A Deep Learning-Based Reverse Design Method for Lightweight Acoustic Black Hole Beam Structures

Abstract

This invention specifically relates to a deep learning-based reverse engineering method for lightweight acoustic black hole beam structures. The method includes: constructing a forward prediction model of the "structural parameters-bandgap" and a reverse design model of the "bandgap-structural parameters" for the acoustic black hole beam based on a first multilayer perceptron network (MLP) and a second LLP, respectively. Specifically, the first LLP is trained using a dimensionality-reduced acoustic black hole beam structure dataset to obtain the forward prediction model; the forward prediction model is then cascaded after the second LLP to obtain a cascaded neural network; and the cascaded neural network is trained to obtain the reverse design model. In practical applications, the upper and lower bound frequencies of the target bandgap are input into the reverse design model, which outputs a target latent vector. The target latent vector is decoded to obtain the target structural parameters, and the acoustic black hole beam is hollowed out according to these parameters, thereby achieving the lightweight design of the acoustic black hole beam.

Description

Technical Field

[0001] This invention relates to the field of acoustic metamaterials technology, specifically to a reverse design method for lightweight acoustic black hole beam structures based on deep learning. Background Technology

[0002] Acoustic black holes, as artificial structures capable of efficiently converging and attenuating elastic wave energy, have attracted widespread attention in the field of vibration and noise control. By introducing a variable cross-section design with thickness gradually varying according to a power-law function into this structure, a unique wave propagation interface is constructed. This interface, similar to the event horizon in physics, fundamentally alters the wave propagation behavior, causing the phase velocity of curved waves to gradually decrease with propagation distance. Energy is continuously compressed and localized during propagation, ultimately achieving near-complete absorption at the theoretical pinch-out point. Based on this precise control over the elastic wave propagation path and energy dissipation process, acoustic black holes show promising engineering application prospects in areas such as broadband vibration reduction of thin plates and shells, wave control of beam structures, and vibration suppression of precision instrument platforms.

[0003] However, several key issues remain before acoustic black hole technology can be truly applied in engineering. Among them, optimizing design parameters under limited structural dimensions to obtain a wider operating bandwidth and higher energy capture efficiency, while mitigating performance degradation caused by cutoff effects during actual manufacturing, is a core challenge that urgently needs to be addressed.

[0004] To address the aforementioned issues, existing research typically employs parametric modeling and topology optimization to improve the performance of acoustic black holes. For example, using semi-analytical methods, finite element methods, and intelligent algorithms to optimize key parameters such as the power-law exponent and material loss factor yields superior results compared to traditional methods in terms of widening the bandwidth, reducing reflection, and enhancing manufacturing robustness.

[0005] Despite this, existing solutions remain focused on forward performance analysis and parameter tuning, i.e., predicting vibration attenuation performance based on given structural parameters, while paying insufficient attention to the more valuable reverse design problem in practical engineering. In fact, engineering applications often require solving for the optimal structural parameters that meet the pre-defined vibration attenuation target. However, due to the complex wave control mechanism of acoustic black hole structures, and the highly nonlinear, strongly coupled, and non-convex mapping relationship between structural parameters and performance indicators, the reverse design process generally suffers from slow model convergence, reliance on initial guesses for solution results, and insufficient design accuracy, making it difficult to meet the demands of high-precision, customized, and efficient engineering design.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of the present invention, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] This invention provides a deep learning-based reverse engineering method for lightweight acoustic black hole beam structures, a computer-readable storage medium, and a computer program product, which can effectively overcome the defects existing in the prior art.

[0008] Other features and advantages of the invention will become apparent from the following detailed description, or may be learned in part by practice of the invention.

[0009] According to a first aspect of the present invention, a reverse engineering method for lightweight acoustic black hole beam structures based on deep learning is provided, the method comprising: The acoustic black hole beam is simulated based on the sample structural parameters to obtain the band structure curve. The upper and lower limits of the sample band gap are extracted from the band structure curve to construct the acoustic black hole beam structure dataset. The acoustic black hole beam structure dataset includes: sample structural parameters, upper and lower limits of the sample band gap, and the sample band gap includes: sample longitudinal wave band gap and sample bending wave band gap. Using the dimensionality-reduced acoustic black hole beam structure dataset, the first multilayer perceptron network is trained to obtain a forward prediction model. The dimensionality-reduced acoustic black hole beam structure dataset includes: sample latent vectors, upper and lower bound frequencies of the sample bandgap. The sample latent vectors are low-dimensional feature representations of the sample structural parameters. The forward prediction model is used to determine the mapping relationship between the sample latent vectors and the upper and lower bound frequencies of the sample bandgap. The forward prediction model is cascaded after the second multilayer perceptron network to obtain a cascaded neural network; and the cascaded neural network is trained based on the dimensionality-reduced acoustic black hole beam structure dataset to obtain the reverse design model. The upper and lower frequency limits of the target bandgap are input into the inverse design model to obtain the target latent vector; and the target latent vector is decoded to obtain the target structure parameters; wherein, the target latent vector is a low-dimensional feature representation of the target structure parameters. The acoustic black hole beam was designed using the target structural parameters, resulting in a lightweight structure for the acoustic black hole beam.

[0010] In some exemplary embodiments, the step of simulating the acoustic black hole beam based on sample structural parameters to obtain bandgap curves, and extracting the upper and lower bandgap frequencies of the sample bandgap from the bandgap curves to construct an acoustic black hole beam structure dataset, includes: Based on the power function variation law of the geometric structure of the acoustic black hole beam, the arrangement of sample structural parameters is set to generate sample structural parameters. Using finite element method software, the acoustic black hole beam was simulated and calculated based on the structural parameters of the sample to obtain the band curve; and the upper and lower band gap frequencies of the sample were extracted from the band curve. Based on the sample structural parameters, the upper and lower bound frequencies of the sample bandgap, an acoustic black hole beam structure dataset is constructed.

[0011] In some exemplary embodiments, the method further includes: By using a variational autoencoder, the sample structure parameters are reduced in dimensionality to obtain the sample latent vector; The dimensionality-reduced acoustic black hole beam structure dataset is determined based on the sample latent vectors, the upper frequency limit of the sample bandgap, and the lower frequency limit.

[0012] In some exemplary embodiments, the step of using the dimensionality-reduced acoustic black hole beam structure dataset to train a first multilayer perceptron network to obtain a positive prediction model includes: The sample latent vector is input into the first multilayer perceptron network to obtain the upper and lower bound frequencies of the first prediction bandgap. The first network prediction error is calculated based on the upper and lower bound frequencies of the first prediction bandgap and the upper and lower bound frequencies of the sample bandgap, according to the first loss function; wherein, the first loss function is the mean square error loss function between the upper and lower bound frequencies of the first prediction bandgap and the upper and lower bound frequencies of the sample bandgap. The network parameters of the first multilayer perceptron network are updated using the backpropagation algorithm to gradually reduce the prediction error of the first network until the network converges, thus obtaining a positive prediction model.

[0013] In some exemplary embodiments, the process of training a cascaded neural network based on the dimensionality-reduced acoustic black hole beam structure dataset to obtain a reverse design model includes: The upper and lower bound frequencies of the sample bandgap are input into the second multilayer perceptron network to obtain the predicted latent vector; By inputting the predicted latent vector into the forward prediction model, the upper and lower bound frequencies of the second prediction bandgap are obtained. For the upper and lower bound frequencies of the sample bandgap and the upper and lower bound frequencies of the second predicted bandgap, the prediction error of the second network is calculated based on the second loss function; wherein, the second loss function is the mean squared error loss function between the upper and lower bound frequencies of the second predicted bandgap and the upper and lower bound frequencies of the sample bandgap. The network parameters of the second multilayer perceptron network are updated using the backpropagation algorithm to gradually reduce the prediction error of the second network until the network converges, thus obtaining the trained second multilayer perceptron network. The trained second-layer perceptron network was selected as the reverse design model.

[0014] In some exemplary embodiments, the positive prediction model includes: Input layer; Multiple hidden layers; each hidden layer is sequentially connected to a batch normalization layer and a ReLU activation layer; The output layer is connected in sequence to the batch normalization layer and the Sigmoid activation layer.

[0015] In some exemplary embodiments, the reverse design model includes: Input layer; Multiple hidden layers; each hidden layer is sequentially connected to a batch normalization layer and a Tanh activation layer; The output layer is connected in sequence to the batch normalization layer and the Sigmoid activation layer.

[0016] According to a second aspect of the present invention, a reverse engineering device for lightweight acoustic black hole beam structures based on deep learning is provided, the device comprising: The acoustic black hole beam structure dataset construction module is used to perform simulation calculations on acoustic black hole beams based on sample structural parameters to obtain bandgap curves; and to extract the upper and lower limits of the sample bandgap frequencies from the bandgap curves to construct the acoustic black hole beam structure dataset; wherein, the acoustic black hole beam structure dataset includes: sample structural parameters, upper and lower limits of the sample bandgap frequencies, and the sample bandgap includes: sample longitudinal wave bandgap and sample bending wave bandgap. The forward prediction model construction module is used to train the first multilayer perceptron network using the dimensionality-reduced acoustic black hole beam structure dataset to obtain the forward prediction model. The dimensionality-reduced acoustic black hole beam structure dataset includes: sample latent vectors, upper and lower bound frequencies of the sample bandgap. The sample latent vectors are low-dimensional feature representations of the sample structural parameters. The forward prediction model is used to determine the mapping relationship between the sample latent vectors and the upper and lower bound frequencies of the sample bandgap. The reverse design model building module is used to cascade the forward prediction model after the second multilayer perceptron network to obtain a cascaded neural network; and to train the cascaded neural network based on the dimensionality-reduced acoustic black hole beam structure dataset to obtain the reverse design model. The target structure parameter prediction module is used to input the upper and lower bound frequencies of the target bandgap into the reverse design model to obtain the target latent vector; and to decode the target latent vector to obtain the target structure parameters; wherein the target latent vector is a low-dimensional feature representation of the target structure parameters. The lightweight reverse design module for acoustic black hole beams is used to design acoustic black hole beams using target structural parameters to obtain lightweight acoustic black hole beam structures.

[0017] According to a third aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium including a stored executable program, wherein, when the executable program is running, the device where the storage medium is located executes the aforementioned reverse engineering method for lightweight acoustic black hole beam structures based on deep learning.

[0018] According to a fourth aspect of the present invention, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the aforementioned deep learning-based reverse engineering method for lightweight acoustic black hole beam structures.

[0019] According to a fifth aspect of the present invention, an electronic device is provided, comprising: Processor; and Memory for storing the executable instructions of the processor; The processor is configured to implement the aforementioned deep learning-based acoustic black hole beam lightweight structure reverse design method by executing the executable instructions.

[0020] This invention provides a deep learning-based reverse engineering method for lightweight acoustic black hole beam structures. The method includes: constructing a forward prediction model of the "structural parameters-bandgap" and a reverse design model of the "bandgap-structural parameters" for the acoustic black hole beam using a first multilayer perceptron network and a second multilayer perceptron network, respectively. Specifically, the first multilayer perceptron network is trained using a dimensionality-reduced acoustic black hole beam structure dataset to obtain the forward prediction model; the forward prediction model is cascaded after the second multilayer perceptron network to obtain a cascaded neural network; and the cascaded neural network is trained to obtain the reverse design model. In practical applications, the upper and lower bound frequencies of the target bandgap are input into the reverse design model, which outputs a target latent vector. The target latent vector is decoded to obtain the target structural parameters, and the acoustic black hole beam is hollowed out according to these parameters, thereby achieving lightweight design of the acoustic black hole beam. Compared to traditional methods, this invention possesses stronger nonlinear modeling capabilities and generalization performance, enabling it to handle complex "performance-structure" mapping relationships. It achieves high-precision reverse design of acoustic black hole beams from the upper and lower limits of the target bandgap frequency to the target structural parameters, effectively reducing the trial-and-error costs in the structural design process, improving design efficiency and accuracy, and thus solving the technical problems of slow convergence speed, strong dependence on initial guesses, and difficulty in meeting the requirements of high-precision customized design in the reverse design process of acoustic black hole beam structures in the prior art.

[0021] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0022] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0023] Figure 1 The flowchart illustrates an exemplary embodiment of the present invention: a reverse design method for lightweight acoustic black hole beam structures based on deep learning. Figure 2 The illustration shows how the sample structure parameters of an exemplary embodiment of the present invention are represented. Figure 3 This schematic diagram illustrates a network architecture of a concatenated neural network, an exemplary embodiment of the present invention. Figure 4 This schematic diagram illustrates the overall process of the reverse engineering method for lightweight acoustic black hole beam structures based on deep learning, an exemplary embodiment of the present invention. Figure 5 This schematic diagram illustrates a reverse design device for lightweight acoustic black hole beam structures based on deep learning, an exemplary embodiment of the present invention. Figure 6 The diagram illustrates the composition of an electronic device according to an exemplary embodiment of the present invention. Detailed Implementation

[0024] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0025] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0026] To address the shortcomings and deficiencies of existing technologies, this example implementation provides a deep learning-based reverse engineering method for lightweight acoustic black hole beam structures. (Reference) Figure 1 As shown, it can specifically include: Step S10: Simulate the acoustic black hole beam based on the sample structural parameters to obtain the bandgap curve; and extract the upper and lower limits of the sample bandgap from the bandgap curve to construct the acoustic black hole beam structure dataset; wherein, the acoustic black hole beam structure dataset includes: sample structural parameters, upper and lower limits of the sample bandgap, and the sample bandgap includes: sample longitudinal wave bandgap and sample bending wave bandgap. Step S12: Using the dimensionality-reduced acoustic black hole beam structure dataset, train the first multilayer perceptron network to obtain a forward prediction model; wherein, the dimensionality-reduced acoustic black hole beam structure dataset includes: sample latent vectors, upper and lower bound frequencies of the sample bandgap, the sample latent vectors are low-dimensional feature representations of the sample structure parameters, and the forward prediction model is used to determine the mapping relationship between the sample latent vectors and the upper and lower bound frequencies of the sample bandgap. Step S14: The forward prediction model is cascaded after the second multilayer perceptron network to obtain a cascaded neural network; and the cascaded neural network is trained based on the dimensionality-reduced acoustic black hole beam structure dataset to obtain the reverse design model. Step S16: Input the upper and lower bound frequencies of the target bandgap into the reverse design model to obtain the target latent vector; and decode the target latent vector to obtain the target structural parameters; wherein, the target latent vector is a low-dimensional feature representation of the target structural parameters. Step S18: Design the acoustic black hole beam using the target structural parameters to obtain a lightweight acoustic black hole beam structure.

[0027] The following will describe in more detail each step of the reverse design method for lightweight acoustic black hole beam structures based on deep learning in this example embodiment, with reference to the accompanying drawings and embodiments.

[0028] For example, in step S10, the simulation calculation of the acoustic black hole beam based on the sample structural parameters is performed to obtain the band structure curve; and the upper and lower band gap frequencies of the sample band gap are extracted from the band structure curve to construct the acoustic black hole beam structure dataset, including: Step S101: Based on the power function variation law of the geometric structure of the acoustic black hole beam, set the arrangement of sample structure parameters and generate sample structure parameters. Step S102: Using finite element software, the acoustic black hole beam is simulated and calculated based on the sample structural parameters to obtain the band curve; and the upper and lower band gap frequencies of the sample are extracted from the band curve. Step S103: Based on the sample structural parameters and the upper and lower limits of the sample bandgap frequency, construct an acoustic black hole beam structure dataset.

[0029] For details, please refer to Figure 2 As shown, Figure 2This is a representation of the sample structure parameters. In the image, pixels have values ​​of 0 or 1, where 0 represents a non-cutout area (black area) and 1 represents a cutout area (white area). The sample structure parameters are the values ​​and spatial arrangement of pixels in the binary image, used to characterize the distribution characteristics of the cutout area in the acoustic black hole beam. Different combinations of pixel values ​​correspond to different cutout structures, thus forming different sample structure parameters.

[0030] Specifically, an initial acoustic black hole beam model is designed based on the power function variation law of the geometric structure and material parameters of the acoustic black hole beam. The pre-defined design area on the initial acoustic black hole beam model is discretized into multiple pixel units according to a predetermined resolution. According to the hollowing-out rules, each pixel unit is assigned a binary value to generate multiple sets of sample structural parameters, where a value of 1 represents a hollowed-out area and a value of 0 represents a non-hollowed-out area. The sample structural parameters can be represented using binary images. Finite element method software is used to apply the multiple sets of sample structural parameters to the initial acoustic black hole beam model, and simulation calculations are performed on the hollowed-out initial acoustic black hole beam model to obtain the band structure curves corresponding to each set of sample structural parameters. The upper and lower limits of the longitudinal wave bandgap and the flexural wave bandgap of the samples are extracted from each bandgap curve to construct an acoustic black hole beam structure dataset. This dataset includes: multiple sets of sample structural parameters, and the upper and lower limits of the sample bandgap corresponding to each set of sample structural parameters. The sample bandgap includes: the longitudinal wave bandgap and the flexural wave bandgap.

[0031] For example, firstly, an initial acoustic black hole beam model is constructed; then, using COMSOL Multiphysics finite element software, multiple sets of sample structural parameters are applied to the initial acoustic black hole beam model to form different hollowing-out shapes. Simulation calculations are then performed on the hollowed-out acoustic black hole beam model to obtain the band structure curves corresponding to each set of sample structural parameters. Finally, the upper and lower band gap frequencies of the samples are extracted from each band gap curve to construct an acoustic black hole beam structure dataset.

[0032] For example, the method further includes: Step S111: Use a variational autoencoder to reduce the dimensionality of the sample structure parameters to obtain the sample latent vector. Step S112: Determine the dimension-reduced acoustic black hole beam structure dataset based on the sample latent vector, the upper frequency of the sample bandgap, and the lower frequency of the sample bandgap.

[0033] The aforementioned latent vectors refer to the low-dimensional feature representation of the sample structure parameters.

[0034] Specifically, a variational autoencoder is introduced to extract features and reduce the dimensionality of the sample structure parameters, mapping the high-dimensional sample structure parameters to low-dimensional sample latent vectors. The sample structure parameters in the acoustic black hole beam structure dataset are replaced with the sample latent vectors, and combined with the upper and lower bound frequencies of the sample bandgap, a dimensionality-reduced acoustic black hole beam structure dataset is generated.

[0035] Furthermore, firstly, the high-dimensional sample structure parameters are input into a variational autoencoder for encoding, converting them into the mean and log-variance of the latent space. Then, based on the mean and log-variance, reparameterization is performed to obtain low-dimensional sample latent vectors. These low-dimensional sample latent vectors then replace the high-dimensional sample structure parameters in the acoustic black hole beam structure data, and are combined with the upper and lower bound frequencies of the sample bandgap to form a dimensionality-reduced acoustic black hole beam structure dataset. This dimensionality-reduced dataset is used for subsequent training of the first and second multilayer perceptron networks.

[0036] For example, a set of sample structural parameters consists of 2500 values. After being encoded by a variational autoencoder, an 8-dimensional latent vector is obtained. Using this latent vector as input data in the model training process can effectively reduce the input dimension, thereby significantly reducing the modeling complexity and computational resource consumption of the neural network.

[0037] For example, in step S12, the step of using the dimensionality-reduced acoustic black hole beam structure dataset to train the first multilayer perceptron network to obtain a positive prediction model includes: Step S121: Input the sample latent vector into the first multilayer perceptron network to obtain the upper and lower bound frequencies of the first prediction bandgap; Step S122: Calculate the first network prediction error using the upper and lower bound frequencies of the first predicted bandgap and the upper and lower bound frequencies of the sample bandgap, based on the first loss function; wherein the first loss function is the mean square error loss function between the upper and lower bound frequencies of the first predicted bandgap and the upper and lower bound frequencies of the sample bandgap. Step S123: Update the network parameters of the first multilayer perceptron network using the backpropagation algorithm, gradually reduce the prediction error of the first network until the network converges, and obtain the positive prediction model.

[0038] For details, please refer to Figure 3 As shown, Figure 3This is a schematic diagram of the network architecture of a cascaded neural network. The forward prediction model includes: an input layer; multiple hidden layers, where each hidden layer is sequentially connected to a batch normalization layer and a ReLU activation layer; and output layers, where each output layer is sequentially connected to a batch normalization layer and a sigmoid activation layer.

[0039] Specifically, the hidden layer or the output layer The weighted input received by each neuron is shown in the following formula: (1) in, Indicates the number of neurons. Indicates the previous level The output of each neuron Indicates input Connection weights between the current neuron and the current neuron This indicates the current neuron's bias.

[0040] The Sigmoid activation function used in the output layer is shown in the following equation: (2) Furthermore, the process of training the first multilayer perceptron network to obtain the positive prediction model is as follows: The training samples in the reduced-dimensional acoustic black hole beam structure dataset are represented as follows: , , , This represents the dimensionality-reduced acoustic black hole beam structure dataset. Each sample latent vector For the first The upper and lower frequency limits of the bandgap for each sample. For the real number field, Let be the dimension of the sample latent vector. This represents the number of training samples.

[0041] The sample latent vector is input into the first multilayer perceptron network to obtain the upper and lower bound frequencies of the first predicted bandgap, where, for the ... The training sample at the th ... The predicted values ​​in each output dimension are denoted as Its true value is denoted as The error between the predicted and actual values, i.e., the first network prediction error, is calculated using the first loss function. The first loss function is the mean squared error loss function between the predicted and actual values, as shown in the following equation: (3) in, Indicates the first Mean squared error loss in each output dimension Indicates the number of training samples. This indicates that the first multilayer perceptron network is related to the second... The training sample at the th ... Predicted values ​​on each output dimension Indicates the first The training sample at the th ... The true value in each output dimension.

[0042] Because excessive prediction error in the first network can easily lead to divergence in the forward prediction model, the backpropagation algorithm is used to update the network parameters of the first multilayer perceptron network, gradually reducing the prediction error until the network converges, thus obtaining the forward prediction model. The backpropagation algorithm is based on a gradient descent strategy, moving along... The negative gradient direction adjusts the network parameters. For a given learning rate η, the update amount of the weight parameters is expressed as: ,in, The gradient of the weight parameters can be expanded using the chain rule as follows: (4) For ease of representation, let

[0043] according to The definition has

[0044] Therefore, the update amount of the weight parameters is summarized as follows:

[0045] According to the weight parameters Using the same derivation method, the bias term can be further obtained. The update formula is given; based on this, the update rule for network parameters by the gradient descent algorithm is as follows: , (5) Through continuous iteration, the most suitable network parameters can be found, thereby constructing the final positive prediction model.

[0046] For example, in step S14, the model training of the cascaded neural network based on the dimensionality-reduced acoustic black hole beam structure dataset to obtain the reverse design model includes: Step S141: Input the upper and lower bound frequencies of the sample bandgap into the second multilayer perceptron network to obtain the predicted latent vector; Step S142: Input the predicted latent vector into the forward prediction model to obtain the upper and lower bound frequencies of the second prediction bandgap. Step S143: For the upper and lower bound frequencies of the sample bandgap and the upper and lower bound frequencies of the second predicted bandgap, calculate the second network prediction error based on the second loss function; wherein, the second loss function is the mean squared error loss function between the upper and lower bound frequencies of the second predicted bandgap and the upper and lower bound frequencies of the sample bandgap. Step S144: Update the network parameters of the second multilayer perceptron network using the backpropagation algorithm, gradually reduce the prediction error of the second network until the network converges, and obtain the trained second multilayer perceptron network. Step S145: The trained second multilayer perceptron network is identified as the reverse design model.

[0047] For details, please refer to Figure 3 As shown, Figure 3 This is a schematic diagram of the network architecture of a cascaded neural network. The reverse-engineered model includes: an input layer; multiple hidden layers, each of which is connected to a batch normalization layer and a Tanh activation layer in sequence; and output layers, each of which is connected to a batch normalization layer and a Sigmoid activation layer in sequence.

[0048] Furthermore, the process of training the second multilayer perceptron network based on the forward prediction model to obtain the reverse design model is as follows: The forward prediction model is cascaded after the second multilayer perceptron network to construct a cascaded neural network; the network parameters of the forward prediction model are fixed, and the upper and lower bound frequencies of the sample bandgap are input into the cascaded neural network. The second multilayer perceptron network is used to calculate the prediction latent vector through forward propagation; the prediction latent vector is input into the forward prediction model to obtain the upper and lower bound frequencies of the second prediction bandgap; for the upper and lower bound frequencies of the sample bandgap and the upper and lower bound frequencies of the second prediction bandgap, the second network prediction is calculated based on the second loss function. The measurement error is calculated, where the second loss function is the mean square error loss function between the upper and lower bound frequencies of the sample bandgap and the upper and lower bound frequencies of the second predicted bandgap. Since excessive prediction error of the second network can easily lead to divergence of the inverse design model, the network parameters of the second multilayer perceptron network are updated using the backpropagation algorithm to gradually reduce the prediction error of the second network until the network converges, thus obtaining the trained second multilayer perceptron network. The trained second multilayer perceptron network is determined as the inverse design model, where the process of updating the network parameters of the second multilayer perceptron network based on the backpropagation algorithm is the same as the process of updating the network parameters of the first multilayer perceptron network.

[0049] For example, in step S16, the upper and lower frequency limits of the target bandgap are reverse-designed based on the reverse design model to output the target latent vector; and the target latent vector is input into the decoding end of the variational autoencoder for decoding to obtain the target structural parameters.

[0050] The method provided in the embodiments of the present invention is referred to Figure 4 As shown, Figure 4 This is a schematic diagram illustrating the overall process of the reverse design method for lightweight acoustic black hole beams based on deep learning. The main steps of the reverse design method for lightweight acoustic black hole beams based on deep learning include: Step 1: Constructing an acoustic black hole beam structure dataset: Based on the power function variation law of the geometric structure of the acoustic black hole beam, the arrangement of sample structural parameters is set to generate sample structural parameters; using finite element software, the acoustic black hole beam is simulated and calculated according to the sample structural parameters to obtain the band structure curve; and the upper and lower band gap frequencies of the sample are extracted from the band gap curve; based on the sample structural parameters and the upper and lower band gap frequencies of the sample, an acoustic black hole beam structure dataset is constructed.

[0051] Specifically, an initial acoustic black hole beam model is designed based on the power function variation law of the geometric structure and material parameters of the acoustic black hole beam. The pre-defined design area on the initial acoustic black hole beam model is discretized into multiple pixel units according to a predetermined resolution. According to the hollowing-out rules, each pixel unit is assigned a binary value to generate multiple sets of sample structural parameters, where a value of 1 represents a hollowed-out area and a value of 0 represents a non-hollowed-out area. The sample structural parameters can be represented using binary images. Finite element method software is used to apply the multiple sets of sample structural parameters to the initial acoustic black hole beam model, and simulation calculations are performed on the hollowed-out initial acoustic black hole beam model to obtain the band structure curves corresponding to each set of sample structural parameters. The upper and lower limits of the longitudinal wave bandgap and the flexural wave bandgap of the samples are extracted from each bandgap curve to construct an acoustic black hole beam structure dataset. This dataset includes: multiple sets of sample structural parameters, and the upper and lower limits of the sample bandgap corresponding to each set of sample structural parameters. The sample bandgap includes: the longitudinal wave bandgap and the flexural wave bandgap.

[0052] For example, firstly, an initial acoustic black hole beam model is constructed; then, using COMSOL Multiphysics finite element software, multiple sets of sample structural parameters are applied to the initial acoustic black hole beam model to form different hollowing-out shapes. Simulation calculations are then performed on the hollowed-out acoustic black hole beam model to obtain the band structure curves corresponding to each set of sample structural parameters. Finally, the upper and lower band gap frequencies of the samples are extracted from each band gap curve to construct an acoustic black hole beam structure dataset.

[0053] Step 2: Perform dimensionality reduction on the acoustic black hole beam dataset to obtain the dimensionality-reduced acoustic black hole beam structure dataset.

[0054] Specifically, the sample structure parameters are input into the variational autoencoder, which outputs the mean and log-variance of the latent space. The mean and log-variance are reparameterized to obtain the sample latent vectors, thus mapping the high-dimensional sample structure parameters to low-dimensional sample latent vectors. The sample latent vectors are used to replace the sample structure parameters in the acoustic black hole beam structure dataset, and combined with the upper and lower bound frequencies of the sample bandgap, the dimension-reduced acoustic black hole beam structure dataset is generated.

[0055] Step 3: Construct a positive prediction model: Based on the first multilayer perceptron network, establish a nonlinear mapping relationship between structural parameters and the upper and lower bandgap frequencies, and train it using the dimensionality-reduced acoustic black hole beam structure dataset until convergence, to obtain the acoustic black hole beam "structural parameters-bandgap" positive prediction model.

[0056] Specifically, the sample latent vector is input into the first multilayer perceptron network to obtain the upper and lower bound frequencies of the first prediction bandgap; using the upper and lower bound frequencies of the first prediction bandgap and the sample bandgap, the prediction error of the first network is calculated according to the first loss function; the network parameters of the first multilayer perceptron network are updated using the backpropagation algorithm to gradually reduce the prediction error of the first network until the network converges, thus obtaining a positive prediction model.

[0057] Step 4: Constructing a cascaded neural network to achieve reverse design: After the second multilayer perceptron network is cascaded into the forward prediction model, a cascaded neural network is obtained; based on the dimensionality-reduced acoustic black hole beam structure dataset, the cascaded neural network is trained to obtain the acoustic black hole beam “bandgap-structural parameters” reverse design model.

[0058] Specifically, a variable scope isolation mechanism is constructed, which allocates independent namespaces to the trained forward prediction model and the reverse design model to be trained, and adds specific prefixes to the variables within them to achieve independent management of model parameters.

[0059] Further, the upper and lower bound frequencies of the sample bandgap are input into the second multilayer perceptron network to obtain the predicted latent vector; the predicted latent vector is input into the forward prediction model to obtain the upper and lower bound frequencies of the second prediction bandgap; for the upper and lower bound frequencies of the sample bandgap and the upper and lower bound frequencies of the second prediction bandgap, the prediction error of the second network is calculated according to the second loss function; the network parameters of the second multilayer perceptron network are updated using the backpropagation algorithm to gradually reduce the prediction error of the second network until the network converges, thus obtaining the trained second multilayer perceptron network; the trained second multilayer perceptron network is determined as the reverse design model.

[0060] Step 5: Implement lightweight design of acoustic black hole beam using reverse design model.

[0061] Specifically, the upper and lower frequency limits of the target bandgap are input into the reverse design model to obtain the target latent vector; the target latent vector is then decoded to obtain the target structural parameters; the target latent vector is a low-dimensional feature representation of the target structural parameters; the acoustic black hole beam is designed using the target structural parameters to obtain a lightweight acoustic black hole beam structure.

[0062] This example implementation provides a deep learning-based reverse engineering device 50 for lightweight acoustic black hole beam structures. (Reference) Figure 5 As shown, it can specifically include: The acoustic black hole beam structure dataset construction module 501 is used to perform simulation calculations on acoustic black hole beams based on sample structural parameters to obtain band curves; and to extract the upper and lower limits of the sample band gap from the band curves to construct the acoustic black hole beam structure dataset; wherein, the acoustic black hole beam structure dataset includes: sample structural parameters, upper and lower limits of the sample band gap, and the sample band gap includes: sample longitudinal wave band gap and sample bending wave band gap; The forward prediction model construction module 502 is used to train the first multilayer perceptron network using the dimensionality-reduced acoustic black hole beam structure dataset to obtain the forward prediction model. The dimensionality-reduced acoustic black hole beam structure dataset includes: sample latent vectors, upper and lower bound frequencies of the sample bandgap. The sample latent vectors are low-dimensional feature representations of the sample structural parameters. The forward prediction model is used to determine the mapping relationship between the sample latent vectors and the upper and lower bound frequencies of the sample bandgap. The reverse design model building module 503 is used to cascade the forward prediction model after the second multilayer perceptron network to obtain a cascaded neural network; and to train the cascaded neural network based on the dimension-reduced acoustic black hole beam structure dataset to obtain the reverse design model. The target structure parameter prediction module 504 is used to input the upper and lower bound frequencies of the target bandgap into the reverse design model to obtain the target latent vector; and to decode the target latent vector to obtain the target structure parameters; wherein the target latent vector is a low-dimensional feature representation of the target structure parameters. The lightweight reverse design module 505 for acoustic black hole beams is used to design acoustic black hole beams using target structural parameters to obtain lightweight acoustic black hole beam structures.

[0063] This invention performs model verification on the trained tandem neural network. Given the true values ​​of the upper and lower limits of the longitudinal wave bandgap and the flexural wave bandgap (the upper and lower limits of the true bandgap), the design results (predicted upper and lower limits of the bandgap) are obtained after processing by the trained tandem neural network, as shown in Tables 1 and 2. Table 1 is the design result and accuracy table for the longitudinal wave bandgap, and Table 2 is the design result and accuracy table for the flexural wave bandgap.

[0064] Let the upper and lower frequency limits of the actual bandgap be respectively... and The upper and lower frequency limits of the predicted bandgap obtained using a cascaded neural network are respectively... and The formula for calculating design accuracy is as follows: (6) As can be seen from the design accuracy calculated in Tables 1 and 2, the design accuracy of the four examples of longitudinal waves and flexural waves is above 95%, indicating that the reverse design model has high reverse design accuracy for longitudinal waves and flexural waves.

[0065] Table 1. Design Results and Accuracy of the Longitudinal Wave Bandgap

[0066] Table 2 Design Results and Accuracy of Bending Wave Bandgap

[0067] The beneficial effects of this invention are as follows: (1) It realizes efficient reverse design from the upper and lower bound frequencies of the target bandgap to the structural parameters: By constructing a reverse design model and combining it with a serial training mechanism, the target latent vector can be quickly deduced from the upper and lower bound frequencies of the target bandgap, and then the target structural parameters can be obtained. This reduces the design cost of relying on repeated simulation and parameter testing in traditional methods and improves the efficiency of reverse design.

[0068] (2) Improved the modeling accuracy of the “complex structural parameters-bandgap” mapping relationship: By constructing a forward prediction model to learn the mapping relationship between structural parameters and the upper and lower limits of the bandgap, and by using the error between the upper and lower limits of the actual bandgap and the upper and lower limits of the predicted bandgap to optimize the reverse design model, thereby improving the accuracy and stability of the reverse design of acoustic black hole beam parameters.

[0069] (3) A lightweight design of acoustic black hole beam structure was achieved: By reverse designing the structural parameters of acoustic black hole beam and applying the obtained structural parameters to the beam hollowing design, the structural mass was reduced while meeting the upper and lower frequency requirements of the target bandgap, thus realizing the lightweight design of acoustic black hole beam in practical applications.

[0070] It should be noted that the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Furthermore, it is readily understood that these processes may, for example, be executed synchronously or asynchronously in multiple modules.

[0071] It should be noted that although several modules or units of the device for performing actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of the present invention, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0072] Figure 6 A schematic diagram of an electronic device suitable for implementing embodiments of the present invention is shown.

[0073] It should be noted that, Figure 6 The electronic device 1000 shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0074] like Figure 6 As shown, the electronic device 1000 includes a Central Processing Unit (CPU) 1001, which can perform various appropriate actions and processes based on programs stored in Read-Only Memory (ROM) 1002 or programs loaded from storage section 1008 into Random Access Memory (RAM) 1003. The RAM 1003 also stores various programs and data required for system operation. The CPU 1001, ROM 1002, and RAM 1003 are interconnected via a bus 1004. An Input / Output (I / O) interface 1005 is also connected to the bus 1004. Furthermore, the electronic device 1000 also includes an FPGA device and a System-on-a-Chip (SoC) device.

[0075] The following components are connected to I / O interface 1005: an input section 1006 including a keyboard, mouse, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN (Local Area Network) card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to I / O interface 1005 as needed. Removable media 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 1010 as needed so that computer programs read from them can be installed into storage section 1008 as needed.

[0076] In particular, according to embodiments of the present invention, the processes described below with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a storage medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 1009, and / or installed from removable medium 1011. When the computer program is executed by central processing unit (CPU) 1001, it performs various functions defined in the system of this application.

[0077] Specifically, the aforementioned electronic devices can be airborne intelligent electronic devices.

[0078] It should be noted that the storage medium shown in the embodiments of the present invention can be a computer-readable signal medium or a computer-readable storage medium, or any combination thereof. A computer-readable storage medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable storage medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), flash memory, optical fiber, portable compact disc read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In the present invention, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, wherein computer-readable program code is carried. Such transmitted data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. The computer-readable signal medium can also be any storage medium other than a computer-readable storage medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, etc., or any suitable combination thereof.

[0079] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0080] The units described in the embodiments of the present invention can be implemented in software or hardware, and the described units can also be located in a processor. The names of these units do not necessarily limit the specific unit itself.

[0081] It should be noted that, as another aspect, this application also provides a storage medium, which may be included in an electronic device or may exist independently without being assembled into the electronic device. The aforementioned storage medium carries one or more programs, which, when executed by an electronic device, cause the electronic device to perform the methods described in the following embodiments. For example, the electronic device may perform... Figure 1 The steps of the method shown.

[0082] In one embodiment, this application provides a computer program product including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0083] Furthermore, the above figures are merely illustrative of the processes included in the method according to exemplary embodiments of the present invention, and are not intended to be limiting. It is readily understood that the processes shown in the above figures do not indicate or limit the temporal order of these processes. Additionally, it is readily understood that these processes may be executed synchronously or asynchronously, for example, in multiple modules.

[0084] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of the invention are indicated by the claims.

[0085] It should be understood that the present invention is not limited to the precise structure described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A reverse design method for lightweight acoustic black hole beam structures based on deep learning, characterized in that, The method includes: The acoustic black hole beam is simulated based on the sample structural parameters to obtain the band structure curve. The upper and lower limits of the sample band gap are extracted from the band structure curve to construct the acoustic black hole beam structure dataset. The acoustic black hole beam structure dataset includes: sample structural parameters, upper and lower limits of the sample band gap, and the sample band gap includes: sample longitudinal wave band gap and sample bending wave band gap. Using the dimensionality-reduced acoustic black hole beam structure dataset, the first multilayer perceptron network is trained to obtain a forward prediction model. The dimensionality-reduced acoustic black hole beam structure dataset includes: sample latent vectors, upper and lower bound frequencies of the sample bandgap. The sample latent vectors are low-dimensional feature representations of the sample structure parameters. The forward prediction model is used to determine the mapping relationship between the sample latent vectors and the upper and lower bound frequencies of the sample bandgap. The forward prediction model is cascaded after the second multilayer perceptron network to obtain a cascaded neural network; and the cascaded neural network is trained based on the dimensionality-reduced acoustic black hole beam structure dataset to obtain the reverse design model. The upper and lower frequency limits of the target bandgap are input into the inverse design model to obtain the target latent vector; and the target latent vector is decoded to obtain the target structure parameters; wherein, the target latent vector is a low-dimensional feature representation of the target structure parameters. The acoustic black hole beam was designed using the target structural parameters, resulting in a lightweight structure for the acoustic black hole beam.

2. The method according to claim 1, characterized in that, The acoustic black hole beam was simulated and calculated based on the sample structural parameters to obtain the band structure curve. Then, the upper and lower band gap frequencies of the sample band gaps were extracted from the band gap curves to construct an acoustic black hole beam structure dataset, including: Based on the power function variation law of the geometric structure of the acoustic black hole beam, the arrangement of sample structural parameters is set to generate sample structural parameters. Using finite element software, the acoustic black hole beam was simulated and calculated based on the structural parameters of the sample to obtain the band curve; and the upper and lower band gap frequencies of the sample were extracted from the band curve. Based on the sample structural parameters, the upper and lower bound frequencies of the sample bandgap, an acoustic black hole beam structure dataset is constructed.

3. The method according to claim 1, characterized in that, The method further includes: By using a variational autoencoder, the sample structure parameters are reduced in dimensionality to obtain the sample latent vector; The dimensionality-reduced acoustic black hole beam structure dataset is determined based on the sample latent vectors, the upper frequency limit of the sample bandgap, and the lower frequency limit.

4. The method according to claim 3, characterized in that, The method of using the dimensionality-reduced acoustic black hole beam structure dataset to train the first multilayer perceptron network to obtain a positive prediction model includes: The sample latent vector is input into the first multilayer perceptron network to obtain the upper and lower bound frequencies of the first prediction bandgap. The first network prediction error is calculated based on the upper and lower bound frequencies of the first prediction bandgap and the upper and lower bound frequencies of the sample bandgap, according to the first loss function; wherein, the first loss function is the mean square error loss function between the upper and lower bound frequencies of the first prediction bandgap and the upper and lower bound frequencies of the sample bandgap. The network parameters of the first multilayer perceptron network are updated using the backpropagation algorithm to gradually reduce the prediction error of the first network until the network converges, thus obtaining a positive prediction model.

5. The method according to claim 4, characterized in that, The dataset of acoustic black hole beam structures with reduced dimensions is used to train a cascaded neural network to obtain a reverse design model, including: The upper and lower bound frequencies of the sample bandgap are input into the second multilayer perceptron network to obtain the predicted latent vector; By inputting the predicted latent vector into the forward prediction model, the upper and lower bound frequencies of the second prediction bandgap are obtained. For the upper and lower bound frequencies of the sample bandgap and the upper and lower bound frequencies of the second predicted bandgap, the prediction error of the second network is calculated based on the second loss function; wherein, the second loss function is the mean squared error loss function between the upper and lower bound frequencies of the second predicted bandgap and the upper and lower bound frequencies of the sample bandgap. The network parameters of the second multilayer perceptron network are updated using the backpropagation algorithm to gradually reduce the prediction error of the second network until the network converges, thus obtaining the trained second multilayer perceptron network. The trained second-layer perceptron network was selected as the reverse design model.

6. The method according to claim 1, characterized in that, The positive prediction model includes: Input layer; Multiple hidden layers; each hidden layer is sequentially connected to a batch normalization layer and a ReLU activation layer; The output layer is connected in sequence to the batch normalization layer and the Sigmoid activation layer.

7. The method according to claim 1, characterized in that, The reverse design model includes: Input layer; Multiple hidden layers; each hidden layer is sequentially connected to a batch normalization layer and a Tanh activation layer; The output layer is connected in sequence to the batch normalization layer and the Sigmoid activation layer.

8. A reverse design device for lightweight acoustic black hole beam structures based on deep learning, characterized in that, The device includes: The acoustic black hole beam structure dataset construction module is used to perform simulation calculations on acoustic black hole beams based on sample structural parameters to obtain bandgap curves; and to extract the upper and lower limits of the sample bandgap frequencies from the bandgap curves to construct the acoustic black hole beam structure dataset; wherein, the acoustic black hole beam structure dataset includes: sample structural parameters, upper and lower limits of the sample bandgap frequencies, and the sample bandgap includes: sample longitudinal wave bandgap and sample bending wave bandgap. The forward prediction model construction module is used to train the first multilayer perceptron network using the dimensionality-reduced acoustic black hole beam structure dataset to obtain the forward prediction model. The dimensionality-reduced acoustic black hole beam structure dataset includes: sample latent vectors, upper and lower bound frequencies of the sample bandgap. The sample latent vectors are low-dimensional feature representations of the sample structural parameters. The forward prediction model is used to determine the mapping relationship between the sample latent vectors and the upper and lower bound frequencies of the sample bandgap. The reverse design model building module is used to cascade the forward prediction model after the second multilayer perceptron network to obtain a cascaded neural network; and to train the cascaded neural network based on the dimensionality-reduced acoustic black hole beam structure dataset to obtain the reverse design model. The target structure parameter prediction module is used to input the upper and lower bound frequencies of the target bandgap into the reverse design model to obtain the target latent vector; and to decode the target latent vector to obtain the target structure parameters; wherein the target latent vector is a low-dimensional feature representation of the target structure parameters. The lightweight reverse design module for acoustic black hole beams is used to design acoustic black hole beams using target structural parameters to obtain lightweight acoustic black hole beam structures.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored executable program, wherein, when the executable program is executed, it controls the device on which the storage medium is located to perform the method according to any one of claims 1 to 7.

10. A computer program product, characterized in that, Includes a computer program that, when executed by a processor, implements the method according to any one of claims 1 to 7.

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