Design and optimization method of multi-layer resonant composite sound absorption structure for large-capacity high-frequency transformer

Abstract

A design and optimization method for a multilayer resonant composite sound-absorbing structure for a large-capacity high-frequency transformer involves comparing and analyzing the sound absorption performance of different composite sound-absorbing structures to determine the optimal composite sound-absorbing structure. Based on the optimal composite sound-absorbing structure, the porous sound-absorbing material with the best sound absorption performance is determined. A three-dimensional simulation model for the electromagnetic field, structural force field, and acoustic field of a high-frequency transformer is established to analyze the noise characteristics of the high-frequency transformer without a sound-absorbing device and determine the analysis frequency. The optimization variables and objective function of the composite sound-absorbing structure are determined, and a central composite experimental design combined with finite element simulation is used to obtain sound field simulation results for the sound-absorbing device with different structural parameters. A radial basis function neural network model is constructed to determine the influence of different structural parameters on the sound pressure level of the high-frequency transformer. The structural parameters of the optimal composite sound-absorbing device are determined using a sparrow search optimization algorithm that integrates sine, cosine, and Cauchy mutations. This method can reduce the impact of noise on the surrounding environment and power equipment.

Description

Technical Field

[0001] The present invention belongs to the technical field of high-frequency transformer design, and in particular relates to a design and optimization method of a multi-layer resonant composite sound absorption structure of a large-capacity high-frequency transformer. Background Art

[0002] Large-capacity high-frequency transformers are indispensable core equipment in power systems and are of great significance to AC / DC hybrid distribution networks, microgrids, flexible ring networks, etc. However, with the increase in the operating frequency and capacity of high-frequency transformers and the reduction in transformer size, the vibration and noise problems of large-capacity high-frequency transformers under service conditions have become more significant, becoming a technical bottleneck that restricts their ability to achieve higher capacity and efficiency. How to effectively suppress the vibration and noise problems of large-capacity high-frequency transformers and ensure their long-term safe and stable operation is one of the key challenges faced in the design of large-capacity high-frequency transformers. Therefore, it is urgent to study methods for suppressing the noise of large-capacity high-frequency transformers under non-sinusoidal excitation conditions. This research not only has important engineering practical value, but also provides new means and reference basis for the subsequent production of prefabricated cabin substation box materials.

[0003] At present, many scholars at home and abroad have conducted extensive research on transformer noise suppression measures, mainly focusing on the low-frequency noise of power frequency transformers and the medium- and high-frequency noise of medium-frequency transformers.

[0004] (1) In terms of power frequency transformers, since the sound power of power frequency transformers is mainly concentrated in the area below 500Hz, mainly low-frequency noise, active noise reduction has become the main method for suppressing low-frequency noise of power frequency transformers. Literature [1]: Li Cailian. Research on noise characteristics of ultra-high voltage transformers and their active noise reduction system [D]. Hebei University of Technology, 2020. Based on the noise characteristics of a 1000kV transformer, an active noise reduction system was built and an active noise reduction experiment was carried out. A noise reduction effect of 7dB was achieved at the error microphone, verifying the feasibility of the active noise reduction system.

[0005] Reference [2]: Zhong Sicong, Zhu Lihua, Wang Qianchao, et al. Analysis of vibration noise of power transformer and its active noise reduction [J]. Transactions of China Electrotechnical Society, 2022, 37(Supplement 1): 11-21. Considering the magnetization characteristics and magnetostrictive characteristics of the transformer core under different harmonic conditions, the active noise reduction analysis method is used to study the sound field distribution and frequency characteristics around the transformer after noise reduction.

[0006] Reference [3]: Qiu Jiangang. Analysis of power transformer vibration noise and research on noise reduction methods [D]. Nanchang University, 2023. A power transformer sound source radiation model was established and the active noise reduction system was studied to achieve effective noise reduction in the transformer spatial domain.

[0007] The common point of the above-mentioned literature is that they all use active noise reduction to suppress low-frequency noise. However, large-capacity high-frequency transformers are mainly characterized by medium- and high-frequency noise. According to basic acoustic theory, high-frequency noise has a shorter wavelength. Within the same layout range, the required secondary sound sources are more densely distributed and require more channels. However, as the number of channels increases, higher requirements are placed on the system hardware operating speed and control methods. Therefore, active noise reduction systems are not suitable for noise control of large-capacity high-frequency transformers.

[0008] (2) In terms of medium-frequency transformers, medium-frequency transformers are mainly characterized by medium- and high-frequency noise. By laying an acoustic covering layer to absorb energy and weaken medium- and high-frequency noise. Reference [4]: ​​P.Shuai and J.Biela,"Influence ofMaterialPropertiesandGeometricShapeofMagneticCoresonAcousticNoiseEmissionofMedium-FrequencyTransformers,"inIEEETransactionsonPowerElectronics,vol.32,no.10,pp.7916-7931,Oct.2017. The vibration noise of annular, rectangular and elliptical cores under high-frequency sinusoidal wave excitation was measured using a laser scanning vibrometer. The core topology with less vibration noise was selected to control the vibration noise of the medium-frequency transformer from the vibration (acoustic) source. This document mainly considers the vibration noise of annular, rectangular and elliptical cores, and does not cover other possible core shapes. There is a certain degree of randomness. Therefore, it is not possible to control the noise of the transformer simply from the core topology.

[0009] Reference [5]: Wang Tianzheng, Zhang Chao, Zhao Xinzhe, et al. Acoustic metamaterial noise reduction method based on power transformer noise characteristics [J]. High Voltage Electrical Appliances, 2019, 55(11): 277-282. Drawing on the Hilbert curve, a maze-type acoustic metamaterial structure suitable for transformer noise reduction is proposed, which achieves better sound transmission loss, but the complex air channel has high requirements on the material volume.

[0010] Reference [6]: Xie Zelong, Yang Tingfang, Liu Hanyao, et al. Design of transformer noise reduction method based on multi-layer hexagonal MAM [J]. Vibration and Shock, 2024, 43(02): 201-207. A composite sound insulation structure based on multi-layer hexagonal film-type acoustic metamaterial is used to suppress the noise of a 110kV power frequency transformer, and there is a high sound transmission loss at the main frequency point of the noise.

[0011] In summary, most measures to suppress noise in high-frequency transformers use acoustic metamaterials or suppress it from the sound source. Few literature studies the spatial distribution characteristics of noise in transformers in the high-frequency band, nor has a sound-absorbing device designed for suppressing noise in a specific frequency range for large-capacity high-frequency transformers. Therefore, there is an urgent need to study methods for suppressing noise in large-capacity high-frequency transformers under non-sinusoidal excitation conditions, which supplements the design and noise control of large-capacity high-frequency transformers. Summary of the Invention

[0012] To address the problem of active noise reduction systems being unsuitable for addressing the noise reduction of large-capacity high-frequency transformers, this paper provides a design and optimization method for a multilayer resonant composite sound absorption structure for large-capacity high-frequency transformers. Using a 10kVA / 5kHz nanocrystalline alloy iron core high-frequency transformer as the research object, this method designs a novel multilayer resonant composite sound absorption structure that significantly suppresses the transformer's noise. Using a radial basis function neural network model and a sparrow search optimization algorithm combining sine-cosine and Cauchy mutations, the optimal structural parameters of the composite sound absorption device are determined. This method provides a new approach for effectively blocking the propagation of high-frequency transformer noise.

[0013] The technical solution adopted by the present invention is:

[0014] The design and optimization method of a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer includes the following steps:

[0015] Step 1: Based on the transfer matrix method, compare and analyze the sound absorption performance of different composite sound absorption structures to determine the optimal composite sound absorption structure;

[0016] Step 2: Based on the optimal composite sound absorbing structure determined in step 1 and the sound absorption performance of different porous sound absorbing materials in the high frequency band, determine the porous sound absorbing material with the best sound absorption performance;

[0017] Step 3: Establish a three-dimensional simulation solution model of the electromagnetic field, structural force field, and acoustic field of the high-frequency transformer, analyze the noise characteristics of the high-frequency transformer without a sound absorption device, and determine the analysis frequency;

[0018] Step 4: Determine the optimization variables and objective function of the composite sound absorption structure, and use a method combining central composite experimental design with finite element simulation to obtain the sound field simulation results of the sound absorption device under different structural parameters;

[0019] Step 5: By constructing a radial basis function neural network model between the sound pressure level at the high-frequency transformer measurement point and the different structural parameters of the sound absorption device, and based on the global sensitivity analysis technology, the degree of influence of different structural parameters on the sound pressure level of the high-frequency transformer is obtained;

[0020] Step 6: Based on the sparrow search optimization algorithm integrating sine, cosine and Cauchy mutation, the structural parameters of the optimal composite sound absorption device are obtained.

[0021] In step 1, the porous sound absorbing material has the advantages of low density and high porosity, and has excellent high-frequency noise reduction performance, while the micro-perforated sound absorbing board as a resonant sound absorbing structure has good sound absorption performance and a wide range of applications. According to the different stacking orders of the micro-perforated sound absorbing board, the porous sound absorbing material and the closed cavity of a certain depth, the following can be formed: Figure 2 The six different composite sound-absorbing structures shown in structures (a) to (f) are compared and analyzed based on the transfer matrix method to determine the sound absorption performance of the six different composite sound-absorbing structures. Figure 2 The middle structure (c) has the best sound absorption performance;

[0022] Transfer matrix T of micro-perforated sound-absorbing panel MPP for:

[0023]

[0024] Where: Z MPP is the acoustic impedance of the micro-perforated sound-absorbing panel, expressed as:

[0025] Z MPP =r+jωm

[0026] Where: ω is the angular frequency; r and m are the acoustic resistance and acoustic mass of the micro-perforated sound-absorbing panel, respectively, expressed as:

[0027]

[0028] Where: μ is the air kinetic viscosity coefficient, which is 1.56×10 -5 m 2 / s; ρ0 is the air density, which is 1.21kg / m 3 ;

[0029] t, d, p, and b are the thickness, pore size, perforation rate, and hole spacing of the micro-perforated sound-absorbing panel, respectively. For micro-pores arranged in a square and circular shape, the perforation rate p = πd 2 / 4b 2 ; ω is the angular frequency; k is the constant of the micro-perforated sound-absorbing panel, k is expressed as:

[0030]

[0031] Transfer matrix T of porous sound-absorbing materials porous for:

[0032]

[0033] Where: D is the thickness of the porous sound-absorbing material; j is the imaginary unit.

[0034] Z p 、k pare the acoustic impedance and wave number of the porous material, respectively, expressed as:

[0035]

[0036] Where: ω is the angular frequency; ρ(ω) and K(ω) are the effective density and effective bulk modulus of the porous material, respectively;

[0037] The Johnson-Champoux-Allard (JCA) porous media acoustic model is used for calculation, which can be expressed as:

[0038]

[0039] Where: α ∞ , φ, σ, Λ, and Λ1 are the bending factor, porosity, flow resistivity, viscous characteristic length, and thermal characteristic length of the porous sound-absorbing material, respectively; γ, ρ0, η, B, and P0 are the specific heat capacity, density, dynamic viscosity, Prandtl number, and static pressure of air, respectively, which are 1.40 and 1.21 kg / m 3 , 1.84×10 -5 Pa·s, 0.707, 1.01325×10 5 Pa.

[0040] Transfer matrix T of the cavity structure air for:

[0041]

[0042] Where: D1 is the cavity depth; k0 = ω / c0 is the wave number of the cavity; ρ0 and c0 are the air density and sound speed, respectively, which are 1.21 kg / m 3 , 340m / s.

[0043] The rule of the transfer matrix method is: multiply the transfer matrices of each sound absorbing layer in sequence to obtain the transfer matrix T of the overall composite sound absorbing structure. total , and then calculate the surface impedance Z of the composite sound-absorbing structure through the transfer matrix f , and finally calculate the sound absorption coefficient α of the composite sound-absorbing structure.

[0044]

[0045] Where: T1 represents the transfer matrix of the first layer acoustic unit; T2 represents the transfer matrix of the second layer acoustic unit; T3 represents the transfer matrix of the third layer acoustic unit; T n is the transfer matrix of the n-th layer acoustic unit; T 11 Represents the element of the first row and first column of the transfer matrix of the overall composite sound-absorbing structure; T 12Represents the element in the first row and second column of the transfer matrix of the overall composite sound-absorbing structure; T 21 Represents the element in the second row and first column of the transfer matrix of the overall composite sound-absorbing structure; T 22 Represents the element in the second row and second column of the transfer matrix of the overall composite sound-absorbing structure.

[0046]

[0047] Where: Z f =T 11 / T 21 is the surface impedance of the composite sound-absorbing structure; Re(Z f / ρ0c0) represents the real part of the complex number; Im(Z f / ρ0c0) represents the imaginary part of the complex number.

[0048] In step 2, the inner layer of the multi-layer resonant composite sound-absorbing structure designed by the present invention is a porous sound-absorbing material. According to step 1, placing the porous sound-absorbing material before the microperforated sound-absorbing panel improves the sound absorption performance of the composite sound-absorbing structure. Therefore, the present invention selects the stacking order of porous sound-absorbing material + microperforated sound-absorbing panel + cavity to further analyze the sound absorption performance of different porous sound-absorbing materials. The present invention selects two types of foam porous sound-absorbing materials: polyurethane and melamine; two types of fiber materials: lightweight glass wool and blown fiber blanket; and the plastic foam selected in step 1 for sound absorption performance analysis. When melamine foam is selected as the porous sound-absorbing material, the composite sound-absorbing structure achieves a sound absorption coefficient of 0.8353 at 10kHz and an average sound absorption coefficient of 0.8309 in the high-frequency range, significantly outperforming the other four sound-absorbing materials. Therefore, the porous sound-absorbing material selected by the present invention is melamine foam.

[0049] In step 3, according to Figure 3 The high frequency transformer structure diagram shown is as follows Figure 4 The three-dimensional structure of the high-frequency transformer is shown in Figure 5(a). Based on the analysis of steps 1 and 2, a sound-absorbing structure with good sound absorption performance is obtained. A three-dimensional simulation solution model of the electromagnetic field, structural force field and acoustic field of the high-frequency transformer equipped with a multi-layer resonant composite sound-absorbing structure is established. The time domain vibration waveform and noise frequency domain characteristics of the core surface of the high-frequency transformer under non-sinusoidal wave excitation are analyzed. Figure 3 The three measurement points A, B, and C shown in the figure are as follows: Figure 6 The time domain diagram of the core surface vibration acceleration is shown by Figure 6It can be seen that under non-sinusoidal voltage excitation, the vibration acceleration amplitude at point B is the largest, followed by point C. This is primarily due to point B's location at a core corner. The higher magnetic flux density at the inner corner creates a greater magnetostrictive stress, resulting in the largest vibration amplitude under this stress. Point C is located at the transformer core's air gap. Due to the Maxwell force at the air gap cross-section, the cores tend to attract each other, leading to collisions. However, the clamping action on the transformer core causes the vibration acceleration amplitude at this measurement point to be smaller than that at point B. Further analysis of the high-frequency transformer's noise frequency domain characteristics revealed the sound pressure levels at different frequencies, as shown in Table 4. Table 4 shows that the sound pressure level is highest at 10 kHz, so the acoustic field analysis frequency was determined to be 10 kHz.

[0050] The influence of nanocrystalline cut core on the stress characteristics of high-frequency transformers was quantitatively evaluated, and the Maxwell force effects with and without air gaps were obtained as shown in Figures 7(a) and 7(b). As shown in Figures 7(a) and 7(b), when there is no air gap at the end face of the core cut, the Maxwell force is mainly distributed at the inner corner of the core due to the high local magnetic flux density, and the maximum Maxwell force density is 4.77×10 -4 N / m 2 If there is an air gap, a Maxwell force will be generated at the cross section of the air gap, and the maximum Maxwell force density reaches 3.82×10 4 N / m 2 Therefore, when there is an air gap at the end face of the transformer core cut, the Maxwell force is the cause of the transformer core vibration.

[0051] In step 4, the thickness t, pore diameter d, perforation rate p, cavity depth D1, porous material thickness D, and distance M from the sound absorbing structure to the center of the transformer of the micro-perforated plate are used as optimization design variables, and the minimum sound pressure level at the measurement point at the analysis frequency determined in step 3 is used as the optimization goal. From the perspective of engineering practice and application, the value range of each optimization variable is determined as shown in Table 5. The central composite experimental design is used to generate 52 sets of test data. Based on the electromagnetic field-structural force field-acoustic field three-dimensional simulation solution model of the high-frequency transformer equipped with a multi-layer resonant composite sound absorbing structure constructed in step 3, the sound field simulation results of the composite sound absorbing structure under different structural parameters are obtained as shown in Table 6.

[0052] In step 5, the radial basis function (RBF) neural network has been widely used in various disciplines due to its advantages such as simple structure, fast convergence speed, and ability to approximate any nonlinear function. It mainly consists of an input layer, a hidden layer, and an output layer, forming a three-layer feedforward neural network structure, such as Figure 8As shown. By selecting the six optimization variables determined in step 4 as the input layer parameters of the radial basis function (RBF) neural network model, the input layer neurons read the sound pressure levels at the high-frequency transformer measurement points under different structural parameters and transmit them to the hidden layer neurons. The hidden layer neurons convert and process the received data and transmit them to the output layer. The training ends when the total error of the training samples reaches the set standard, thereby establishing a multidimensional nonlinear mapping relationship between the structural parameters of the composite sound absorption device and the sound pressure levels at the high-frequency transformer measurement points, as shown in the following formula.

[0053]

[0054] Where: c n represents the center of the nth hidden layer connection point, σ represents the width of the basis function; ||x m -c n || 2 Represents the squared Euclidean distance between the mth input vector and the center of the nth hidden layer connection point, and the output layer is the output vector y, which is equivalent to the response, ω ij Represents the connection weight from the i-th node in the hidden layer to the j-th node in the output layer.

[0055] Finally, the radial basis function (RBF) neural network model can be used to predict the sound pressure level at the measurement point under different structural parameters of the composite sound absorption device:

[0056] According to the 52 groups of experimental data generated by the central composite experimental design in step 4, 42 groups of data were randomly selected as the training set of the model and the remaining 10 groups of data were used as the prediction set to test the accuracy of the model. Figure 9 、 Figure 10 The RBF model training output and prediction output results are shown. The RBF model can be used to predict the sound pressure level at the measurement point under different structural parameters of the composite sound absorption device.

[0057] In step 5, the relevant evaluation indexes of the total predicted value of the sound pressure level at the measurement point are calculated. The two evaluation indexes used are the root mean square error (RMSE) and the correlation coefficient (R 2 ).

[0058] The formula for calculating the root mean square error is:

[0059]

[0060] The correlation coefficient calculation formula is:

[0061]

[0062] Where: y i is the actual value of the i-th sample; is the predicted value of the i-th estimated sample; is the sample mean.

[0063] Based on the radial basis function (RBF) neural network model constructed in step 5 and using global sensitivity analysis technology, the influence of the total effect index on the output variables is considered to analyze the influence of the six optimization variables determined in step 4 on the sound pressure level of the large-capacity high-frequency transformer. The total effect index is defined as:

[0064]

[0065] Where: X i is the i-th input parameter; Y is about X i Output parameters; represents the conditional variance, where the matrix X ～i Indicates division by X i All input parameters except E X～i Indicates division by X i The expected values ​​of all input parameters except Y|X ～i Represents X ～i Accepts division by X when fixed ～i The output parameter when the external input parameter changes; Var(Y) represents the total variance of Y. Figure 11 The influence of the six optimized variables on the vibration noise of the high-frequency transformer is shown.

[0066] In step 6, according to the radial basis function (RBF) neural network model constructed in step 5, the structural parameters of the optimal composite sound absorption device are obtained based on the sparrow search optimization algorithm (SCSSA) that integrates sine, cosine and Cauchy mutations. The sparrow search optimization algorithm (SCSSA) based on the integration of sine, cosine and Cauchy mutations introduces sine and cosine inertia weights and Cauchy mutation strategies on the basis of the traditional sparrow algorithm, aiming to improve the global search capability and global optimization capability of the algorithm. Compared with the traditional sparrow algorithm, the SCSSA algorithm has better global solution capability and computational efficiency. The specific flow chart of the algorithm is as follows: Figure 12 shown.

[0067] The step search factor of the basic sine and cosine algorithm shows a linear decreasing trend, which is not conducive to balancing the global search and local development capabilities of the sparrow optimization algorithm. Therefore, the step search factor is improved to speed up the acquisition of the optimal solution. The expression is as follows:

[0068]

[0069] Where: r′1 represents the step search factor of the sine-cosine algorithm; η is the adjustment coefficient, η≥1; a is a constant, set to 1; t is the number of iterations; Iter max is the maximum number of iterations.

[0070] Considering that during the entire search process of the SSA algorithm, the update of the positions of the population individuals is usually affected by the current positions, a non-linear weight factor ω1 is introduced to adjust the dependence of the position update on the current individual information, and thus the new position of the discoverer is obtained. The update formula is as follows:

[0071]

[0072] In the formula: Iter max represents the maximum number of iterations; represents the position of the i-th new discoverer sparrow in the j-th dimension at the current iteration number t + 1; r2 ∈ [0, 2π] is a random number that determines the moving distance of the sparrow; r3 ∈ [0, 2π] is a random number that controls the influence of the optimal individual on the next position of the sparrow; is the position of the i-th sparrow in the j-th dimension at the current iteration number t; R2 (R2 ∈ [0, 1]) and ST (ST ∈ [0.5, 1]) represent the warning value and the safety value respectively; R2 < ST indicates that the warning value is small, indicating that no natural enemy has appeared; R2 ≥ ST indicates that the warning value is large, indicating that the natural enemy of the sparrow has appeared; X F-best is the overall optimal position of the current discoverer.

[0073] During the foraging process, followers usually forage around the best discoverer, and at the same time, food competition may also occur, causing followers to become new discoverers. To prevent the algorithm from falling into local optima, a Cauchy mutation strategy is introduced in the follower update formula to improve the global optimization ability. The new follower position update formula is as follows:

[0074]

[0075] In the formula: cauchy(0, 1) is the standard Cauchy distribution function; represents the multiplication meaning; represents the position of the i-th new follower sparrow in the j-th dimension at the current iteration number t + 1; X G-best (t) represents the overall optimal position of the current followers.

[0076] Considering their own safety and the ability to successfully obtain food, sparrows will select 10% - 20% of the individuals from the population for scouting and warning. The position update is as follows:

[0077]

[0078] In the formula: represents the position of the i-th new scout sparrow in the j-th dimension at the current iteration number t + 1; X Z-best (t) represents the overall optimal position of the current scouts; represents the worst overall position of the current scout; β is the step length correction coefficient, which obeys the standard normal distribution; f i This is the fitness of the sparrow at this time; f ω Indicates the overall worst fitness at this time; f g Indicates the overall optimal fitness at this time; when f>f g When f=f g When , it means that the sparrows in the middle of the group sense the threat of natural enemies and should immediately move towards other sparrows to get rid of the danger; k∈(0,1) is a random number; ε is a very small constant.

[0079] Also includes step 7:

[0080] The feasibility of the composite sound absorption structure design is verified by electromagnetic field-structural force field-acoustic field coupling simulation, including:

[0081] The electromagnetic field-structural force field-acoustic field coupling simulation method is adopted. The calculation results of the core surface vibration acceleration in COMSOL are loaded as loads into the pressure acoustic solution module in COMSOL for coupling simulation to verify the noise reduction effect of the multi-layer resonant composite sound-absorbing structure.

[0082] The present invention discloses a method for designing and optimizing a multilayer resonant composite sound-absorbing structure for a large-capacity high-frequency transformer, which has the following beneficial effects: 1) In step 1 of the present invention, the transfer matrix method is a method for evaluating the acoustic performance of a multilayer composite sound-absorbing structure. This method can accurately and precisely analyze and predict the sound absorption effect of the composite sound-absorbing structure at different frequencies. The present invention utilizes the relevant theories of the transfer matrix method to systematically compare and analyze the sound absorption performance of six different composite sound-absorbing structures, comprehensively evaluate the sound absorption characteristics of each structure, and further obtain a sound-absorbing structure with significant sound absorption performance, laying the foundation for further analysis of the sound absorption performance of different porous sound-absorbing materials. This step has high practical value in the design and optimization of multilayer resonant composite sound-absorbing structures.

[0083] 2) Step 2 of the present invention evaluates the high-frequency sound absorption performance of different porous sound-absorbing materials based on the optimal composite sound-absorbing structure. Since the optimal composite sound-absorbing structure has been determined in step 1, the acoustic performance evaluation in step 2 is more targeted and more efficient.

[0084] 3) Step 3 of the present invention comprehensively analyzes the noise characteristics of a high-frequency transformer by establishing a three-dimensional coupled simulation model of the electromagnetic field, structural force field, and acoustic field, thereby resolving the complexities inherent in high-frequency transformer noise analysis and improving the accuracy of noise analysis. Meanwhile, prior art methods for analyzing high-frequency transformer noise often employ single-field simulation or experimental methods. Step 3 comprehensively analyzes the noise characteristics of a high-frequency transformer through multi-field coupled simulation, enabling a comprehensive assessment of its vibration noise characteristics.

[0085] 4) In step 4 of the present invention, by clarifying the optimization variables and objective function of the composite sound absorbing structure and combining it with the central composite experimental design, it is possible to systematically study the effect of different structural parameters of the multilayer resonant composite sound absorbing device on the sound absorption performance and comprehensively evaluate the sound absorption performance of the sound absorbing device.

[0086] 5) Step 5 of the present invention, by constructing a radial basis neural network model, can effectively capture the complex multidimensional nonlinear mapping relationship between the structural parameters of the composite sound absorption device and the sound pressure level of the high-frequency transformer measurement point, and predict the impact of different structural parameters on the sound pressure level of the high-frequency transformer, thereby improving the accuracy of the sound field prediction; at the same time, using global sensitivity analysis technology, it can analyze the structural parameters (optimization variables) that have the greatest impact on the sound pressure level of the measurement point, thereby improving the optimization efficiency;

[0087] 6) In step 6 of the present invention, the algorithm combines the advantages of sine and cosine mutations to enhance global search capabilities and Cauchy mutations to improve search efficiency, and can more comprehensively search for optimization variables, avoid falling into local optimal solutions, and increase the possibility of finding a global optimal solution. BRIEF DESCRIPTION OF THE DRAWINGS

[0088] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0089] Figure 1 This is a flow chart for the design and optimization of the multi-layer resonant composite sound-absorbing structure of the present invention.

[0090] Figure 2 Schematic diagrams of six different multi-layer resonant composite sound absorption structures;

[0091] in:

[0092] 1. Porous material 2. Cavity I 3. Microperforated plate 4. Cavity II 5. Rigid wall 6. Cavity III

[0093] Figure 3 This is a schematic diagram of the high-frequency transformer structure.

[0094] Figure 4 This is the three-dimensional structure diagram of the high-frequency transformer;

[0095] 7-Epoxy resin casting part, 8-Fixed clamp part, 9-Secondary winding, 10-Primary winding, 11-Air gap, 12-Iron core. Figure 5(a) is a three-dimensional diagram of a high-frequency transformer with a multi-layer resonant composite sound absorption structure.

[0096] Figure 5(b) is a plan view of the high-frequency transformer xoy equipped with a multi-layer resonant composite sound-absorbing structure.

[0097] Figure 6 This is the time domain diagram of vibration acceleration at different measurement points on the surface of the high-frequency transformer core.

[0098] Figure 7(a) shows the Maxwell stress distribution of the high-frequency transformer core when there is an air gap;

[0099] Figure 7(b) shows the Maxwell stress distribution of the high-frequency transformer core when there is no air gap.

[0100] Figure 8 Schematic diagram of the basic structure of the radial basis neural network model.

[0101] Figure 9 Output results for radial basis neural network training.

[0102] Figure 10 The output result of radial basis neural network prediction.

[0103] Figure 11 It is the sensitivity of the optimization variables to the optimization target of high-frequency transformer.

[0104] Figure 12 This is the specific flow chart of the SCSSA algorithm.

[0105] Figure 13 These are the sound absorption characteristic curves of different multi-layer resonant composite sound absorption structures.

[0106] Figure 14 This is the sound pressure level cloud diagram of the high-frequency transformer when no composite sound-absorbing structure is installed.

[0107] Figure 15 This is the sound pressure level cloud diagram of the high-frequency transformer when a composite sound-absorbing structure is installed.

[0108] Figure 16 This is the sound pressure level distribution cloud diagram of the high-frequency transformer under the optimal parameters.

[0109] Figure 17 is the polar plot of the sound pressure level. DETAILED DESCRIPTION

[0110] This paper proposes a design and optimization method for a multi-layer resonant composite sound-absorbing structure. This structure is suitable for solving the vibration noise problem of large-capacity high-frequency transformers. The parameters of the multi-layer resonant composite sound-absorbing structure are optimized based on a sparrow search algorithm that integrates sine, cosine, and Cauchy variations. The overall design and optimization flow chart is shown in the figure below. Figure 1 shown.

[0111] A design and optimization method for a multi-layer resonant composite sound-absorbing structure is disclosed. The method is suitable for solving the vibration noise problem of large-capacity high-frequency transformers. The method comprises the following steps: forming six composite sound-absorbing devices with different structures according to the different stacking orders of micro-perforated sound-absorbing panels, porous sound-absorbing materials, and closed cavities of a certain depth; comparing and analyzing the sound absorption characteristics of the six different sound-absorbing devices and four different porous sound-absorbing materials based on the transfer matrix method to determine the multi-layer resonant composite sound-absorbing structure; establishing a three-dimensional simulation solution model of the electromagnetic field, structural force field, and acoustic field of a high-frequency transformer based on the structure to determine the acoustic field analysis frequency; and determining the acoustic field analysis frequency according to the structural characteristics of the composite sound-absorbing device with the thickness t of the micro-perforated panel and the aperture d of the micro-perforated panel. , perforation ratio p, cavity depth D1, porous material thickness D, and the distance M of the sound-absorbing structure from the transformer center are used as optimization variables and the range is determined according to actual conditions. The minimum sound pressure level at the measurement point of 10kHz is set as the optimization goal. A central composite experimental design is combined with the finite element method to obtain sample data. Based on this sample data, an RBF neural network model is constructed to analyze the relationship between the sound pressure level at the high-frequency transformer measurement point and the different structural parameters of the sound-absorbing device. Global sensitivity analysis is used to determine the degree of influence of different structural parameters on the sound pressure level of the high-frequency transformer. Finally, the optimal structural parameters of the composite sound-absorbing device are obtained based on the SCSSA optimization algorithm and verified through simulation. The method of this invention is expected to provide a new technical approach and implementation means for noise control of high-frequency transformers and other power equipment, reducing the impact of noise on the surrounding environment and power equipment.

[0112] Taking a 10kVA / 5kHz nanocrystalline alloy core high-frequency transformer as the research object, the noise suppression effect of the multi-layer resonant composite sound absorption structure on the high-frequency transformer is analyzed. The basic structure is as follows Figure 4 As shown. The primary and secondary windings of the high-frequency transformer are both 40 turns, with a rated voltage of 540V, and are wound with 1mm×4mm flat copper wire; the iron core is made of The nanocrystalline ribbons are wound and the following are listed in Table 1: Figure 3 The relevant dimensional parameters of the high-frequency transformer core are shown.

[0113] Table 1 Dimensional parameters of high-frequency transformer core

[0114]

[0115] Step 1: According to Figure 2 The six different composite sound-absorbing structures shown in the figure are used to compare and analyze the sound absorption performance of the six different composite sound-absorbing structures based on the transfer matrix method. The sound absorption characteristic curves of different structures are shown in Figure 2. Figure 11 As shown in Table 2, the sound absorption performance index statistics are shown in Table 2. By comparison, it can be determined Figure 2 The structure (c) composed of melamine foam porous sound-absorbing material + micro-perforated sound-absorbing board + cavity stacked in sequence has better sound absorption performance.

[0116] Table 2 Comparison of sound absorption performance of different multi-layer resonant composite sound absorption structures

[0117]

[0118] Step 2: Based on the determined Figure 2 The middle structure (c) is a composite sound-absorbing structure. The sound absorption performance of two foam porous sound-absorbing materials, polyurethane and melamine, and two fiber materials, lightweight glass wool and melt-blown fiber blanket, are compared. The sound absorption performance is shown in Table 3 below, and it is determined that the porous sound-absorbing material is melamine material.

[0119] Table 3 Comparison of sound absorption performance of different porous sound-absorbing materials

[0120]

[0121] Step 3: Based on the multi-layer resonant composite sound absorption structure determined in Steps 1 and 2, a three-dimensional simulation solution model of the electromagnetic field, structural force field and acoustic field of the high-frequency transformer is established as shown in Figure 5(a), and the following is obtained: Figure 14 、 Figure 15 The sound pressure level cloud diagram of the high-frequency transformer is shown in Figure 4, with and without a composite sound-absorbing structure. Table 4 shows the sound pressure level at different frequencies, and 10kHz is determined as the sound field analysis frequency.

[0122] Table 4 Sound pressure levels at different frequencies

[0123]

[0124] Step 4: The minimum sound pressure level at the 10 kHz measurement point is selected as the optimization target. Based on the structural characteristics of the composite sound absorption device, structural parameters that may affect its noise suppression effect are selected as optimization variables. These parameters mainly include the thickness t of the micro-perforated plate, the aperture d, the perforation ratio p, the cavity depth D1, the thickness D of the porous material, and the distance M between the sound absorption structure and the center of the transformer. The relevant structural parameters are shown in Figures 5(a) and 5(b).

[0125] The composite sound absorption device has two main constraints: the structural parameters of the microperforated sound absorption panel, which are primarily based on engineering practice and application; and the thickness of the porous sound absorption material, which depends primarily on the actual installation space. Based on these two constraints, the range of values ​​for each optimization variable is determined, as shown in Table 5.

[0126] Table 5 Optimization variable value range

[0127]

[0128] The central composite test design combined with the finite element method was used to obtain 52 sets of test data as shown in Table 6, and the sound field simulation results of the sound absorption device under different structural parameters were obtained;

[0129] Table 6 Calculation results of central composite experimental design

[0130]

[0131] Step 5: Use the data in Table 6 to construct a radial basis function neural network model between the sound pressure level at the high-frequency transformer measurement point and the different structural parameters of the sound absorption device. Randomly select 42 groups of data as the training set of the model and the remaining 10 groups of data as the prediction set to test the accuracy of the model. Figure 9 、 Figure 10 The RMSE between the predicted data and the original data of the RBF neural network model is 0.9302 and R 2 The correlation coefficient of the constructed RBF model is 0.9736. Since the correlation coefficient of the constructed RBF model is close to 1.0, it can be considered that the model has a high degree of fit, thereby verifying the accuracy of its prediction.

[0132] Based on the global sensitivity analysis technology, the influence of different structural parameters on the sound pressure level of high-frequency transformer is obtained. Figure 11 As shown in the figure, it can be seen that the six optimized variables have a certain impact on the vibration noise of the high-frequency transformer, and all the impacts are positive, especially the optimized variable D has a particularly significant impact.

[0133] Step 6: Based on the RBF neural network model solved above, combined with the SCSSA optimization algorithm, the relevant parameters of the optimization algorithm are set as follows: the population size is 50, the maximum number of iterations is 100, the ratio of discoverers to alerters is 0.8 and 0.1 respectively, and the safety threshold is 0.7. The optimal structural parameters of the composite sound absorption device are shown in Table 7 below. The specific flow chart of the algorithm is shown in Figure 12 shown.

[0134] Table 7 Optimal structural parameters

[0135]

[0136] Step 7: Use electromagnetic field-structural force field-acoustic field coupling simulation to obtain the following Figure 16 The sound pressure level distribution cloud diagram of the high-frequency transformer under the optimal parameters is shown. From the results, it can be seen that the composite sound absorption structure has a significant noise suppression effect on the high-frequency transformer, verifying the feasibility of the composite sound absorption structure design.

[0137] In order to further verify the noise suppression effect of the multi-layer resonant composite sound absorption device on the high-frequency transformer under the optimal structural parameters, the sound pressure levels of different measurement points of the high-frequency transformer were extracted with and without the composite sound absorption device. According to the national standard GB / T1094.10-2022, the data extraction points were set on the circumference of the circle 0.3m away from the center of the high-frequency transformer, and a data extraction point was set every 2° and the counterclockwise direction was set as the positive direction. The following results were obtained: Figure 17 The sound pressure level polar diagram shown is composed of Figure 17 It can be clearly seen that the multi-layer resonant composite sound absorption device significantly reduces the overall sound pressure level of the high-frequency transformer, providing a new means and reference basis for the subsequent production of prefabricated cabin-type substation box materials.

Claims

1. Design and optimization method of multi-layer resonant composite sound absorption structure of large-capacity high-frequency transformer, characterized by The following steps are involved: Step 1: Based on the transfer matrix method, compare and analyze the sound absorption performance of different composite sound absorption structures to determine the optimal composite sound absorption structure; Step 2: Based on the optimal composite sound absorbing structure determined in step 1 and the sound absorption performance of different porous sound absorbing materials in the high frequency band, determine the porous sound absorbing material with the best sound absorption performance; Step 3: Establish a three-dimensional simulation solution model of the electromagnetic field, structural force field, and acoustic field of the high-frequency transformer, analyze the noise characteristics of the high-frequency transformer without a sound absorption device, and determine the analysis frequency; Step 4: Determine the optimization variables and objective function of the composite sound absorption structure, and use a method combining central composite experimental design with finite element simulation to obtain the sound field simulation results of the sound absorption device under different structural parameters; Step 5: By constructing a radial basis function neural network model between the sound pressure level at the high-frequency transformer measurement point and different structural parameters of the sound absorption device, the influence of different structural parameters on the sound pressure level of the high-frequency transformer is obtained; Step 6: Based on the sparrow search optimization algorithm integrating sine, cosine and Cauchy mutation, the structural parameters of the optimal composite sound absorption device are obtained.

2. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 1 is characterized in that: In step 1, different composite sound-absorbing structures can be formed according to the stacking order of the micro-perforated sound-absorbing panel, the porous sound-absorbing material, and the closed cavity of a certain depth; the sound absorption performance of the different composite sound-absorbing structures is compared and analyzed based on the transfer matrix method, and it is determined that the structure composed of the melamine foam porous sound-absorbing material, the micro-perforated sound-absorbing panel, and the cavity stacked in this order has the best sound absorption performance; Transfer matrix T of micro-perforated sound-absorbing panel MPP for: Where: Z MPP is the acoustic impedance of the micro-perforated sound-absorbing panel, expressed as: WITH MPP =r+jωm Where: ω is the angular frequency; r and m are the acoustic resistance and acoustic mass of the micro-perforated sound-absorbing panel, respectively, expressed as: Where: μ is the air kinetic viscosity coefficient; ρ0 is the air density; t, d, p, and b are the thickness, pore size, perforation rate, and pore spacing of the micro-perforated sound-absorbing panel, respectively; ω is the angular frequency; and k is the constant of the micro-perforated sound-absorbing panel, which can be expressed as: Transfer matrix T of porous sound-absorbing materials porous for: Where: D is the thickness of the porous sound-absorbing material; j is the imaginary unit; Z p 、k p are the acoustic impedance and wave number of the porous material, respectively, expressed as: Where: ω is the angular frequency; ρ(ω) and K(ω) are the effective density and effective bulk modulus of the porous material, respectively; The Johnson-Champoux-Allard (JCA) porous media acoustic model is used for calculation, which is expressed as: Where: α ∞ , φ, σ, Λ, Λ1 are the bending factor, porosity, flow resistivity, viscous characteristic length and thermal characteristic length of the porous sound absorbing material respectively; γ, ρ0, η, B, P0 are the specific heat capacity, density, dynamic viscosity, Prandtl number and static pressure of air respectively; Transfer matrix T of the cavity structure air for: Where: D1 is the cavity depth; k0 = ω / c0 is the wave number of the cavity; ρ0 and c0 are the air density and sound speed respectively; The rule of the transfer matrix method is: multiply the transfer matrices of each sound absorbing layer in sequence to obtain the transfer matrix T of the overall composite sound absorbing structure. total , and then calculate the surface impedance Z of the composite sound-absorbing structure through the transfer matrix f , and finally calculate the sound absorption coefficient α of the composite sound absorption structure; Where: T1 represents the transfer matrix of the first layer acoustic unit; T2 represents the transfer matrix of the second layer acoustic unit; T3 represents the transfer matrix of the third layer acoustic unit; T n is the transfer matrix of the n-th layer acoustic unit; T 11 Represents the element of the first row and first column of the transfer matrix of the overall composite sound-absorbing structure; T 12 Represents the element in the first row and second column of the transfer matrix of the overall composite sound-absorbing structure; T 21 Represents the element in the second row and first column of the transfer matrix of the overall composite sound-absorbing structure; T 22 Represents the element in the second row and second column of the transfer matrix of the overall composite sound-absorbing structure; Where: Z f =T 11 / T 21 is the surface impedance of the composite sound-absorbing structure; Re(Z f / ρ0c0) represents the real part of the complex number; Im(Z f / ρ0c0) represents the imaginary part of the complex number.

3. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 2 is characterized in that: In step 2, two types of porous sound-absorbing foam materials, polyurethane and melamine, two types of fiber materials, lightweight glass wool and melt-blown fiber blanket, and the plastic foam selected in step 1 were selected for sound absorption performance analysis. When melamine foam was selected as the porous sound-absorbing material, the sound absorption coefficient of the composite sound-absorbing structure reached 0.8353 at 10 kHz and the average sound absorption coefficient in the high-frequency band was as high as 0.8309. The sound absorption performance was significantly better than that of the other four sound-absorbing materials. Therefore, melamine foam was selected as the porous sound-absorbing material.

4. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 3 is characterized by: In step 3, a three-dimensional structure of a high-frequency transformer is constructed according to the structure of the high-frequency transformer. Based on the analysis of steps 1 and 2, a sound-absorbing structure with good sound absorption performance is obtained. A three-dimensional simulation solution model of the electromagnetic field, structural force field, and acoustic field of a high-frequency transformer equipped with a multi-layer resonant composite sound-absorbing structure is established. The time domain vibration waveform and noise frequency domain characteristics of the core surface of the high-frequency transformer under non-sinusoidal wave excitation are analyzed, and the influence of the nanocrystalline cutting core of the high-frequency transformer on the stress characteristics is quantitatively evaluated.

5. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 4 is characterized in that: In step 4, the thickness t, pore diameter d, perforation rate p, cavity depth D1, porous material thickness D, and distance M between the sound-absorbing structure and the transformer center of the micro-perforated plate are used as optimization design variables, and the minimum sound pressure level at the measurement point at the analysis frequency determined in step 3 is used as the optimization target; a central composite experimental design is used to generate multiple groups of test data. And according to the electromagnetic field-structural force field-acoustic field three-dimensional simulation solution model of the high-frequency transformer equipped with a multi-layer resonant composite sound-absorbing structure built in step 3, the sound field simulation results of the composite sound-absorbing structure under different structural parameters are obtained.

6. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 5 is characterized in that: In step 5, by selecting the optimization variables determined in step 4 as the input layer parameters of the radial basis RBF neural network model, the input layer neurons read the sound pressure levels of the high-frequency transformer measurement points under different structural parameters and transmit them to the hidden layer neurons. The hidden layer neurons convert and process the received data and transmit them to the output layer. The training ends when the total error of the training samples reaches the set standard, thus establishing a multi-dimensional nonlinear mapping relationship between the structural parameters of the composite sound absorption device and the sound pressure level of the high-frequency transformer measurement point, as shown in the following formula; Where: c n represents the center of the nth hidden layer connection point, σ represents the width of the basis function; ||x m -c n || 2 Represents the squared Euclidean distance between the mth input vector and the center of the nth hidden layer connection point, and the output layer is the output vector y, which is equivalent to the response, ω ij Represents the connection weight from the i-th node in the hidden layer to the j-th node in the output layer; Finally, the radial basis function (RBF) neural network model can be used to predict the sound pressure level at the measurement point under different structural parameters of the composite sound absorption device.

7. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 6 is characterized in that: In step 5, the relevant evaluation indexes of the total predicted value of the sound pressure level at the measurement point are calculated; the two evaluation indexes used are the root mean square error (RMSE) and the correlation coefficient (R 2 ); The formula for calculating the root mean square error is: The correlation coefficient calculation formula is: Where: y i is the actual value of the i-th sample; is the predicted value of the i-th estimated sample; y i is the sample mean.

8. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 7 is characterized in that: Based on the radial basis function (RBF) neural network model constructed in step 5 and using global sensitivity analysis technology, the influence of the total effect index on the output variables is considered to analyze the influence of the six optimization variables determined in step 4 on the sound pressure level of the large-capacity high-frequency transformer. The total effect index is defined as: Where: X i is the i-th input parameter; Y is about X i Output parameters; represents the conditional variance, where the matrix X ～i Indicates division by X i All input parameters except E X～i Indicates division by X i The expected values ​​of all input parameters except Y|X ～i Represents X ～i Accepts division by X when fixed ～i Output parameter when external input parameter changes; Var(Y) represents the total variance of Y.

9. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 1 is characterized in that: In step 6, the structural parameters of the optimal composite sound absorbing device are obtained based on the radial basis function (RBF) neural network model constructed in step 5 and the sparrow search optimization algorithm (SCSSA) that integrates sine, cosine and Cauchy variations. The SCSSA algorithm (SCSSA) that integrates sine, cosine and Cauchy variations introduces sine, cosine inertia weights and Cauchy variation strategies on the basis of the traditional sparrow algorithm. The step search factor of the basic sine-cosine algorithm shows a linear decreasing trend. Improving the step search factor can speed up the acquisition of the optimal solution. The expression is as follows: Where: r1 represents the step size search factor of the sine-cosine algorithm; η is the adjustment coefficient, η ≥ 1; a is a constant, set to 1; t is the number of iterations; Iter max is the maximum number of iterations; A nonlinear weight factor ω1 is introduced to adjust the dependence of the position update on the current individual information, thereby obtaining the new discoverer position. The update formula is as follows: where: Iter max represents the maximum number of iterations; represents the position of the i-th newly discovered sparrow at the j-th dimension under the current iteration number t+1; r2 is a random number in [0, 2π], determining the moving distance of the sparrow; r3 is a random number in [0, 2π], controlling the influence of the optimal individual on the next position of the sparrow; is the position of the i-th sparrow at the j-th dimension under the current iteration number t; R2 (R2 ∈ [0, 1]) and ST (ST ∈ [0.5, 1]) represent the warning value and the safety value respectively; R2 < ST indicates that the warning value is small, indicating that no natural enemy appears; R2 ≥ ST indicates that the warning value is large, indicating that the natural enemy of the sparrow appears; X F-best is the overall optimal position of the current discoverers; During the foraging process, followers usually forage around the best finder. At the same time, food competition may occur, making the follower become the new finder. To prevent the algorithm from falling into the local optimum, the Cauchy mutation strategy is introduced into the follower update formula to improve the global optimization ability. The new follower position update formula is as follows: Where: cauchy(0,1) is the standard Cauchy distribution function; ⊕ means multiplication; Indicates that at the current iteration number t+1, the i-th new follower sparrow is in the j-dimensional position; X G-best (t) represents the current optimal position of the follower; Considering their own safety and the ability to successfully obtain food, sparrows will select 10% to 20% of the population for reconnaissance and surveillance. The location updates are as follows: Where: Indicates that at the current iteration number t+1, the i-th new scout sparrow is at the j-dimensional position; X Z-best (t) represents the current optimal position of the scout; represents the worst overall position of the current investigator; β is the step length correction coefficient, which obeys the standard normal distribution; f i This is the fitness of the sparrow at this time; f ω Indicates the overall worst fitness at this time; f g Indicates the overall optimal fitness at this time; when f>f g When f=f g When , it means that the sparrows in the middle of the group sense the threat of natural enemies and should immediately move towards other sparrows to get rid of the danger; k∈(0,1) is a random number; ε is a very small constant.

10. The method for designing and optimizing a multi-layer resonant composite sound absorption structure for a large-capacity high-frequency transformer according to claim 1 is characterized in that: It also includes step 7: using electromagnetic field-structural force field-acoustic field coupling simulation to verify the feasibility of the composite sound absorption structure design, specifically including: The electromagnetic field-structural force field-acoustic field coupling simulation method is adopted. The calculation results of the core surface vibration acceleration in COMSOL are loaded as loads into the pressure acoustic solution module in COMSOL for coupling simulation to verify the noise reduction effect of the multi-layer resonant composite sound-absorbing structure.

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