Method for predicting relative acoustic impedance of composite micro-perforated panel structure based on proxy model

Abstract

This invention discloses a relative acoustic impedance prediction method for composite microperforated plate structures based on a surrogate model, belonging to the field of vibration and noise control technology. This invention considers the structural parameters of variable cross-section series-parallel composite microperforated plate structures and uses Latin hypercube sampling to generate parameter samples. Relative acoustic impedance data for different structures are obtained through numerical simulation. Fourier series functions are constructed using the relative acoustic impedance data to solve for the fitting coefficients, thus achieving a fit to the relative acoustic impedance. A multi-input / output multilayer perceptron neural network is built to predict the fitting coefficients based on the structural parameters, forming a relative acoustic impedance prediction surrogate model with the fitting coefficients as an intermediate bridge. The relative acoustic impedance prediction method of this invention effectively solves the contradictory problems of high accuracy but long time consumption in numerical simulation of acoustic superstructures, and high requirements for mathematical theory and low accuracy in analytical solution derivation, thus balancing the accuracy and efficiency of acoustic superstructure design.

Description

Technical Field

[0001] This invention relates to a method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model, belonging to the field of vibration and noise control technology. Background Technology

[0002] Micro-perforated acoustic metastructures have advantages such as being lightweight and easy to install, and in recent years they have been increasingly used in scenarios with high requirements for vibration and noise control, such as high-speed trains and helicopters. However, the sound absorption performance of micro-perforated acoustic metastructures is an important factor limiting their widespread application. Therefore, improving the sound absorption performance of micro-perforated acoustic metastructures is of great significance and can expand their application areas, especially in fields with high requirements for vibration and noise control.

[0003] Traditional methods for controlling vibration and noise, such as dampers, vibration isolators, and rigid sheet metal sound insulation, are typically large in size and may have limited effectiveness for certain equipment or parts of equipment (underwater vehicles, dynamic multi-condition applications). Given the frequent occurrence of vibration fatigue and acoustic fatigue, as well as the multi-functional requirements for weight reduction and lightweight mechanical components, superstructures offer significant potential for vibration and noise reduction. They possess advantages such as adjustable sound absorption frequency bands, lightweight materials, and strong design flexibility. However, designing sound-absorbing structures based on numerical simulation requires substantial computational power and time. Furthermore, the analytical solution derivation of the structure relies on strong mathematical skills and ignores many influencing parameters. Therefore, it is necessary to propose a method for predicting acoustic impedance based on numerical simulation. Based on this, the sound absorption coefficient can be obtained, enabling rapid and high-precision design of sound-absorbing superstructures. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the relative acoustic impedance of composite microperforated plate structures based on a surrogate model, so as to replace the numerical model for solving the relative acoustic impedance of composite microperforated plate structures.

[0005] This invention discloses a method for predicting the relative acoustic impedance of a composite micro-perforated plate structure based on a surrogate model. The method includes the following steps:

[0006] Step 1: Based on the established variable cross-section series-parallel composite micro-perforated plate structure model, determine the structural parameters and give the range of values ​​for the structural parameters.

[0007] Step 2: Based on the range of structural parameter values, Latin hypercube sampling is used to uniformly generate parameter samples in the structural parameter variation space;

[0008] Step 3: Conduct numerical simulations based on structural parameter samples to establish a structural parameter-frequency-relative acoustic impedance database;

[0009] Step 4: Based on the structural parameters-frequency-relative acoustic impedance database, construct a mathematical model of the fitting function and calculate the fitting coefficients of the fitting function.

[0010] Step 5: Based on the fitting coefficients of the fitting function and the structural parameter samples, establish a structural parameter-fitting coefficient database, and build a neural network mapping model with structural parameters as input and fitting coefficients as output.

[0011] Furthermore, step 1 also includes the following steps:

[0012] Step 11: Draw a sketch in the modeling software and generate a composite micro-perforated structure model. The outer boundary of the overall structure and the length and width of each substructure are set as known fixed parameters, while the remaining structural parameters are variable parameters.

[0013] Step 12: For each substructure within the structural model, the cavity depth, perforation diameter, and number of perforations are treated as variable structural parameters, with the given parameter value range:

[0014] ;

[0015] Where, N i1 D represents the number of holes in the i1th microperforated plate. j1 Let H be the diameter of the hole in the j1th micro-perforated plate. k1 Represents the k1th variable back cavity depth parameter, where I and J are the number of micro-perforated plates, I=J, and K is the number of variable depth back cavities;

[0016] Make N min =(n 1,L , n 2,L ,…, n I,L ), N max =(n 1,U , n 2,U ,…, n I,U ), N=(N1, N2,…, N I );D min =(d 1,L , d 2,L ,…, d J,L ), D max =(d 1,U , d 2,U ,…, d J,U ), D=(D1, D2,…, D J ); H min =(h 1,L , h 2,L ,…,h K,L ), H max =(h 1,U , h 2,U ,…, hK,U H = (H1, H2, ..., H) K Determine the range of values ​​N for the number of holes in the structural parameters. min ≤N≤N max The range of hole diameter values ​​D min ≤D≤D max The cavity depth range is H. min ≤H≤H max .

[0017] Furthermore, in step 2, based on the range of structural parameters and the Latin hypercube sampling formula, the required sample size M is given, and the upper bound V of each structural parameter value is set. max Lower bound V min As the sampling boundary; the algorithm file is compiled in MATLAB, and the Latin hypercube sampling algorithm file can be run to collect M structural parameter samples S(N, D, H), and the samples are output for numerical simulation.

[0018] The Latin hypercube sampling formula is:

[0019] ;

[0020] Where i2 is the sample number and j2 is the sample dimension. For a standard uniform distribution, For standard uniformly distributed random numbers, A random permutation of 1 to M. These are sampled values.

[0021] Furthermore, step 3 also includes the following steps:

[0022] Step 31: Add the "Pressure Acoustics, Frequency Domain" module to the modeling software, select "Frequency Domain" and "Parametric Scan" to build a simulation model, including a perfectly matched layer model, a background pressure field model, and an acoustic superstructure model, and add air as the material for each domain;

[0023] Step 32: Define the structure parameters N, D, and H in the "Parameters" section of "Global Definition" and give them an initial value within the range of possible values.

[0024] Step 33: Set the relative acoustic impedance expression through "Variables" and set the area value of the acoustic impedance calculation plane through "Integral"; add the "Background Pressure Field", "Plane Wave Radiation", and "Internal Perforated Plate" modules in "Pressure Acoustics, Frequency Domain" and complete the corresponding parameter settings;

[0025] Step 34: Set the simulation frequency band f in the research section, import the generated structural parameter sample S(N, D, H) in the parameterized scan section, and set the scan type to "specified combination";

[0026] Step 35: Click Calculate in the “Parametric Scan” settings box. After the numerical simulation is completed, obtain the real and imaginary parts of the relative acoustic impedance through “Derived Value” in the “Results” section. Export the data in tabular form using “Export”. Each set of structural parameters will obtain a set of frequency-relative acoustic impedance real and imaginary part data. Merge the frequency-relative acoustic impedance real and imaginary part data corresponding to all structural parameter samples S(N, D, H) to obtain the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z).

[0027] Furthermore, step 4 also includes the following steps:

[0028] Step 41: Based on the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), with frequency f as the independent variable and the real and imaginary parts of the relative acoustic impedance as the dependent variables, construct a structure to fit the real part Z of the relative acoustic impedance. real And the imaginary part Z imag The nth order Fourier series:

[0029] ;

[0030] in, , , The coefficients are the fitting function coefficients for the real part of the impedance. For order, , , The coefficients are the fitting function coefficients for the imaginary part of the impedance. For the maximum frequency, Minimum frequency;

[0031] Step 42: Use MATLAB to compile code files to read the frequency-real part data and frequency-imaginary part data from the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), respectively. Fit each set of data and determine the Fourier series fitting coefficients for each set of data. Use the root mean square error (RMSE) as the standard for judging the fitting effect, and adjust the order n to make the fitting error meet the requirements.

[0032] The RMSE of the Fourier series fitting function for impedance is expressed as:

[0033] ;

[0034] in, For frequency points, The impedance value at the k3th frequency point, To fit the impedance value, Let t be real or img, where real represents the real part and img represents the imaginary part. When t is real... , That is, the real part of the impedance value; conversely, the imaginary part of the impedance value.

[0035] Step 43: After determining the order n, run the MATLAB code to obtain the Fourier series fitting coefficients for each set of data, and output them for use in building a neural network model.

[0036] Furthermore, step 5 also includes the following steps:

[0037] Step 51, referring to the construction method of the structural parameter-frequency-relative acoustic impedance database, the fitting coefficients B(a) obtained by fitting the real and imaginary parts of the acoustic impedance using Fourier series are... r, n1 , b r,n , c i, n1 , d i,n Each parameter is associated with a structural parameter sample S(N, D, H), and a structural parameter-coefficient database A2(S, B) is constructed, where n1 = 0, 1, ..., n0.

[0038] Step 52: Divide the structural parameter-coefficient database A2(S, B) into 3 sub-databases, namely the training set A 21 (S, B), Test set A 22 (S, B) and validation set A 23 (S, B), using MATLAB code files to construct a system with structural parameters S(N, D, H) as input and coefficients B(a) as input. r, n1 , b r,n , c i, n1 , d i,n The output is a multi-input multi-output multilayer perceptron neural network model;

[0039] Step 53, using training set A 21 (S, B) Train the network model, adjusting the number of hidden layer nodes p, the number of layers m, and the learning rate l of the neural network model. r Number of iterations I t The root mean square error between given impedance data As a metric for evaluating model training performance:

[0040] ;

[0041] in, For training sample size, To output the number of dimensions, For the first Sample size For the first One output dimension, For network training output, This is the original output;

[0042] Step 54, using test set A 22 Substituting (S, B) into the neural network to test the accuracy and generalization performance of the model, we can achieve a relationship between the structural parameters S(N, D, H) and the fitting coefficients B(a). r, n1 , b r,n , c i, n1 , d i,n High-precision prediction.

[0043] Furthermore, in step 53, a momentum factor is added. The improved mean squared error partial derivative is obtained and used for backpropagation of the neural network and updating the connection weights, thereby accelerating the convergence speed of the network model and enabling the model performance to meet the requirements.

[0044] ;

[0045] This is a momentum factor added to accelerate the convergence speed of the network model.

[0046] Furthermore, the relative acoustic impedance prediction method for composite microperforated plate structures based on the surrogate model also includes:

[0047] Step 6, based on sub-database A 23 Numerical simulations were performed using (S, B) data and compared with the fitting coefficients of the real and imaginary parts predicted in step 5 to verify the effectiveness and correctness of the method of the present invention.

[0048] The beneficial effects achieved by this invention are:

[0049] This invention considers the structural parameters of composite microperforated plate structures and uses Latin hypercube sampling to generate parameter samples. Relative acoustic impedance data for different structures are obtained through numerical simulation. A Fourier series function is constructed using the relative acoustic impedance data to solve for its fitting coefficients, thus achieving a fit to the relative acoustic impedance. A multi-input / output multilayer perceptron neural network is built to predict the fitting coefficients based on the structural parameters, forming a relative acoustic impedance prediction surrogate model with the fitting coefficients as an intermediary bridge. This invention's relative acoustic impedance prediction method effectively solves the contradictory problems of high accuracy but long processing time in acoustic hyperstructure numerical simulation, and high mathematical requirements and low accuracy in analytical solution derivation, thus balancing the accuracy and efficiency of acoustic hyperstructure design. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the relative acoustic impedance prediction method for composite microperforated plate structures based on the surrogate model of the present invention.

[0051] Figure 2 This is a simplified diagram of the composite microperforated plate structure model according to an embodiment of the present invention;

[0052] Figure 3 These are the numerical simulation results of the real and imaginary parts of the relative acoustic impedance of a set of structural parameters of this invention;

[0053] Figure 4 This is a comparison chart of the fitting results of the two sets of numerical simulation data of the real and imaginary parts of relative acoustic impedance in this invention.

[0054] Figure 5 This is a schematic diagram of the multilayer perceptron (MLP) neural network model of the present invention;

[0055] Figure 6 This is a graph of the loss function curve, which is the fitting coefficient of the real part of the relative acoustic impedance data, as the network output of this invention.

[0056] Figure 7 This is a set of comparison charts showing the training effects of the network output of this invention, which is the fitting coefficient of the real part of the relative acoustic impedance data.

[0057] Figure 8 This is a set of test results comparison charts showing the fitting coefficients of the real part of the relative acoustic impedance data as the network output of this invention;

[0058] Figure 9 This is a loss function curve of the network output of the present invention, which is the fitting coefficient of the imaginary part of the relative acoustic impedance data;

[0059] Figure 10 This is a set of comparison charts showing the training effects of the network output of this invention, which is the fitting coefficient of the imaginary part of the relative acoustic impedance data.

[0060] Figure 11 This is a set of test results comparison charts showing the fitting coefficients of the imaginary part of the relative acoustic impedance data as the network output of this invention;

[0061] Figure 12 This is a set of real part data fitting coefficient diagrams obtained from the neural network model to verify the relative acoustic impedance prediction method of this invention;

[0062] Figure 13 This is a set of imaginary part data fitting coefficient diagrams obtained from the neural network model to verify the relative acoustic impedance prediction method of this invention;

[0063] Figure 14 This is a comparison chart of the real part of the relative acoustic impedance predicted by the method of this invention and the numerical simulation data;

[0064] Figure 15 This is a comparison chart of the imaginary part of the relative acoustic impedance predicted by the method of this invention and the numerical simulation data. Detailed Implementation

[0065] The present invention will be further described below with reference to specific embodiments, and the advantages and features of the present invention will become clearer as a result. However, these embodiments are merely exemplary and do not constitute any limitation on the scope of the present invention. Those skilled in the art should understand that modifications or substitutions can be made to the details and form of the technical solutions of the present invention without departing from the spirit and scope of the present invention, but all such modifications and substitutions fall within the protection scope of the present invention.

[0066] Example 1:

[0067] like Figure 1 As shown, a method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model includes the following steps:

[0068] Step 1: Based on the established variable cross-section series-parallel composite micro-perforated plate structure model, determine the structural parameters (N, D, H) and specify the parameter value range N. min ≤N≤N max D min ≤D≤D max H min ≤H≤H max ;

[0069] Specifically, step 1 includes:

[0070] Step 11: Launch COMSOL Multiphysics and enter the modeling interface. Set the length unit at "Geometry 1" to "mm". Draw a sketch at "Geometry 1" and generate a composite micro-perforated plate structure model. The outer boundary of the overall structure and the length and width of each substructure are set as known fixed parameters, while the remaining parameters are variable parameters. For variable parameters, the generated 3D model only represents one state.

[0071] Step 12: For structural parameters such as cavity depth, perforation diameter, and number of perforations of each substructure within the structural model, the given parameter value range is:

[0072]

[0073] Where, N i1 D represents the number of holes in the i1th microperforated plate. j1 Let H be the diameter of the hole in the j1th micro-perforated plate. k1 N represents the k1th variable back cavity depth parameter, where I and J are the number of micro-perforated plates, I=J, and K is the number of variable depth back cavities. min =(n 1,L , n 2,L ,…,n I,L ), N max =(n 1,U , n 2,U ,…, nI,U ), N=(N1, N2,…, N I );D min =(d 1,L , d 2,L ,…, d J,L ), D max =(d 1,U ,d 2,U ,…, d J,U ), D=(D1, D2,…, D J ); H min =(h 1,L , h 2,L ,…, h K,L ), H max =(h 1,U , h 2,U ,…, h K,U H = (H1, H2, ..., H) K ).

[0074] Step 2: Based on the range of structural parameters, Latin hypercube sampling is used to uniformly generate parameter samples S(N, D, H) in the structural parameter variation space.

[0075] Specifically, step 2 includes:

[0076] Based on the range of structural parameters and the Latin hypercube sampling formula, the required sample size M is given, and the upper bound V of each structural parameter value is set. max Lower bound V min As the sampling boundary, an algorithm file is compiled in MATLAB, and the Latin hypercube sampling algorithm file is run to collect M structural parameter samples S(N, D, H), and the samples are output for numerical simulation.

[0077] The Latin hypercube sampling formula is:

[0078]

[0079] Where i2 is the sample number and j2 is the sample dimension. For a standard uniform distribution, For standard uniformly distributed random numbers, A random permutation of 1 to M. These are sampled values.

[0080] Step 3: Conduct numerical simulations based on the structural parameter samples S(N, D, H) to establish a structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z);

[0081] Specifically, step 3 includes:

[0082] Step 31: Add the "Pressure Acoustics, Frequency Domain" module to the physics field in COMSOL Multiphysics. Select "Frequency Domain" and "Parametric Scan" for the study. After entering the modeling interface, change the length unit at "Geometry 1" to "mm". Build a simulation model at "Geometry 1", including the perfect matching layer model, background pressure field model, acoustic superstructure model, etc., and add air as the material for each domain.

[0083] Step 32: Define the structure parameters N, D, and H in the "Parameters" section of "Global Definition" and give them an initial value within the range of possible values.

[0084] Step 33: In the "Definition" section of "Component 1", set the relative acoustic impedance expression through "Variable" and set the area value of the acoustic impedance calculation plane through "Integral"; in the "Pressure Acoustics, Frequency Domain" section, add modules such as "Background Pressure Field", "Plane Wave Radiation", and "Internal Perforated Plate" and complete the corresponding parameter settings.

[0085] Step 34: Set the simulation frequency band in the research area, import the generated structural parameter sample S(N,D,H) in the parameterized scan area, and set the scan type to "specified combination";

[0086] Step 35: Click Calculate in the “Parametric Scan” settings box. After the numerical simulation is completed, obtain the real and imaginary parts of the relative acoustic impedance through “Derived Value” in the “Results” section. Export the data in tabular form using “Export”. Each set of structural parameters will obtain a set of frequency-relative acoustic impedance real and imaginary parts data. Merge the data corresponding to all structural parameter samples S(N, D, H) to obtain the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z).

[0087] Step 4: Based on the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), construct the mathematical model of the fitting function Z=F(f) and solve for the fitting coefficients B(a). r, n1 , b r,n , c i, n1 , d i,n );

[0088] Specifically, step 4 includes:

[0089] Step 41: Based on the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), with frequency f as the independent variable and the real and imaginary parts of the relative acoustic impedance as the dependent variables, construct a structure to fit the real part Z of the relative acoustic impedance. real And the imaginary part Z imag The nth order Fourier series:

[0090]

[0091] Step 42: Use MATLAB to compile code files to read the frequency-real part data and frequency-imaginary part data from the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), respectively. Fit each set of data and determine the Fourier series fitting coefficients for each set of data. Use the root mean square error (RMSE) as the criterion for judging the fitting effect, and adjust the order n to make the fitting error meet the requirements.

[0092] The RMSE of the Fourier series fitting function for impedance is expressed as:

[0093]

[0094] in, For frequency points, The impedance value at the k3th frequency point, To fit the impedance value, Let t be real or img, where real represents the real part and img represents the imaginary part. When t is real... , That is, the real part of the impedance value; conversely, the imaginary part of the impedance value.

[0095] Step 43: After determining the order n, run the MATLAB code to obtain the Fourier series fitting coefficients for each set of data, and output them for use in building a neural network model.

[0096] Step 5, based on the fitting coefficients B(a) of the fitting function r, n1 , b r,n , c i, n1 , d i,n ), and construct a structural parameter-coefficient database A2(S, B) using structural parameter samples S(N, D, H) as input and coefficients B(a) as input. r, n1 , b r,n , c i, n1 , d i,n ) is the output neural network mapping model.

[0097] Specifically, step 5 includes:

[0098] Step 51, referring to the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), the fitting coefficients B(a) obtained by fitting the real and imaginary parts of the acoustic impedance using Fourier series are... r, n1 , b r,n , c i, n1 , d i,nEach parameter corresponds one-to-one with the structural parameter sample S(N, D, H), and a structural parameter-coefficient database A2(S, B) is constructed.

[0099] Step 52: Divide the structural parameter-coefficient database A2(S, B) into 3 sub-databases, namely the training set A 21 (S, B), Test set A 22 (S, B) and validation set A 23 (S, B), using MATLAB code files to construct a system with structural parameters S(N, D, H) as input and coefficients B(a) as input. r, n1 , b r,n , c i, n1 , d i,n The output is a multi-input multi-output multilayer perceptron (MLP) neural network model;

[0100] Step 53, using training set A 21 (S, B) Train the network model, adjusting the number of hidden layer nodes p, the number of layers m, and the learning rate l of the neural network model. r Number of iterations I t Parameters such as the root mean square error between the predicted values ​​of the neural network model and the true labels on the training set of the network model are used. As a metric for evaluating model training performance:

[0101] ;

[0102] Simultaneously add momentum factor The improved mean squared error partial derivative is obtained and used for backpropagation of the neural network and updating the connection weights, thereby accelerating the convergence speed of the network model and ensuring that the model performance meets the requirements, i.e.: ,in This is a momentum factor added to accelerate the convergence speed of the network model.

[0103] Step 54, using test set A 22 Substituting (S, B) into the neural network to test the accuracy and generalization performance of the model, we can achieve a relationship between the structural parameters S(N, D, H) and the fitting coefficients B(a). r, n1 , b r,n , c i, n1 , d i,n High-precision prediction.

[0104] Step 6, based on sub-database A 23 Numerical simulations were performed using (S, B) data and compared with the relative acoustic impedance prediction method of the present invention to verify the effectiveness and correctness of the method of the present invention.

[0105] By applying the above technical solution, and considering fitting the relative acoustic impedance instead of directly fitting the second-order parameter of sound absorption coefficient, this solution can more realistically reflect the acoustic mechanism of the acoustic superstructure and has a certain degree of physical interpretability. Furthermore, by using Fourier series and fitting the real and imaginary parts of the acoustic impedance separately with frequency as the independent variable, without considering structural parameters in the Fourier series, the difficulty of constructing the surrogate model is reduced, ensuring that the order of the fitting function is within a reasonable range and achieving high accuracy. In addition, by establishing a neural network model for mapping the coefficients of the structure-participating fitting function through a multilayer perceptron, the coefficients of the fitting function are cleverly used as a "link" to establish the connection between structural parameters and relative acoustic impedance, indirectly realizing the prediction of relative acoustic impedance by structural parameters.

[0106] In one implementation, with Figure 2 Taking the composite microperforated plate structure shown as an example, the present invention provides the following optional specific embodiments:

[0107] Figure 2 It is a composite micro-perforated plate structure, and its external geometric dimensions are all 50 mm. Figure 2 (b) It can be seen that the upper part consists of two sub-series structures, and the lower part consists of four sub-parallel structures, each of which is composed of two second-level sub-series structures. There are a total of 10 micro-perforated plates, with the number of perforations being N1, N2, N3, N4, N5, N6, N7, N8, N9, and N... 10 The corresponding perforation diameters are D1, D2, D3, D4, D5, D6, D7, D8, D9, and D. 10 The dimension representing the cavity depth of the upper series structure is H1, and the dimensions representing the cavity depth of the secondary sub-series structures within the lower sub-parallel structure are H2, H3, H4, and H5, respectively. There are abrupt changes in cross-section between the perforated plates of the upper sub-series structure and each of the lower sub-parallel structures. By combining the two parts, a variable cross-section series-parallel composite micro-perforated plate structure is formed.

[0108] Step 1: Based on the variable cross-section series-parallel composite micro-perforated plate structure model, determine the structural parameters N, D, and H and specify their value ranges. Specifically:

[0109] First, the hyperstructure model is drawn directly using COMSOL Multiphysics, such as... Figure 2 As shown in the figure. Only the structural parameters N, D, and H are labeled in the figure, totaling 25. The number of perforations in each micro-perforated plate is denoted as N. i (i1=1,2,……,10), the corresponding perforation diameter is D. j1 (j1=1,2,……,10), where the subscript is the perforation plate number, and the parameter representing the depth of the back cavity is H. k1(k1=1,2,……,5). See Table 1 for its range of values.

[0110] Table 1

[0111]

[0112] Step 2: Based on the range of structural parameters, Latin hypercube sampling is used to uniformly generate quantitative parameter samples S(N, D, H) in the structural parameter variation space. Specifically:

[0113] according to Figure 2 In the 3D model of the acoustic superstructure, the minimum number of holes in the two upper perforated plates is defined as N. min1 =30, maximum number of holes is set to N max1 =38, that is, N min1 ≤N1, N2≤N max1 The remaining minimum number of perforations N min2 =5, maximum N max2 =13 The range is: N min2 ≤N3, N4, N5, N6, N7, N8, N9, N 10 ≤N max2 Minimum perforation diameter D min =0.8 mm, maximum D max =1 mm, i.e., D min ≤D1, D2, D3, D4, D5, D6, D7, D8, D9, D 10 ≤D max The minimum value of the position of perforated plate 2 is H. min1 =32 mm, maximum H max1 =36mm, i.e., H min1 ≤H1≤H max1 The perforated plates 4, 6, 8, and 10 have the smallest back cavity depth H. min2 =5mm, maximum value H max2 =25mm are all H min2 ≤H1, H2, H3, H4, H5≤H max2 The sample size was determined to be 200.

[0114] Secondly, the values ​​of the parameters in the j2 dimension for the i2th sample are calculated based on Latin hypercube sampling, where... For a random permutation of j2-dimensional parameters, The sample follows a U(0, 1) distribution, where M is the sample size and has a value of 200. The Latin hypercube sampling formula is:

[0115] (1)

[0116] Next, Mapping to the value space of each parameter generates sampled data, i.e.:

[0117] (2)

[0118] Where V min V is the vector of minimum values ​​for each parameter. max It is the maximum value vector.

[0119] Finally, based on the aforementioned Latin hypercube sampling mathematical model, MATLAB code files were compiled, and given the parameter value ranges in Table 1, a total of 200 sets of sampling data were generated. Table 2 lists some of the collected data.

[0120] Table 2

[0121]

[0122] Step 3: Perform numerical simulation analysis based on the structural parameter sample S(N, D, H) to establish a structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), specifically:

[0123] First, add the "Pressure Acoustics, Frequency Domain" physics module in COMSOL Multiphysics. Select "Frequency Domain" and "Parametric Scan" for the study. After entering the modeling interface, change the length unit in "Geometry 1" to "mm". Build a simulation model in "Geometry 1", including a perfectly matched layer model, a background pressure field model, and an acoustic superstructure model, and add air as the material for each domain. Define structural parameter variables in the "Parameters" section of "Global Definition" and assign any initial value within the range. In the "Definition" section of "Component 1", set the relative acoustic impedance expression through "Variable" and set the area value of the acoustic impedance calculation plane through "Integral". Add modules such as "Background Pressure Field", "Plane Wave Radiation", and "Internal Perforated Plate" in "Pressure Acoustics, Frequency Domain" and complete the corresponding parameter settings.

[0124] Next, import the generated data into COMSOL Multiphysics, set the simulation frequency range to 201~1001Hz, the step size to 10Hz, and the simulation frequency point E. f =81, and a parametric scan was performed. Table 3 lists some of the simulation data for a set of structural parameters. Figure 3 The table presents the numerical simulation results of the real and imaginary parts of the relative acoustic impedance for two sets of structural parameters. The data in the table are rounded to three decimal places.

[0125] Table 3

[0126]

[0127] Step 4: Based on the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), construct the mathematical model of the fitting function Z=F(f) and solve for the fitting coefficients B(a) of the fitting function. r, n1 , b r,n , c i, n1 , d i,n ), n=1,2,…,n0, n1=0,1,…,n0, specifically:

[0128] First, based on the data in Tables 2 and 3, a database A1(N, D, H, fZ) is constructed. Then, an nth-order Fourier series fitting function is created, with frequency as the independent variable and the real and imaginary parts of the relative acoustic impedance as the dependent variables, respectively:

[0129] (3)

[0130] Secondly, MATLAB code files were compiled to read the real and imaginary frequency data from A1(N, D, H, f, Z), and to fit each set of data, determining the Fourier series fitting coefficients for each set. The order n of the Fourier series was adjusted, and the root mean square error (RMSE) was used as the criterion for judging the fitting effect, ensuring that the fitting error of each set was less than 0.5. The formula for calculating the root mean square error (RMSE) is as follows:

[0131] (4)

[0132] Finally, after determining the fitting order n=5, the MATLAB code was run again to obtain the Fourier series fitting coefficients for each set of data. Table 4 lists some of the fitting coefficients and their root mean square error (RMSE). Figure 4 This is a comparison chart of the fitting results of two sets of data.

[0133] Table 4

[0134]

[0135] Step 5, based on the calculated fitting function, the fitting coefficients B(a) r, n1 , b r,n , c i, n1 , d i,n ), and construct a structural parameter-coefficient database A2(S, B) based on structural parameter samples S(N, D, H), specifically:

[0136] By matching the structural parameter samples in Table 2 with the real part fitting coefficients and imaginary part fitting coefficients in Table 4, a structural parameter-coefficient database is constructed.

[0137] Based on the structural parameter-coefficient database A2(S, B), it is divided into 3 sub-databases A21 (S, B), A 22 (S, B), A 23 (S, B), construct the structural parameters S(N, D, H) to the coefficients B(a). r, n1 , b r,n , c i, n1 , d i,n The neural network mapping model is as follows:

[0138] To facilitate neural network training, the structural parameter-coefficient database was randomly divided into three sub-databases for neural network model training, testing, and method validation, respectively. The training set comprised 0.8%, the test set 0.15%, and the validation set 0.05%. Due to the significant differences in the physical meaning of each parameter, all data were normalized using the following formula:

[0139] (4)

[0140] Where y is the original data, y max The maximum value of this type of data, y min It is the minimum value.

[0141] A neural network model is constructed with the following structure: input layer consists of structural parameters S (25 dimensions), output layer consists of fitting coefficients B (11 dimensions), and three hidden layers with nodes q1, q2, and q3 respectively. The connection weight matrix between the input and hidden layers is W1, between hidden layers W2 and W3, and between the input and output layers is W4. The learning rate is l. r The number of iterations is I t The input layer and hidden layers, and the hidden layers and output layer, use a linear propagation mechanism. The activation function of each hidden layer is Leaky ReLU, i.e.:

[0142] (5)

[0143] Where, 0 < <1, x1 is the output of the previous layer network.

[0144] The loss function for the neural network is set to the root mean square value:

[0145] (6)

[0146] Where C1 is the number of training samples and C2 is the number of output dimensions. output It is the network training output, y train This is the original output. Simultaneously, the mean squared value is used for backpropagation of the neural network's error and to update the connection weights, i.e.:

[0147] (7)

[0148] in, This is a momentum factor added to accelerate the convergence speed of the network model.

[0149] Table 5 shows the network model parameters obtained by debugging with the real part fitting coefficients and the imaginary part fitting coefficients as outputs, respectively.

[0150] Table 5

[0151]

[0152] Figure 5 This is a schematic diagram of a neural network model. Figure 6 It is the loss function curve whose output is the real part data fitting coefficients. Figure 7 Here is a set of comparison charts showing the training effects. Figure 8 This is a comparison chart of the test results. Figure 9 The network output is the loss function curve representing the fitting coefficients for the imaginary part of the data. Figure 10 This is a comparison chart of the training effects of a set of data. Figure 11 The table below shows a comparison of the test results. Table 6 lists the root mean square error (RMSE) of the training and test sets. According to the data in the figure and table, the neural network model built in this invention performs well.

[0153] Table 6

[0154]

[0155] Step 6, based on sub-database A 23 Numerical simulations were performed using (S, B) data and compared with relative acoustic impedance prediction methods to verify the effectiveness and correctness of the method of the present invention; specifically:

[0156] Table 7 lists one set of structural parameters used to verify the method of the present invention. These parameters are used as input to the trained neural network model to predict the network output and obtain the coefficients of the fitting function.

[0157] Table 7

[0158]

[0159] Figure 12 , Figure 13 These are the fitting coefficients for the real and imaginary parts of the network prediction, respectively. Based on these fitting coefficients, the expression for the fitting function can be obtained, and further calculations can be performed to obtain the real and imaginary curves of the relative acoustic impedance. Figure 14 , Figure 15 These are comparison graphs showing the real and imaginary parts of the relative acoustic impedance predicted by the method of this invention, and the numerical simulation results. Figure 14 , Figure 15It can be seen that the prediction accuracy of the method of the present invention is high, the method of the present invention is correct, and the prediction of relative acoustic impedance by structural parameters is realized.

[0160] Example 2:

[0161] A method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model includes: a determination module: based on an established variable cross-section series-parallel composite microperforated plate structure model, determining the structural parameters (N, D, H) and specifying the parameter value range N. min ≤N≤N max D min ≤D≤D max H min ≤H≤H max The generation module generates parameter samples S(N, D, H) uniformly across the structural parameter variation space using Latin hypercube sampling, based on the range of structural parameter values. The first establishment module performs numerical simulations based on the structural parameter samples S(N, D, H) to establish a structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z). The construction module constructs a fitting function mathematical model Z=F(f) based on the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z) and calculates the fitting coefficients B(a). r, n1 , b r,n , c i, n1 , d i,n The second module is established based on the fitting coefficients B(a) of the fitting function. r, n1 , b r,n , c i, n1 , d i,n ), structural parameter samples S(N, D, H); Module construction: establish a structural parameter-coefficient database A2(S, B), and construct a system with structural parameters S(N, D, H) as input and coefficients B(a r, n1 , b r,n , c i, n1 , d i,n The output is the neural network mapping model; the verification module is based on sub-library A. 23 Numerical simulations were performed using (S, B) data and compared with the relative acoustic impedance prediction method of the present invention to verify the effectiveness and correctness of the method of the present invention.

[0162] Example 3:

[0163] A processor for running a program, wherein the program executes any of the above-mentioned methods for predicting the relative acoustic impedance of composite microperforated plate structures based on a surrogate model.

[0164] Example 4:

[0165] A computer-readable storage medium includes a stored program that, when the program is executed, controls the device where the computer-readable storage medium is located to execute any of the above-described methods for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model.

[0166] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the scope of protection of the present invention; all technical solutions formed by equivalent transformations or equivalent substitutions fall within the scope of protection of the present invention; the parts of the present invention not described in detail are well-known technologies to those skilled in the art.

Claims

1. A method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model, characterized in that, The relative acoustic impedance prediction method for composite microperforated plate structures based on the surrogate model includes the following steps: Step 1: Based on the established variable cross-section series-parallel composite micro-perforated plate structure model, determine the structural parameters and give the range of values ​​for the structural parameters. Step 2: Based on the range of structural parameter values, Latin hypercube sampling is used to uniformly generate parameter samples in the structural parameter variation space; Step 3: Conduct numerical simulations based on structural parameter samples to establish a structural parameter-frequency-relative acoustic impedance database; Step 4: Based on the structural parameters-frequency-relative acoustic impedance database, construct a mathematical model of the fitting function and calculate the fitting coefficients of the fitting function. Step 5: Based on the fitting coefficients of the fitting function and the structural parameter samples, establish a structural parameter-fitting coefficient database, and build a neural network mapping model with structural parameters as input and fitting coefficients as output.

2. The method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model according to claim 1, characterized in that, Step 1 also includes the following steps: Step 11: Draw a sketch in the modeling software and generate a composite micro-perforated structure model. The outer boundary of the overall structure and the length and width of each substructure are set as known fixed parameters, while the remaining structural parameters are variable parameters. Step 12: For each substructure within the structural model, the cavity depth, perforation diameter, and number of perforations are treated as variable structural parameters, with a given range of values: ； Where, N i1 D represents the number of holes in the i1th microperforated plate. j1 Let H be the diameter of the hole in the j1th micro-perforated plate. k1 Represents the k1th variable back cavity depth parameter, where I and J are the number of micro-perforated plates, I=J, and K is the number of variable depth back cavities; Make N min =(n 1,L , n 2,L ,…, n I,L ), N max =(n 1,U , n 2,U ,…, n I,U ), N=(N1, N2,…, N I );D min =(d 1,L , d 2,L ,…, d J,L ), D max =(d 1,U , d 2,U ,…, d J,U ), D=(D1, D2,…, D J ); H min =(h 1,L , h 2,L ,…,h K,L ), H max =(h 1,U , h 2,U ,…, h K,U H = (H1, H2, ..., H) K Determine the range of values ​​N for the number of holes in the structural parameters. min ≤N≤N max The range of hole diameter values ​​D min ≤D≤D max The cavity depth range is H. min ≤H≤H max .

3. The method for predicting the relative acoustic impedance of a composite micro-perforated plate structure based on a surrogate model according to claim 1, characterized in that, In step 2, based on the range of structural parameters and the Latin hypercube sampling formula, the required sample size M is given, and the upper bound V of each structural parameter value is set. max Lower bound V min As the sampling boundary; the algorithm file is compiled in MATLAB, and the Latin hypercube sampling algorithm file can be run to collect M structural parameter samples S(N, D, H), and the samples are output for numerical simulation. The Latin hypercube sampling formula is: ； Where i2 is the sample number and j2 is the sample dimension. For a standard uniform distribution, For standard uniformly distributed random numbers, A random permutation of 1 to M. These are sampled values.

4. The method for predicting the relative acoustic impedance of a composite micro-perforated plate structure based on a surrogate model according to claim 1, characterized in that, Step 3 also includes the following steps: Step 31: Add the "Pressure Acoustics, Frequency Domain" module to the modeling software, select "Frequency Domain" and "Parametric Scan" to build a simulation model, including a perfectly matched layer model, a background pressure field model, and an acoustic superstructure model, and add air as the material for each domain; Step 32: Define the structure parameters N, D, and H in the "Parameters" section of "Global Definition" and give them an initial value within the range of possible values; Step 33: Set the relative acoustic impedance expression through "Variables" and set the area value of the acoustic impedance calculation plane through "Integral"; add the "Background Pressure Field", "Plane Wave Radiation", and "Internal Perforated Plate" modules in "Pressure Acoustics, Frequency Domain" and complete the corresponding parameter settings; Step 34: Set the simulation frequency band f in the research section, import the generated structural parameter sample S(N, D,H) in the parameterized scan section, and set the scan type to "specified combination"; Step 35: Click Calculate in the "Parametric Scan" settings box. After the numerical simulation is completed, obtain the real and imaginary parts of the relative acoustic impedance through "Derived Values" in the "Results" section. Export the data in tabular form using "Export". Each set of structural parameters will obtain a set of frequency-relative acoustic impedance real and imaginary part data. Merge the frequency-relative acoustic impedance real and imaginary part data corresponding to all structural parameter samples S(N, D, H) to obtain the structural parameter-frequency-relative acoustic impedance database A1(N,D, H, f, Z).

5. The method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model according to claim 1, characterized in that, Step 4 also includes the following steps: Step 41: Based on the structural parameter-frequency-relative acoustic impedance database A1(N, D, H, f, Z), with frequency f as the independent variable and the real and imaginary parts of the relative acoustic impedance as the dependent variables, construct a structure to fit the real part Z of the relative acoustic impedance. real And the imaginary part Z imag The nth order Fourier series: ； in, , , The coefficients are the fitting function coefficients for the real part of the impedance. For order, , , The coefficients are the fitting function coefficients for the imaginary part of the impedance. For the maximum frequency, Minimum frequency; Step 42: Use MATLAB to compile code files to read the frequency-real part data and frequency-imaginary part data from the structural parameter-frequency-relative acoustic impedance database A1(N,D, H, f, Z), respectively. Fit each set of data and determine the Fourier series fitting coefficients for each set of data. Use the root mean square error (RMSE) as the standard for judging the fitting effect, and adjust the order n to make the fitting error meet the requirements. The RMSE of the Fourier series fitting function for impedance is expressed as: ； in, For frequency points, The impedance value at the k3th frequency point, To fit the impedance value, Let t be real or img, where real represents the real part and img represents the imaginary part. When t is real... , That is, the real part of the impedance value; conversely, the imaginary part of the impedance value. Step 43: After determining the order n, run the MATLAB code to obtain the Fourier series fitting coefficients for each set of data, and output them for use in building a neural network model.

6. The method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model according to claim 1, characterized in that, Step 5 also includes the following steps: Step 51, referring to the construction method of the structural parameter-frequency-relative acoustic impedance database, the fitting coefficients B(a) obtained by fitting the real and imaginary parts of the acoustic impedance using Fourier series are... r, n1 , b r,n , c i, n1 , d i,n Each parameter is associated with a structural parameter sample S(N, D, H), and a structural parameter-coefficient database A2(S, B) is constructed, where n1 = 0, 1, ..., n0. Step 52: Divide the structural parameter-coefficient database A2(S, B) into 3 sub-databases, namely the training set A 21 (S,B), Test set A 22 (S, B) and validation set A 23 (S, B), using MATLAB code files to construct a system with structural parameters S(N,D, H) as input and coefficients B(a) as input. r, n1 , b r,n , c i, n1 , d i,n The output is a multi-input multi-output multilayer perceptron neural network model; Step 53, using training set A 21 (S, B) Train the network model, and adjust the number of hidden layer nodes p, the number of layers m, and the learning rate l of the neural network model. r Number of iterations I t The root mean square error between given impedance data As a metric for evaluating model training performance: ； in, For training sample size, To output the number of dimensions, For the first Sample size, For the first One output dimension, For network training output, This is the original output; Step 54, using test set A 22 Substituting (S, B) into the neural network to test the accuracy and generalization performance of the model, we can achieve a relationship between the structural parameters S(N, D, H) and the fitting coefficients B(a). r, n1 , b r,n , c i, n1 , d i,n High-precision prediction.

7. The method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model according to claim 6, characterized in that, In step 53, the momentum factor is added. The improved mean squared error partial derivative is obtained and used for backpropagation of the neural network and updating the connection weights, thereby accelerating the convergence speed of the network model and ensuring that the model performance meets the requirements. ； This is a momentum factor added to accelerate the convergence speed of the network model.

8. The method for predicting the relative acoustic impedance of a composite microperforated plate structure based on a surrogate model according to claim 1, characterized in that, The relative acoustic impedance prediction method for composite microperforated plate structures based on the surrogate model also includes: Step 6, based on sub-database A 23 Numerical simulations were performed using (S, B) data and compared with the fitting coefficients of the real and imaginary parts predicted in step 5 to verify the effectiveness and correctness of the method of the present invention.

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