Porous material parameter identification method based on impedance tube test hardware

Abstract

The invention discloses a porous material parameter identification method based on impedance tube test hardware. The method comprises the following steps: S1, acquiring an original sound pressure signal by using the impedance tube test hardware; s2, performing fast Fourier transform operation on the original test signal set to generate a spectrum feature matrix; s3, constructing a multi-scale Fourier neural operator model, and outputting a multi-scale spectrum feature fusion result; s4, inputting the multi-scale spectrum feature fusion result into an output prediction layer to obtain an initial material parameter prediction result; s5, calculating and reconstructing a spectrum curve in combination with a material acoustics theoretical model, and constructing a target error function; s6, initializing a sparrow search algorithm population to obtain a final optimal neural operator configuration; and S7, updating the multi-scale Fourier neural operator model, performing reasoning operation on the frequency spectrum characteristic matrix again, and outputting a final material parameter identification result. According to the method, a multi-scale neural operator and a sparrow search algorithm are adopted, and high-precision recognition of the acoustic parameters of the porous material is achieved.

Description

Technical Field

[0001] The present invention relates to the technical field of acoustic material parameter identification, and in particular to a porous material parameter identification method based on impedance tube testing hardware. Background Art

[0002] In the research and engineering applications of acoustic material properties, porous materials are widely used in the fields of noise control, acoustic environment regulation and material structure design due to their excellent sound absorption properties. In order to accurately evaluate the acoustic performance parameters of porous materials, such as flow resistivity, porosity, equivalent sound velocity, structure factor and viscosity correction factor, researchers usually use impedance tube testing systems to obtain the acoustic response characteristics of materials under different frequency conditions. The impedance tube experimental method has the advantages of strong controllability and high measurement accuracy, and is widely used in the inversion of material acoustic parameters. In traditional methods, the reflection coefficient and absorption coefficient are usually calculated from the sound pressure signals collected by upstream and downstream microphones based on the transfer function method, and then the relevant parameters are solved by fitting the theoretical model.

[0003] In existing research, most parameter identification methods use least squares fitting to estimate material parameters by optimizing frequency domain errors. While these methods can estimate material parameters, they have limited generalization capabilities for different materials and exhibit significant uncertainty when dealing with nonlinear coupling relationships and non-steady-state frequency response issues. To improve prediction accuracy, some methods attempt to introduce machine learning models to model experimental data, such as neural network regression models based on reflection coefficients or absorption coefficients. However, most of these models ignore frequency band structure and multi-scale characteristics, and are prone to overlooking differences in the acoustic response of materials at different frequency bands, resulting in large prediction errors.

[0004] In recent years, Fourier neural network operators have demonstrated potential in modeling complex frequency-domain responses and are suitable for frequency-domain signal modeling tasks. However, existing technologies often construct Fourier neural network structures using a single-scale approach, making it difficult to integrate the contributions of low-frequency and high-frequency information to material parameter identification, and insufficiently analyzing the spectral response characteristics of porous materials. Furthermore, existing deep model-based recognition schemes rely on manual design of network structures and lack adaptive optimization mechanisms, which can lead to high model complexity or unstable recognition accuracy.

[0005] In terms of model structure optimization, some studies have introduced evolutionary algorithms, such as genetic algorithms and particle swarm optimization, to search for neural network hyperparameters. However, these algorithms have limited search efficiency in high-dimensional structural spaces and fail to combine the objective error function with physical constraints to guide the optimization process, making it difficult to obtain a global optimal solution for the structural configuration. At the same time, the optimization objectives often focus only on minimizing the prediction error and lack joint constraints on frequency domain modeling capabilities and physical consistency. Existing methods also lack a fitness function that jointly evaluates frequency domain residuals, structural complexity, and physical rationality, making it impossible to achieve a coordinated improvement in structural optimization and parameter identification.

[0006] Therefore, how to provide a porous material parameter identification method based on impedance tube testing hardware is a problem that those skilled in the art urgently need to solve. Summary of the Invention

[0007] One purpose of the present invention is to propose a method for identifying parameters of porous materials based on impedance tube testing hardware. The present invention makes full use of the impedance tube acoustic testing device, the fast Fourier transform algorithm, the frequency domain feature extraction mechanism, the multi-scale Fourier neural operator modeling technology and the sparrow search algorithm optimization strategy, and describes in detail the complete process from the acquisition of the sound pressure response signal, the construction of the spectrum feature matrix, the training and reasoning of the neural operator model, the reconstruction and fitting of the acoustic theory model, to the intelligent optimization of the structural parameter configuration and the accurate identification of the final material parameters. This method effectively extracts the multi-scale spectral features in the acoustic signal through multi-band hierarchical modeling and complex domain convolution operations, and at the same time introduces an adaptive structural optimization algorithm to achieve efficient search and dynamic update of the model structure parameters, thereby improving the accuracy and stability of identification. The present invention has the advantages of high recognition accuracy, strong physical consistency of parameters, high model optimization efficiency and wide adaptability to different types of porous materials.

[0008] According to an embodiment of the present invention, a method for identifying porous material parameters based on impedance tube testing hardware includes the following steps:

[0009] S1. Use impedance tube test hardware to acoustically excite the porous material sample to be tested, collect the original sound pressure signal, and generate an original test signal set;

[0010] S2. Perform a fast Fourier transform operation on the original test signal set to generate a spectrum feature matrix;

[0011] S3. Construct a multi-scale Fourier neural operator model, wherein the multi-scale Fourier neural operator model includes multiple parallel Fourier convolution sublayers, each of which receives components of the spectrum feature matrix in a low-frequency subband, a mid-frequency subband, and a high-frequency subband, and outputs a multi-scale spectrum feature fusion result;

[0012] S4. Input the multi-scale spectral feature fusion result into the output prediction layer of the multi-scale Fourier neural operator model, perform a forward propagation operation, and obtain the initial material parameter prediction result;

[0013] S5. Based on the initial material parameter prediction results, the material acoustic theoretical model is combined to calculate and reconstruct the spectrum curve and construct the target error function;

[0014] S6. Initialize the sparrow search algorithm population, set each sparrow individual to represent a neural operator configuration of a multi-scale Fourier neural operator model and optimize it to obtain the final optimal neural operator configuration;

[0015] S7. Based on the final optimal neural operator configuration, update the multi-scale Fourier neural operator model, re-perform the inference operation on the spectral feature matrix, and output the final material parameter identification result.

[0016] Optionally, the original test signal set includes an excitation sound source signal, a sound pressure response signal collected by a first position microphone, a sound pressure response signal collected by a second position microphone, a sampling time label, a channel number identifier, and a signal collection sequence number;

[0017] The excitation sound source signal is a broadband excitation signal applied by an impedance tube speaker; the sound pressure response signal collected by the first position microphone is a sound pressure time series collected by an acoustic measuring point located on the upstream side of the porous material to be measured; and the sound pressure response signal collected by the second position microphone is a sound pressure time series collected by an acoustic measuring point located on the downstream side of the porous material to be measured.

[0018] Optionally, the S2 specifically includes:

[0019] S21, performing equally spaced discrete sampling on the excitation sound source signal, the sound pressure response signal collected by the first position microphone, and the sound pressure response signal collected by the second position microphone in the original test signal set to obtain corresponding excitation signal sequences, first sound pressure sequences, and second sound pressure sequences;

[0020] S22, performing fast Fourier transform operations on the excitation signal sequence, the first sound pressure sequence, and the second sound pressure sequence, respectively, to obtain complex spectrum data of each sequence in the frequency domain, thereby obtaining an excitation spectrum, a first sound pressure spectrum, and a second sound pressure spectrum;

[0021] S23. Calculate the complex reflection coefficient, absorption coefficient, and transfer function value at each frequency point based on a transfer function method, where the complex reflection coefficient is calculated as the complex ratio of the first and second sound pressure spectra, the absorption coefficient is the unit value minus the square of the reflection coefficient modulus, and the transfer function is the complex ratio of the second sound pressure spectrum to the first sound pressure spectrum;

[0022] S24. Arrange the complex reflection coefficient, absorption coefficient, and transfer function value in order from low to high frequency to construct a spectrum feature matrix.

[0023] Optionally, the S3 specifically includes:

[0024] S31. Construct a multi-scale Fourier neural operator model, wherein the multi-scale Fourier neural operator model includes multiple sets of parallel Fourier convolution sublayers, a frequency domain channel fusion module, and an output prediction layer;

[0025] S32, dividing the spectrum feature matrix into three frequency domain sub-matrices: low frequency sub-band, medium frequency sub-band, and high frequency sub-band according to frequency, inputting each into the corresponding Fourier convolution sub-layer, and performing frequency domain feature modeling operation;

[0026] S33. Each Fourier convolution sublayer performs frequency domain projection on the input subband data, maps each input frequency vector to a complex frequency domain channel, and performs complex multiplication convolution. The convolution kernel weight is represented by a complex parameter to generate a subband feature output.

[0027] S34, inputting the sub-band feature output of each sub-band convolution sub-layer into the frequency domain channel fusion module, performing spectrum feature splicing and nonlinear mapping operations, and obtaining a multi-scale spectrum feature fusion result;

[0028] S35. Input the multi-scale spectrum feature fusion result into the output prediction layer, where the output prediction layer is composed of a set of complex fully connected mapping units and outputs a corresponding set of material parameters.

[0029] Optionally, the S33 specifically includes:

[0030] S331, assuming that the input data of the spectrum feature matrix in the kth frequency sub-band is a real-valued frequency domain vector sequence X k (f), where k∈{low frequency, medium frequency, high frequency}, f represents the frequency variable;

[0031] S332, input frequency domain vector X k (f) Perform complex frequency domain transform operation to obtain complex spectrum representation Z k (f), where each element contains amplitude information and phase information;

[0032] S333, define the Fourier convolution kernel weight as W k , where each weight value represents the frequency domain convolution kernel response coefficient at the corresponding frequency point, and the convolution kernel size matches the subband channel dimension;

[0033] S334. Perform a Fourier convolution operation on the complex spectrum input data in each frequency subband in the frequency dimension. Centered on the current frequency point, select the complex spectrum input values ​​corresponding to the current frequency point and several adjacent frequency points before and after it to construct a frequency local window. Within the frequency local window, perform a complex multiplication operation on the input complex value of each frequency point by a preset complex convolution kernel weight. Perform a weighted sum of all product results along the frequency dimension to obtain a subband frequency domain convolution output result.

[0034] S335. Apply a complex domain activation function to the sub-band frequency domain convolution output result to generate a sub-band feature output.

[0035] Optionally, the initial material parameter prediction results include flow resistivity, porosity, equivalent sound velocity, structure factor and viscosity correction factor; the flow resistivity indicates the magnitude of the viscous resistance encountered by air in the process of penetrating the porous material structure; the porosity describes the proportional relationship between the internal pore volume and the total volume of the porous material; the equivalent sound velocity reflects the equivalent propagation speed of sound waves when propagating in the porous material; the structure factor characterizes the influence of the internal microstructure morphology of the material on the length of the sound wave propagation path; the viscosity correction factor corrects the viscous damping effect encountered by air when propagating in the pores of the material.

[0036] Optionally, the S5 specifically includes:

[0037] S51. Receive initial material parameter prediction results, and calculate a set of frequency domain response eigenvalues ​​corresponding to the predicted parameters based on a theoretical acoustic model of the porous material, wherein the frequency domain response eigenvalues ​​include a theoretical reflection coefficient, a theoretical absorption coefficient, and a theoretical acoustic impedance at each frequency point;

[0038] S52. Based on the physical relationship between various parameter variables in the acoustic theoretical model of the porous material, a theoretical response curve of the material is calculated according to the input material parameters and frequency, and a reconstructed spectrum curve is generated;

[0039] S53, matching the reconstructed spectrum curve with the measured reflection coefficient and absorption coefficient in the spectrum feature matrix frequency by frequency point, and constructing a frequency domain residual mapping relationship;

[0040] S54. Define a coupled residual function for jointly evaluating the deviation relationship between material parameter prediction and frequency domain physical response, and construct a target error function, wherein the target error function is composed of a complex reflection error term, an absorption error term, and a physical compatibility regularization term:

[0041]

[0042] in, is the target error function, i is the frequency point index, N fis the total number of frequency sampling points, λ1 is the reflection coefficient error, λ2 is the absorption coefficient error, λ3 is the weight parameter of the regularization term, R recon (f i ) is the reconstructed reflection coefficient, R meas (f i ) is the measured reflection coefficient, α recon (f i ) is the reconstruction absorption coefficient, α meas (f i ) is the measured absorption coefficient, Ω(P init ) is the parameter regularization term, P init is the prediction result of initial material parameters, f i is the i-th frequency sampling point.

[0043] Optionally, the S6 specifically includes:

[0044] S61. Define the structural search space of the multi-scale Fourier neural operator model, which is composed of the neural operator configurations of multiple Fourier convolution sublayers. The neural operator configurations include the number of convolution kernels, the Fourier channel dimension and the activation function encoding, and construct the structural parameter configuration vector S j ;

[0045] S62, use Latin hypercube sampling to initialize the sparrow search algorithm population, construct multiple sparrow individuals, each sparrow individual corresponds to a neural operator configuration S j , and respectively give the marks of discoverer role, joiner role and vigilant role;

[0046] S63, constructing a fitness function, wherein the fitness function is based on the target error function and introduces a structural complexity penalty term and a physical constraint penalty term of the initial material parameter prediction result;

[0047] S64, performing a position update operation on all sparrow individuals, recalculating the fitness value of the structural parameter configuration vector after each round of update, and recording the current global optimal neural operator configuration;

[0048] S65. When the fitness function value converges to the preset threshold θ or reaches the maximum number of iterations N, the final optimal neural operator configuration S is output. best .

[0049] Optionally, the location update operation includes discoverer individual update, joiner individual update and alerter individual update;

[0050] The discoverer individual update performs an exponential decrease strategy to search global structural parameters for sparrow individuals with the discoverer role; the joiner individual update introduces position perturbation to optimize local structural parameters for sparrow individuals marked as joiner roles; the guard individual update uses Gaussian perturbation combined with a jumping search strategy to update sparrows with the guard role.

[0051] Optionally, the S7 specifically includes:

[0052] S71, based on the final optimal neural operator configuration S best , replacing the original multi-scale Fourier neural operator model structure configuration to obtain a multi-scale Fourier neural operator model with updated structure;

[0053] S72, inputting the spectral feature matrix as input data into the multi-scale Fourier neural operator model after the structure update, performing Fourier domain convolution operations through each Fourier convolution sublayer in turn, and obtaining an updated multi-scale spectral feature fusion result;

[0054] S73, inputting the updated multi-scale spectrum feature fusion result into the output prediction layer, performing a forward propagation operation, and obtaining the final material parameter identification result;

[0055] S74. The final material parameter identification results include flow resistivity, porosity, equivalent sound velocity, structure factor and viscosity correction factor.

[0056] The beneficial effects of the present invention are:

[0057] The porous material parameter identification method based on impedance tube testing hardware proposed in the present invention has achieved systematic improvements in the accuracy of acoustic performance parameter inversion, modeling efficiency and physical consistency of the results. By performing a fast Fourier transform on the original sound pressure response signal, a spectral feature matrix containing complex reflection coefficients, absorption coefficients and transfer functions is obtained, and a stable mapping relationship from experimental data to frequency domain features is established to ensure that the input data has high precision and high availability. A multi-scale Fourier neural operator model is further used to perform parallel modeling of low-frequency, medium-frequency and high-frequency sub-bands of spectral features. The local frequency response characteristics of each sub-band are extracted through complex frequency domain convolution, which effectively retains the coupling relationship between frequencies and enhances the modeling ability of complex acoustic behaviors.

[0058] During the model inference process, the initially identified material parameters are used as input. Combined with the material acoustics theoretical model, the theoretical reflection and absorption curves are calculated. A joint residual error function is constructed, introducing reflection error, absorption error, and parameter regularization terms to achieve comprehensive constraints on the prediction results, thereby improving the physical rationality and interpretability of the material parameter output results. At the same time, the sparrow search algorithm is used to optimize the structural parameters of the multi-scale Fourier neural operator model. Combined with Latin hypercube sampling and role allocation mechanisms, the convergence efficiency of structural search in high-dimensional space is effectively improved. The fitness function incorporates structural complexity penalties and parameter physical constraints on the basis of error measurement, enabling the final model to achieve an optimal balance between accuracy, complexity control, and physical consistency.

[0059] By combining the above methods, the present invention not only achieves high-precision identification of the acoustic parameters of porous materials, but also ensures the stability of the spectral modeling process and the engineering applicability of the output results. This method demonstrates strong capabilities in processing non-stationary frequency domain data, extracting complex material response characteristics, and optimizing neural model structures, providing reliable technical support for parameter acquisition of porous materials in noise control and sound absorption material design. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0061] Figure 1 This is a flow chart of the porous material parameter identification method based on impedance tube testing hardware proposed in the present invention;

[0062] Figure 2 This is a schematic diagram of the functional modules of the multi-scale Fourier neural operator model structure in the porous material parameter identification method based on impedance tube testing hardware proposed in the present invention;

[0063] Figure 3 This is a processing flow chart of the sparrow search algorithm optimizing the neural operator configuration in the porous material parameter identification method based on impedance tube testing hardware proposed in the present invention. DETAILED DESCRIPTION

[0064] The present invention will now be described in further detail with reference to the accompanying drawings, which are simplified schematic diagrams that illustrate the basic structure of the present invention in a schematic manner.

[0065] refer to Figure 1-3 , a porous material parameter identification method based on impedance tube testing hardware includes the following steps:

[0066] S1. Use impedance tube test hardware to acoustically excite the porous material sample to be tested, collect the original sound pressure signal, and generate an original test signal set;

[0067] S2. Perform a fast Fourier transform operation on the original test signal set to generate a spectrum feature matrix;

[0068] S3. Construct a multi-scale Fourier neural operator model, wherein the multi-scale Fourier neural operator model includes multiple parallel Fourier convolution sublayers, each of which receives components of the spectrum feature matrix in a low-frequency subband, a mid-frequency subband, and a high-frequency subband, and outputs a multi-scale spectrum feature fusion result;

[0069] S4. Input the multi-scale spectral feature fusion result into the output prediction layer of the multi-scale Fourier neural operator model, perform a forward propagation operation, and obtain the initial material parameter prediction result;

[0070] S5. Based on the initial material parameter prediction results, the material acoustic theoretical model is combined to calculate and reconstruct the spectrum curve and construct the target error function;

[0071] S6. Initialize the sparrow search algorithm population, set each sparrow individual to represent a neural operator configuration of a multi-scale Fourier neural operator model and optimize it to obtain the final optimal neural operator configuration;

[0072] S7. Based on the final optimal neural operator configuration, update the multi-scale Fourier neural operator model, re-perform the inference operation on the spectral feature matrix, and output the final material parameter identification result.

[0073] The porous material parameter identification method based on impedance tube testing hardware provided by the present invention can achieve high-precision, automated identification of key acoustic parameters of porous materials. By integrating a multi-scale Fourier neural operator model with a sparrow search algorithm, deep mining of frequency domain features and efficient optimization of model structure are achieved, improving the accuracy of parameter prediction and the generalization ability of the model. The proposed method effectively overcomes the strong reliance on manual experience, low recognition efficiency, and poor adaptability of traditional parameter identification, significantly improving the automation and intelligence level of porous material parameter testing, and providing reliable data support for material acoustic performance evaluation and product development.

[0074] In this embodiment, the original test signal set includes an excitation sound source signal, a sound pressure response signal collected by a first position microphone, a sound pressure response signal collected by a second position microphone, a sampling time label, a channel number identifier, and a signal collection sequence number;

[0075] The excitation sound source signal is a broadband excitation signal applied by an impedance tube speaker; the sound pressure response signal collected by the first position microphone is a sound pressure time series collected by an acoustic measuring point located on the upstream side of the porous material to be measured; and the sound pressure response signal collected by the second position microphone is a sound pressure time series collected by an acoustic measuring point located on the downstream side of the porous material to be measured.

[0076] This method achieves comprehensive acquisition of the acoustic pressure response at both ends of a porous material by synchronously collecting acoustic signals at multiple points within an impedance tube. The use of broadband excitation and multi-channel labeling effectively improves the integrity and timing accuracy of signal data. The collected acoustic pressure time series, combined with sampling labels, provides a precise data foundation for subsequent spectrum analysis and parameter identification, significantly enhancing the reliability and automation of material acoustic property measurements.

[0077] In this embodiment, S2 specifically includes:

[0078] S21, performing equally spaced discrete sampling on the excitation sound source signal, the sound pressure response signal collected by the first position microphone, and the sound pressure response signal collected by the second position microphone in the original test signal set to obtain corresponding excitation signal sequences, first sound pressure sequences, and second sound pressure sequences;

[0079] S22, performing fast Fourier transform operations on the excitation signal sequence, the first sound pressure sequence, and the second sound pressure sequence, respectively, to obtain complex spectrum data of each sequence in the frequency domain, thereby obtaining an excitation spectrum, a first sound pressure spectrum, and a second sound pressure spectrum;

[0080] S23. Calculate the complex reflection coefficient, absorption coefficient, and transfer function value at each frequency point based on a transfer function method, where the complex reflection coefficient is calculated as the complex ratio of the first and second sound pressure spectra, the absorption coefficient is the unit value minus the square of the reflection coefficient modulus, and the transfer function is the complex ratio of the second sound pressure spectrum to the first sound pressure spectrum;

[0081] S24. Arrange the complex reflection coefficient, absorption coefficient, and transfer function value in order from low to high frequency to construct a spectrum feature matrix, wherein the spectrum feature matrix uses the three types of frequency domain features corresponding to each frequency point as matrix column vectors.

[0082] This method obtains complex spectrum data in the frequency domain by performing equally spaced sampling and fast Fourier transforms on a multi-channel acoustic signal sequence. The transfer function method is then used to accurately calculate the complex reflection coefficient, absorption coefficient, and transfer function value at each frequency point. The three core frequency domain features are systematically integrated into a feature matrix, providing a high-dimensional, high-resolution data foundation for subsequent parameter identification. This process effectively improves the accuracy of parameter extraction and the scientific and automated level of acoustic performance analysis for porous materials.

[0083] In this embodiment, S3 specifically includes:

[0084] S31. Construct a multi-scale Fourier neural operator model, wherein the multi-scale Fourier neural operator model includes multiple sets of parallel Fourier convolution sublayers, a frequency domain channel fusion module, and an output prediction layer;

[0085] S32, dividing the spectrum feature matrix into three frequency domain sub-matrices: low frequency sub-band, medium frequency sub-band, and high frequency sub-band according to frequency, inputting each into the corresponding Fourier convolution sub-layer, and performing frequency domain feature modeling operation;

[0086] S33. Each Fourier convolution sublayer performs frequency domain projection on the input subband data, maps each input frequency vector to a complex frequency domain channel, and performs complex multiplication convolution. The convolution kernel weight is represented by a complex parameter to generate a subband feature output.

[0087] S34, inputting the sub-band feature output of each sub-band convolution sub-layer into the frequency domain channel fusion module, performing spectrum feature splicing and nonlinear mapping operations, and obtaining a multi-scale spectrum feature fusion result;

[0088] S35. Input the multi-scale spectral feature fusion result into the output prediction layer, which is composed of a set of complex fully connected mapping units and outputs the corresponding material parameter set as the initial material parameter prediction result for subsequent error calculation and optimization process.

[0089] The present invention constructs a multi-scale Fourier neural operator model, divides the spectral feature matrix into low-frequency, medium-frequency and high-frequency sub-bands according to frequency, and inputs them into multiple sets of parallel Fourier convolution sub-layers respectively, so as to achieve detailed modeling of acoustic features in different frequency bands. Each convolution sub-layer uses complex weights to perform frequency domain convolution operations, which can capture amplitude and phase information at the same time, and improve the ability to characterize complex spectral characteristics. Feature splicing and nonlinear mapping are performed through the frequency domain channel fusion module to fully integrate multi-scale frequency domain information. Finally, the key parameters of the porous material are directly output through the complex fully connected unit mapping of the output prediction layer, providing a basis for subsequent error evaluation and model optimization. This method enhances the modeling accuracy of multi-scale acoustic features, improves the accuracy of parameter prediction, and provides strong technical support for the automated and efficient identification of porous material properties.

[0090] In this embodiment, the S33 specifically includes:

[0091] S331, assuming that the input data of the spectrum feature matrix in the kth frequency sub-band is a real-valued frequency domain vector sequence X k (f), where k∈{low frequency, medium frequency, high frequency}, f represents the frequency variable;

[0092] S332, input frequency domain vector X k(f) Perform complex frequency domain transform operation to obtain complex spectrum representation Z k (f), where each element contains amplitude information and phase information;

[0093] S333, define the Fourier convolution kernel weight as W k , where each weight value represents the frequency domain convolution kernel response coefficient at the corresponding frequency point, and the convolution kernel size matches the subband channel dimension;

[0094] S334. Perform a Fourier convolution operation on the complex spectrum input data in each frequency subband in the frequency dimension. Centered on the current frequency point, select the complex spectrum input values ​​corresponding to the current frequency point and several adjacent frequency points before and after it to construct a frequency local window. Within the frequency local window, perform a complex multiplication operation on the input complex value of each frequency point by a preset complex convolution kernel weight. Perform a weighted sum of all product results along the frequency dimension to obtain a subband frequency domain convolution output result.

[0095] S335. Apply a complex domain activation function to the sub-band frequency domain convolution output result so that the convolution result retains the inter-frequency coupling information and generates a sub-band feature output.

[0096] The present invention performs a complex frequency domain transform on the input data of each frequency subband to obtain a complex spectral representation that contains both amplitude and phase information. Using complex convolution kernel weights, complex multiplication and weighted accumulation are performed on the frequency domain data within a local frequency window, effectively extracting correlations and local features between different frequency points. The convolution results are processed with a complex activation function to enhance the nonlinear expression capability, enabling the output features to more accurately reflect the complex acoustic properties of the material. This method significantly improves the accuracy of porous material parameter identification and the model's sensitivity to spectral details.

[0097] In this embodiment, the initial material parameter prediction results include flow resistivity, porosity, equivalent sound velocity, structure factor and viscosity correction factor; the flow resistivity indicates the magnitude of the viscous resistance encountered by air in the process of penetrating the porous material structure; the porosity describes the proportional relationship between the internal pore volume and the total volume of the porous material; the equivalent sound velocity reflects the equivalent propagation speed of sound waves when propagating in the porous material; the structure factor characterizes the influence of the internal microstructure of the material on the length of the sound wave propagation path; the viscosity correction factor corrects the viscous damping effect encountered by air when propagating in the pores of the material.

[0098] This method can simultaneously predict resistivity, porosity, equivalent sound velocity, structure factor, and viscosity correction factor, achieving a comprehensive characterization of the microstructure and acoustic performance of porous materials. Each parameter has a clear physical meaning, encompassing the material's sound transmission, energy dissipation, and microstructural influences. Accurately identifying these parameters provides a scientific basis for the design, performance optimization, and engineering applications of porous materials, improving the accuracy and efficiency of acoustic material performance evaluation and development.

[0099] In this embodiment, the S5 specifically includes:

[0100] S51. Receive initial material parameter prediction results, and calculate a set of frequency domain response eigenvalues ​​corresponding to the predicted parameters based on a theoretical acoustic model of the porous material, wherein the frequency domain response eigenvalues ​​include a theoretical reflection coefficient, a theoretical absorption coefficient, and a theoretical acoustic impedance at each frequency point;

[0101] S52. Based on the physical relationship between various parameter variables in the acoustic theoretical model of the porous material, a theoretical response curve of the material is calculated according to the input material parameters and frequency, and a reconstructed spectrum curve is generated;

[0102] S53, matching the reconstructed spectrum curve with the measured reflection coefficient and absorption coefficient in the spectrum feature matrix frequency by frequency point, and constructing a frequency domain residual mapping relationship;

[0103] S54. Define a coupled residual function for jointly evaluating the deviation relationship between material parameter prediction and frequency domain physical response, and construct a target error function, wherein the target error function is composed of a complex reflection error term, an absorption error term, and a physical compatibility regularization term:

[0104]

[0105] in, is the target error function, i is the frequency point index, N f is the total number of frequency sampling points, λ1 is the reflection coefficient error, λ2 is the absorption coefficient error, λ3 is the weight parameter of the regularization term, R recon (f i ) is the reconstructed reflection coefficient, R meas (f i ) is the measured reflection coefficient, α recon (f i ) is the reconstruction absorption coefficient, α meas (f i ) is the measured absorption coefficient, Ω(P init ) is the parameter regularization term, P init is the prediction result of initial material parameters, f i is the i-th frequency sampling point.

[0106] The present invention substitutes the initial material parameter prediction results into the theoretical acoustic model of porous materials, calculates the theoretical reflection coefficient and absorption coefficient corresponding to each predicted parameter, and realizes a comparative analysis of the theoretical and measured spectral characteristics. Based on the physical relationship between the parameters, a theoretical spectrum curve is generated, and a frequency-point residual mapping is performed with the measured spectrum data. By defining a joint error function, the reflection coefficient, absorption coefficient residual and parameter physical rationality regularization term are weighted and combined, and each term in the formula measures the spectrum fitting error and parameter physical constraint respectively. This method effectively improves the accuracy and physical consistency of parameter identification, and provides a scientific basis for the precise modeling and optimization of the acoustic properties of porous materials.

[0107] In this embodiment, S6 specifically includes:

[0108] S61. Define the structural search space of the multi-scale Fourier neural operator model, which is composed of the neural operator configurations of multiple Fourier convolution sublayers. The neural operator configurations include the number of convolution kernels, the Fourier channel dimension and the activation function encoding, and construct the structural parameter configuration vector S j ;

[0109] S62, use Latin hypercube sampling to initialize the sparrow search algorithm population, construct multiple sparrow individuals, each sparrow individual corresponds to a neural operator configuration S j , and respectively give the marks of discoverer role, joiner role and vigilant role;

[0110] S63, constructing a fitness function, wherein the fitness function is based on the target error function and introduces a structural complexity penalty term and a physical constraint penalty term of the initial material parameter prediction result;

[0111] S64, performing a position update operation on all sparrow individuals, recalculating the fitness value of the structural parameter configuration vector after each round of update, and recording the current global optimal neural operator configuration;

[0112] S65. When the fitness function value converges to the preset threshold θ or reaches the maximum number of iterations N, the final optimal neural operator configuration S is output. best .

[0113] The present invention defines the structural search space of the multi-scale Fourier neural operator model and uses Latin hypercube sampling combined with the sparrow search algorithm for efficient structural optimization. By setting the number of convolution kernels, Fourier channel dimensions and activation function encoding, neural operator models of different structures can be flexibly constructed. The fitness function integrates the target error, model complexity and physical constraints to achieve a unified evaluation of model performance and physical rationality. The algorithm dynamically updates the structural configuration in each round of iteration and continuously searches for the global optimal solution, thereby improving the efficiency and accuracy of the model structure search. This method significantly enhances the adaptive optimization capability and generalization performance of the porous material parameter identification model.

[0114] In this embodiment, the location update operation includes individual updates of discoverers, individual updates of joiners, and individual updates of alerters;

[0115] The discoverer individual update performs an exponential decrease strategy to search global structural parameters for sparrow individuals with the discoverer role; the joiner individual update introduces position perturbation to optimize local structural parameters for sparrow individuals marked as joiner roles; the guard individual update uses Gaussian perturbation combined with a jumping search strategy to update sparrows with the guard role.

[0116] This method effectively combines global search with local optimization by dividing individual sparrows into the roles of discoverers, joiners, and sentinels. The discoverers use an exponentially decreasing strategy to explore global parameters, increasing the search range; the joiners optimize local structural parameters through positional perturbations, enhancing the ability to adjust model details; and the sentinels combine Gaussian perturbations with jump search to effectively avoid being trapped in local optima. This method improves the globality and convergence speed of structural parameter optimization, helping to achieve more optimal neural operator structure configurations.

[0117] In this embodiment, the S7 specifically includes:

[0118] S71, based on the final optimal neural operator configuration S best , replacing the original multi-scale Fourier neural operator model structure configuration to obtain a multi-scale Fourier neural operator model with updated structure;

[0119] S72, inputting the spectral feature matrix as input data into the multi-scale Fourier neural operator model after the structure update, performing Fourier domain convolution operations through each Fourier convolution sublayer in turn, and obtaining an updated multi-scale spectral feature fusion result;

[0120] S73, inputting the updated multi-scale spectrum feature fusion result into the output prediction layer, performing a forward propagation operation, and obtaining the final material parameter identification result;

[0121] S74. The final material parameter identification results include flow resistivity, porosity, equivalent sound velocity, structure factor and viscosity correction factor.

[0122] This method utilizes an optimized multi-scale Fourier neural operator model structure to deeply fuse and extract spectral features, enhancing the model's ability to represent complex spectral information. During forward propagation, the model more accurately outputs resistivity, porosity, equivalent sound velocity, structure factor, and viscosity correction factor, enabling high-precision identification of key parameters of porous materials. This method effectively improves the accuracy of material parameter prediction and the generalization capability of the model.

[0123] Example 1:

[0124] To verify the feasibility of the present invention, it was applied to a parameter identification project for porous sound-absorbing materials conducted in an acoustic materials laboratory. In this scenario, the experimenters hoped to rapidly and non-destructively obtain the key acoustic performance parameters of material samples for subsequent material classification, structural modeling, and acoustic simulation analysis. However, traditional parameter identification methods rely on manual selection of initial parameters and optimization using least squares fitting. This not only results in slow convergence but also easily falls into local optimality or produces non-physically plausible solutions when faced with materials with complex spectral characteristics and drastically varying reflection coefficients.

[0125] In actual application, the experimenters used impedance tube test hardware to perform broadband excitation on the sample, collected the sound pressure response signals at the upstream and downstream positions, and combined with the excitation source signal to construct a set of original test signals containing original time domain data and annotated labels. Subsequently, the collected signals were processed by fast Fourier transform to extract the complex reflection coefficient, absorption coefficient and transfer function value at each frequency point, and construct a spectral feature matrix. The spectral data was input into the multi-scale Fourier neural operator model constructed by the present invention. The model performs frequency domain modeling through three groups of sub-band convolution sub-layers of low frequency, medium frequency and high frequency, and fuses them into a unified multi-scale feature representation.

[0126] The model provides a first-round prediction of material parameters under the initial structure, including resistivity, porosity, equivalent acoustic velocity, structure factor, and viscosity correction factor. Subsequently, a joint error function is constructed, the residuals of the predicted results are compared with the theoretical spectral response, reflection and absorption error terms are introduced, and the structural configuration of the neural operator is iteratively optimized using a sparrow search algorithm. Ultimately, a converged optimal structural model is obtained and the final parameter identification results are output.

[0127] To evaluate the performance of our method, we compared the recognition accuracy, average error, and computational time of a traditional transfer function fitting method (TFM), a standard neural network fitting method (SNN), and our method on three different material samples. The results show that our method outperforms the comparison methods in terms of prediction accuracy, model convergence speed, and recognition stability. In particular, for samples with complex cavity structures, the absorption coefficient residual is significantly reduced, demonstrating that our model more effectively captures the multi-scale characteristics of the spectral response.

[0128] Table 1 compares the test results for three typical material samples, listing the deviation between the predicted and measured values ​​for five key parameters, the average residual, and the calculation time (in seconds). All experiments were conducted on the same test platform and using the same acoustic testing hardware. The data were averaged over three replicates, demonstrating statistical stability and engineering reference value.

[0129] Table 1: Comparison of parameter identification effects of different methods on three types of porous material samples

[0130]

[0131] As can be seen from the above table, the present invention has significant improvements in multiple key performance indicators compared with the traditional transfer function fitting method (TFM) and the standard neural network method (SNN) in the task of acoustic parameter identification of porous materials. First, in terms of recognition accuracy, the average parameter residuals of the method of the present invention on three types of typical material samples were 3.7%, 3.6% and 4.2%, respectively, which were significantly lower than the 12.3%, 12.7% and 14.6% of the TFM method, and the overall average error was reduced by more than 70%. Compared with the SNN method, the error of the method of the present invention is also smaller, reflecting the enhancement of the ability to model spectral features, especially in the identification of structural factors and viscosity correction factors, the error control is more stable, showing a higher physical consistency of parameters.

[0132] Among the specific parameter items, the resistivity recognition accuracy is an important indicator to measure the model's ability to perceive the aerodynamic resistance inside the material. The resistivity error of the method of the present invention on all material samples is controlled within 4%, while the TFM method is generally higher than 12%, and the SNN method is mostly between 6% and 9%, indicating that the multi-scale frequency domain modeling mechanism of the present invention can more fully reflect the characteristic information of the low-frequency band. In addition, in terms of porosity and equivalent sound velocity, two important indicators that reflect the overall properties of the material structure, the method of the present invention shows higher accuracy. In particular, on material B, the equivalent sound velocity error is only 3.9%, the lowest among the three methods, indicating that it can effectively suppress the interference of structural noise on the recognition results in the mid-frequency modeling stage.

[0133] In terms of recognition efficiency, the average calculation time of the method of the present invention is controlled at about 10 seconds, which is significantly better than the TFM method (more than 16 seconds on average) and slightly better than the SNN method. This is mainly due to the rapid convergence of the sparrow search algorithm on the neural structure and the ability to control the structural complexity, which enables the model to greatly improve the calculation efficiency while maintaining the structural expression ability. In addition, the stability advantage of the present invention on complex materials (such as material C) is particularly obvious, the error fluctuation is small, and the recognition results are more balanced between different parameter dimensions.

[0134] In summary, the tabular data fully verify that the method of the present invention is superior to the existing comparative methods in terms of recognition accuracy, calculation efficiency and stability in porous material parameter identification, and has good engineering practicality and promotion value.

[0135] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any technician familiar with the technical field, within the technical scope disclosed by the present invention, who makes equivalent replacements or changes based on the technical solution and inventive concept of the present invention, should be covered by the scope of protection of the present invention.

Claims

1. A porous material parameter identification method based on impedance tube testing hardware, characterized in that: The steps include: S1. Use impedance tube test hardware to acoustically excite the porous material sample to be tested, collect the original sound pressure signal, and generate an original test signal set; S2. Perform a fast Fourier transform operation on the original test signal set to generate a spectrum feature matrix; S3. Construct a multi-scale Fourier neural operator model, wherein the multi-scale Fourier neural operator model includes multiple parallel Fourier convolution sublayers, each of which receives components of the spectrum feature matrix in a low-frequency subband, a mid-frequency subband, and a high-frequency subband, and outputs a multi-scale spectrum feature fusion result; S4. Input the multi-scale spectral feature fusion result into the output prediction layer of the multi-scale Fourier neural operator model, perform a forward propagation operation, and obtain the initial material parameter prediction result; S5. Based on the initial material parameter prediction results, the reconstructed spectrum curve is calculated and reconstructed in combination with the acoustic theoretical model of porous materials to construct the target error function; S6. Initialize the sparrow search algorithm population, set each sparrow individual to represent a neural operator configuration of a multi-scale Fourier neural operator model and optimize it to obtain the final optimal neural operator configuration; S7. Based on the final optimal neural operator configuration, update the multi-scale Fourier neural operator model, re-perform the inference operation on the spectral feature matrix, and output the final material parameter identification result.

2. The porous material parameter identification method based on impedance tube testing hardware according to claim 1, characterized in that: The original test signal set includes an excitation sound source signal, a sound pressure response signal collected by a first position microphone, a sound pressure response signal collected by a second position microphone, a sampling time label, a channel number identifier, and a signal collection sequence number; The excitation sound source signal is a broadband excitation signal applied by an impedance tube speaker; the sound pressure response signal collected by the first position microphone is a sound pressure time series collected by an acoustic measuring point located on the upstream side of the porous material to be measured; and the sound pressure response signal collected by the second position microphone is a sound pressure time series collected by an acoustic measuring point located on the downstream side of the porous material to be measured.

3. The porous material parameter identification method based on impedance tube testing hardware according to claim 1, characterized in that: The S2 specifically includes: S21, performing equally spaced discrete sampling on the excitation sound source signal, the sound pressure response signal collected by the first position microphone, and the sound pressure response signal collected by the second position microphone in the original test signal set to obtain corresponding excitation signal sequences, first sound pressure sequences, and second sound pressure sequences; S22, performing fast Fourier transform operations on the excitation signal sequence, the first sound pressure sequence, and the second sound pressure sequence, respectively, to obtain complex spectrum data of each sequence in the frequency domain, thereby obtaining an excitation spectrum, a first sound pressure spectrum, and a second sound pressure spectrum; S23. Calculate the complex reflection coefficient, absorption coefficient, and transfer function value at each frequency point based on a transfer function method, where the complex reflection coefficient is calculated as the complex ratio of the first and second sound pressure spectra, the absorption coefficient is the unit value minus the square of the reflection coefficient modulus, and the transfer function is the complex ratio of the second sound pressure spectrum to the first sound pressure spectrum; S24. Arrange the complex reflection coefficient, absorption coefficient, and transfer function value in order from low to high frequency to construct a spectrum feature matrix.

4. The porous material parameter identification method based on impedance tube testing hardware according to claim 1, characterized in that: The S3 specifically includes: S31. Construct a multi-scale Fourier neural operator model, wherein the multi-scale Fourier neural operator model includes multiple sets of parallel Fourier convolution sublayers, a frequency domain channel fusion module, and an output prediction layer; S32, dividing the spectrum feature matrix into three frequency domain sub-matrices: low frequency sub-band, medium frequency sub-band, and high frequency sub-band according to frequency, inputting each into the corresponding Fourier convolution sub-layer, and performing frequency domain feature modeling operation; S33. Each Fourier convolution sublayer performs frequency domain projection on the input subband data, maps each input frequency vector to a complex frequency domain channel, and performs complex multiplication convolution. The convolution kernel weight is represented by a complex parameter to generate a subband feature output. S34, inputting the sub-band feature output of each sub-band convolution sub-layer into the frequency domain channel fusion module, performing spectrum feature splicing and nonlinear mapping operations, and obtaining a multi-scale spectrum feature fusion result; S35. Input the multi-scale spectrum feature fusion result into the output prediction layer, where the output prediction layer is composed of a set of complex fully connected mapping units and outputs a corresponding set of material parameters.

5. The porous material parameter identification method based on impedance tube testing hardware according to claim 4 is characterized in that: The S33 specifically includes: S331, assuming that the input data of the spectrum feature matrix in the kth frequency sub-band is a real-valued frequency domain vector sequence X k (f), where k∈{low frequency, medium frequency, high frequency}, f represents the frequency variable; S332, input frequency domain vector X k (f) Perform complex frequency domain transform operation to obtain complex spectrum representation Z k (f), where each element contains amplitude information and phase information; S333, define the Fourier convolution kernel weight as W k , where each weight value represents the frequency domain convolution kernel response coefficient at the corresponding frequency point, and the convolution kernel size matches the subband channel dimension; S334. Perform a Fourier convolution operation on the complex spectrum input data in each frequency subband in the frequency dimension. Centered on the current frequency point, select the complex spectrum input values ​​corresponding to the current frequency point and several adjacent frequency points before and after it to construct a frequency local window. Within the frequency local window, perform a complex multiplication operation on the input complex value of each frequency point by a preset complex convolution kernel weight. Perform a weighted sum of all product results along the frequency dimension to obtain a subband frequency domain convolution output result. S335. Apply a complex domain activation function to the sub-band frequency domain convolution output result to generate a sub-band feature output.

6. The porous material parameter identification method based on impedance tube testing hardware according to claim 1, characterized in that: The initial material parameter prediction results include flow resistivity, porosity, equivalent sound velocity, structure factor and viscosity correction factor; The flow resistivity indicates the magnitude of the viscous resistance encountered by air when penetrating the porous material structure; the porosity describes the proportional relationship between the pore volume and the total volume of the porous material; the equivalent sound velocity reflects the equivalent propagation speed of sound waves when propagating in the porous material; the structure factor characterizes the influence of the internal microstructure of the material on the length of the sound wave propagation path; the viscosity correction factor corrects the viscous damping effect encountered by air when propagating in the pores of the material.

7. The porous material parameter identification method based on impedance tube testing hardware according to claim 1, characterized in that: The S5 specifically includes: S51. Receive initial material parameter prediction results, and calculate a set of frequency domain response eigenvalues ​​corresponding to the predicted parameters based on a theoretical acoustic model of the porous material, wherein the frequency domain response eigenvalues ​​include a theoretical reflection coefficient, a theoretical absorption coefficient, and a theoretical acoustic impedance at each frequency point; S52. Based on the physical relationship between various parameter variables in the acoustic theoretical model of the porous material, a theoretical response curve of the material is calculated according to the input material parameters and frequency, and a reconstructed spectrum curve is generated; S53, matching the reconstructed spectrum curve with the measured reflection coefficient and absorption coefficient in the spectrum feature matrix frequency by frequency point, and constructing a frequency domain residual mapping relationship; S54. Define a coupled residual function for jointly evaluating the deviation relationship between material parameter prediction and frequency domain physical response, and construct a target error function, wherein the target error function is composed of a complex reflection error term, an absorption error term, and a physical compatibility regularization term: in, is the target error function, i is the frequency point index, N f is the total number of frequency sampling points, λ1 is the reflection coefficient error, λ2 is the absorption coefficient error, λ3 is the weight parameter of the regularization term, R recon (f i ) is the reconstructed reflection coefficient, R meas (f i ) is the measured reflection coefficient, α recon (f i ) is the reconstruction absorption coefficient, α meas (f i ) is the measured absorption coefficient, Ω(P init ) is the parameter regularization term, P init is the prediction result of the initial material parameters, f i is the i-th frequency sampling point.

8. The porous material parameter identification method based on impedance tube testing hardware according to claim 1, characterized in that: The S6 specifically includes: S61. Define the structural search space of the multi-scale Fourier neural operator model, which is composed of the neural operator configurations of multiple Fourier convolution sublayers. The neural operator configurations include the number of convolution kernels, the Fourier channel dimension and the activation function encoding, and construct the structural parameter configuration vector S j ; S62, use Latin hypercube sampling to initialize the sparrow search algorithm population, construct multiple sparrow individuals, each sparrow individual corresponds to a neural operator configuration S j , and respectively give the marks of discoverer role, joiner role and vigilant role; S63, constructing a fitness function, wherein the fitness function is based on the target error function and introduces a structural complexity penalty term and a physical constraint penalty term of the initial material parameter prediction result; S64, performing a position update operation on all sparrow individuals, recalculating the fitness value of the structural parameter configuration vector after each round of update, and recording the current global optimal neural operator configuration; S65. When the fitness function value converges to the preset threshold θ or reaches the maximum number of iterations N, the final optimal neural operator configuration S is output. best .

9. The porous material parameter identification method based on impedance tube testing hardware according to claim 8, characterized in that: The location update operation includes discoverer individual update, joiner individual update and alerter individual update; The discoverer individual update performs an exponential decrease strategy to search global structural parameters for sparrow individuals with the discoverer role; the joiner individual update introduces position perturbation to optimize local structural parameters for sparrow individuals marked as joiner roles; the guard individual update uses Gaussian perturbation combined with a jumping search strategy to update sparrows with the guard role.

10. The porous material parameter identification method based on impedance tube testing hardware according to claim 1, characterized in that: The S7 specifically includes: S71, based on the final optimal neural operator configuration S best , replacing the original multi-scale Fourier neural operator model structure configuration to obtain a multi-scale Fourier neural operator model with updated structure; S72, inputting the spectral feature matrix as input data into the multi-scale Fourier neural operator model after the structure update, performing Fourier domain convolution operations through each Fourier convolution sublayer in turn, and obtaining an updated multi-scale spectral feature fusion result; S73, inputting the updated multi-scale spectrum feature fusion result into the output prediction layer, performing a forward propagation operation, and obtaining the final material parameter identification result; S74. The final material parameter identification results include flow resistivity, porosity, equivalent sound velocity, structure factor and viscosity correction factor.

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