Fibonacci array design method for equivalent source method near-field acoustical holography and application of Fibonacci array design method

Abstract

The invention discloses a Fibonacci array design method for equivalent source method near-field acoustical holography and application thereof, and the method comprises the steps: determining the shape of an array to be a circular plane, a rectangular plane, a spherical surface or a cylindrical surface, and generating corresponding Fibonacci lattice point coordinates according to the shape and size of the array and the number of microphones; a microphone is arranged at the position of the Fibonacci lattice point, and a required Fibonacci array is obtained; the array is used for measuring a sound field, and a measurement signal is input into an equivalent source method near-field acoustical holography algorithm to reconstruct the sound field. According to the invention, the space utilization rate of the microphone can be effectively improved, the comprehensiveness and uniformity of the near-field acoustical holography sound pressure acquisition of the equivalent source method are ensured, and relatively low transfer matrix condition number and column correlation are also considered. Under the condition of the same array surface shape, the same number of microphones and the same solving method, compared with a conventional uniformly-distributed array and a randomly-distributed array, the array provided by the invention has higher acoustical holography reconstruction stability and precision.

Description

Technical Field

[0001] The present invention relates to the technical field of sound source identification and positioning, and more specifically to a Fibonacci array design method for equivalent source method near-field acoustic holography and its application. Background Art

[0002] Near-field acoustic holography is an effective means of sound source identification and sound field visualization, and has important application value for the low-noise design of various types of equipment. Its principle is to use a microphone array to measure the acoustic parameters such as sound pressure and vibration velocity radiated by the sound source, and reconstruct the acoustic quantities on the surface of the sound source or in any three-dimensional space through sound field reconstruction algorithms such as spatial Fourier transform method, boundary element method, equivalent source method, and spherical / plane wave superposition method. Among the many reconstruction algorithms, the equivalent source method has been widely used and studied due to its theoretical simplicity and the advantage of being applicable to sound sources of any shape.

[0003] In order to ensure the reliability of the equivalent source method to reconstruct the sound field, the first is to improve the stability of the solution, and the second is to ensure the comprehensiveness of the sampling of the sound field information. The key factors affecting the stability of the solution are the condition number and column correlation of the transfer matrix. The smaller the value, the better the stability of the solution. The properties of the transfer matrix are closely related to the distribution of the microphone array. At present, in actual acoustic holography tests, the conventional arrays commonly used have microphones that are evenly distributed at equal intervals according to rectangular coordinates, polar coordinates, spherical coordinates, and cylindrical coordinates. Although such arrays are simple in design and easy to implement, they often lead to high condition numbers and column correlations of the transfer matrix, affecting the stability and accuracy of the solution. On the other hand, although the microphones of the above array are evenly distributed at equal intervals on the coordinate axis, their overall distribution in space is not uniform. For example, a spherical array sampled at equal intervals according to spherical coordinates has dense sampling near the poles and sparse sampling near the equator; a circular plane array sampled at equal intervals according to polar coordinates has dense sampling near the center and sparse sampling near the edge. This results in the microphone being unable to fully and fully sample the sound field information within the array surface. In order to reduce column correlation, some researchers have proposed using randomly distributed microphone arrays. However, in practical applications, random arrays have uneven coverage of the sound field and are likely to miss key sound field information, and the reliability of reconstruction cannot be guaranteed. In addition, there are also schemes to determine the optimal array distribution by calculating the minimum condition number or minimum column correlation of the transfer matrix, but this scheme only considers the solution stability and ignores the uniformity of the array distribution, and it is still difficult to guarantee the reliability of reconstruction. Summary of the invention

[0004] The present invention aims to solve the shortcomings of microphone arrays in the existing equivalent source method near-field acoustic holography technology, and provides a Fibonacci array design method and application for equivalent source method near-field acoustic holography, so that the Fibonacci array takes into account uniformity and lower transfer matrix condition number and column correlation, while comprehensively collecting sound field information, improving the stability of the solution.

[0005] The Fibonacci array design method for equivalent source method near-field acoustic holography of the present invention is carried out according to the following steps:

[0006] Step a, determining the shape and size of the Fibonacci array, and setting the number N of microphones in the Fibonacci array;

[0007] The shape of the Fibonacci array is a circular plane, a rectangular plane, a spherical surface or a cylindrical surface;

[0008] The dimensions of the Fibonacci array are: the radius r1 of the circular plane, the length and width a×b of the rectangular plane, the radius r2 of the spherical surface, and the radius r3 and height L of the cylindrical surface;

[0009] The number N of microphones is not less than 8;

[0010] Step b: Calculate the coordinates of N array grid points corresponding to the N microphones in a one-to-one manner according to the grid point generation algorithm of the Fibonacci array, which are:

[0011] The coordinates of the N array grid points of the Fibonacci array with a circular plane shape are calculated by formula (1):

[0012]

[0013] The coordinates of the N array grid points of the Fibonacci array in the shape of a rectangular plane are calculated by formula (2):

[0014]

[0015] The coordinates of the N array grid points of the Fibonacci array with a spherical shape are calculated by formula (3):

[0016]

[0017] The coordinates of the N array grid points of the cylindrical Fibonacci array are calculated by formula (4):

[0018]

[0019] in:

[0020] n represents the nth Fibonacci point or the nth microphone;

[0021] Let x(n), y(n) and z(n) represent the position coordinates of the nth Fibonacci grid point respectively;

[0022] z0 represents the set array height, z0 is a constant;

[0023] mod(n / φ,1) represents the fractional part of n / φ;

[0024] Step c: setting a microphone at the Fibonacci grid point coordinate position calculated in step b to obtain a Fibonacci array for equivalent source method near-field acoustic holography.

[0025] The equivalent source method near-field acoustic holography method of the present invention is to use the Fibonacci array of the present invention to perform the following process:

[0026] First, the frequency domain sound pressure vector P is detected as follows: H

[0027] Determine the array shape according to the structure of the sound source to be measured, and obtain a Fibonacci array of corresponding shape according to the method of step b and step c in claim 1; use the Fibonacci array to measure in the near field area of ​​the sound source to be measured, and obtain the frequency domain sound pressure vector P represented by formula (5) H :

[0028]

[0029] in:

[0030] r Hn Represents the position coordinates of the nth microphone, i.e. r Hn =(x(n),y(n),z(n));

[0031] p(r Hn ) represents the frequency domain sound pressure detected by the nth microphone;

[0032] Secondly, solve the equivalent source intensity vector Q as follows:

[0033] Set M equivalent source points, with m representing the mth equivalent source point, and transform the sound pressure vector p H As the input information of the near-field acoustic holography using the equivalent source method, the matrix equation of the near-field acoustic holography using the equivalent source method represented by equation (6) is used to solve the equivalent source intensity vector Q;

[0034] p H =G H Q (6)

[0035] in:

[0036] Q=[q(r E1 ),q(r E2 ),…,q(r EM )] T ,q(r Em ) represents the source intensity of the mth equivalent source point;

[0037] Transfer matrix G H for:

[0038]

[0039] With [G H ] nm Characterize the transfer matrix G H The element in the nth row and mth column is:

[0040]

[0041] |r Hn -r Em | represents the nth microphone position r Hn and the mth equivalent source point position r Em The distance between

[0042] k is the wave number;

[0043] Finally, the sound pressure vector p on the reconstruction surface is calculated as follows: R

[0044] According to the equivalent source intensity vector Q, the sound pressure vector p on the reconstruction surface is calculated according to formula (8): R :

[0045] p R =G R Q (8)

[0046] The sound pressure vector p on the reconstruction surface R For: p R =[p(r R1 ),p(r R2 ),…,p(r RW )] T , W represents the total number of reconstruction points;

[0047] Transfer matrix G R for:

[0048]

[0049] With [G R ]wm Characterize the transfer matrix G R The element at row w and column m is:

[0050]

[0051] |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.

[0052] The characteristics of the equivalent source method near-field acoustic holography method of the present invention are also:

[0053] The matrix equation of the equivalent source method near-field acoustic holography represented by formula (6) is used to solve the equivalent source intensity vector Q by using the following method 1 or method 2:

[0054] Method 1: When the sound source is spatially continuous and distributed, a solution method under a non-sparse framework is used

[0055] That is, Tikhonov regularization is used to solve the l2 norm problem shown in formula (10):

[0056]

[0057] Method 2: When the sound source is spatially discrete and concentrated, a solution method under a sparse framework is used

[0058] That is, the sparse regularization based on the CVX toolbox is used to solve the 1-norm problem shown in equation (11):

[0059]

[0060] In formula (10) and formula (11):

[0061] Indicates the value of Q when the following formula reaches the minimum value;

[0062] ||·||2 represents the 2-norm, ||·||1 represents the 1-norm, and ε represents an error term related to noise.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] 1. The Fibonacci array of the present invention optimizes the space utilization of the microphone, and takes into account the comprehensiveness and uniformity of sound pressure collection while ensuring that the condition number and column correlation of the equivalent source method transfer matrix are low.

[0065] 2. Compared with conventional uniformly distributed arrays and randomly distributed arrays, the Fibonacci array of the present invention has higher acoustic holographic reconstruction stability and accuracy under the conditions of the same holographic measurement surface shape, the same number of microphones and the same solution method. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 , Figure 6 , Fig.11 , Fig.16 The comparison of the measurement point positions of three distributions, namely, conventional uniform distribution, a certain random distribution, and the Fibonacci distribution of the present invention, in a circular plane, a rectangular plane, a spherical surface, and a cylindrical array. At the same time, the distribution positions of the reconstruction points, the equivalent source points, and the sound source points are also shown in the figure.

[0067] Figure 2 , Figure 7 , Fig.12 , Fig.17 The transfer matrix condition numbers of the measurement points of the three distributions, namely, conventional uniform distribution, 10 random distributions, and the Fibonacci distribution of the present invention, are compared in the circular plane, rectangular plane, spherical surface, and cylindrical arrays;

[0068] Figure 3 , Figure 8 , Fig.13 , Fig.18 The comparison of the average column correlation of the transfer matrices of the measurement points of three distributions, namely, conventional uniform distribution, 10 kinds of random distribution, and the Fibonacci distribution of the present invention, in the circular plane, rectangular plane, spherical surface, and cylindrical array respectively;

[0069] Figure 4 , Fig. 9 , Fig.14 , Fig.19 The relative errors of the sound field reconstruction obtained by solving the l2 norm problem using Tikhonov regularization for the three measurement points of conventional uniform distribution, 10 random distributions, and the Fibonacci distribution of the present invention in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0070] Figure 5 , Fig.10 , Fig.15 , Fig. 20 The relative errors of the sound field reconstruction obtained by solving the 1-norm problem using sparse regularization based on the CVX toolbox for the three measurement points of conventional uniform distribution, 10 random distributions, and the Fibonacci distribution of the present invention in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0071] Markings in the figure:

[0072] h11, h12, h13, and h14 are the conventionally uniformly distributed measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0073] h21, h22, h23, and h24 are randomly distributed measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0074] h31, h32, h33, and h34 are the measurement points of Fibonacci distribution in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0075] r1, r2, r3, and r4 are reconstruction points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0076] q1, q2, q3, and q4 are the equivalent source points in the circular plane, rectangular plane, spherical surface, and cylindrical array respectively;

[0077] s1, s2, s3, and s4 are the sound source points in the circular plane, rectangular plane, spherical surface, and cylindrical array respectively;

[0078] c11, c12, c13, c14 are the transfer matrix condition numbers or average column correlations of conventional uniformly distributed measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0079] c21, c22, c23, and c24 are the transfer matrix condition numbers or average column correlations of randomly distributed measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0080] c31, c32, c33, and c34 are the transfer matrix condition numbers or average column correlations of Fibonacci-distributed measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0081] e11, e12, e13, and e14 are the calculated relative errors of conventional uniformly distributed measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0082] e21, e22, e23, and e24 are the calculated relative errors of randomly distributed measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively;

[0083] e31, e32, e33, and e34 are the calculated relative errors of the Fibonacci distribution measurement points in the circular plane, rectangular plane, spherical surface, and cylindrical array, respectively. DETAILED DESCRIPTION

[0084] The Fibonacci array design method for equivalent source near-field acoustic holography in this embodiment is performed in the following steps:

[0085] Step a, determining the shape and size of the Fibonacci array, and setting the number N of microphones in the Fibonacci array;

[0086] According to actual engineering needs, the shape of the Fibonacci array can be set to a circular plane, a rectangular plane, a spherical surface, or a cylindrical surface;

[0087] The dimensions of the Fibonacci array are: the radius r1 of the circular plane, the length and width a×b of the rectangular plane, the radius r2 of the spherical surface, and the radius r3 and height L of the cylinder surface;

[0088] The number of microphones N is not less than 8;

[0089] Step b: Calculate the coordinates of N array grid points corresponding to the N microphones in a one-to-one manner according to the grid point generation algorithm of the Fibonacci array, which are:

[0090] The coordinates of the N array grid points of the Fibonacci array with a circular plane shape are calculated by formula (1):

[0091]

[0092] The coordinates of the N array grid points of the Fibonacci array in the shape of a rectangular plane are calculated by formula (2):

[0093]

[0094] The coordinates of the N array grid points of the Fibonacci array with a spherical shape are calculated by formula (3):

[0095]

[0096] The coordinates of the N array grid points of the cylindrical Fibonacci array are calculated by formula (4):

[0097]

[0098] in:

[0099] n represents the nth Fibonacci point or the nth microphone;

[0100] Let x(n), y(n) and z(n) represent the position coordinates of the nth Fibonacci grid point respectively;

[0101] z0 represents the set array height, z0 is a constant;

[0102] mod(n / φ,1) represents the fractional part of n / φ;

[0103] Step c, setting a microphone at the Fibonacci grid coordinate position calculated by step b to obtain a Fibonacci array for equivalent source method near-field acoustic holography, which is used to measure the sound pressure in the near field of the sound source as the input required for the equivalent source method near-field acoustic holography.

[0104] The near-field acoustic holography method using the equivalent source method of the Fibonacci array in this embodiment is performed as follows:

[0105] First, the frequency domain sound pressure vector P of the near field of the sound source is detected as follows: H

[0106] Determine the array shape according to the structure of the sound source to be measured, and obtain a Fibonacci array of corresponding shape according to the method of step b and step c in claim 1; use the Fibonacci array to measure in the near field area of ​​the sound source to be measured, and obtain the frequency domain sound pressure vector P represented by formula (5) H :

[0107] p H =[p(r H1 ),p(r H2 ),…,p(r HN )] T (5)

[0108] in:

[0109] r Hn Represents the position coordinates of the nth microphone, i.e. r Hn =(x(n),y(n),z(n));

[0110] p(r Hn ) represents the frequency domain sound pressure detected by the nth microphone;

[0111] Secondly, solve the equivalent source intensity vector Q as follows:

[0112] Set M equivalent source points, with m representing the mth equivalent source point, and transform the sound pressure vector p H As the input information of the near-field acoustic holography using the equivalent source method, the matrix equation of the near-field acoustic holography using the equivalent source method represented by equation (6) is used to solve the equivalent source intensity vector Q;

[0113] p H =G H Q (6)

[0114] in:

[0115] Q=[q(r E1 ),q(r E2 ),…,q(r EM )]T ,q(r Em ) represents the source intensity of the mth equivalent source point;

[0116] Transfer matrix G H for:

[0117]

[0118] With [G H ] nm Characterize the transfer matrix G H The element in the nth row and mth column is:

[0119]

[0120] |r Hn -r Em | represents the nth microphone position r Hn and the mth equivalent source point position r Em The distance between

[0121] k is the wave number;

[0122] Finally, the sound pressure vector p on the reconstruction surface is calculated as follows: R

[0123] According to the equivalent source intensity vector Q, the sound pressure vector p on the reconstruction surface is calculated according to formula (8): R :

[0124] p R =G R Q (8)

[0125] The sound pressure vector p on the reconstruction surface R For: p R =[p(r R1 ),p(r R2 ),…,p(r RW )] T , W represents the total number of reconstruction points;

[0126] Transfer matrix G R for:

[0127]

[0128] With [G R ] wm Characterize the transfer matrix G R The element at row w and column m is:

[0129]

[0130] |rR wr E m| represents the position of the w-th reconstruction point r R w and the mth equivalent source position r E m distance between.

[0131] In a specific implementation, the matrix equation of the equivalent source method near-field acoustic holography represented by equation (6) is used to solve the equivalent source intensity vector Q, which is solved by the following method 1 or method 2:

[0132] Method 1: When the sound source is distributed continuously in space, the equivalent source intensity vector is non-sparse, so it is easy to use the solution method under the non-sparse framework

[0133] That is, Tikhonov regularization is used to solve the l2 norm problem shown in formula (10):

[0134]

[0135] Method 2: When the sound source is spatially discrete and concentrated, the equivalent source intensity vector is sparse, so it is easy to use the solution method under the sparse framework.

[0136] That is, the sparse regularization based on the CVX toolbox is used to solve the l1 norm problem shown in formula (11):

[0137]

[0138] In formula (10) and formula (11):

[0139] Indicates the value of Q when the following formula reaches the minimum value;

[0140] ||·||2 represents the 2-norm, ||·||1 represents the 1-norm, and ε represents an error term related to noise.

[0141] The arrays of four shapes in the present invention are tested as follows:

[0142] Simulation experiment

[0143] Simulation purpose: to verify the effect of the Fibonacci distribution array of the present invention in sound field reconstruction. Specifically, it is verified that the Fibonacci distribution array has uniform and comprehensive sampling within the coverage range of the holographic surface, and its transfer matrix condition number and average column correlation are no higher than those of conventional uniform arrays and random arrays. Moreover, within the calculation frequency range, the Fibonacci distribution array can obtain sound field reconstruction accuracy that is significantly better than conventional uniform arrays and random arrays.

[0144] Simulation process: The invented array can be used for four regular shaped array surface areas: circular plane, rectangular plane, spherical surface and cylindrical surface. Therefore, these four shape areas are considered separately in the simulation. For each shape area, the transfer matrix condition number, transfer matrix average column correlation and sound field reconstruction error of the three distributions: conventional uniform distribution, random distribution and Fibonacci distribution are compared. Since the possibility of randomly distributed arrays is infinite in theory, only 10 random arrays are selected in the simulation for result comparison and analysis. The specific simulation parameter settings of the four arrays are as follows:

[0145] Array 1: Circular Planar Array

[0146] The circular planar array model is as follows Figure 1 As shown, the array surface is located on the plane of z = 0.1m, the center coordinates are (0, 0, 0.1)m, and the radius is 1m. The number of measurement points of the conventional uniform distribution h11, random distribution h21, and Fibonacci distribution h31 are all set to 90. Among them, the coordinates of the measurement points of the Fibonacci distribution are generated using formula (1). The sound field is generated by two point sound sources s1 located on the plane of z = -0.2m, with coordinates of (0, 0.3, -0.2)m and (0, -0.3, -0.2)m respectively. The sound pressure radiated by the point sound source at space r can be calculated by formula (12):

[0147]

[0148] Among them, r s represents the position of the point sound source in space, |rr s | represents r and r s The distance between them. The reconstruction point r1 is set to 5, all located on the plane of z=0m, with coordinates of (0,0,0)m, (0.4,0.4,0)m, (-0.4,0.4,0)m, (-0.4,-0.4,0)m, (0.4,-0.4,0)m. The equivalent source point q1 is located on the plane of z=-0.1m, and is evenly distributed in a circular area with a center coordinate of (0,0,-0.1)m and a radius of 0.8m. The number of equivalent sources is 301. The simulation frequency is set to 100Hz-1000Hz.

[0149] Array 2: Rectangular Planar Array

[0150] Rectangular planar array model such as Figure 6As shown, its array surface is located on the plane of z = 0.1m, and the distribution area is a rectangle of 0.6m×1.4m. The number of measurement points of the conventional uniform distribution h12, random distribution h22, and Fibonacci distribution h32 is set to 105. Among them, the coordinates of the measurement points of the Fibonacci distribution are generated using formula (2). The sound field is generated by two point sound sources s2 located on the plane of z = -0.3m, with coordinates of (0.3, 1.03, -0.3)m and (0.3, 0.34, -0.3)m respectively. The sound pressure radiated by the point sound source at space r is calculated by formula (12). The reconstruction point r2 is located on the plane of z = 0m and is uniformly distributed in a rectangle of 0.4m×1.2m. The equivalent source point q2 is located on the plane of z = -0.1m and is uniformly distributed in a rectangle of 0.4m×1.2m. The number of equivalent sources is 231. The simulation frequency is set to 100Hz-3000Hz.

[0151] Array 3: Spherical Array

[0152] Spherical array model Fig.11 As shown, the center of the sphere is located at the origin of the coordinate system, and the radius is 1m. The number of measurement points of the conventional uniform distribution h13, random distribution h23, and Fibonacci distribution h33 is set to 184. Among them, the coordinates of the measurement points of the Fibonacci distribution are generated using formula (3). The sound field is generated by two point sound sources s3 located on the plane z = 0m, with coordinates of (0, 0.1, 0)m and (0, -0.1, 0)m respectively. The sound pressure radiated by the point sound source at space r is calculated by formula (12). Six reconstruction points r3 are set, with coordinates of (0, 0.9, 0)m, (0, -0.9, 0)m, (0.9, 0, 0)m, (-0.9, 0, 0)m, (0, 0, 0.9)m, and (0, 0, -0.9)m respectively. The equivalent source points q3 are distributed on a sphere with a center at the origin of the coordinate system and a radius of 0.3m. The number of equivalent sources is 464. The simulation frequency is set to 100Hz-3000Hz.

[0153] Array 4: Cylindrical Array

[0154] The cylindrical array model is as follows Fig.16As shown, the center of its bottom surface is located at the origin of the coordinate system, and the radius is 0.159m. The number of measurement points of the conventional uniform distribution h14, random distribution h24, and Fibonacci distribution h34 are all set to 110. Among them, the coordinates of the measurement points of the Fibonacci distribution are generated using formula (4). The sound field is generated by two point sound sources s4 located on the axis of the cylinder, with coordinates of (0,0,0.4)m and (0,0,0.8)m respectively. The sound pressure radiated by the point sound source at space r is calculated by formula (12). Three reconstruction points r4 are set, with coordinates of (0,0.11,0.3)m, (0,0.11,0.6)m, and (0,0.11,0.9)m respectively. The equivalent source point q4 is distributed on a cylinder with the center of the bottom surface located at the origin of the coordinate system and a radius of 0.477m. The number of equivalent sources is 208 in total. The simulation frequency is set to 100Hz-3000Hz.

[0155] In the simulation of the above four array shapes, the transfer matrix condition number is calculated by formula (13):

[0156]

[0157] The value of the condition number can reflect the solution stability, that is, the stability of the l2 norm problem solved by Tikhonov regularization in the non-sparse framework in equation (10). The smaller the condition number, the better the solution stability.

[0158] The average column correlation of the transfer matrix is ​​calculated by formula (14):

[0159]

[0160] Among them, the transfer matrix G H See formula (6); G H (:,i) and G H (:,j) represent the transfer matrix G H The i-th and j-th columns of ; represents the total number of combinations of any two columns from N columns. The average column correlation of the transfer matrix can reflect the solution stability under the sparse framework, that is, the stability of the sparse regularization based on the CVX toolbox in equation (11) to solve the l1 norm problem. The smaller the average column correlation, the better the solution stability.

[0161] In the process of reconstruction using the equivalent source method, the sampled sound pressure of the array is the sound pressure radiated by the point source s1 at the corresponding measurement point, that is, p in equation (5) H During simulation, at p H Add Gaussian white noise with a signal-to-noise ratio of 30dB. Next, construct the transfer matrix G according to formula (6): H. Then, the source intensity Q can be solved. In order to compare the reconstruction errors of the invented array under sparse and non-sparse solution methods, both solution methods are compared here. Among them, the non-sparse solution method uses Tikhonov regularization to solve the l2 norm problem of equation (10), and the sparse solution method uses sparse regularization based on the CVX toolbox to solve the l1 norm problem of equation (11). After obtaining the source intensity vector Q, substitute it into equation (8) to obtain the sound pressure vector p at the reconstruction point R .

[0162] Finally, the relative error of sound pressure is calculated using formula (15):

[0163]

[0164] 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, and ε(f) represents the relative error at frequency f.

[0165] Figure 2 , Figure 7 , Fig.12 and Fig.17 The comparison of the transfer matrix condition numbers of the measurement points under three distribution modes, namely, conventional uniform distribution, 10 random distributions and the Fibonacci distribution of the present invention, is shown in circular plane, rectangular plane, spherical surface and cylindrical array respectively. Figure 3 , Figure 8 , Fig.13 , Fig.18 The comparison of the average column correlation of the transfer matrix of the measurement points under the three distribution modes of conventional uniform distribution, 10 random distributions and the Fibonacci distribution of the present invention is shown respectively in the circular plane, rectangular plane, spherical surface and cylindrical array. It can be observed from these figures that the transfer matrix condition number (c31, c32, c33, c34) and the average column correlation (c31, c32, c33, c34) of the Fibonacci distribution array are significantly lower than or not higher than the conventional uniform distribution array (c11, c12, c13, c14) and the random distribution array (c21, c22, c23, c24), indicating that in these cases, the solution stability of the Fibonacci distribution array in the sparse and non-sparse framework is not inferior to that of the conventional uniform distribution array and the random distribution array.

[0166] Figure 4 , Fig. 9 , Fig.14 , Fig.19The relative errors of sound field reconstruction are obtained by using Tikhonov regularization to solve the l2 norm problem in three distribution modes: conventional uniform distribution, 10 random distributions and the Fibonacci distribution of the present invention in circular plane, rectangular plane, spherical surface and cylindrical array. Figure 5 , Fig.10 , Fig.15 , Fig. 20 The relative errors of the sound field reconstruction obtained by solving the l1 norm problem using sparse regularization based on the CVX toolbox in the three distribution modes of conventional uniform distribution, 10 kinds of random distribution and the Fibonacci distribution of the present invention in the circular plane, rectangular plane, spherical plane and cylindrical array, respectively. It can be seen from these figures that under the same array shape, the same number of measurement points and the same solution method, within the working frequency range, the reconstruction errors (e31, e32, e33, e34) of the Fibonacci distribution proposed by the present invention are lower than those of the conventional uniform distribution (e11, e12, e13, e14) and the random distribution (e21, e22, e23, e24). This verifies that the array of the present invention is superior to the conventional uniform array and the random array.

Claims

1. A Fibonacci array design method for equivalent source method near-field acoustic holography, characterized in that Proceed as follows: Step a, determining the shape and size of the Fibonacci array, and setting the number N of microphones in the Fibonacci array; The shape of the Fibonacci array is a circular plane, a rectangular plane, a spherical surface or a cylindrical surface; The dimensions of the Fibonacci array are: the radius r1 of the circular plane, the length and width a×b of the rectangular plane, the radius r2 of the spherical surface, and the radius r3 and height L of the cylindrical surface; The number N of microphones is not less than 8; Step b: Calculate the coordinates of N array grid points corresponding to the N microphones in a one-to-one manner according to the grid point generation algorithm of the Fibonacci array, which are: The coordinates of the N array grid points of the Fibonacci array with a circular plane shape are calculated by formula (1): The coordinates of the N array grid points of the Fibonacci array in the shape of a rectangular plane are calculated by formula (2): The coordinates of the N array grid points of the Fibonacci array with a spherical shape are calculated by formula (3): The coordinates of the N array grid points of the cylindrical Fibonacci array are calculated by formula (4): in: n represents the nth Fibonacci point or the nth microphone; Let x(n), y(n) and z(n) represent the position coordinates of the nth Fibonacci grid point respectively; z0 represents the set array height, z0 is a constant; mod(n / φ,1) represents the fractional part of n / φ; Step c: setting a microphone at the Fibonacci grid point coordinate position calculated in step b to obtain a Fibonacci array for equivalent source method near-field acoustic holography.

2. An equivalent source method near-field acoustic holography method, characterized by The Fibonacci array of claim 1 is used in the following process: First, the frequency domain sound pressure vector P is detected as follows: H Determine the array shape according to the structure of the sound source to be measured, and obtain a Fibonacci array of corresponding shape according to the method of step b and step c in claim 1; use the Fibonacci array to measure in the near field area of ​​the sound source to be measured, and obtain the frequency domain sound pressure vector P represented by formula (5) H : p H =[p(r H1 ),p(r H2 ),…,p(r HN )] T (5) in: r Hn Represents the position coordinates of the nth microphone, i.e. r Hn =(x(n),y(n),z(n)); p(r Hn ) represents the frequency domain sound pressure detected by the nth microphone; Secondly, solve the equivalent source intensity vector Q as follows: Set M equivalent source points, with m representing the mth equivalent source point, and transform the sound pressure vector p H As the input information of the near-field acoustic holography using the equivalent source method, the matrix equation of the near-field acoustic holography using the equivalent source method represented by equation (6) is used to solve the equivalent source intensity vector Q; p H =G H Q (6) in: Q=[q(r E1 ),q(r E2 ),…,q(r EM )] T ,q(r Em ) represents the source intensity of the mth equivalent source point; Transfer matrix G H for: With [G H ] nm Characterize the transfer matrix G H The element in the nth row and mth column is: r Hn -r Em | represents the nth microphone position r Hn and the mth equivalent source point position r Em The distance between k is the wave number; Finally, the sound pressure vector p on the reconstruction surface is calculated as follows: R According to the equivalent source intensity vector Q, the sound pressure vector p on the reconstruction surface is calculated according to formula (8): R : p R =G R Q (8) The sound pressure vector p on the reconstruction surface R For: p R =[p(r R1 ),p(r R2 ),…,p(r RW )] T , W represents the total number of reconstruction points; the transfer matrix G R for: With [G R ] wm Characterize the transfer matrix G R The element at row w and column m is: |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.

3. The equivalent source method near-field acoustic holography method according to claim 2 is characterized in that: The matrix equation of the equivalent source method near-field acoustic holography represented by formula (6) is used to solve the equivalent source intensity vector Q by using the following method 1 or method 2: Method 1: When the sound source is spatially continuous and distributed, a solution method under a non-sparse framework is used That is, Tikhonov regularization is used to solve the l2 norm problem shown in formula (10): Method 2: When the sound source is spatially discrete and concentrated, a solution method under a sparse framework is used That is, the sparse regularization based on the CVX toolbox is used to solve the l1 norm problem shown in formula (11): In formula (10) and formula (11): Indicates the value of Q when the following formula reaches the minimum value; ||·||2 represents the 2-norm, ||·||1 represents the 1-norm, and ε represents an error term related to noise.

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