A Machine Learning Optimization Method for a Low-Frequency Sound Absorbing Structure Based on 3D Printing

Abstract

The present invention discloses a machine learning optimization method for a low-frequency sound absorption structure based on three-dimensional printing, belonging to the technical field of artificial intelligence acoustics. The low-frequency sound absorption structure is prepared by photocuring three-dimensional printing of a photosensitive resin material, and includes side slits, extended cavities, circular perforations, resonant cavities, a first partition, a second partition, and a third partition, having good scalability and can be adjusted according to different noise control requirements; through the machine learning optimization method, it is possible to quickly adjust the structural parameters to cope with the noise control task on the premise of ensuring a small size, so as to obtain a significant sound absorption effect in a specific low-frequency band; this application adopts a machine learning method based on a multi-layer perceptron and a genetic algorithm to optimize the geometric parameters of the low-frequency sound absorption structure, and through the use of a commercial finite element solver COMSOL Multiphysics for simulation calculations, further verifies and optimizes the sound absorption performance of the structure.

Description

Technical Field

[0001] The present invention relates to the technical field of artificial intelligence acoustics, and in particular to a machine learning optimization method for a low-frequency sound absorption structure based on three-dimensional printing. Background Art

[0002] With the acceleration of the urbanization process and the expansion of industrial production, the problem of noise pollution has become increasingly serious, and low-frequency noise ranks first among various noise pollution problems. At present, noise suppression structures based on structures such as Helmholtz resonators have been successfully manufactured on a small scale through additive manufacturing technology. However, traditional sound absorption structures cannot use small-sized structures to regulate large-wavelength sound waves, resulting in difficult problems in controlling low-frequency noise. In addition, the parameter design of sound absorption structures requires a large amount of time and economic costs. The booming development of machine learning enables sound absorption structures to control the parameter space through more effective methods to ensure the ultimate achievement of the ideal sound absorption effect. However, it is still difficult to select a neural network architecture that can optimize more effectively with lower computational costs and faster extraction of dataset features. Summary of the Invention

[0003] Technical problems to be solved: Aiming at technical problems such as the long wavelength of low-frequency noise and the difficulty of traditional material sound absorption structures in suppressing and regulating large-wavelength sound waves in the case of small sizes, the present application provides a machine learning optimization method for a low-frequency sound absorption structure based on three-dimensional printing, which is prepared by three-dimensional printing stereolithography technology and has convenient structural parameter adjustment; aiming at the problem of high time and economic costs of traditional structural parameter design, a multi-layer perceptron and a genetic algorithm are combined for machine learning optimization to optimize its structural parameters, and the sound absorption performance is calculated and verified through COMSOL Multiphysics finite element simulation; finally, the optimized structure has an advantage in the sound absorption effect in a specific low-frequency band, realizing the low-frequency noise suppression function on a small-sized unit.

[0004] Technical solution: A machine learning optimization method for a low-frequency sound absorption structure based on three-dimensional printing, the steps are as follows:

[0005] Step 1, construct a low-frequency sound absorption structure for realizing low-frequency sound absorption: The low-frequency sound absorption structure is prepared by three-dimensional photocuring printing with a photosensitive resin material. The low-frequency sound absorption structure is composed of a side slit, an extended cavity, a circular perforation, a resonance cavity, a first partition, a second partition, and a third partition. Among them, the side slit is located 1 mm above the bottom of the right side of the low-frequency sound absorption structure, and the extended cavity extends into the low-frequency sound absorption structure along the side slit to form an extended cavity; the resonance cavity is arranged above the extended cavity, and the bottom surface of the resonance cavity is connected to the top surface of the extended cavity through a circular perforation, and the circular perforation is arranged at one end of the extended cavity away from the side slit; the first partition, the second partition, and the third partition are evenly and staggeredly arranged in the resonance cavity, and the first partition, the second partition, and the third partition are successively relatively far away from the circular perforation; the material density of the low-frequency sound absorption structure is between 1.0 g / cm³ and 1.2 g / cm³, and the Young's modulus is between 2000 MPa and 4000 MPa;

[0006] Step 2: Use the commercial finite element solver COMSOL Multiphysics to simulate and calculate the low-frequency sound absorption structure, set and record the lengths of the first partition, the second partition, and the third partition, calculate the sound absorption performance of the low-frequency sound absorption structure at 200 Hz to 350 Hz, and record the sound absorption performance at a step of 5 Hz; record the sound absorption coefficients at 31 frequencies corresponding to 3 geometric parameters in each group to form a complete data set; the data set contains the geometric parameters of the input features and the sound absorption coefficients of the target output, and is used for the training and verification of subsequent machine learning models;

[0007] Step 3, perform machine learning optimization on the sound absorption performance of the low-frequency sound absorption structure based on a multi-layer perceptron and a genetic algorithm. Specifically, it includes the following sub-steps:

[0008] 3.1. Construct a multi-layer perceptron neural network model to model the mapping relationship between geometric parameters and sound absorption coefficients, train the model with the data set collected in Step 2, and use cross-validation to evaluate the generalization performance of the model, so as to optimize the prediction ability of the model;

[0009] 3.2. Use the genetic algorithm to optimize the geometric parameters and output the optimized geometric parameters;

[0010] Step 4: Substitute the optimized geometric parameters into COMSOL Multiphysics for recalculation and verification, obtain the final sound absorption coefficient distribution curve, and compare it with the sound absorption performance of the initial geometric parameters to verify the optimization effect.

[0011] Preferably, the length of the resonance cavity in the low-frequency sound absorption structure L = 40 - 45 mm, the width W = 23 - 25 mm, the height H = 23 - 25 mm, the height of the side slitt = 1 - 2 mm, the wall thickness of the resonant cavity b = 1 mm, the distance between the circular perforations and the side seam D L = 30 - 40 mm, the diameter of the circular perforations D n = 1 - 2 mm.

[0012] Preferably, the length of the resonant cavity in the low - frequency sound - absorbing structure L = 42 mm, the width W = 24 mm, the height H = 24 mm, the height of the side seam t = 2 mm, the wall thickness of the resonant cavity b = 1 mm, the distance between the circular perforations and the side seam D L = 35 mm, the diameter of the circular perforations D n = 2 mm.

[0013] Preferably, the top and bottom surfaces of the first partition, the second partition, and the third partition are fixedly connected to the top and bottom surfaces inside the resonant cavity respectively.

[0014] Preferably, the right - hand side surfaces of the first partition and the third partition are fixedly connected to the right - hand side surface inside the resonant cavity, and the left - hand side surface of the second partition is fixedly connected to the left - hand side surface inside the resonant cavity.

[0015] Preferably, the extending lengths of the first partition, the second partition, and the third partition inside the resonant cavity are adjustable.

[0016] Preferably, during the calculation process of the commercial finite - element solver COMSOL Multiphysics in step 2, the entire model uses a hard boundary to limit the air domain, the side seam and the circular perforations are selected as narrow regions, the circular perforations use a thermoviscous acoustic interface, a plane wave with an amplitude of 1 Pa is used to simulate the incident harmonic wave, and the Young's modulus attenuation coefficient of the metamaterial is adjusted between 0.02 and 0.3.

[0017] Preferably, the model structure of the multi - layer perceptron neural network model in step 3.1 includes:

[0018] Input layer: The input data contains 3 features, which are the extending lengths of the first partition, the second partition, and the third partition inside the resonant cavity respectively;

[0019] Hidden layer: Two hidden layers are set, and the ReLU activation function is used after each hidden layer. Among them, the first hidden layer contains 64 neurons, and the second hidden layer contains 128 neurons;

[0020] Dropout layer: A Dropout layer is set after each hidden layer with a Dropout probability of 0.5 to reduce overfitting;

[0021] Output layer: Finally, 31 values are output, representing the sound absorption performance in the range of 200 Hz to 350 Hz with a step of 5 Hz.

[0022] Preferably, the model training and validation process of the multi-layer perceptron neural network model in step 3.1 includes:

[0023] Using the mean squared error MSE as the loss function: ;

[0024] Among them, n is the total number of samples in the dataset, taking the value n = 9540; y i is the actual value, is the predicted value; is the L2 regularization term, used to prevent overfitting, where λ is the regularization coefficient, ω represents the weight parameters in the neural network;

[0025] The L2 regularization formula is as follows: ;

[0026] Among them, R(ω) represents the regularization term, ω represents the weight parameters in the neural network; λ is the regularization coefficient, taking the value λ = 10 -5 ; ω j is the j th weight parameter; p is the total number of parameters;

[0027] Using the Adam optimizer to optimize the parameters of the neural network, and its update formula includes:

[0028] (1) Calculation of the first-order and second-order momentum estimates of the gradient:

[0029] m t =β 1 m t-1 + (1 -β 1) g t

[0030] v t =β 2 v t-1+(1 -β 2) g t 2

[0031] wherein, t is the number of iterations; m t is the first-order momentum estimate of the gradient at the t -th iteration, representing the moving average; v t is the second-order momentum estimate of the gradient at the t -th iteration, representing the moving average of the square; m t-1 , v t-1 are the first-order and second-order momentum estimates of the gradient at the t -1-th iteration; β 1 and β 2 are the decay coefficients, with values β 1 = 0.9, β 2 = 0.999; g t is the gradient at the t -th iteration;

[0032] (2) Bias correction: , ;

[0033] wherein, is the first-order momentum after bias correction; is the second-order momentum after bias correction; and are respectively β 1 and β 2 to the t -th power, representing the decay effect of β 1 and β 2 after t iterations;

[0034] (3) Parameter update rule: ;

[0035] wherein, θ t is the model parameter at the t -th update iteration, θ t+1 is the model parameter at the t +1-th update iteration; η is the learning rate, set to η = 0.001; is the smoothing term, with a value of = 10-8 , to avoid a zero denominator;

[0036] The model validation uses the KFold cross - validation method. The dataset is divided into 5 subsets, and 5 - fold cross - validation is used for training and validation. The cross - validation calculation formula is as follows: ;

[0037] Among them, K represents the number of folds of cross - validation, with a value K = 5, score k is the validation score of the k th fold.

[0038] Preferably, for the genetic algorithm described in step 3.2, the initial population size is set to 100, and the number of genetic iterations is 40 generations. The following steps are used to optimize the geometric parameter data:

[0039] (1) Construct the fitness function

[0040] Taking the extension lengths of the first partition, the second partition, and the third partition of the low - frequency sound - absorbing structure in the resonance cavity as inputs, use the trained multi - layer perceptron model to predict the sound - absorption coefficients of the low - frequency sound - absorbing structure at multiple frequencies; determine the fitness value by calculating the total sound - absorption coefficient and combining the sound - absorption performance near the target low - frequency of 200 Hz. The fitness value is represented by the following formula: ;

[0041] Among them, m is the number of frequency points. Frequency points are selected in the range from 200 Hz to 350 Hz with a step of 5 Hz, and the value m = 31; a i is the sound - absorption coefficient at the i th frequency; f peak is the frequency in Hz corresponding to the maximum sound - absorption coefficient; f target is the target frequency, that is, 200 Hz; δ is the penalty factor, with a value δ = 0.2, used to adjust the trade - off between the total sound - absorption coefficient and the deviation from the target frequency;

[0042] Among them, the sound - absorption coefficient is calculated using the following formula: ;

[0043] Among them, the reflection coefficient R is defined as ; Z H is the acoustic impedance of the sound - absorbing structure; Z 0 = ρ 0 c0 is the characteristic impedance of air, where the density of air ρ 0 = 1.21 kg / m 3 , the speed of sound in air c 0 = 343 m / s ;

[0044] (2) Based on the fitness function, optimize by simulating the natural selection process, including:

[0045] Crossover operation: Use the two-point crossover operation cxTwoPoint to perform crossover on individuals, with a crossover probability of 0.5; By randomly selecting two crossover points c 1 and c 2 update the gene expression of the offspring individuals O 1 and O 2 as follows:

[0046] O 1 = P 1[: c 1] + P 2 c 1: c 2] + P 1 c 2:]

[0047] O 2 = P 2[: c 1] + P 1 c 1: c 2] + P 2 c 2:]

[0048] Among them, P 1 and P 2 are the gene sequences of two parent individuals, [: c 1] is the part from the start position of the sequence to before the crossover point c 1; c 1: c 2] is the part of the sequence from the crossover point c 1 to the crossover point c 2; c 2:] is the part of the sequence from the crossover point c 2 to the end of the sequence;

[0049] Mutation operation: Mutate individuals through the Gaussian mutation operation mutGaussian, with a mutation probability of 0.2; For the individual I = x 1, x 2, x 3], each gene xi Perform Gaussian mutation with a probability of 0.2:

[0050] x’ = x + N (0, σ 2 )

[0051] where, N (0, σ 2 ) is Gaussian distributed noise with a mean of 0 and a variance of σ 2 ;

[0052] Selection operation: Through the tournament selection operation selTournament, the tournament size is 3, randomly select 3 individuals from the population { I 1, I 2, I 3}, calculate their fitness values F , and select the individual with the highest fitness:

[0053] I selected = arg max i∈{1,2,3} F ( I i )

[0054] where, I i represents the i th individual selected; F ( I i ) is the fitness function; I i 's fitness value is calculated by the fitness function F ( I i ), arg max i∈{1,2,3} F ( I i ) means to select the individual index in the set { I 1, I 2, I 3} that makes the function F ( I i ) take the maximum value i .

[0055] Compared with the prior art, the present invention has at least the following beneficial effects:

[0056] 1. The low-frequency sound absorption structure of the present invention can quickly adjust the structural parameters to cope with different noise control tasks while ensuring a small size. Aiming at the problem that the wavelength of low-frequency noise is long and the structural size of traditional sound absorption materials is small and cannot effectively control large-wavelength sound waves, compared with traditional sound absorption structures, the low-frequency sound absorption structure of the present invention is prepared by a photosensitive resin metamaterial through three-dimensional printing and photocuring technology, which can effectively suppress low-frequency noise in the case of a small size and achieve better low-frequency noise control. At the same time, the low-frequency sound absorption structure of the present invention has good scalability, and the parameters of the three partitions can be flexibly adjusted, which is convenient for parameter design and optimization through methods such as machine learning to cope with different applications that meet different frequency bands and different noise control requirements.

[0057] 2. The machine learning optimization method combining a multi-layer perceptron and a genetic algorithm used in the present invention can effectively optimize the geometric parameters of the sound absorption structure in a short time. Through the prediction of the neural network model and the adaptive optimization of the genetic algorithm, the time and economic costs in the traditional design method are reduced, and the efficiency and accuracy of the design process are improved. Combining with the commercial finite element solver COMSOL Multiphysics for simulation calculations further verifies and optimizes the performance of the designed sound absorption structure. The optimization scheme integrating the algorithm and simulation calculations can ensure the reliability of the optimization results and avoid the uncertainty and high costs brought by the method that purely relies on experiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic structural diagram of the low-frequency sound absorption structure of the embodiment of the present application.

[0059] Figure 2 It is a structural diagram of the neural network model for predicting sound absorption performance.

[0060] Figure 3 is Figure 1 The sound pressure level diagram calculated by the commercial finite element solver COMSOL Multiphysics for the medium and low-frequency sound absorption structure, with a frequency of 265 Hz.

[0061] Figure 4 It is a comparison diagram of the sound absorption coefficient before and after optimization.

[0062] Description of the reference numerals: 100, low-frequency sound absorption structure; 1, side seam; 2, extended cavity; 3, circular perforation; 4, resonant cavity; 5, first partition; 6, second partition; 7, third partition. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0063] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described in conjunction with the attached Figures 1 - 4 drawings.

[0064] Example 1: As Figure 1 shown, the present invention provides a three-dimensional printed low-frequency sound absorption structure. The low-frequency sound absorption structure 100 is a related structure for realizing low-frequency noise suppression, and is prepared by photocuring three-dimensional printing with a photosensitive resin material. The low-frequency sound absorption structure 100 is composed of a side slit 1, an extended cavity 2, a circular perforation 3, a resonance cavity 4, a first partition 5, a second partition 6, and a third partition 7. Among them, the side slit 1 is provided at a position 1 mm above the bottom of the right side of the low-frequency sound absorption structure 100, and the extended cavity 2 extends into the low-frequency sound absorption structure 100 along the side slit 1 to form the extended cavity 2; the resonance cavity 4 is provided above the extended cavity 2, and the bottom surface of the resonance cavity 4 is connected to the top surface of the extended cavity 2 through the circular perforation 3, and the circular perforation 3 is provided at one end of the extended cavity 2 away from the side slit 1; the first partition 5, the second partition 6, and the third partition 7 are evenly and staggeredly arranged in the resonance cavity 4, and the top and bottom surfaces of the first partition 5, the second partition 6, and the third partition 7 are fixedly connected to the top and bottom surfaces inside the resonance cavity 4 respectively, the right side surfaces of the first partition 5 and the third partition 7 are fixedly connected to the right side surface inside the resonance cavity 4, the left side surface of the second partition 6 is fixedly connected to the left side surface inside the resonance cavity 4, the extending lengths of the first partition 5, the second partition 6, and the third partition 7 in the resonance cavity 4 are adjustable, and the first partition 5, the second partition 6, and the third partition 7 are successively relatively far away from the circular perforation 3; the material density of the low-frequency sound absorption structure 100 is between 1.0 g / cm³ and 1.2 g / cm³ to increase sound damping, and the Young's modulus is between 2000 MPa and 4000 MPa.

[0065] In the low-frequency sound absorption structure 100, the length of the resonance cavity 4 L = 40 - 45 mm, the width W = 23 - 25 mm, the height H = 23 - 25 mm, the height of the side slit 1 t = 1 - 2 mm, the wall thickness of the resonance cavity 4 b = 1 mm, the circular perforation 3 is at a distance of D L = 30 - 40 mm from the side slit 1, and the diameter of the circular perforation 3 D n = 1 - 2 mm.

[0066] In the low-frequency sound absorption structure 100 of the present invention, the parameters of the first partition 5, the second partition 6, and the third partition 7 are convenient to adjust, which is beneficial to optimization using machine learning methods. Combining parameter optimization, a low-frequency sound absorption structure provided by the present invention can regulate large-wavelength sound waves in a smaller size and effectively suppress low-frequency noise.

[0067] Example 2: The present invention also discloses a machine learning optimization method for a three-dimensional printed low-frequency sound absorption structure, including the following steps:

[0068] Step 1: Construct a low-frequency sound absorption structure 100 for realizing low-frequency sound absorption based on the parameters of Embodiment 1. In the low-frequency sound absorption structure 100, the length of the resonant cavity 4 L = 42 mm, the width W = 24 mm, the height H = 24 mm, the height of the side slit 1 t = 2 mm, the wall thickness of the resonant cavity 4 b = 1 mm, the distance between the circular perforation 3 and the side slit 1 D L = 35 mm, the diameter of the circular perforation 3 D n = 2 mm.

[0069] Step 2, finite element calculation and data set collection: The data set uses the commercial finite element solver COMSOL Multiphysics to simulate and calculate the low-frequency sound absorption structure 100. The entire model uses a hard boundary to limit the air domain. The side slit 1 and the circular perforation 3 are selected as narrow areas. At the same time, the circular perforation 3 adopts a thermoviscous acoustic interface. A plane wave with an amplitude of 1 Pa is used to simulate the incident harmonic wave. The Young's modulus attenuation coefficient of the metamaterial is adjusted between 0.02 and 0.3;

[0070] Set and record the lengths of the first partition 5, the second partition 6, and the third partition 7, calculate the sound absorption performance of the low-frequency sound absorption structure 100 from 200 Hz to 350 Hz, and record the sound absorption performance at a step of 5 Hz; record the sound absorption coefficients of 31 frequencies corresponding to 3 geometric parameters in each group to form a complete data set; the data set contains the geometric parameters of the input features and the sound absorption coefficients of the target output, which are used for the training and verification of the subsequent machine learning model. The neural network structure is as Figure 2 shown;

[0071] As Figure 3 shown in the sound pressure level diagram, compared with the sound pressure of 90 dB at the sound source inlet, the sound pressure is concentrated in the resonant cavity area, significantly increased to 106 dB, an increase of 17%, indicating that the sound energy is effectively coupled and controlled in this area; the first partition 5, the second partition 6, and the third partition 7 further optimize the propagation mode of the sound wave in the cavity;

[0072] Step 3, machine learning optimization of the sound absorption performance of the low-frequency sound absorption structure 100 based on a multi-layer perceptron and a genetic algorithm. Specifically, it includes the following sub-steps:

[0073] 3.1. Construct a multi-layer perceptron neural network model to model the mapping relationship between geometric parameters and sound absorption coefficients. Train the model with the data set collected in Step 2, and use cross-validation to evaluate the generalization performance of the model, so as to optimize the prediction ability of the model;

[0074] The structure of the multi - layer perceptron neural network model is as follows Figure 2 shown, and the model structure includes:

[0075] Input layer: The input data contains 3 features, namely the extension lengths of the first partition 5, the second partition 6, and the third partition 7 in the resonant cavity 4;

[0076] Hidden layer: Two hidden layers are set, and the ReLU activation function is used after each hidden layer. Among them, the first hidden layer contains 64 neurons, and the second hidden layer contains 128 neurons;

[0077] Dropout layer: A Dropout layer is set after each hidden layer, and the Dropout probability is 0.5, which is used to reduce overfitting;

[0078] Output layer: Finally, 31 values are output, representing the sound absorption performance in the range of 200 Hz to 350 Hz, with a step size of 5 Hz;

[0079] According to the data set collected in step 2, model training and verification are carried out, and the process includes:

[0080] Use the mean square error MSE as the loss function: ;

[0081] Among them, n is the total number of samples in the data set, n = 9540; y i is the actual value, is the predicted value; is the L2 regularization term, which is used to prevent overfitting. Among them, λ is the regularization coefficient, ω represents the weight parameters in the neural network;

[0082] The L2 regularization formula is as follows: ;

[0083] Among them, R(ω) represents the regularization term, ω represents the weight parameters in the neural network; λ is the regularization coefficient, and λ is set to -5 ; ω j is the j th weight parameter; p is the total number of parameters;

[0084] Use the Adam optimizer to optimize the parameters of the neural network, and its update formula includes:

[0085] (1) Calculation of the first - order and second - order momentum estimates of the gradient:

[0086] m t =β 1 m t-1 + (1 -β 1) g t

[0087] v t =β 2 v t-1 + (1 -β 2) g t 2

[0088] where t is the number of iterations; m t is the first - order momentum estimate of the gradient at the t -th iteration, representing the moving average; v t is the second - order momentum estimate of the gradient at the t -th iteration, representing the moving average of the squares; m t-1 , v t-1 are the first - order and second - order momentum estimates of the gradient at the t -1 - th iteration; β 1 and β 2 are decay coefficients, with values β 1 = 0.9, β 2 = 0.999; g t is the gradient at the t -th iteration;

[0089] (2) Bias correction: , ;

[0090] where is the first - order momentum after bias correction; is the second - order momentum after bias correction; and are respectively β 1 and β 2 to the t -th power, representing the decay effect of β 1 and β 2 after t iterations;

[0091] (3) Parameter update rule: ;

[0092] Among them, θ t is the model parameter of the t th update iteration, θ t+1 while t is the model parameter of the η +1th update iteration; η is the learning rate, set to = 0.001; = 10 -8 is used to avoid the denominator being zero;

[0093] The model is verified using the KFold cross - validation method. The dataset is divided into 5 subsets, and 5 - fold cross - validation is used for training and validation. The cross - validation calculation formula is as follows: ;

[0094] Among them, K represents the number of folds of cross - validation, with a value of K = 5, score k is the validation score of the k th fold;

[0095] 3.2. Optimize the geometric parameters using the genetic algorithm and output the optimized geometric parameters. For the genetic algorithm, the initial population size is set to 100, and the number of genetic iterations is 40 generations. The following steps are used to optimize the geometric parameter data:

[0096] (1) Construct the fitness function

[0097] Taking the extension lengths of the first partition 5, the second partition 6, and the third partition 7 of the low - frequency sound - absorbing structure 100 in the resonance cavity 4 as the input, use the trained multi - layer perceptron model to predict the sound - absorption coefficients of the low - frequency sound - absorbing structure 100 at multiple frequencies; determine the fitness value by calculating the total sound - absorption coefficient and combining the sound - absorption performance near the target low - frequency of 200 Hz. The fitness value is expressed by the following formula: ;

[0098] Among them, m is the number of frequency points, and frequency points are selected in the range from 200 Hz to 350 Hz with a step of 5 Hz, with a value of m = 31; a i is the sound - absorption coefficient at the i th frequency; f peak is the frequency in Hz corresponding to the maximum sound - absorption coefficient; f target is the target frequency, i.e., 200 Hz;δ is the penalty factor, and its value δ = 0.2, which is used to adjust the trade-off between the total absorption coefficient and the deviation from the target frequency;

[0099] The absorption coefficient is calculated using the following formula: ;

[0100] where the reflection coefficient R is defined as ; Z H is the acoustic impedance of the sound absorption structure; Z 0 = ρ 0 c 0 is the characteristic impedance of air, where the density of air ρ 0 = 1.21 kg / m 3 , and the speed of sound in air c 0 = 343 m / s ;

[0101] (2) Based on the fitness function, optimize by simulating the process of natural selection, including:

[0102] Crossover operation: Use the two-point crossover operation cxTwoPoint to perform crossover on individuals, and the crossover probability is 0.5; By randomly selecting two crossover points c 1 and c 2 to update the gene expression of the offspring individuals O 1 and O 2 as follows:

[0103] O 1 = P 1[: c 1] + P 2 c 1: c 2] + P 1 c 2:]

[0104] O 2 = P 2[: c 1] + P 1 c 1: c 2] + P 2 c 2:]

[0105] where P 1 and P 2 are the gene sequences of the two parent individuals, [: c 1] is the part from the start position of the sequence to before the crossover point c 1; c 1:c 2] is the part of the sequence from intersection point c 1 to intersection point c 2; c 2:] is the part of the sequence from intersection point c 2 to the end of the sequence;

[0106] Mutation operation: The individual is mutated through the Gaussian mutation operation mutGaussian with a mutation probability of 0.2; for the individual I = x 1, x 2, x 3], each gene x i undergoes Gaussian mutation with a probability of 0.2:

[0107] x’ = x + N (0, σ 2 )

[0108] where N (0, σ 2 ) is Gaussian distributed noise with a mean of 0 and a variance of σ 2 ;

[0109] Selection operation: Through the tournament selection operation selTournament, the tournament size is 3, and 3 individuals { I 1, I 2, I 3} are randomly selected from the population, and their fitness values F are calculated, and the one with the highest fitness is selected:

[0110] I selected =arg max i∈{1,2,3} F ( I i );

[0111] where I i represents the i -th individual selected; F ( I i ) is the fitness function; I i The fitness value of F ( I i ) is calculated by the fitness function maxi∈{1,2,3} F ( I i ) represents selecting the individual index that makes the function I 1, I 2, I 3} reach the maximum value in the set F ([[]] I i ) i .

[0112] Step 4: As Figure 4 shown, substitute the optimized geometric parameters into COMSOL Multiphysics for recalculation and verification, obtain the final sound absorption coefficient distribution curve, and compare it with the sound absorption performance of the initial geometric parameters to verify the optimization effect;

[0113] As Figure 4 shown, compare the sound absorption coefficients of the sound absorption structure before and after optimization. The effects are as follows: the peak value rises from 0.8604 to 0.9649, an increase of 12.2%; the 3dB bandwidth broadens from 51.4Hz to 55.9Hz, an expansion of 8.8%; the center frequency drops from 292Hz to 267Hz, a decrease of 8.6%. It can be seen that the sound absorption coefficient of the optimized structure is improved, the effective sound absorption range is expanded and shifted towards low frequencies, meeting the design objectives.

[0114] The present invention relates to the field of acoustics, particularly regarding the quantitative analysis of the interaction between sound waves and sound absorption structures and its application in the calculation of sound absorption coefficients. To place the practical application within the framework of basic acoustic theory, the present invention discusses the interaction between sound waves and materials, which is quantitatively described by the key parameter of acoustic impedance. In acoustic theory, acoustic impedance Z H is used to describe the response characteristics of materials to external acoustic excitation. For the calculation of the sound absorption coefficient α of acoustic metamaterials under normal incidence conditions, the present invention adopts the following formula: ;

[0115] where the reflection coefficient R is defined as ; Z H is the acoustic impedance of the sound absorption structure; Z 0 = ρ 0 c 0 is the characteristic impedance of air, and its value is jointly determined by the density ρ 0 of air and the speed of sound c 0 in air. Specifically, the density ρ 0 = 1.21 kg / m 3 , and the speed of sound in airc 0 = 343 m / s ; When the impedance of the sound absorption structure Z H matches the impedance of the air Z 0, a perfect vibration absorption effect can be achieved. Among them, precisely controlling the acoustic impedance of the sound absorption structure plays a crucial role in optimizing its sound absorption performance. The present invention designs a Figure 1 low-frequency sound absorption structure as shown. To avoid parameter redundancy, the acoustic impedance of the sound absorption structure is controlled by designing the lengths of the first partition 5, the second partition 6, and the third partition 7 in the cavity.

[0116] In the entire optimization workflow, the machine learning model is combined with the genetic algorithm. Through model training, cross-validation, iterative optimization, and finite element simulation, a small-sized structure that can not only meet the requirements of low-frequency sound absorption performance but also has good scalability is finally obtained. As Figure 4 shown, the sound absorption coefficient calculated by the formula can be represented by a two-dimensional curve. The peak value of the sound absorption coefficient of the optimized structure increases by 12.2%, and the sound absorption effect is optimized; the 3dB bandwidth expands by 8.8%, and the effective sound absorption range expands; the center frequency decreases by 8.6% and shifts to the low frequency, meeting the design goal.

[0117] The above is the preferred implementation manner of the present invention. It should be noted that for those of ordinary skill in the art of this technology, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing, characterized in that: Here are the steps: Step 1, constructing a low-frequency sound absorbing structure (100) for achieving low-frequency sound absorption: the low-frequency sound absorbing structure (100) is made of a photosensitive resin material through photocuring three-dimensional printing, and the low-frequency sound absorbing structure (100) is composed of a side seam (1), an extended cavity (2), a circular perforation (3), a resonant cavity (4), a first baffle (5), a second baffle (6) and a third baffle (7), wherein the side seam (1) is arranged 1 mm above the bottom of the right side surface of the low-frequency sound absorbing structure (100), and the extended cavity (2) extends along the side seam (1) into the low-frequency sound absorbing structure (100) to form an extended cavity (2); the resonant cavity (4) is formed by a first baffle (5), a second baffle (6) and a third baffle (7). The cavity (4) is arranged above the extended cavity (2); the bottom surface of the resonant cavity (4) and the top surface of the extended cavity (2) are connected via a circular perforation (3); the circular perforation (3) is arranged at an end of the extended cavity (2) away from the side seam (1); the first baffle (5), the second baffle (6) and the third baffle (7) are evenly staggered in the resonant cavity (4); the first baffle (5), the second baffle (6) and the third baffle (7) are relatively far away from the circular perforation (3) in sequence; the material density of the low-frequency sound absorbing structure (100) is between 1.0 g / cm³ and 1.2 g / cm³, and the Young's modulus is between 2000 MPa and 4000 MPa; Step 2: Dataset: Use the commercial finite element solver COMSOL Multiphysics to simulate and calculate the low-frequency sound absorption structure (100), set and record the lengths of the first baffle (5), the second baffle (6) and the third baffle (7), calculate the sound absorption performance of the low-frequency sound absorption structure (100) from 200 Hz to 350 Hz, and record the sound absorption performance in steps of 5 Hz; record the sound absorption coefficients of 31 frequencies corresponding to each group of 3 geometric parameters to form a complete data set; the data set contains the geometric parameters of the input features and the sound absorption coefficient of the target output, which is used for the subsequent training and verification of the machine learning model; Step 3, performing machine learning optimization of the sound absorption performance of the low-frequency sound absorption structure (100) based on a multi-layer perceptron and a genetic algorithm, specifically, comprising the following sub-steps: 3.

1. Construct a multi-layer perceptron neural network model to model the mapping relationship between geometric parameters and sound absorption coefficients, train the model using the data set collected in step 2, and use cross-validation to evaluate the generalization performance of the model, thereby optimizing the prediction ability of the model; 3.

2. Use genetic algorithm to optimize geometric parameters and output optimized geometric parameters; Step 4: Substitute the optimized geometric parameters into COMSOL Multiphysics for recalculation and verification, obtain the final sound absorption coefficient distribution curve, and compare it with the sound absorption performance of the initial geometric parameters to verify the optimization effect.

2. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to claim 1, characterized in that: The length of the resonant cavity (4) in the low-frequency sound absorbing structure (100) is L =40-45mm, width W =23-25mm, height H = 23-25 ​​mm, height of the side seam (1) t = 1-2 mm, the wall thickness of the resonant cavity (4) b = 1mm, circular perforation (3) distance from side seam (1) D L = 30-40 mm, diameter of the circular perforation (3) D n =1-2mm.

3. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to claim 2, characterized in that: The length of the resonant cavity (4) in the low-frequency sound absorbing structure (100) is L =42mm, width W =24mm, height H = 24 mm, height of side seam (1) t = 2 mm, the wall thickness of the resonant cavity (4) b = 1mm, circular perforation (3) distance from side seam (1) D L = 35 mm, diameter of the circular perforation (3) D n =2mm.

4. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to claim 1, characterized in that: The top surface and bottom surface of the first partition plate (5), the second partition plate (6) and the third partition plate (7) are respectively fixedly connected to the top surface and bottom surface inside the resonance cavity (4).

5. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to claim 1, characterized in that: The right side surfaces of the first partition plate (5) and the third partition plate (7) are fixedly connected to the right side surface inside the resonance cavity (4), and the left side surface of the second partition plate (6) is fixedly connected to the left side surface inside the resonance cavity (4).

6. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to claim 1, characterized in that: The first partition plate (5), the second partition plate (6) and the third partition plate (7) have adjustable extension lengths in the resonance cavity (4).

7. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to any one of claims 1 to 6, characterized in that: In the calculation process of the commercial finite element solver COMSOL Multiphysics in step 2, the entire model uses hard boundaries to restrict the air domain. The side slits (1) and circular perforations (3) are selected as narrow areas. At the same time, the circular perforations (3) use the thermoviscous acoustic interface, and a plane wave with an amplitude of 1 Pa is used to simulate the incident harmonics. The Young's modulus attenuation coefficient of the metamaterial is adjusted between 0.02 and 0.

3.

8. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to any one of claims 1 to 6, characterized in that: The model structure of the multilayer perceptron neural network model in step 3.1 includes: Input layer: The input data includes three features, namely, the extension lengths of the first partition (5), the second partition (6), and the third partition (7) in the resonant cavity (4); Hidden layer: Two hidden layers are set, and ReLU activation function is used after each hidden layer. The first hidden layer contains 64 neurons and the second hidden layer contains 128 neurons. Dropout layer: A Dropout layer is set after each hidden layer with a Dropout probability of 0.5 to reduce overfitting; Output layer: The final output is 31 values, representing the sound absorption performance in the range of 200Hz to 350Hz, with a step size of 5Hz.

9. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to any one of claims 1 to 6, characterized in that: The model training and verification process of the multi-layer perceptron neural network model in step 3.1 includes: Use mean square error MSE as the loss function: ； in, n is the total number of samples in the data set, taking n =9540; y i is the actual value, is the predicted value; is the L2 regularization term, which is used to prevent overfitting. λ is the regularization coefficient, ω Represents the weight parameters in the neural network; The L2 regularization formula is as follows: ； in, R(ω) represents the regularization term, ω Represents the weight parameters in the neural network; λ is the regularization coefficient, and its value is λ =10 -5 ; ω j For the j Weight parameters; p is the total number of parameters; The Adam optimizer is used to optimize the parameters of the neural network. The update formula includes: (1) Calculation of first-order and second-order momentum estimates of gradients: m t =β 1 m t-1 + （1 -β 1） g t v t =β 2 v t-1 + （1 -β 2） g t 2 in, t is the number of iterations; m t For the t The first-order momentum estimate of the gradient of the iteration, representing the moving average; v t For the t The second-order momentum estimate of the gradient of the iteration, which represents the moving average of the square; m t-1 , v t-1 The first t -1 iteration of gradient first-order momentum estimation and gradient second-order momentum estimation; β 1 and β 2 is the attenuation coefficient, which is β 1=0.9, β 2=0.999; g t For the t The gradient at iteration ; (2) Deviation correction: ， ； in, is the first-order momentum after bias correction; is the bias-corrected second-order momentum; and They are β 1 and β 2 of t The second square represents β 1 and β 2 Pass t The attenuation effect of the iterations; (3) Parameter update rules: ； in, θ t It is t Update the model parameters of the iteration, θ t+1 The t +1 update iteration of model parameters; η is the learning rate, set to η =0.001; is the smoothing term, The value is = 10 -8 , used to avoid the denominator being zero; The model validation uses the KFold cross-validation method, which divides the data set into 5 subsets and uses 5-fold cross-validation for training and validation. The cross-validation calculation formula is as follows: ； in, K Indicates the number of cross-validation folds, value K =5, score k For the k The verification score of the fold.

10. The machine learning optimization method for low-frequency sound absorption structure based on three-dimensional printing according to any one of claims 1 to 6, characterized in that: In the genetic algorithm described in step 3.2, the initial population size is set to 100, the number of genetic iterations is set to 40, and the following steps are used to optimize the geometric parameter data: (1) Constructing fitness function The extended lengths of the first baffle (5), the second baffle (6) and the third baffle (7) of the low-frequency sound absorbing structure (100) in the resonant cavity (4) are used as inputs, and the sound absorption coefficient of the low-frequency sound absorbing structure (100) at multiple frequencies is predicted using a trained multi-layer perceptron model; the fitness value is determined by calculating the total sound absorption coefficient and combining the sound absorption performance near the target low frequency of 200 Hz; the fitness value is expressed by the following formula: ； in, m is the number of frequency points, and the frequency points are selected in the range of 200Hz to 350Hz with a step size of 5Hz. m =31; a i It is i The sound absorption coefficient of each frequency; f peak is the frequency Hz corresponding to the maximum sound absorption coefficient; f target is the target frequency, i.e. 200 Hz; δ is the penalty factor, with a value of δ =0.2, used to adjust the trade-off between the total sound absorption coefficient and the target frequency deviation; The sound absorption coefficient is calculated using the following formula: ； Among them, the reflection coefficient R Defined as ; Z H is the acoustic impedance of the sound absorbing structure; Z 0= ρ 0 c 0 is the characteristic impedance of air, where the density of air ρ 0=1.21 kg / m 3 , the speed of sound in air c 0=343 m / s ; (2) Based on the fitness function, simulate the natural selection process for optimization, including: Crossover operation: The two-point crossover operation cxTwoPoint is used to cross the individuals, with a crossover probability of 0.5; two crossover points are randomly selected c 1 and c 2 pairs of offspring O 1 and O The gene expression of 2 is updated as follows: O 1= P 1[: c 1]+ P 2[ c 1: c 2]+ P 1[ c 2:] O 2= P 2[: c 1]+ P 1[ c 1: c 2]+ P 2[ c 2:] in, P 1 and P 2 is the gene sequence of two parent individuals, [: c 1] is from the beginning of the sequence to the intersection point c 1 before the part; [ c 1: c 2] For the sequence from the intersection c 1 to the intersection c 2 part between; [ c 2:] is the sequence from the intersection c 2 to the end of the sequence; Mutation operation: The individual is mutated through the Gaussian mutation operation mutGaussian, with a mutation probability of 0.2; for individual I =[ x 1, x 2, x 3], each gene x i Gaussian mutation occurs with probability 0.2: x’ = x + N （0， σ 2 ） in, N (0, σ 2 ) has a mean of 0 and a variance of σ 2 Gaussian distributed noise; Selection operation: Through the tournament selection operation selTournament, the tournament size is 3, and 3 individuals are randomly selected from the population { I 1, I 2, I 3}, calculate its fitness value F , and select the one with the highest fitness: I selected =arg max i∈{1,2,3} F ( I i ) in, I i Indicates the extracted i individual; F ( I i ) is the fitness function; I i The fitness value is determined by the fitness function F ( I i ) is calculated, arg max i∈{1,2,3} F ( I i ) means in the set { I 1, I 2, I 3} Select the function F ( I i ) The individual index with the maximum value i .

Images