Piezoelectric metamaterial adaptive vibration suppression method based on deep learning reverse design

Abstract

The invention relates to a piezoelectric metamaterial self-adaptive vibration suppression method based on deep learning reverse design. The piezoelectric metamaterial self-adaptive vibration suppression method comprises the steps that a nonlinear digital piezoelectric metamaterial is acquired, and a circuit parameter and vibration response signal data set of the metamaterial is acquired; wherein the circuit parameter and vibration response signal data set comprises a circuit parameter vector and a band gap tag vector of the nonlinear digital piezoelectric metamaterial; constructing a reverse design network model based on deep learning; training a reverse design network model based on deep learning according to the circuit parameters and the vibration response signal data set; and obtaining circuit parameters of the nonlinear digital piezoelectric metamaterial. According to the piezoelectric metamaterial, a nonlinear shunt circuit with programmability is formed by a single chip microcomputer, a deep learning neural network is combined, corresponding circuit parameters can be accurately and automatically designed according to expected vibration suppression response, the vibration suppression flexibility, the self-adaptive capacity and the design efficiency are improved, and the application range is wide. And a good vibration suppression effect is shown.

Description

Technical Field

[0001] The present invention relates to the field of vibration control technology, and in particular to a piezoelectric metamaterial adaptive vibration suppression method based on deep learning reverse design. Background Art

[0002] Applications requiring high precision, such as precision machining and measurement, space remote sensing, and observation, can be subject to vibrations from the external environment or within the device, severely degrading its precision and accuracy. To ensure proper operation, structural vibrations must be effectively controlled. Common vibration suppression methods include passive vibration isolation, semi-active vibration suppression, and active vibration suppression. Semi-active vibration suppression, based on the bandgap properties of piezoelectric metamaterials, has attracted extensive research due to its increased flexibility and low power consumption.

[0003] Traditional piezoelectric metamaterials are typically based on analog shunt circuits. Analog circuit design is complex, and changing circuit parameters after design is complete is inconvenient and lacks flexibility. Furthermore, designers require a certain level of prior knowledge and experience to ensure effective designs. Therefore, finding a more efficient and convenient way to design piezoelectric metamaterials that achieve the desired vibration suppression performance has become a pressing challenge for those skilled in the art. Summary of the Invention

[0004] The present invention addresses the technical problems existing in the prior art. By utilizing the band gap characteristics of piezoelectric metamaterials, it provides a piezoelectric metamaterial adaptive vibration control method based on deep learning reverse design. By obtaining the vibration response signal of the nonlinear piezoelectric metamaterial under different circuit parameters, a neural network model corresponding to the circuit parameters and the response signal is constructed to achieve reverse design of the vibration suppression characteristics of the nonlinear piezoelectric metamaterial and perform structural vibration suppression.

[0005] To achieve the above-mentioned objectives, the present invention adopts the following technical solutions: a piezoelectric metamaterial adaptive vibration control method based on deep learning reverse design, comprising constructing a nonlinear piezoelectric metamaterial; obtaining a data set of circuit parameters and a vibration response signal of a nonlinear digital piezoelectric metamaterial; the data set of circuit parameters and vibration response signal comprises a circuit parameter vector and a bandgap label vector of the nonlinear digital piezoelectric metamaterial; constructing a reverse design network model based on deep learning; training the reverse design network model based on deep learning according to the data set of circuit parameters and vibration response signal; and obtaining the circuit parameters of the nonlinear digital piezoelectric metamaterial for vibration suppression according to the trained reverse design network model based on deep learning.

[0006] As an improvement to the present invention, the nonlinear digital piezoelectric metamaterial includes: a local resonant unit, an excitation signal sensor, and a response signal sensor. The local resonant units are arranged periodically, and two or more one-dimensionally periodically arranged local resonant units constitute multiple vibration control channels. The two or more vibration control channels and their parameter adjustment cause the metamaterial's vibration waves of a specified frequency to attenuate. It should be noted that as the number of integrated local resonant units increases, the vibration suppression capability of the nonlinear digital piezoelectric metamaterial will be further enhanced. In an embodiment constructed by the present invention, the nonlinear digital piezoelectric metamaterial can achieve a vibration wave attenuation effect of up to 37.75dB.

[0007] As an improvement to the present invention, the local resonance unit includes a piezoelectric transducer and a nonlinear shunt circuit. The local resonance units are periodically arranged on the substrate, and the piezoelectric transducer in the local resonance unit is attached to one side surface of the substrate. This helps to simplify the structural layout and reduce the mechanical coupling interference that may be caused by double-sided layout, thereby improving the stability and consistency of the system. At the same time, this unilateral layout method can achieve directional coupling control of the structural vibration direction, enhance the ability to control specific modal vibrations, and further improve the vibration suppression performance.

[0008] As an improvement of the present invention, the piezoelectric transducers in the local resonance unit are respectively connected to the nonlinear shunt circuit, wherein the nonlinear shunt circuit includes a digital part and an analog part, the analog part is built using an operational amplifier, a capacitor and a resistor, and the digital part is built using a single-chip microcomputer, and the analog part and the digital part are connected using a digital-to-analog conversion module, wherein the upper and lower surfaces of the piezoelectric transducer are respectively connected to the output port and the ground wire of the nonlinear shunt circuit. Through the above structural design, the nonlinear term is effectively integrated into the piezoelectric metamaterial system. By utilizing the programmable characteristics of the single-chip microcomputer, the parameters of the nonlinear term can be flexibly adjusted, thereby giving the system a higher nonlinear response control capability. After adding the nonlinear term, the piezoelectric metamaterial showed characteristics such as widening of the vibration suppression frequency band, offset of the jump point of the vibration transmission rate curve, and change in the degree of vibration wave attenuation in the experiment, which significantly enhanced the flexibility and adaptability of the vibration suppression system.

[0009] As an improvement of the present invention, the digital part of the nonlinear shunt circuit is implemented by a single chip microcomputer. The digital part converts the nonlinear circuit into the form of a transfer function in the s domain and further discretizes it into a differential equation, which is:

[0010]

[0011] Where y[n] is the output value at the current moment, y[nj] is the output value at the previous j sampling moments, x[n] is the input value at the current moment, x[ni] is the input value at the previous i sampling moments, m is the numerator order, n is the denominator order, and b i is the numerator coefficient, a j is the denominator coefficient, K2 is the coefficient of the nonlinear quadratic term, and K3 is the coefficient of the nonlinear cubic term. Since s-domain analysis methods cannot directly handle nonlinear terms, the above design allows the nonlinear control strategy to be written into the microcontroller in differential form and implemented through programming, effectively integrating it into the piezoelectric metamaterial system and improving the adjustability and response flexibility of the vibration control process.

[0012] As an improvement of the present invention, the shape of the piezoelectric transducer on the substrate is any one of circular, elliptical, rectangular, diamond, triangular or hexagonal.

[0013] As an improvement of the present invention, the shape of the substrate in the local resonance unit is any one of a rectangle, a square or a hexagon, and the substrate is made of metal.

[0014] As an improvement of the present invention, the number of the vibration control channels is two or more.

[0015] As an improvement of the present invention, the number of local resonance units in each vibration control channel is one.

[0016] As an improvement to the present invention, the reverse design network model based on deep learning is composed of two network models: a pre-trained network and a reverse design network. The circuit parameter vector is used as the input of the pre-trained network, and the bandgap label vector is used as the output of the pre-trained network. The bandgap label vector is used as the input of the reverse design network, and the circuit parameter vector is used as the output of the reverse design network. Based on this, the reverse design network is used for reverse design from vibration response to circuit parameters, and the pre-trained network is used to verify whether the predicted circuit parameters can produce corresponding vibration responses, thereby constructing a network model with integrated design and verification functions. In this way, not only the accuracy and reliability of reverse design are improved, but also the network model's ability to self-verify the design results is realized.

[0017] As an improvement to the present invention, training the deep learning-based serial pipeline model includes: using a pipeline training method to train the pre-trained network and the reverse-designed network separately, with the process being divided into the following two stages. In the first stage, the pre-trained network is trained to achieve a mapping from the circuit parameters of the nonlinear piezoelectric metamaterial to the bandgap characteristics; in the second stage, the reverse-designed network and the pre-trained network are constructed into a serial pipeline. First, the reverse-designed network completes the mapping from the bandgap characteristics to the circuit parameters of the nonlinear piezoelectric metamaterial, and then the output of the reverse-designed network is used as the input of the pre-trained network to generate new target characteristics. The reverse-designed network is a Transformer network combining a 1DCNN neural network and a Transformer network. During the back-propagation process, the Adam optimizer is used, with a learning rate of 0.0001.

[0018] The loss function of the cascaded network is:

[0019]

[0020] Where L is the data length, To reverse engineer the network’s predictions, is the predicted value of the pretrained network, and λ is the weight assigned to the reverse-engineered network. This multi-objective loss function design helps improve the network's stability and prediction accuracy in practical applications. In an embodiment constructed by the present invention, the reverse-engineered network achieved an accuracy of up to 98.916% on the test set.

[0021] Compared to the prior art, the present invention offers the following advantages: the nonlinear piezoelectric metamaterial provided herein can achieve adaptive vibration control. By implementing the shunt circuit using a single-chip microcomputer, the parameters of the linear portion of the shunt circuit can be flexibly adjusted, thereby adjusting the frequency range of vibration suppression, etc., adding programmability to the metamaterial and significantly improving the flexibility of vibration suppression. Furthermore, by adjusting the coefficients of the nonlinear terms in the digital shunt circuit to control the nonlinear response of the metamaterial, it can provide a wider range of vibration suppression effects than linear piezoelectric metamaterials. The transition point of the vibration transmissibility and the degree of vibration wave attenuation can also be flexibly adjusted, further enhancing the metamaterial's flexibility and adaptability. In an embodiment constructed by the present invention, the vibration suppression range can be widened by up to 1.36 times, demonstrating the metamaterial's superior performance in vibration control. In the neural network model established by the present invention, the pre-trained network can replace the finite element method to accurately predict the structural vibration response, and the reverse design network can accurately predict the circuit parameters of the desired response. In an embodiment constructed by the present invention, the prediction accuracy rate can reach 98.916%. This method significantly improves the efficiency of the reverse design process of metamaterial structural parameters. Compared to traditional design methods, this approach reduces reliance on prior knowledge and the time-consuming debugging experiments, making metamaterial design simpler and more intelligent. The present invention provides a piezoelectric metamaterial adaptive vibration suppression method based on deep learning reverse design. This method combines nonlinear digital piezoelectric metamaterials with a deep learning reverse design model. This method not only effectively suppresses vibration but also improves design efficiency, enabling efficient and accurate intelligent reverse design. This enhances the application value of nonlinear piezoelectric metamaterials in complex working conditions and provides new ideas for building intelligent vibration control systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 Schematic diagram of the structure of the nonlinear piezoelectric metamaterial of the present invention;

[0023] Figure 2 Schematic diagram of a single piezoelectric transducer of a nonlinear piezoelectric metamaterial and a programmable shunt circuit thereof according to the present invention;

[0024] Figure 3 This is a structural diagram of the reverse design network pipeline training model based on deep learning in the present invention;

[0025] Figure 4 Iteration diagram of the loss function during pipeline training network;

[0026] Figure 5 This is a diagram showing the vibration suppression effect of the reverse design of nonlinear piezoelectric metamaterials.

[0027] In the figure: 1, 2, and 3 are all piezoelectric transducers, 4. Local resonance unit, 5. Operational amplifier, 6. Resistor, 7. Analog-to-digital conversion module, 8. Microcontroller, 9. Digital-to-analog conversion module, 10. Target bandgap label vector, 11. Convolution block, 12. Fully connected layer, 13. Predicted circuit parameter vector, 14. Transformer block, 15. Predicted bandgap label vector, 16. Loss value, 17. Training set loss value, 18. Test set loss value, 19. Number of iterations. DETAILED DESCRIPTION

[0028] The present invention will be described in more detail below with reference to the accompanying drawings and examples. The following examples will help those skilled in the art further understand the present invention, but are not intended to limit the present invention in any way. It should be noted that those skilled in the art may make various variations and modifications without departing from the scope of the present invention. Such variations and modifications are within the scope of the present invention.

[0029] In addition, in the description of the present application specification and the appended claims, the terms "first", "second", "third", etc. are only used to distinguish the descriptions and cannot be understood as indicating or implying relative importance.

[0030] In order to illustrate the technical solution described in this application, a specific implementation method is provided below.

[0031] Embodiment: This embodiment provides a method for adaptively suppressing vibration of a piezoelectric metamaterial based on deep learning reverse design, comprising the following steps:

[0032] Step 1: Build nonlinear piezoelectric metamaterial. Figure 1 As shown in FIG, a monolithic square piezoelectric transducer is periodically fixed on one side of the substrate by gluing with epoxy resin, and the piezoelectric transducer is connected to the nonlinear shunt circuit via a wire. Figure 2 As shown, the piezoelectric transducer is connected to the analog part of the nonlinear shunt circuit through a wire and the digital shunt circuit is realized by programming the single chip microcomputer and controlling the real-time interaction between the digital-to-analog conversion module and the analog-to-digital conversion module and the analog circuit signal. Figure 1 As shown, an excitation signal is applied through the piezoelectric transducer 1 and a response signal is obtained through the piezoelectric transducer 3 .

[0033] Step 2: Obtain the circuit parameters and response signal dataset of the piezoelectric metamaterial. The circuit parameters and response signal dataset include the nonlinear circuit parameter vector and bandgap label vector of the piezoelectric metamaterial. Figure 1 The vibration response of the piezoelectric metamaterial shown is used as sample data for design, and its circuit parameters are respectively represented by three parameters x1, x2, and x3 to represent the coefficients and frequencies of the quadratic term and the cubic term, and are normalized.

[0034] The response signal corresponding to the circuit parameters is divided into the target frequency range [f min ,f max ] is divided into N segments, where N = 2000. Then a label vector y = (y1, y2, ..., y N ), by assigning a value to the label vector to indicate whether the vibration wave is suppressed. i =1, frequency f i is a passband, otherwise it is a forbidden band.

[0035] Step 3: Build the network model. To address the issue of piezoelectric metamaterials exhibiting identical response signals for identical circuit parameters, this example uses a pretrained network and a reverse-engineered network. The pretrained network takes the circuit parameter vector as input and outputs the bandgap label vector. The reverse-engineered network takes the bandgap label vector as input and outputs the circuit parameter vector.

[0036] Step 4: Model training. This example uses the pipeline training method to train the pre-trained network and the reverse-designed network respectively. The process is divided into the following two stages: In the first stage, the pre-trained network is trained to achieve the mapping from circuit parameters to response signals; in the second stage, the reverse-designed network and the pre-trained network are connected in series to form a pipeline-like model. First, the response signal is input into the reverse-designed network to obtain the predicted circuit parameters, and then the predicted circuit parameters are input into the trained pre-trained network to obtain the predicted response signal. The adam optimizer is selected for network training, and the learning rate is 0.0001. The loss function of the series network is:

[0037]

[0038] Where L is the sample size, To reverse engineer the network’s predictions, is the predicted value of the pre-trained network, and λ is the weight assigned to the reverse-engineered network.

[0039] The data set obtained in step 2 is divided into a training set and a test set according to a ratio of 9:1, and the network is trained. Figure 4 This is an iterative diagram of the loss function of the tandem network during the training process. It can be seen that the loss function of the network gradually decreases to convergence, and the training set and test set are relatively consistent, indicating that the network training is in good condition.

[0040] Step 5: After the series network is trained through step 4, the target bandgap vector is input into the trained reverse design network to obtain the circuit parameters that meet the design. The parameters are then programmed into the MCU online to obtain the actual response of the piezoelectric metamaterial under the circuit. The actual bandgap vector of the response signal is compared with the target bandgap vector to verify the accuracy of the neural network. Figure 5 As shown in the figure, the gray area indicates that the vibration wave is suppressed within this frequency band. It can be seen that the target suppression interval and the actual suppression interval are basically consistent, indicating that the reverse design network predicts the band gap well.

[0041] The piezoelectric metamaterial designed in this paper effectively achieves adaptive vibration suppression by leveraging its structural response to the vibrations of a nonlinear shunt circuit. Furthermore, the deep learning-based reverse design model established in this paper accurately and automatically reverse-engineers circuit parameters, streamlining the design process and improving efficiency.

[0042] The above-described embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. A piezoelectric metamaterial adaptive vibration suppression method based on deep learning reverse design, characterized in that: include: Obtain nonlinear digital piezoelectric metamaterials to obtain the circuit parameters and vibration response signal data sets of metamaterials; The circuit parameter and vibration response signal dataset includes the circuit parameter vector and bandgap label vector of the nonlinear digital piezoelectric metamaterial; a reverse design network model based on deep learning is constructed; and the reverse design network model based on deep learning is trained based on the circuit parameter and vibration response signal dataset; The circuit parameters of the nonlinear digital piezoelectric metamaterial are obtained according to the trained deep learning-based reverse design network model.

2. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 1, characterized in that: The nonlinear digital piezoelectric metamaterial includes a local resonance unit, an excitation signal sensor, and a response signal sensor. The local resonance units are arranged periodically. Two or more one-dimensional periodically arranged local resonance units constitute multiple vibration control channels. The two or more vibration control channels and their parameter adjustment cause the metamaterial's specified frequency vibration wave to attenuate.

3. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 2, characterized in that: The local resonance unit includes a piezoelectric transducer and a nonlinear shunt circuit. The local resonance unit is periodically arranged on a substrate. The piezoelectric transducer in the local resonance unit is pasted on one side surface of the substrate.

4. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 1, 2 or 3, characterized in that: The piezoelectric transducers in the local resonance unit are respectively connected to the nonlinear shunt circuit, wherein the nonlinear shunt circuit includes a digital part and an analog part, the analog part is constructed using an operational amplifier, a capacitor and a resistor, and the digital part is constructed using a single-chip microcomputer, and the analog part and the digital part are connected using a digital-to-analog conversion module, wherein the upper and lower surfaces of the piezoelectric transducer are respectively connected to the output port and the ground wire of the nonlinear shunt circuit.

5. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 4, characterized in that: The digital part of the nonlinear shunt circuit is implemented by a single chip microcomputer. The digital part converts the nonlinear circuit into the form of a transfer function in the s domain and further discretizes it into a differential equation. The differential equation is: Where y[n] is the output value at the current moment, y[nj] is the output value at the previous nj sampling moments, x[n] is the input value at the current moment, x[ni] is the input value at the previous ni sampling moments, m is the numerator order, n is the denominator order, and b i is the numerator coefficient, a j is the denominator coefficient, K2 is the coefficient of the nonlinear quadratic term, and K3 is the coefficient of the nonlinear cubic term.

6. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 3, characterized in that: The shape of the piezoelectric transducer on the substrate is any one of circular, elliptical, rectangular, diamond, triangular or hexagonal; The shape of the substrate in the local resonance unit is any one of rectangular, square or hexagonal, and the substrate is made of metal.

7. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 2, characterized in that: The number of the vibration control channels is two or more; the number of the local resonance units in each vibration control channel is one.

8. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 1, characterized in that: The reverse design network model based on deep learning is composed of two network models: a pre-trained network and a reverse design network; the circuit parameter vector is used as the input of the pre-trained network, and the bandgap label vector is used as the output of the pre-trained network; The bandgap label vector is used as the input of the reverse design network, and the circuit parameter vector is used as the output of the reverse design network.

9. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 8, characterized in that: The deep learning-based serial pipeline model is trained, including: using the pipeline training method to train the pre-trained network and the reverse design network respectively. The process is divided into the following two stages. In the first stage, the pre-trained network is trained to realize the mapping from the circuit parameters of the nonlinear piezoelectric metamaterial to the bandgap characteristics; in the second stage, the reverse design network and the pre-trained network are constructed into a serial pipeline. First, the reverse design network completes the mapping from the bandgap characteristics to the circuit parameters of the nonlinear piezoelectric metamaterial, and then the output of the reverse design network is used as the input of the pre-trained network to generate new target characteristics; the pre-trained network is a 1DCNN network; the reverse design network is a network composed of a 1DCNN neural network and a Transformer network, including a complete 1DCNN network branch and a Transformer network branch; in the back-propagation process, the adam optimizer is selected, and the learning rate is 0.0001. The loss function of the cascaded network is: Where L is the data length, To reverse engineer the network’s predictions, is the predicted value of the pre-trained network, and λ is the weight assigned to the reverse-engineered network.

10. The method for adaptive vibration suppression of piezoelectric metamaterials based on deep learning reverse design according to claim 9, characterized in that: The trained reverse design network is used to reverse design the shunt circuit parameters of the nonlinear digital piezoelectric metamaterial, thereby realizing customized vibration suppression requirements and forming an intelligent vibration suppression scheme. The specific process includes: first, applying a swept frequency excitation to the structure to select the frequency band that needs to be suppressed, and dividing this frequency band into N equal parts. Then, using MATLAB software, the part that needs to be suppressed is set to 0, and the part that does not need to be suppressed is set to 1. This label vector is input into the trained reverse design network to obtain the predicted circuit parameters. Then, this circuit parameter is written into the microcontroller through online programming to realize the nonlinear digital piezoelectric metamaterial of the corresponding structure. Finally, applying a swept frequency excitation to the structure again can see the customized vibration suppression effect.

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