Orthogonal matching pursuit sound field reconstruction method based on joint weighted transfer matrix mode and improved cosine similarity

Abstract

The invention discloses an orthogonal matching pursuit sound field reconstruction method of joint weighted transfer matrix mode and improved cosine similarity, comprising: setting a measurement surface and dividing it evenly, obtaining a number of grid points, installing microphones through the grid points, and forming a holographic surface; arranging a reconstruction surface, arranging an equivalent source surface on the side of the reconstruction surface away from the holographic surface, using the relationship between the equivalent source source intensity and the measured sound pressure and the reconstruction surface sound pressure, establishing a sound field reconstruction model under sparse sampling based on the transfer matrix mode; implementing a transfer matrix mode weighting strategy, using the orthogonal matching pursuit method of improved cosine similarity, solving the weighted sparse coefficient vector of the equivalent source intensity; according to the weighted sparse coefficient of the equivalent source intensity and the transfer relationship between the reconstructed sound pressure and the equivalent source source intensity, the sound field reconstruction under sparse sampling is realized. The invention improves the sound field reconstruction accuracy and stability of the orthogonal matching pursuit method.

Description

Technical Field

[0001] The invention relates to the technical field of noise sound field, in particular to an orthogonal matching pursuit sound field reconstruction method combining weighted transfer matrix mode and improved cosine similarity. Background Art

[0002] As a powerful sound field reconstruction technology, near-field acoustic holography has been widely used in the field of noise control. However, since traditional near-field acoustic holography is based on the Nyquist sampling theorem, its sound field reconstruction accuracy is limited by the spatial sampling rate. Usually, a large number of sampling microphones are required to achieve a good reconstruction effect, which greatly increases the measurement cost of the sound source identification system. With the introduction and application of compressed sensing theory, near-field acoustic holography breaks through the limitations of the Nyquist sampling theorem and can achieve high-precision sound field reconstruction while significantly reducing the number of sampling points. At present, there are related technologies that use compressed sensing theory in the field of sound field reconstruction. As a classic greedy algorithm, the orthogonal matching pursuit method is widely used because of its simple process, fast calculation speed, and easy hardware implementation. In each iteration, this method selects the atom with the strongest correlation with the residual (i.e., the column vector of the transfer matrix) according to the inner product criterion, and gradually forms a support set to approximate the original signal. The key step of the method lies in the atom selection strategy, which directly determines whether the optimal atom can be selected for sound field reconstruction. In fact, each atom of the transfer matrix corresponds to each order transfer matrix mode in the sound field reconstruction model. If the atom corresponding to the transfer matrix mode that contributes the most to the sound field can be accurately selected in the atom selection step, the sound field can be well reconstructed. However, as the frequency increases, the sound field becomes more and more complex, and the spatial sparsity decreases, thereby weakening the distinction between high-order modes and low-order modes in the transfer matrix. This makes it difficult to select the correct atom for matching according to the inner product criterion, resulting in reduced performance of the orthogonal matching pursuit method when reconstructing high-frequency sound fields. In addition, if the orthogonal matching pursuit method does not correctly handle the transfer matrix mode when looking for a sparse solution, the noise contained in the high-order transfer matrix mode will be amplified in the sound field reconstruction, which will lead to low accuracy of sound field reconstruction.

[0003] Currently, truncation orders can be used to limit the impact of high-order modes on reconstruction results. However, the determination of the optimal truncation criterion varies with frequency and is easily affected by the signal-to-noise ratio. There is a lack of universal criteria for selecting the optimal truncation order. Summary of the invention

[0004] To solve the above technical problems, the present invention proposes an orthogonal matching pursuit sound field reconstruction method that combines weighted transfer matrix modes and improved cosine similarity, which can achieve high-precision sound field reconstruction with fewer microphones and can significantly reduce the testing cost in practical applications.

[0005] To achieve the above object, the present invention provides an orthogonal matching pursuit sound field reconstruction method combining weighted transfer matrix mode and improved cosine similarity, comprising:

[0006] Determine a research area, set a measurement surface based on the research area, set grid points on the measurement surface, install microphones through the grid points, and form a holographic surface, wherein the grid points correspond to the microphones one by one;

[0007] Arrange a reconstruction surface between the sound source in the study area and the holographic surface, arrange an equivalent source surface on the side of the reconstruction surface away from the holographic surface, and establish a sound field reconstruction model under sparse sampling based on transfer matrix mode by using the relationship between the equivalent source intensity and the measured sound pressure and the reconstruction surface sound pressure;

[0008] Based on the sound field reconstruction model under sparse sampling, a transfer matrix modal weighting strategy is implemented, and the weighted sparse coefficient vector of the equivalent source intensity is solved by using the orthogonal matching pursuit method of improved cosine similarity;

[0009] According to the weighted sparse coefficient of the equivalent source intensity and the transmission relationship between the reconstructed sound pressure and the equivalent source intensity, the sound field reconstruction under sparse sampling is achieved.

[0010] Preferably, a sound field reconstruction model under sparse sampling based on transfer matrix mode is established, including:

[0011] Establishing the relationship between the equivalent source intensity on the equivalent source surface and the measured sound pressure on the holographic surface, the relationship between the equivalent source intensity on the equivalent source surface and the reconstructed sound pressure on the reconstruction surface, and the relationship between the reconstructed sound pressure on the reconstruction surface and the measured sound pressure on the holographic surface respectively;

[0012] Based on the transfer matrix G r Perform singular value decomposition to establish the sound field reconstruction model under sparse sampling based on the transfer matrix mode, where the transfer matrix G r It is a transfer matrix between the reconstructed sound pressure on the reconstruction surface and the equivalent source intensity on the equivalent source surface.

[0013] Preferably, the relationship between the equivalent source intensity on the equivalent source surface and the measured sound pressure on the holographic surface is:

[0014] P h =G h q(1)

[0015] Where P h =[p h (r1),…,p h (r m ),…,p h (r M )] Tis the measured sound pressure of M microphones on the holographic surface H, p h (r m ) is the sound pressure signal measured by the mth microphone, r m is the position vector of the mth microphone, m=1,2,3,…,M; is the equivalent source strength vector, represents the source intensity of the nth equivalent source on the equivalent source surface, n=1,2,3,…,N, is the position vector of the nth equivalent source; G h is the transfer matrix between the sound pressure of the sampling point on the holographic surface H and the equivalent source intensity on the equivalent source surface S;

[0016] The relationship between the equivalent source intensity on the equivalent source surface and the reconstructed sound pressure on the reconstruction surface is:

[0017] P r =G r q(2)

[0018] In the formula, is the reconstructed sound pressure of L reconstruction points on the reconstruction surface R, is the reconstructed sound pressure at the lth reconstruction point, is the position vector of the lth reconstruction point, l=1,2,3,…,L; G r is the transfer matrix between the reconstructed sound pressure on the reconstruction surface R and the equivalent source intensity on the equivalent source surface S;

[0019] The relationship between the reconstructed sound pressure on the reconstruction surface and the measured sound pressure on the holographic surface is:

[0020] P h =G h (G r ) + P r (3)

[0021] Where the superscript “+” indicates the generalized inverse of the matrix.

[0022] Preferably, based on the transfer matrix G r The method for singular value decomposition is:

[0023] P r =UΣV H q=Uθ(4)

[0024] In the formula, U=[U1,…,U n ,…,U N ] and V=[V1,…,V n ,…,V N ] are the left singular vector and the right singular vector respectively, U n and V nare the column vectors of left singular vectors and right singular vectors respectively. The superscript “H” represents the conjugate transpose. Σ=diag(σ1,…,σ n ,…,σ N ) is a diagonal matrix consisting of real positive singular values, satisfying σ1≥…≥σ n ≥…≥σ N >0; θ is the sparse coefficient vector of equivalent source intensity.

[0025] Preferably, the sound field reconstruction model under sparse sampling based on transfer matrix mode is:

[0026] P h =Hθ(5)

[0027] In the formula, H = G h (G r ) + U is the perception matrix.

[0028] Preferably, when the number of sampling points is much smaller than the number of equivalent sources, the sound field reconstruction under sparse sampling conditions is regarded as an underdetermined problem, and according to the compressed sensing theory, the sparse coefficient vector of the equivalent source intensity in the following formula (6) is expressed as a l0 norm minimization problem, and weighted by a real-time transfer matrix modal weighting strategy;

[0029]

[0030] Where θ is the sparse coefficient vector of equivalent source intensity.

[0031] Preferably, the real-time transfer matrix modal weighting strategy comprises:

[0032] Each column of the transfer matrix U is normalized, and then the corresponding singular value is used to weight the mode of each order transfer matrix, that is:

[0033]

[0034] In the formula, is the weighted transfer matrix, D U is the weighting matrix;

[0035] Then the measured sound pressure on the holographic surface in equation (5) is expressed as:

[0036]

[0037] In the formula, is the weighted perception matrix, is the weighted sparse coefficient vector of equivalent source intensity, is the weight matrix D U The generalized inverse of .

[0038] Preferably, the weighted sparse coefficient vector of the equivalent source intensity is solved by using an orthogonal matching pursuit method of improved cosine similarity, including:

[0039] S1.1. Initialize residual γ0 = P h , iteration number t = 1, index set is an empty set, and the maximum number of iterations is determined according to the number of microphones M and the number of equivalent source points N. in It means rounding to the largest integer not greater than the real number;

[0040] S1.2, define the improved cosine similarity criterion;

[0041] S1.3, using the improved cosine similarity criterion to select the best atom, in the weighted perception matrix Find the atomic position that best matches the current residual.

[0042]

[0043] Update index set Γ t =Γ t-1 ∪j t , Γ t is the index set of the tth iteration, Γ t-1 is the index set of the previous iteration, j t is the weighted perception matrix The index value of the optimal atom position in ;

[0044] S1.4. Using the index set Γ t From the weighted perception matrix The corresponding atomic composition support matrix is ​​selected from And use the least squares method to calculate the current approximate solution is the support set of the tth iteration, Representation Matrix The transpose of

[0045] S1.5. Update residual

[0046] S1.6, the number of iterations is t = t + 1, and the iteration is repeated until the termination condition t = T is met, and the weighted sparse coefficient vector of the equivalent source intensity is output as the final solution

[0047] Preferably, during the iteration process, the optimal weight coefficient for each iteration is Determined by the following process:

[0048] For the weight coefficient α in the tth iteration (t)Traverse from 0 to 1 with an increment of 0.01 to calculate the corresponding weighted sparse coefficient vector of equivalent source intensity And use Estimate the sound pressure at the M sampling points on the holographic surface, and then minimize the measured sound pressure P on the holographic surface h and reconstructed sound pressure The relative error between them determines the optimal weight coefficient

[0049]

[0050] When the weight coefficient is set to When , the weighted sparse coefficient vector of the equivalent source intensity of the tth iteration is obtained.

[0051] Preferably, the method further comprises:

[0052] In obtaining the weighted sparse coefficient vector of the equivalent source intensity Then, according to formula (4), the reconstructed sound pressure on the reconstruction surface is calculated Realize sound field reconstruction under sparse sampling.

[0053] Compared with the prior art, the present invention has the following advantages and technical effects:

[0054] 1. The present invention realizes high-precision sound field reconstruction under sparse sampling by implementing a weighting strategy for transfer matrix modes and improving the atomic matching criterion; by establishing a weighting strategy for transfer matrix modes, low-order transfer matrix modes are preferentially selected when constructing a support set, thereby reducing the instability risk caused by selecting high-order modes containing noise; by introducing a measure of the spatial distance between vectors to improve the cosine similarity criterion, an improved cosine similarity atomic matching criterion is used to replace the original inner product criterion to measure the correlation between atoms and residuals, thereby overcoming the problem of incorrect atom selection caused by the high complexity of high-frequency sound fields; the method of the present invention improves the sound field reconstruction accuracy and stability of the orthogonal matching pursuit method, and broadens the frequency application range of the orthogonal matching pursuit method.

[0055] 2. The method of the present invention has stable performance in sound field reconstruction, higher noise resistance and robustness, and its reconstruction accuracy under different signal-to-noise ratio conditions is better than that of the traditional orthogonal matching pursuit method.

[0056] 3. The method of the present invention adopts random arrangement when installing microphones, and the test process is efficient and convenient. It can also achieve high-precision sound field reconstruction when there are fewer microphones, which can significantly reduce the test cost in practical applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0058] Figure 1 A schematic diagram of a sound field reconstruction model under sparse sampling according to an embodiment of the present invention;

[0059] Figure 2 A schematic diagram of the distribution of microphone positions used in an embodiment of the present invention;

[0060] Figure 3 1 is a comparison diagram of the reconstructed sound pressure distribution results at 500 Hz, 1000 Hz, 1500 Hz and 2000 Hz of the embodiment of the present invention;

[0061] Figure 4 This is a comparison diagram of the average error of 100 sound field reconstructions at different frequencies according to an embodiment of the present invention;

[0062] Figure 5 This is a comparison diagram of the reconstructed sound pressure distribution results of an embodiment of the present invention when the frequency is 500 Hz and the signal-to-noise ratio is 10 dB, 20 dB and 30 dB respectively;

[0063] Figure 6 This is a comparison diagram of the reconstructed sound pressure distribution results of an embodiment of the present invention when the frequency is 2000 Hz and the signal-to-noise ratio is 10 dB;

[0064] Figure 7 1 is a comparison diagram of the reconstructed sound pressure distribution results of an embodiment of the present invention when the frequency is 500 Hz and the number of sampling points is 36, 49 and 64 respectively;

[0065] Figure 8 This is a comparison diagram of the reconstructed sound pressure distribution results of an embodiment of the present invention when the frequency is 2000 Hz and the number of sampling points is 36. DETAILED DESCRIPTION

[0066] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0067] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0068] Example 1

[0069] The present invention proposes an orthogonal matching pursuit sound field reconstruction method combining weighted transfer matrix mode and improved cosine similarity, comprising:

[0070] Determine a research area, set a measurement surface based on the research area and evenly divide the measurement surface to obtain a number of grid points, install microphones through the grid points to form a holographic surface, wherein the grid points correspond to the microphones one by one;

[0071] A reconstruction surface is arranged between the sound source and the holographic surface in the study area, and an equivalent source surface is arranged on the side of the reconstruction surface away from the holographic surface. The relationship between the equivalent source intensity and the measured sound pressure and the reconstruction surface sound pressure is used to establish a sound field reconstruction model under sparse sampling based on the transfer matrix mode;

[0072] Based on the sound field reconstruction model under sparse sampling, the transfer matrix modal weighting strategy is implemented, and the weighted sparse coefficient vector of equivalent source intensity is solved by using the orthogonal matching pursuit method with improved cosine similarity.

[0073] According to the weighted sparse coefficient of the equivalent source intensity and the transmission relationship between the reconstructed sound pressure and the equivalent source intensity, the sound field reconstruction under sparse sampling is achieved.

[0074] This embodiment implements a weighting strategy for the transfer matrix mode and improves the atomic matching criterion to achieve high-precision sound field reconstruction under sparse sampling. By establishing a weighting strategy for the transfer matrix mode, low-order transfer matrix modes are given priority when constructing the support set, reducing the risk of instability caused by selecting high-order modes containing noise. By introducing a measure of the spatial distance between vectors to improve the cosine similarity criterion, the improved cosine similarity atomic matching criterion is used to replace the original inner product criterion to measure the correlation between atoms and residuals, thereby overcoming the problem of incorrect atom selection caused by the high complexity of high-frequency sound fields.

[0075] Specifically, a rectangular measurement surface is set in the near field area of ​​the sound source, and the measurement surface is evenly divided into L grid points in rows and columns, where L x is the number of rows of L grid points, L y is the number of columns of L grid points, L = L x ×L y Randomly select M grid points from the L grid points as sampling points to install microphones, the M grid points correspond to M microphones one by one, M<L, and form an M-sparse holographic surface H. Use M microphones to synchronously measure the sound pressure at each sampling point on the holographic surface H.

[0076] A reconstruction plane R is arranged between the sound source and the holographic plane H, an equivalent source plane S is arranged on the side of the reconstruction plane R away from the holographic plane H, the number of equivalent source points arranged on the equivalent source plane S is N, and the number of reconstruction points arranged on the reconstruction plane R is L.

[0077] Furthermore, a sound field reconstruction model based on sparse sampling of transfer matrix modes is established, including:

[0078] Establishing the relationship between the equivalent source intensity on the equivalent source surface and the measured sound pressure on the holographic surface, the relationship between the equivalent source intensity on the equivalent source surface and the reconstructed sound pressure on the reconstruction surface, and the relationship between the reconstructed sound pressure on the reconstruction surface and the measured sound pressure on the holographic surface respectively;

[0079] Based on the transfer matrix G r Singular value decomposition is performed and a sound field reconstruction model based on sparse sampling of transfer matrix modes is established.

[0080] Specifically, according to the free-field Green's function and the principle of equivalent source method, a sound field reconstruction model based on sparse sampling of transfer matrix modes is established. The specific process is as follows:

[0081] Step 3.1: Establish the equivalent source intensity q on the equivalent source surface S and the measured sound pressure P on the holographic surface H h The relationship between:

[0082] P h =G h q(1)

[0083] Among them, P h =[p h (r1),…,p h (r m ),…,p h (r M )] T is the measured sound pressure of M microphones on the holographic surface H, p h (r m ) is the sound pressure signal measured by the mth microphone, r m is the position vector of the mth microphone, m=1,2,3,…,M; is the equivalent source strength vector, represents the source intensity of the nth equivalent source on the equivalent source surface, n=1,2,3,…,N, is the position vector of the nth equivalent source; G h is the transfer matrix between the sound pressure at the sampling point on the holographic surface H and the equivalent source intensity on the equivalent source surface S, which can be expressed as:

[0084]

[0085] In the formula, i is the imaginary unit, ρ is the air density, c is the speed of sound, and k is the wave number.

[0086] Step 3.2: Establish the equivalent source intensity q on the equivalent source surface S and the reconstructed sound pressure P on the reconstruction surface R r The relationship between:

[0087] P r =G r q (3)

[0088] in, is the reconstructed sound pressure of L reconstruction points on the reconstruction surface R, is the reconstructed sound pressure at the lth reconstruction point, is the position vector of the lth reconstruction point, l=1,2,3,…,L; G r is the transfer matrix between the reconstructed sound pressure on the reconstruction surface R and the equivalent source intensity on the equivalent source surface S, which can be expressed as:

[0089]

[0090] In the formula,

[0091] Step 3.3: Establish the reconstructed sound pressure P on the reconstruction surface R r The sound pressure P is measured on the holographic surface H h The relationship between:

[0092] P h =G h (G r ) + P r (5)

[0093] The superscript "+" indicates the generalized inverse of the matrix.

[0094] Step 3.4: Transfer matrix G r Perform singular value decomposition and express equation (3) as follows:

[0095] P r =UΣV H q=Uθ (6)

[0096] Among them, U=[U1,…,U n ,…,U N ] and V=[V1,…,V n ,…,V N ] are left singular vectors and right singular vectors, respectively, and both are orthogonal unitary matrices, U n and V n are their column vectors respectively. The superscript “H” represents the conjugate transpose, Σ=diag(σ1,…,σ n ,…,σ N ) is a diagonal matrix consisting of real positive singular values, satisfying σ1≥…≥σ n ≥…≥σ N >0; θ is the sparse coefficient vector of the equivalent source intensity. In this way, the transfer matrix G is represented by the column vector of the left singular vector U r, U, as a sparse basis matrix, can be regarded as a transfer matrix mode.

[0097] Step 3.5: Establish a sound field reconstruction model based on sparse sampling of transfer matrix modes. Substitute equation (6) into equation (5):

[0098] P h =Hθ (7)

[0099] Where H = G h (G r ) + U is the perception matrix.

[0100] When the number of sampling points is much smaller than the number of equivalent sources (i.e., M<<N), the sound field reconstruction under sparse sampling conditions is an underdetermined problem. According to the theory of compressed sensing, solving the sparse coefficient vector θ of the equivalent source intensity in equation (7) can be expressed as a l0 norm minimization problem:

[0101]

[0102] By solving the sparse coefficient vector θ of the equivalent source intensity in equation (8) and substituting it into equation (6), the reconstructed sound pressure of the reconstruction surface R can be obtained, that is, the sound field reconstruction under sparse sampling is realized. However, in the solution process, if too many high-order transfer matrix modes are selected as candidate bases, the noise contained in the high-order transfer matrix modes will be amplified in the sound field reconstruction, resulting in low accuracy of sound field reconstruction. Therefore, by suppressing high-order transfer matrix modes and weighting low-order transfer matrix modes, the probability of selecting low-order modes to participate in sound field reconstruction can be increased, thereby enhancing the accuracy and stability of sound field reconstruction.

[0103] Furthermore, the real-time transfer matrix modal weighting strategy includes:

[0104] Since the singular values ​​corresponding to the low-order transfer matrix modes are much larger than the singular values ​​corresponding to the high-order transfer matrix modes, this embodiment uses the corresponding singular values ​​to perform weighted processing on the transfer matrix modes, thereby giving priority to the low-order transfer matrix modes in the selection of sound field reconstruction and suppressing the selection of high-order transfer matrix modes.

[0105] The implementation of the weighting strategy includes two steps: first, normalize each column of the transfer matrix U, and then use the corresponding singular value to weight each order of the transfer matrix mode. That is, the weighting process of the transfer matrix mode is characterized as:

[0106]

[0107] in, is the weighted transfer matrix, D U is the weighting matrix, which can be expressed as:

[0108]

[0109] Among them, U n is the nth column of the transfer matrix U, σ n is the nth singular value in the diagonal matrix Σ.

[0110] After weighting the transfer matrix modes using the corresponding singular values, the measured sound pressure on the holographic surface R in equation (7) can be expressed as:

[0111]

[0112] in, is the weighted perception matrix, is the weighted sparse coefficient vector of equivalent source intensity, D U The generalized inverse of .

[0113] The orthogonal matching pursuit method based on improved cosine similarity is used to solve the weighted sparse coefficient vector β of the equivalent source intensity in equation (11), which specifically includes:

[0114] Step 5.1: Initialize residual γ0 = P h , iteration number t = 1, index set is an empty set, and the maximum number of iterations is determined according to the number of microphones M and the number of equivalent source points N. in Represents the largest integer that is rounded to a real number not greater than the real number.

[0115] Step 5.2: Define the improved cosine similarity criterion. For two vectors x = (x1, x2, ..., x n ) and y=(y1,y2,…,y n ), the improved cosine similarity criterion is defined as:

[0116]

[0117] Among them, α∈[0,1] is the weight coefficient, is the Euclidean distance between two vectors.

[0118] Step 5.3: Use the improved cosine similarity criterion to select the best atom and add it to the weighted perception matrix according to the following formula: Find the atomic position that best matches the current residue:

[0119]

[0120] Step 5.4: Update the index set Γ t =Γ t-1 ∪jt ;

[0121] Among them, Γ t is the index set of the tth iteration, Γ t-1 is the index set of the previous iteration, j t is the weighted perception matrix The index value of the optimal atom position in .

[0122] Step 5.5: Using the index set Γ t From the weighted perception matrix The corresponding atomic composition support matrix is ​​selected from And use the least squares method to calculate the current approximate solution

[0123] in, is the support set of the tth iteration, Representation Matrix The transpose of .

[0124] Step 5.6: Update the residual

[0125] Step 5.7: Iterate again for t=t+1 times until the termination condition t=T is met, then stop iterating and output the weighted sparse coefficient vector of the equivalent source intensity as the final solution

[0126] In the above process, the optimal weight coefficient for each iteration This is determined through the following process:

[0127] For the weight coefficient α in the tth iteration (t) Traverse from 0 to 1 with an increment of 0.01 to calculate the corresponding weighted sparse coefficient vector of equivalent source intensity And use To estimate the sound pressure at the M sampling points on the holographic surface, and then minimize the measured sound pressure P on the holographic surface h and reconstructed sound pressure The relative error between them determines the optimal weight coefficient

[0128]

[0129] When the weight coefficient is set to When , the weighted sparse coefficient vector of the equivalent source intensity of the tth iteration is obtained.

[0130] In obtaining the weighted sparse coefficient vector of equivalent source intensity After that, according to formula (6), the reconstructed sound pressure on the reconstruction surface R can finally be expressed as This enables sound field reconstruction under sparse sampling.

[0131] Compared with the traditional orthogonal matching pursuit method, the method of the present invention has better sound field reconstruction performance.

[0132] Example 2

[0133] In order to more clearly express the technical solution of the present invention, the following specific embodiments are provided to introduce the solution:

[0134] In numerical simulation, the sound source, holographic surface H, equivalent source surface S and reconstruction surface R are distributed as follows: Figure 1 As shown in the figure, the simulated sound source is a simply supported steel plate with a thickness of 3 mm and a size of 0.5 m × 0.5 m. A harmonic force with an amplitude of 1 N is applied to the center of the steel plate. The Poisson's ratio of the steel plate is 0.28 and the density is 7.85 × 10 3 kg / m 3 , Young's modulus is 2.1×10 11 Pa. The holographic surface H is 0.05m away from the steel plate, and its size is 0.5m×0.5m. A total of 441 grid points of 21×21 are evenly divided on H, that is, the grid spacing is 0.025m. In order to simulate the actual environment, Gaussian white noise with a signal-to-noise ratio of 30dB is added to the measured sound pressure. The reconstruction surface R is 0.02m away from the steel plate, and the size of the reconstruction surface R and the distribution of the grid points on it are consistent with the distribution of the grid points on the holographic surface H. The equivalent source surface S is arranged on the side of the reconstruction surface R away from the holographic surface H, 0.05m away from the steel plate, and the size of the equivalent source surface S and the distribution of the equivalent source points on it are consistent with the distribution of the grid points on the holographic surface H. In order to quantitatively evaluate the sound field reconstruction performance, the reconstruction relative error is defined as:

[0135]

[0136] Among them, P r and P th are the reconstructed sound pressure and the theoretical sound pressure, respectively.

[0137] In the simulation, 64 grid points are randomly selected from the 441 grid points on the holographic surface H to install microphones to measure the sound pressure. The distribution of microphone positions is as follows: Figure 2 shown.

[0138] Figure 3The figure shows the comparison of the reconstructed sound pressure distribution results at frequencies of 500Hz, 1000Hz, 1500Hz and 2000Hz using the traditional orthogonal matching pursuit method and the method of this embodiment. It can be seen that compared with the traditional orthogonal matching pursuit method, the reconstructed sound pressure distribution of the method of this embodiment is more consistent with the theoretical sound pressure distribution. The reconstruction errors of the method of this embodiment at the four frequencies are significantly lower than those of the traditional orthogonal matching pursuit method. The reconstruction errors of the traditional orthogonal matching pursuit method at the four frequencies are 9.17%, 34.77%, 46.61% and 52.93%, respectively, while the reconstruction errors of the method of this embodiment are reduced to 2.72%, 4.32%, 5.65% and 7.98%, respectively. Although the sound field becomes more complex as the frequency increases, the method of this embodiment still has a lower sound field reconstruction error at high frequencies, indicating the advantage of the method of this embodiment in sound field reconstruction performance.

[0139] Example 3

[0140] like Figure 1-4 As shown in the figure, compared with the traditional orthogonal matching pursuit method, this method has better sound field reconstruction performance in a wide frequency band.

[0141] In the numerical simulation, the holographic surface H, the equivalent source surface S and the reconstruction surface R are distributed as follows: Figure 1 The parameters of the equivalent source surface and the reconstruction surface are set the same as those in Example 1.

[0142] 100 different random microphone distributions are selected on the holographic surface for sound field reconstruction, and the average value of the relative error of these 100 sound field reconstructions is taken as the evaluation index. Figure 4 The figure shows the average error curve of 100 times of sound field reconstruction using the traditional orthogonal matching pursuit method and this method in the frequency range of 100-2000Hz. It can be seen that the sound field reconstruction accuracy of this method is significantly better than that of the traditional orthogonal matching pursuit method in the entire frequency band. As the frequency increases, the sound field becomes more and more complex, which will lead to a decrease in the accuracy of atom selection in the orthogonal matching pursuit method and a gradual increase in the error of sound field reconstruction. However, this method has a more excellent sound field reconstruction performance in the entire frequency range.

[0143] Example 4

[0144] like Figure 1-5 As shown, compared with the traditional orthogonal matching pursuit method, the method of the present invention has better noise resistance and robustness.

[0145] In the numerical simulation, the holographic surface R, the equivalent source surface S and the reconstruction surface R are distributed as follows: Figure 1 The sound source frequency is 500 Hz, and the parameters of the holographic surface, equivalent source surface and reconstruction surface are set the same as those in Example 1.

[0146] Figure 5The figure shows the comparison of the reconstructed sound pressure distribution results of the traditional orthogonal matching pursuit method and the method of the present invention when the signal-to-noise ratio is 10dB, 20dB and 30dB respectively. When the signal-to-noise ratio is 10dB, the reconstructed sound pressure distribution of the traditional orthogonal matching pursuit method in a high noise environment cannot be well matched with the theoretical value, and the reconstruction error reaches 26.91%, indicating that the noise resistance and robustness of the traditional method are poor, while the method of the present invention can accurately reconstruct the sound pressure distribution with an error of only 8.71%, and has better noise resistance and robustness; when the signal-to-noise ratio is 20dB, the reconstructed sound pressure distribution of the traditional orthogonal matching pursuit method is more consistent with the theoretical value with an error of 12.29% as the signal-to-noise ratio increases, while the method of the present invention can accurately reconstruct the sound pressure distribution with a reconstruction error of only 6.71%; when the signal-to-noise ratio is 30dB, both methods can accurately reconstruct the sound pressure distribution, but the reconstruction error of the method of the present invention is only 2.72%, which is also lower than the 9.17% of the traditional orthogonal matching pursuit method.

[0147] Example 5

[0148] like Figure 1-6 As shown, compared with the traditional orthogonal matching pursuit method, the method of the present invention has better noise resistance and robustness at high frequencies.

[0149] In the numerical simulation, the holographic surface R, the equivalent source surface S and the reconstruction surface R are distributed as follows: Figure 1 The sound source frequency is 2000 Hz, and Gaussian white noise with a signal-to-noise ratio of 10 dB is added in the simulation. The parameters of the holographic surface, equivalent source surface and reconstruction surface are set the same as those in Example 1.

[0150] Figure 6 The figure shows the comparison of the reconstructed sound pressure distribution results of the traditional orthogonal matching pursuit method and the method of the present invention when the frequency is 2000Hz and the signal-to-noise ratio is 10dB. It can be seen that in high-frequency and high-noise environments, the reconstructed sound pressure distribution of the traditional orthogonal matching pursuit method is less consistent with the theoretical value, with a reconstruction error of 40.92%, while the method of the present invention can still accurately reconstruct the sound pressure distribution with an error of only 15.06%, and has better noise resistance and robustness at high frequencies.

[0151] Example 6

[0152] like Figure 1-7 As shown, compared with the traditional orthogonal matching pursuit method, the method of the present invention has higher sound field reconstruction performance when using fewer sampling points at high frequencies.

[0153] In the numerical simulation, the holographic surface R, the equivalent source surface S and the reconstruction surface R are distributed as follows: Figure 1 The sound source frequency is 500 Hz, and the parameters of the holographic surface, equivalent source surface and reconstruction surface are set the same as those in Example 1.

[0154] Figure 7 The figure shows the comparison of the reconstructed sound pressure distribution results of the traditional orthogonal matching pursuit method and the method of the present invention when the number of sampling points is 36, 49 and 64 respectively. When the number of sampling points is 36, the traditional orthogonal matching pursuit method cannot obtain accurate sound pressure distribution, and the reconstruction error is 38.81%, while the method of the present invention can obtain accurate sound pressure distribution, with an error of only 5.16%, and has better sound field reconstruction performance when the number of sampling points is small; when the number of sampling points is 49, the accuracy of reconstructed sound pressure distribution of the traditional orthogonal matching pursuit method is improved, with a reconstruction error of 26.91%, while the reconstruction error of the method of the present invention is only 3.31%; when the number of sampling points is 64, the traditional orthogonal matching pursuit method can basically obtain sound pressure distribution results that are relatively consistent with the theoretical value as the number of sampling points increases, with a reconstruction error of 9.17%, while the method of the present invention can still achieve high-precision sound field reconstruction, with a reconstruction error of 2.72%, indicating that the method of the present invention can achieve high-precision sound field reconstruction with fewer sampling points.

[0155] Example 7

[0156] like Figure 1-8 As shown, compared with the traditional orthogonal matching pursuit method, the method of the present invention can use fewer sampling points to achieve sound field reconstruction at high frequencies.

[0157] In the numerical simulation, the holographic surface R, the equivalent source surface S and the reconstruction surface R are distributed as follows: Figure 1 The sound source frequency is 2000 Hz, and microphones are installed at 36 grid points randomly selected from the 441 grid points on the holographic surface H to measure the sound pressure.

[0158] Figure 8 The figure shows the comparison of the reconstructed sound pressure distribution results of the traditional orthogonal matching pursuit method and the method of the present invention when the frequency is 2000Hz and 36 sampling points are used. It can be seen that under the condition of high frequency and small number of sampling points, the reconstructed sound pressure distribution of the traditional orthogonal matching pursuit method cannot match the theoretical value, and the reconstruction error is as high as 76.59%, while the method of the present invention can still reconstruct the sound pressure distribution more accurately, with an error of 24.83%, indicating that the method of the present invention can achieve sound field reconstruction using fewer sampling points at high frequencies, significantly reducing the test cost in practical applications.

[0159] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. An orthogonal matching pursuit sound field reconstruction method based on joint weighted transfer matrix modality and improved cosine similarity, characterized in that: include: Determine a research area, set a measurement surface based on the research area, set grid points on the measurement surface, install microphones through the grid points, and form a holographic surface, wherein the grid points correspond to the microphones one by one; Arrange a reconstruction surface between the sound source in the study area and the holographic surface, arrange an equivalent source surface on the side of the reconstruction surface away from the holographic surface, and establish a sound field reconstruction model under sparse sampling based on transfer matrix mode by using the relationship between the equivalent source intensity and the measured sound pressure and the reconstruction surface sound pressure; Based on the sound field reconstruction model under sparse sampling, a transfer matrix modal weighting strategy is implemented, and the weighted sparse coefficient vector of the equivalent source intensity is solved by using the orthogonal matching pursuit method of improved cosine similarity; According to the weighted sparse coefficient of the equivalent source intensity and the transmission relationship between the reconstructed sound pressure and the equivalent source intensity, the sound field reconstruction under sparse sampling is realized; The sound field reconstruction model under sparse sampling based on the transfer matrix mode is established, including: Establishing the relationship between the equivalent source intensity on the equivalent source surface and the measured sound pressure on the holographic surface, the relationship between the equivalent source intensity on the equivalent source surface and the reconstructed sound pressure on the reconstruction surface, and the relationship between the reconstructed sound pressure on the reconstruction surface and the measured sound pressure on the holographic surface respectively; Based on the transfer matrix Perform singular value decomposition to establish the sound field reconstruction model under sparse sampling based on the transfer matrix mode, wherein the transfer matrix It is a transfer matrix between the reconstructed sound pressure on the reconstruction surface and the equivalent source intensity on the equivalent source surface.

2. The method according to claim 1, characterized in that The relationship between the equivalent source intensity on the equivalent source surface and the measured sound pressure on the holographic surface is: （1） In the formula, is the measured sound pressure of M microphones on the holographic surface H, is the sound pressure signal measured by the mth microphone, is the position vector of the mth microphone, ; is the equivalent source strength vector, represents the source intensity of the nth equivalent source on the equivalent source surface, , is the position vector of the nth equivalent source; is the transfer matrix between the sound pressure of the sampling point on the holographic surface H and the equivalent source intensity on the equivalent source surface S; The relationship between the equivalent source intensity on the equivalent source surface and the reconstructed sound pressure on the reconstruction surface is: （2） In the formula, is the reconstructed sound pressure of L reconstruction points on the reconstruction surface R, is the reconstructed sound pressure at the lth reconstruction point, is the position vector of the lth reconstruction point, ; is the transfer matrix between the reconstructed sound pressure on the reconstruction surface R and the equivalent source intensity on the equivalent source surface S; The relationship between the reconstructed sound pressure on the reconstruction surface and the measured sound pressure on the holographic surface is: （3） Where the superscript "+" indicates the generalized inverse of the matrix.

3. The method according to claim 2, characterized in that Based on the transfer matrix The method for singular value decomposition is: （4） In the formula, and are the left singular vector and the right singular vector respectively, and are the column vectors of left singular vectors and right singular vectors respectively. The superscript "H" represents the conjugate transpose. is a diagonal matrix consisting of real positive singular values, satisfying ; is the sparse coefficient vector of the equivalent source intensity.

4. The method according to claim 3, characterized in that The sound field reconstruction model under sparse sampling based on transfer matrix mode is: （5） In the formula, is the perception matrix.

5. The method according to claim 4, characterized in that When the number of sampling points is much smaller than the number of equivalent sources, the sound field reconstruction under sparse sampling conditions is regarded as an underdetermined problem. According to the compressed sensing theory, the sparse coefficient vector of the equivalent source intensity in the following formula (6) is expressed as a l0 norm minimization problem and weighted by the real-time transfer matrix modal weighting strategy; （6） In the formula, is the sparse coefficient vector of the equivalent source intensity.

6. The method according to claim 5, characterized in that The real-time transfer matrix modal weighting strategy includes: Each column of the transfer matrix U is normalized, and then the corresponding singular value is used to weight the mode of each order transfer matrix, that is: （7） In the formula, is the weighted transfer matrix, is the weighting matrix; Then the measured sound pressure on the holographic surface in equation (5) is expressed as: （8） In the formula, is the weighted perception matrix, is the weighted sparse coefficient vector of equivalent source intensity, is the weight matrix The generalized inverse of .

7. The method according to claim 6, characterized in that The weighted sparse coefficient vector of equivalent source intensity is solved by using the orthogonal matching pursuit method with improved cosine similarity, including: S1.

1. Initialize residual , number of iterations , index set , is an empty set, and the maximum number of iterations is determined according to the number of microphones M and the number of equivalent source points N. ,in It means rounding to the largest integer not greater than the real number; S1.2, define the improved cosine similarity criterion; S1.3, using the improved cosine similarity criterion to select the best atom, in the weighted perception matrix Find the atomic position that best matches the current residual. , ）（9） Update Index Set , is the index set of the tth iteration, is the index set of the previous iteration, is the weighted perception matrix The index value of the optimal atom position in ; S1.

4. Using Index Sets From the weighted perception matrix The corresponding atomic composition support matrix is ​​selected from , and use the least squares method to calculate the current approximate solution , is the support set of the tth iteration, Representation Matrix The transpose of S1.

5. Update residual ; S1.6, the number of iterations is , re-iterate and update until the termination condition is met , output the weighted sparse coefficient vector of equivalent source intensity, the final solution .

8. The method according to claim 7, characterized in that During the iteration process, the optimal weight coefficient of each iteration , determined by the following process: For the weight coefficient in the tth iteration Traverse from 0 to 1 with an increment of 0.01 to calculate the corresponding weighted sparse coefficient vector of equivalent source intensity , and use Estimate the sound pressure at M sampling points on the holographic surface, and then minimize the measured sound pressure on the holographic surface and reconstructed sound pressure The relative error between them determines the optimal weight coefficient : （10） When the weight coefficient is set to When , the weighted sparse coefficient vector of the equivalent source intensity of the tth iteration is obtained.

9. The method according to claim 7, characterized in that: The method further comprises: In obtaining the weighted sparse coefficient vector of the equivalent source intensity Then, according to formula (4), the reconstructed sound pressure on the reconstruction surface is calculated , to achieve sound field reconstruction under sparse sampling.

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