Cellular topology microphone array for equivalent source method near field acoustical holography

Abstract

The invention discloses a honeycomb topology microphone array for equivalent source method near-field acoustical holography, which is characterized in that according to the geometrical shape and geometrical parameters of the honeycomb topology microphone array, the space coordinates of N array lattice points in one-to-one correspondence with N microphones are calculated and obtained based on a honeycomb lattice point generation algorithm; further obtaining a cellular topology microphone array with N array lattice points; measuring by using the cellular topology microphone array to obtain sound field measurement data; and further utilizing the sound field measurement data to obtain a sound field distribution result of a reconstruction surface through an equivalent source method, and completing the design of the honeycomb topology microphone array for the equivalent source method near-field acoustical holography. According to the method, the spatial distribution of the array is optimized, the condition number of the transfer matrix is remarkably reduced while the coverage uniformity of the sound field is ensured, and then the stability and precision of sound field reconstruction based on the equivalent source method are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of noise source identification and positioning, and more specifically to a cellular topology microphone array for equivalent source method near-field acoustic holography, which is particularly suitable for sound field reconstruction in near-field acoustic holography measurement. Background Art

[0002] Near-field acoustic holography is a highly efficient method for sound source identification and sound field visualization, with significant application value for the low-noise design and acoustic performance optimization of various devices. Its principle is to use a microphone array to measure acoustic parameters such as the sound pressure and vibration velocity radiated by the sound source. Then, through sound field reconstruction algorithms such as spatial Fourier transform, boundary element method, equivalent source method, and Helmholtz equation least squares method, the distribution of acoustic quantities on the surface of the sound source or in three-dimensional space is reconstructed. The equivalent source method has been widely used and studied due to its theoretical simplicity and applicability to sound sources of arbitrary shapes.

[0003] In actual acoustic holography testing, conventional microphone arrays often employ uniformly spaced distributions in rectangular, polar, spherical, or cylindrical coordinates, which are simple to design and easy to implement. However, the overall spatial distribution of these arrays exhibits significant non-uniformity. For example, equally spaced sampling based on spherical coordinates results in dense microphone distribution in the polar regions and sparse distribution in the equatorial region; while equally spaced sampling of circular planar arrays in polar coordinates results in dense microphone distribution in the center and sparse distribution in the edge regions. This spatial non-uniformity not only makes it difficult to fully and comprehensively acquire the sound field information within the array plane, but also results in a high condition number of the transfer matrix, thus affecting the accuracy and reliability of sound field reconstruction. Summary of the Invention

[0004] In order to avoid the shortcomings of the above-mentioned existing technologies, the present invention provides a cellular topology microphone array for near-field acoustic holography based on the equivalent source method. By optimizing the spatial distribution of the array, the condition number of the transfer matrix is significantly reduced while ensuring the uniformity of the sound field coverage, thereby improving the stability and accuracy of the sound field reconstruction based on the equivalent source method.

[0005] The present invention adopts the following technical solutions to solve the technical problems:

[0006] The cellular topology microphone array for equivalent source method near-field acoustic holography of the present invention is characterized in that, based on the geometric shape and geometric parameters of the cellular topology microphone array, the spatial coordinates of N array grid points corresponding one to one to the N microphones are calculated based on a cellular grid point generation algorithm, thereby obtaining a cellular topology microphone array with N array grid points; the cellular topology microphone array is then used to perform measurements to obtain sound field measurement data; and the sound field measurement data is further used to obtain a sound field distribution result of a reconstructed surface through the equivalent source method, thereby completing the design of the cellular topology microphone array for equivalent source method near-field acoustic holography.

[0007] The cellular topology microphone array for equivalent source method near-field acoustic holography of the present invention is also characterized in that:

[0008] The geometric shapes of the cellular topology microphone array include a rectangular plane microphone array, a cylindrical microphone array and a spherical microphone array;

[0009] The method of obtaining the sound field measurement data by measuring with a cellular topology microphone array is to measure in the near field area of the sound source to be measured by using the cellular topology microphone array to obtain the frequency domain sound pressure vector p represented by formula (1): H :

[0010] p H =[p(r H1 ),p(r H2 ),…,p(r HN )] T (1)

[0011] H represents the holographic surface;

[0012] With r Hn represents the position coordinates of the nth microphone on the holographic surface H, n = 1, 2, 3...N;

[0013] With p(r Hn ) represents the frequency domain sound pressure data measured by the n-th microphone on the holographic surface H;

[0014] Set M equivalent source points inside the sound source, where m represents the mth equivalent source point, and measure the sound pressure vector p H As the input information of the equivalent source method near-field acoustic holography, the equivalent source intensity vector Q is solved by inverting the matrix equation of the equivalent source method near-field acoustic holography represented by formula (2):

[0015] p H =G H Q (2)

[0016] Where Q = [q(r E1 ),q(r E2 ),…,q(r EM )]T ;

[0017] E represents the equivalent source surface; r Em Represents the position coordinates of the mth equivalent source on the equivalent source surface E, m = 1, 2, 3...M;

[0018] q(r Em ) represents the mth equivalent source intensity on the equivalent source surface E; G H It is the transfer matrix represented by formula (3):

[0019]

[0020] [G H ] nm Characterization transfer matrix G H The element in the nth row and mth column is as shown in formula (4):

[0021]

[0022] Among them, |r Hn -r Em | represents the nth microphone position r Hn and the mth equivalent source point position r Em the distance between them; k is the wave number;

[0023] On the basis of obtaining the equivalent source intensity vector Q, the sound pressure on the reconstruction surface is calculated according to formula (5):

[0024] p R =G R Q (5)

[0025] in,

[0026] R represents the reconstruction surface; p R Represents the sound pressure vector on the reconstruction surface, that is, p R =[p(r R1 ),p(r R2 ),…,p(r RW )] T ;

[0027] W represents the total number of reconstruction points;

[0028] r Rw Represents the position coordinates of the w-th reconstruction point on the reconstruction surface R, w=1,2,3……W;

[0029] p(r Rw ) represents the sound pressure at the w-th reconstruction point on the reconstruction surface R;

[0030] G Ris the transfer matrix represented by formula (6):

[0031]

[0032] [G R ] wm Denotes the transfer matrix G R The element in the wth row and mth column, [G R ] wm Characterized by formula (7):

[0033]

[0034] Among them, |r Rw -r Em | represents the position r of the w-th reconstruction point Rw and the mth equivalent source position r Em The distance between them.

[0035] The cellular topology microphone array for equivalent source method near-field acoustic holography of the present invention is also characterized in that:

[0036] For a rectangular planar microphone array, the spatial coordinates of N array grid points in a cellular topology microphone array are calculated using formula (8):

[0037]

[0038] Where: n=1,2,3......N;

[0039] X n and Y n are the number of regular hexagonal units in the X and Y directions respectively;

[0040] L represents the side length of the regular hexagonal unit, and h represents the half-height of the regular hexagon;

[0041] x 奇 (n) and x 偶 (n) are the coordinates of the odd and even columns in the x-direction of the rectangular planar microphone array;

[0042] Moreover, x 奇 (n) and x 偶 (n) are commonly represented as x 矩形平面 (n);

[0043] y 奇 (n) and y 偶 (n) are the coordinates of the odd and even rows in the y direction of the rectangular planar microphone array;

[0044] And, y 奇 (n) and y 偶 (n) Commonly characterized as y 矩形平面(n);

[0045] For the cylindrical microphone array, the spatial coordinates of N array grid points in the cellular topology microphone array are calculated by formula (9):

[0046]

[0047] Where r represents the cross-sectional radius of the cylindrical array;

[0048] x(n), y(n), z(n) represent the coordinates of the generated cylindrical microphone array in the x, y, and z directions, respectively.

[0049] The cellular topology microphone array for equivalent source method near-field acoustic holography of the present invention is also characterized in that:

[0050] For the spherical microphone array, the spatial coordinates of N array grid points in the cellular topology microphone array are calculated by equations (10) and (11):

[0051]

[0052] Where: n = 1, 2, 3 ... N; i = 1, 2, 3 ... 11; r is the radius of the sphere;

[0053] a, b are the coordinates of the vertices in the regular hexagon, where a=1 and b is the golden ratio. Constructed, b = 1 / φ;

[0054] Construct a set of regular hexagon vertex base coordinates V from a and b base ;

[0055] Represents the coordinates of the vertex base coordinates in the x, y, and z directions. x(n), y(n), and z(n) represent the coordinates of the generated spherical microphone array in the x, y, and z directions, respectively. base The generated x(n), y(n), and z(n) can be used as the next set of base coordinates to iteratively generate new x(n), y(n), and z(n), thereby obtaining a spherical microphone array with more measurement points.

[0056] Compared with the existing technology, the beneficial effects of the present invention are embodied in:

[0057] 1. The present invention optimizes the design of the honeycomb topology array, takes into account the uniformity of the sound field coverage, significantly reduces the condition number of the transfer matrix, and effectively improves the accuracy of the sound field reconstruction.

[0058] 2. The present invention is based on the idea of equivalent source and is not limited to the shape of the holographic surface. It can comprehensively and fully measure the sound field information of various types of complex-shaped equipment.

[0059] 3. Compared with the conventional uniformly distributed array, the cellular topology microphone array of the present invention can make fuller use of the sound field information under undersampling conditions to obtain more stable reconstruction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 The cellular topology microphone array of the present invention is distributed in a rectangular plane space;

[0061] Figure 2a The cellular topology microphone array of the present invention is distributed in the cylindrical space;

[0062] Figure 2b The cellular topology microphone array of the present invention is distributed in the spherical space;

[0063] Figure 2c 、 Figure 2d and Figure 2e The measurement point position distributions of cellular topology microphone array, conventional uniform array and random array under rectangular plane are shown respectively;

[0064] Figure 2f Design the spatial arrangement of the measurement surface, reconstruction surface, and equivalent source surface for a rectangular planar cellular topology microphone array.

[0065] Figure 3a 、 Figure 3b and Figure 3c The measurement point distributions of the honeycomb topology microphone array, conventional uniform array and random array under the cylindrical surface are shown respectively; Figure 3d To design the spatial arrangement of the measurement surface, reconstruction surface and equivalent point source surface based on the cylindrical honeycomb topology microphone array, Figure 3e Arrange a top view of the space;

[0066] Figure 4a 、 Figure 4b and Figure 4c The measurement point distributions of the spherical honeycomb topology microphone array, conventional uniform array, and random array are respectively. Figure 4d Design the spatial arrangement of the measurement surface, reconstruction surface and equivalent point source surface for a microphone array based on a spherical honeycomb topology;

[0067] Figure 5a 、 Figure 5b and Figure 5c The transfer matrix condition number results are obtained by measuring the radiated sound pressure of a point source at position (0,0,0)m at an analysis frequency of 100Hz to 2000Hz using a rectangular planar cellular topology microphone array, a cylindrical cellular topology microphone array, and a spherical cellular topology microphone array according to the present invention. Furthermore, the transfer matrix condition number results obtained by measuring a uniform array and two random arrays are given for easy comparison.

[0068] Figure 6a 、 Figure 6b and Figure 6c The relative error results of sound field reconstruction calculated based on the rectangular planar honeycomb topology microphone array, cylindrical honeycomb topology microphone array, and spherical honeycomb topology microphone array of the present invention are shown respectively. The relative error curves of sound field reconstruction obtained by measurements based on a uniform array and two random arrays are also given.

[0069] Figure 7a 、 Figure 7b and Figure 7c The relative error curves of the sound field reconstruction of the cellular topology microphone array of the present invention and the conventional uniform array under underdetermined sampling conditions are respectively given in rectangular plane, cylindrical and spherical arrays. DETAILED DESCRIPTION

[0070] In this embodiment, the cellular topology microphone array used for near-field acoustic holography using the equivalent source method is as follows: based on the geometric shape and geometric parameters of the cellular topology microphone array, the spatial coordinates of N array grid points corresponding one to one to the N microphones are calculated based on the cellular grid point generation algorithm, thereby obtaining a cellular topology microphone array with N array grid points; the cellular topology microphone array is then used to perform measurements to obtain sound field measurement data; the sound field measurement data is further used to obtain the sound field distribution result of the reconstructed surface through the equivalent source method, thereby completing the design of the cellular topology microphone array used for near-field acoustic holography using the equivalent source method.

[0071] In this embodiment, the cellular topology microphone array used for equivalent source method near-field acoustic holography has a geometric shape including a rectangular plane microphone array, a cylindrical microphone array, and a spherical microphone array according to actual engineering needs.

[0072] In this embodiment, a cellular topology microphone array is used to measure the near field area of the sound source to be measured, and the frequency domain sound pressure vector p represented by formula (1) is obtained. H , as the input required for the equivalent source method near-field acoustic holography.

[0073] p H =[p(r H1 ),p(r H2 ),…,p(r HN )] T (12)

[0074] H represents the holographic surface;

[0075] With r Hn represents the position coordinates of the nth microphone on the holographic surface H, n = 1, 2, 3...N;

[0076] p(r Hn) represents the frequency domain sound pressure data measured by the n-th microphone on the holographic surface H;

[0077] M equivalent source points are set inside the sound source, where m represents the mth equivalent source point. The equivalent source intensity vector Q is solved by inverting the matrix equation of the equivalent source method near-field acoustic holography represented by formula (2):

[0078] p H =G H Q (13)

[0079] Where Q = [q(r E1 ),q(r E2 ),…,q(r EM )] T ;

[0080] E represents the equivalent source surface; r Em Represents the position coordinates of the mth equivalent source on the equivalent source surface E, m = 1, 2, 3...M;

[0081] q(r Em ) represents the mth equivalent source intensity on the equivalent source surface E;

[0082] G H It is the transfer matrix represented by formula (3):

[0083]

[0084] [G H ] nm Characterization transfer matrix G H The element in the nth row and mth column is as shown in formula (4):

[0085]

[0086] Among them, |r Hn -r Em | represents the nth microphone position r Hn and the mth equivalent source point position r Em the distance between them; k is the wave number;

[0087] On the basis of obtaining the equivalent source intensity vector Q, the sound pressure on the reconstruction surface is calculated according to formula (5):

[0088] p R =G R Q (16)

[0089] in,

[0090] R represents the reconstruction surface; p R Represents the sound pressure vector on the reconstruction surface, that is, p R=[p(r R1 ),p(r R2 ),…,p(r RW )] T ;

[0091] W represents the total number of reconstruction points;

[0092] r Rw Represents the position coordinates of the w-th reconstruction point on the reconstruction surface R, w=1,2,3……W;

[0093] p(r Rw ) represents the sound pressure at the w-th reconstruction point on the reconstruction surface R;

[0094] G R is the transfer matrix represented by formula (6):

[0095]

[0096] [G R ] wm Denotes the transfer matrix G R The element in the wth row and mth column, [G R ] wm Characterized by formula (7):

[0097]

[0098] Among them, |r Rw -r Em | represents the position r of the w-th reconstruction point Rw and the mth equivalent source position r Em The distance between them.

[0099] In this embodiment, for the rectangular plane microphone array, the spatial coordinates of N array grid points in the cellular topology microphone array are calculated by formula (8), and the generated rectangular plane microphone array is as follows: Figure 1 As shown:

[0100]

[0101] Where: n=1,2,3......N;

[0102] X n and Y n are the number of regular hexagonal units in the X and Y directions respectively;

[0103] L represents the side length of the regular hexagonal unit, and h represents the half-height of the regular hexagon;

[0104] x 奇 (n) and x 偶(n) are the coordinates of the odd and even columns in the x direction of the rectangular plane microphone array, collectively represented by x 矩形平面 (n);

[0105] y 奇 (n) and y 偶 (n) are the coordinates of the odd and even rows in the y direction of the rectangular plane microphone array, collectively represented by y 矩形平面 (n);

[0106] In this embodiment, for the cylindrical microphone array, the spatial coordinates of N array grid points in the cellular topology microphone array are calculated by formula (9), and the generated cylindrical microphone array is as follows: Figure 2a As shown:

[0107]

[0108] Where r represents the cross-sectional radius of the cylindrical array;

[0109] x(n), y(n), z(n) represent the coordinates of the generated cylindrical microphone array in the x, y, and z directions, respectively.

[0110] In this embodiment, for a spherical microphone array, the spatial coordinates of N array grid points in a cellular topology microphone array are calculated by equations (10) and (11), and the generated spherical microphone array is as follows: Figure 2b As shown:

[0111]

[0112] Where: n=1,2,3......N;

[0113] a, b are the coordinates of the vertices in the regular hexagon, where a=1 and b is the golden ratio. Constructed, b = 1 / φ;

[0114] Construct a set of regular hexagon vertex base coordinates V from a and b base ,in and Represents the x, y, and z coordinates of the vertex base coordinates, i = 1, 2, 3, ... 11;

[0115] r is the radius of the sphere;

[0116] x(n), y(n), z(n) represent the coordinates of the generated spherical microphone array in the x, y, and z directions, respectively. base The generated x(n), y(n), and z(n) can be used as the next set of base coordinates to iteratively generate new x(n), y(n), and z(n), thereby obtaining a spherical microphone array with more measurement points.

[0117] The cellular topology microphone array of the present invention is tested as follows:

[0118] Simulation process: The arrays were used for three regular array surface areas: rectangular planes, spheres, and cylinders. Therefore, these three shapes were considered separately in the simulation. For each shape, the transfer matrix condition number and acoustic field reconstruction error were compared for the three distributions: conventional uniform distribution, random distribution, and honeycomb distribution. The specific simulation parameters for the three arrays are set as follows:

[0119] Array 1: Rectangular planar array

[0120] Figure 2c 、 Figure 2d 、 Figure 2e The following are array model diagrams of cellular topology microphone array, conventional uniform array and random array in rectangular plane. The array is located on the plane of z = 0.1m, and the distribution area is a rectangle of 0.4m × 0.4m. The number of measurement points of conventional uniform array, random array and cellular topology microphone array are 143, 137 and 137 respectively. The sound field is generated by a point sound source located at (0m, 0m, 0m). The reconstruction surface is located on the plane of z = 0.09m and is evenly distributed in a rectangle of 0.4m × 0.4m. The reconstruction surface consists of 137 reconstruction points. The equivalent source points are located on the plane of z = 0.05m and are evenly distributed in a rectangle of 0.4m × 0.4m. The number of equivalent sources is 137, as shown in the figure. Figure 2f The simulation frequency is set to 100Hz-2000 Hz.

[0121] Array 2: Cylindrical Array

[0122] Figure 3a 、 Figure 3b 、 Figure 3c The following are the array model diagrams of the cellular topology microphone array, the conventional uniform array and the random array under the cylindrical surface, respectively. The array radius is 0.25m and the height is 0.5m. The number of measurement points of the conventional uniform array, the random array and the cellular topology microphone array are 186, 184 and 184 respectively. The sound field is generated by a point sound source located at (0m, 0m, 0m). The reconstruction surface consists of 216 reconstruction points, which are evenly distributed on the cylindrical surface with a radius of 0.077m coaxial with the holographic array. The equivalent source points are evenly distributed on the cylindrical surface with a radius of 0.047m coaxial with the holographic array. The total number of equivalent sources is 198, as shown in the figure. Figure 3d and Figure 3e The simulation frequency is set to 100Hz-2000 Hz.

[0123] Array 3: Spherical Array

[0124] Figure 4a 、 Figure 4b 、 Figure 4c The following are the array model diagrams of the cellular topology microphone array, the conventional uniform array, and the random array on the sphere. The center of the sphere is located at the coordinate origin, and the radius is 0.1m. The number of measurement points of the conventional uniform array, the random array, and the cellular topology microphone array are 165, 162, and 162, respectively. The sound field is generated by a point sound source located at (0m, 0m, 0m). The reconstruction surface consists of 416 reconstruction points, which are evenly distributed on a sphere with a radius of 0.07m. The equivalent source points are evenly distributed on a sphere with a radius of 0.05m. The total number of equivalent sources is 116, as shown in the following figure. Figure 4d The simulation frequency is set to 100Hz-2000 Hz.

[0125] To verify the effectiveness of the proposed honeycomb topology microphone array in sound field reconstruction, array configurations were designed for three regular array surface areas: rectangular, cylindrical, and spherical. For each area, the transfer matrix condition number and sound field reconstruction error of the three distributions (uniform, random, and honeycomb) were compared.

[0126] Here the condition number of the transfer matrix is defined as

[0127]

[0128] in, Indicates G H The generalized inverse matrix of max and σ min Represent the maximum and minimum singular values of the transfer matrix, respectively. Generally speaking, the larger the condition number of the transfer matrix, the greater the magnification of the holographic sound pressure measurement error, and the more serious the pathological nature of the inversion.

[0129] In order to measure the accuracy of the sound field reconstruction based on the array measurement of the present invention, the relative error of the reconstructed sound pressure is defined as:

[0130]

[0131] Among them, p R (f) and p(f) represent the reconstructed sound pressure and theoretical sound pressure vector of all reconstruction points at frequency f, respectively; ε(f) represents the relative error at frequency f.

[0132] Figure 5a 、 Figure 5b 、 Figure 5c The transfer matrix condition number results obtained by measuring the cellular topology microphone array, uniform array and two random arrays of the present invention are given in rectangular plane, cylindrical and spherical arrays respectively.

[0133] Figure 6a 、 Figure 6b 、 Figure 6cThe relative error results of the sound field reconstruction obtained by measuring the cellular topology microphone array of the present invention, a uniform array, and two random arrays for rectangular planes, cylindrical surfaces, and spherical arrays are presented. As can be seen from the figure, under the same array shape, number of measurement points, and solution method, the transfer matrix condition number and relative error of the sound field reconstruction of the cellular topology microphone array proposed in the present invention are lower than those of the uniform array and the random array, thus verifying that the array of the present invention is superior to conventional uniform arrays and random arrays.

[0134] Figure 7a 、 Figure 7b and Figure 7c The results of the relative reconstruction errors of the cellular topology microphone array of the present invention and the conventional uniform array under underdetermined sampling conditions are given for rectangular plane, cylindrical, and spherical arrays. For the rectangular plane array, the number of equivalent source points is set to 263, the number of measurement points of the cellular topology microphone array is 137, and the number of measurement points of the uniform array is set to 143, 165, and 195, respectively. For the cylindrical array, the number of equivalent source points is set to 205, the number of measurement points of the cellular topology microphone array is 133, and the number of measurement points of the uniform array is set to 138, 150, and 190, respectively. For the spherical array, the number of equivalent source points is set to 250, the number of measurement points of the cellular topology microphone array is 162, and the number of measurement points of the uniform array is set to 162, 180, and 209, respectively. As can be seen from the figure, the cellular topology microphone array proposed in the present invention can achieve a lower relative reconstruction error than the uniform array with a smaller number of measurement points, thereby verifying that the measurement array of the present invention can make more full use of the sound field information.

Claims

1. A cellular topology microphone array for equivalent source method near-field acoustic holography, characterized by: According to the geometric shape and geometric parameters of the cellular topology microphone array, the spatial coordinates of N array grid points corresponding one to one to the N microphones are calculated based on the cellular grid point generation algorithm, thereby obtaining a cellular topology microphone array with N array grid points; the cellular topology microphone array is then used to perform measurements to obtain sound field measurement data; the sound field measurement data is further used to obtain the sound field distribution results of the reconstructed surface through the equivalent source method, thereby completing the design of the cellular topology microphone array for equivalent source method near-field acoustic holography.

2. The cellular topology microphone array for equivalent source near-field acoustic holography according to claim 1, characterized in that: The geometric shapes of the cellular topology microphone array include a rectangular plane microphone array, a cylindrical microphone array and a spherical microphone array; The method of obtaining the sound field measurement data by measuring with a cellular topology microphone array is to measure in the near field area of the sound source to be measured by using the cellular topology microphone array to obtain the frequency domain sound pressure vector p represented by formula (1): H : p H =[p(r H1 ),p(r H2 ),…,p(r HN )] T (1) H represents the holographic surface; With r Hn represents the position coordinates of the nth microphone on the holographic surface H, n = 1, 2, 3...N; With p(r Hn ) represents the frequency domain sound pressure data measured by the n-th microphone on the holographic surface H; Set M equivalent source points inside the sound source, where m represents the mth equivalent source point, and measure the sound pressure vector p H As the input information of the equivalent source method near-field acoustic holography, the equivalent source intensity vector Q is solved by inverting the matrix equation of the equivalent source method near-field acoustic holography represented by formula (2): p H =G H Q (2) Where Q = [q(r E1 ),q(r E2 ),…,q(r EM )] T ; E represents the equivalent source surface; r Em Represents the position coordinates of the mth equivalent source on the equivalent source surface E, m = 1, 2, 3...M; q(r Em ) represents the mth equivalent source intensity on the equivalent source surface E; G H It is the transfer matrix represented by formula (3): [G H ] nm Characterization transfer matrix G H The element in the nth row and mth column is as shown in formula (4): Among them, |r Hn -r Em | represents the nth microphone position r Hn and the mth equivalent source point position r Em the distance between them; k is the wave number; On the basis of obtaining the equivalent source intensity vector Q, the sound pressure on the reconstruction surface is calculated according to formula (5): p R =G R Q (5) in, R represents the reconstruction surface; p R Represents the sound pressure vector on the reconstruction surface, that is, p R =[p(r R1 ),p(r R2 ),,p(r RW )] T ; W represents the total number of reconstruction points; r Rw Represents the position coordinates of the w-th reconstruction point on the reconstruction surface R, w=1,2,3……W; p(r Rw ) represents the sound pressure at the w-th reconstruction point on the reconstruction surface R; G R is the transfer matrix represented by formula (6): [G R ] wm Denotes the transfer matrix G R The element in the wth row and mth column, [G R ] wm Characterized by formula (7): Among them, |r Rw -r Em | represents the position r of the w-th reconstruction point Rw and the mth equivalent source position r Em The distance between them.

3. The cellular topology microphone array for equivalent source near-field acoustic holography according to claim 2, characterized in that: For a rectangular planar microphone array, the spatial coordinates of N array grid points in a cellular topology microphone array are calculated using formula (8): Where: n=1,2,3......N; X n and Y n are the number of regular hexagonal units in the X and Y directions respectively; L represents the side length of the regular hexagonal unit, and h represents the half-height of the regular hexagon; x 奇 (n) and x 偶 (n) are the coordinates of the odd and even columns in the x-direction of the rectangular planar microphone array; Moreover, x 奇 (n) and x 偶 (n) are commonly represented as x 矩形平面 (n); y 奇 (n) and y 偶 (n) are the coordinates of the odd and even rows in the y direction of the rectangular planar microphone array; And, y 奇 (n) and y 偶 (n) Commonly characterized as y 矩形平面 (n); For the cylindrical microphone array, the spatial coordinates of N array grid points in the cellular topology microphone array are calculated by formula (9): Where r represents the cross-sectional radius of the cylindrical array; x(n), y(n), z(n) represent the coordinates of the generated cylindrical microphone array in the x, y, and z directions, respectively.

4. The cellular topology microphone array for equivalent source near-field acoustic holography according to claim 2, characterized in that: For the spherical microphone array, the spatial coordinates of N array grid points in the cellular topology microphone array are calculated by equations (10) and (11): Where: n = 1, 2, 3 ... N; i = 1, 2, 3 ... 11; r is the radius of the sphere; a, b are the coordinates of the vertices in the regular hexagon, where a=1 and b is the golden ratio. Constructed, b = 1 / φ; Construct a set of regular hexagon vertex base coordinates V from a and b base ; and Represents the x, y, and z coordinates of the vertex base coordinates; x(n), y(n), z(n) represent the coordinates of the generated spherical microphone array in the x, y, and z directions, respectively. base The generated x(n), y(n), and z(n) can be used as the next set of base coordinates to iteratively generate new x(n), y(n), and z(n), thereby obtaining a spherical microphone array with more measurement points.

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