is represented by the following formula:

[0017] z = μ + ε × σ

[0018] Wherein μ is the mean, and σ is the standard deviation.

[0019] Further, the Gaussian distribution predicted by the PGN model is sampled multiple times to generate multiple groups of structural parameters that meet the conditions.

[0020] Advantages: Compared with the prior art, the present application has the following obvious advantages:

[0021] The application is based on a PGN model (a probability generation network model) to design acoustic metamaterials, which not only overcomes the one-to-many mapping problem of spectral response to structural parameters in the traditional acoustic metamaterial design process, but also can significantly reduce the overall calculation time and improve the design efficiency by predicting the solution immediately after the training phase, and for any complex acoustic structure, the optimal structure meeting the conditions can be retrieved through the probability generation method. BRIEF DESCRIPTION OF DRAWINGS

[0022] Figure 1 is a method flowchart of the application;

[0023] Figure 2 is a schematic diagram of an acoustic magic cube structure and its spectral response;

[0024] Figure 3 is the architecture of the PGN model;

[0025] Figure 4 is the design result based on the PGN model. DETAILED DESCRIPTION

[0026] The application will be further described in detail below with reference to the accompanying drawings.

[0027] The application embodiments take an acoustic magic cube sound absorber as an example to specifically introduce the acoustic metamaterial design method, and the acoustic magic cube sound absorber is a sound absorbing structure composed of five channels placed at the end of a waveguide tube.

[0028] In combination with Figure 1 , the acoustic metamaterial design method comprises the following steps:

[0029] Step 1: Construct a data set through acoustic theory analysis.

[0030] As Figure 2 , the mapping from the element structure to the spectral response is forward prediction, and the mapping from the spectral response to the element structure is reverse retrieval. The structural parameters D are randomly sampled in the interval from 200 to 300 mm, and thus a data set composed of 80000 training data, 10000 validation data and 10000 test data is established. Each set of samples corresponds to the structural parameters D of the five channels of the tube length D = [l1, l2, l3, l4, l5], and the corresponding spectral response R is a sound absorption spectrum R = [α1, α2…α 101 ] composed of 101 discrete points.

[0031] Step 2: Construct a forward DNN model and a reverse GRU model.

[0032] The forward DNN model comprises an input layer, a hidden layer and an output layer, full connection is used between layers, and an activation function ReLu and an optimizer Adam are used.

[0033] The reverse GRU model comprises two activation gates in each unit: an update gate and a reset gate, as shown in Figure 3 The update gate Z t and the reset gate R t are calculated using the following formula:

[0034] Z t =sigmoid(W z x t +U z h t-1 +b z ),

[0035] R t =sigmoid(W r x t +U r h t-1 +b r ),

[0036] wherein W and U are learnable weight matrices, and b is a learnable bias matrix. h t-1 is the hidden state passed down from the previous node, x t is an input vector at time t; sigmoid(·) represents an activation function; subscripts z and r represent information related to the update gate and the reset gate, such as weights, biases, etc.

[0037] Step 3: Considering the multi-value problem between the function and the structure of the acoustic metamaterial, the forward DNN is pre-trained using a dataset to establish a forward mapping from the structure parameters to the spectral response, and the dataset is normalized before being input into the forward DNN; during the training process, the structure parameters are used as the input of the forward DNN model, and the spectral response is used as the output of the forward DNN model, and the training is stopped when the loss function converges, and the weights of the model are fixed. The loss function of the forward DNN model is the error between the predicted spectral response and the real spectral response, and MAE is used as the measurement index.

[0038] Step 4: To ensure that the reverse neural network can converge during the training process, the forward DNN model with fixed weights in step 3 is cascaded after the reverse GRU model to form a PGN model; then the dataset is input into the PGN model for training; as Figure 3As shown, the output of the inverse GRU model is used as the input of the forward DNN model, and the prediction cell structure is obtained by Gaussian sampling in a probabilistic generation manner. The loss function is constructed by the difference between the spectrum response input into the PGN model and the predicted spectrum response output by the model. In order to ensure that the generated probability distribution is Gaussian distribution, the KL divergence and the regularization term are added to the loss function. When the loss function converges, the training is stopped, and the model parameters are saved.

[0039] The loss function in the PGN model is configured as:

[0040]

[0041] Where N is the total number of training samples, i is the sample number, M represents the dimension of the structure parameter, μ j represents the jth component of the mean of the generated Gaussian distribution, σ j 2 represents the jth component of the variance vector of the generated Gaussian distribution, represents the reciprocal of the variance.

[0042] Step 5: input the customized spectrum into the PGN model trained in step 4, and perform multiple probability sampling on the Gaussian distribution predicted by the PGN model to generate multiple candidate cell structures that meet the conditions, so as to realize on-demand design.

[0043] As Figure 3 shown, the process of probability sampling is to sample an ε from the Gaussian distribution N(0, 1), and the generated cell structure z is represented by the following expression:

[0044] z = μ + ε × σ

[0045] Where μ is the mean, and σ is the standard deviation.

[0046] As shown in (a) of Figure 4 To verify the performance of the PGN model, a sound absorption spectrum with perfect sound absorption characteristics (α = 1) in the range of 300-400 Hz (corresponding to f1, f2) is customized. The customized spectrum is input into the trained PGN model, and a predicted spectrum with high sound absorption characteristics (α > 0.8) in the range of 284-414 Hz is generated, as shown in (b) of Figure 4 The high-precision prediction result proves the effectiveness of the acoustic metamaterial design method based on the PGN model proposed by the application.

Claims

1. A design method for acoustic metamaterials based on the PGN model, characterized in that: Includes the following steps: (1) Construct a dataset that includes the structural parameters of acoustic metamaterials and their corresponding spectral responses; (2) A PGN model is constructed by cascading an inverse GRU model first and a forward DNN model pre-trained on the dataset later. The PGN model is trained using the dataset. The candidate metastructure obtained by Gaussian sampling of the output of the inverse GRU model is used as the input of the pre-trained forward DNN model. (3) Input the customized spectrum into the trained PGN model, perform probability sampling on the Gaussian distribution predicted by the PGN model, and generate structural parameters that meet the conditions; The pre-training process of a forward DNN model involves taking structural parameters as input and spectral response as output to establish a forward mapping from structural parameters to spectral response. The forward DNN model uses the error between the predicted spectral response and the true spectral response as the loss function and MAE as the metric. Training stops when the loss function converges and the model weights are fixed. The loss function of the PGN model is constructed by the difference between the spectral response input to the PGN model and the predicted spectral response output by the PGN model; KL divergence and regularization terms are added to the loss function to ensure that the generated probability distribution is Gaussian. The loss function of the PGN model is: Where N is the total number of training samples, i is the sample number, and MAE represents the measurement metric. M represents the dimension of the structural parameters, μ j Let σ represent the j-th component of the mean of the Gaussian distribution. j 2 Let j represent the j-th component of the variance vector that generates the Gaussian distribution. It represents the reciprocal of the variance.

2. The design method according to claim 1, characterized in that: A forward DNN model consists of an input layer, hidden layers, and an output layer. The layers are connected by a fully connected method and use the ReLU activation function and the Adam optimizer.

3. The design method according to claim 1, characterized in that: The inverse GRU model consists of an input layer, a hidden layer, and an output layer. The hidden layer uses a GRU module and a fully connected layer module, and employs the ReLU activation function and the Adam optimizer.

4. The design method according to claim 1, characterized in that: The process of probability sampling the Gaussian distribution predicted by the PGN model is as follows: An ε is sampled from the Gaussian distribution N(0,1), and the resulting metastructure z is expressed by the following equation: z=μ+ε×σ Where μ is the mean and σ is the standard deviation.

5. The design method according to claim 4, characterized in that: Multiple probability samplings are performed on the Gaussian distribution predicted by the PGN model to generate multiple sets of structural parameters that meet the conditions.

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