Method for in-situ measurement of surface acoustic impedance of materials using mosaic microphone array

Abstract

The application provides a method for in-situ measuring surface acoustic impedance of material by using a mosaic microphone array, wherein a rectangular microphone array is arranged on a surface of a material to be measured; the microphones are divided into two groups; an acoustic wave incidence angle is set; an acoustic source is arranged in a half space on one side of the surface of the material based on the acoustic wave incidence angle; sound pressures are collected by the two groups of microphones; spherical wave basis functions are used to respectively describe sound field radiated by the acoustic source and reflected by the boundary; a particle velocity component in the direction of a unit normal vector is obtained based on the two groups of spherical wave basis functions; the particle normal velocity at the first group of microphones is reconstructed by using the sound pressure distribution collected by the two groups of microphones; the acoustic impedance ratio at the first group of microphones is calculated based on the sound pressure and the particle normal velocity of the surface of the material collected by the first group of microphones; and the surface acoustic impedance ratio of the material to be measured is obtained by taking an average value. The method avoids the influence of acoustic scattering of components on the sound field and improves the sound pressure measurement accuracy.

Description

Technical Field

[0001] This invention relates to the field of acoustic impedance measurement technology, and specifically to a method for in-situ measurement of the acoustic impedance of a material surface using an embedded microphone array. Background Technology

[0002] The surface acoustic impedance of a material is an important physical quantity characterizing its acoustic properties. The classic methods for measuring acoustic impedance are the impedance tube method and the reverberation chamber method, both of which require standard acoustic equipment and environmental conditions. In practical engineering environments, by using a microphone array to collect sound pressure distribution and calculating the boundary acoustic quantity distribution based on near-field acoustic holographic reconstruction, the boundary acoustic impedance can be obtained, enabling in-situ measurement of the surface acoustic impedance of materials.

[0003] Current in-situ measurement methods for acoustic impedance require the deployment of a microphone array in a half-space on one side of the boundary to collect sound pressure distribution, followed by calculation of the boundary sound pressure and particle normal velocity distribution based on near-field acoustic holography reconstruction. Depending on the near-field acoustic holography method used, the deployed microphone array can be a double-layer planar array, a double-layer closed curved surface array, a single-layer spherical array, or a single-layer planar array, etc. Regardless of the complexity of the array structure, the presence of components such as array supports and cables will affect the sound field distribution in the half-space, thereby affecting the sound pressure measurement and acoustic quantity reconstruction calculation results, and ultimately affecting the acoustic impedance calculation results. Summary of the Invention

[0004] This invention proposes a method for in-situ measurement of the acoustic impedance of a material surface using an embedded microphone array, in order to solve the technical problem that existing acoustic impedance measurement methods are inaccurate due to the influence of components such as array supports and cables on the sound field distribution.

[0005] To address the aforementioned technical problems, this invention provides a method for in-situ measurement of the acoustic impedance of a material surface using an embedded microphone array, comprising the following steps:

[0006] Step S1: Arrange a rectangular microphone array uniformly on the surface of the material to be tested; divide the microphones into two groups, the sum of the row and column numbers of the first group is even, and the sum of the row and column numbers of the second group is odd.

[0007] The measurement points of the first set of microphones are flush with the surface of the material to be tested, while the measurement points of the second set of microphones are higher than the surface of the material to be tested.

[0008] Step S2: Set the sound wave incident angle, and based on the sound wave incident angle, arrange the sound source in the half space on one side of the material surface, and collect the sound pressure through the two sets of microphones;

[0009] Step S3: Use two sets of spherical wave basis functions to describe the sound field of source radiation and boundary reflection respectively;

[0010] Step S4: Based on the two sets of spherical wave basis functions, obtain the particle velocity component in the unit normal vector direction, and reconstruct the particle normal velocity at the first set of microphones using the sound pressure distribution collected by the two sets of microphones.

[0011] Step S5: Based on the material surface acoustic pressure and the normal vibration velocity of the particle collected by the first group of microphones, calculate the acoustic impedance at the first group of microphones, and obtain the surface acoustic impedance of the material to be tested by taking the average value.

[0012] Preferably, the measuring aperture of the microphones arranged in a rectangular array is greater than half the wavelength of the sound wave emitted by the sound source in step S2 in the dimensions of the two sides of the rectangle.

[0013] Preferably, the spacing between the microphones arranged in a rectangular array is less than one-sixth of the wavelength of the sound wave emitted by the sound source in step S2.

[0014] Preferably, the distance of the microphone beyond the surface of the material to be tested is greater than one-tenth of the wavelength of the sound wave emitted by the sound source.

[0015] Preferably, step S3 includes:

[0016] Step S31: Establish a global coordinate system with the center of the microphone array as the origin O and the plane where the boundary of the material to be measured is located as the xy coordinate plane; denote the mirror image point of the sound source center O1 about the boundary as O2, translate the global coordinate system to O1 and O2, establish two local coordinate systems, and denote the coordinates of any field point x in the half space in the two local coordinate systems as x1 and x2 respectively.

[0017] Step S32: In two local coordinate systems, the sound pressure response of the sound source radiation and boundary reflection at the field point x is described by a linear superposition of a set of spherical wave functions.

[0018] Preferably, the expression for step S32 is:

[0019]

[0020] In the formula, ψ 1,j (x1; ω) and ψ 2,j (x2; ω) are the spherical wave basis functions with O1 and O2 as the origins, respectively; c 1,j (ω) and c 2,j (ω) represents the coefficients of the two sets of basis function expansion terms; ω is the angular frequency of the sound wave; j is the ordinal number of the basis function expansion term; J is the number of basis function expansion terms; (r1,θ1,φ1) and (r2,θ2,φ2) represent the spherical coordinates of the field point in the two local coordinate systems, respectively; For a sphere of the first kind, Hankel function is used; k = ω / c is the wave number of the sound wave, and c is the speed of sound. It is a spherical harmonic function; integers n, l, and j satisfy the relation j = n 2 +n+l+1, where -n≤l≤n, 0≤n≤N, and N is the cutoff value for n.

[0021] Preferably, in step S4, the method for obtaining the particle velocity components in the unit normal vector direction includes:

[0022] Step S411: Increase the half-space sound pressure p at field point x. half (x;ω) represents the linear superposition of sound source radiation and boundary reflection;

[0023] Step S412: By utilizing the relationship between the sound pressure in half-space and the particle velocity of the fluid medium to satisfy the conditions of the Euler equation, the particle velocity component in the unit normal vector direction is obtained.

[0024] Preferably, in step S412, the particle velocity component in the unit normal vector direction The expression is:

[0025]

[0026] In the formula, ρ0 is the density of the fluid medium; Indicates the direction of the unit normal vector.

[0027] Preferably, in step S4, the method for reconstructing the normal velocity of the particles at the first set of microphones using the sound pressure distribution collected by the two sets of microphones includes:

[0028] Step S421: Set the global coordinates of all microphones on the rectangular array to x m m = 1, 2, ..., M, where M is the number of microphones, and their coordinates in the two local coordinate systems are denoted as x and y respectively. 1,m and x 2,m The sound pressure values ​​collected by the array Represented in the following matrix form:

[0029]

[0030] Step S422: For the coefficient vector {c(ω)} 2J×1 Solve for the problem, and you will get the following results.

[0031]

[0032] In the formula, the superscript T denotes the transpose of the vector; the superscript T... Represents the pseudo-inverse of a matrix;

[0033] Step S423: Reconstruct the normal vibration velocity of the mass points at the first set of measurement points on the material surface:

[0034]

[0035] In the formula, x m′ The global coordinates of the first set of measurement points. This indicates rounding up to the nearest integer.

[0036] Preferably, the expression for the surface acoustic impedance is:

[0037]

[0038] The beneficial effects of the present invention include at least the following:

[0039] 1) This invention utilizes a microphone array to collect sound pressure information and combines it with near-field acoustic holography to calculate the surface acoustic impedance of materials, enabling in-situ acquisition of surface acoustic impedance in actual engineering environments without relying on impedance measuring instruments.

[0040] 2) The microphone array used in this invention is embedded in the material, which avoids the influence of sound scattering from components such as array supports and cables on the sound field when the microphone array is arranged in space, and can improve the accuracy of sound pressure measurement.

[0041] 3) This invention utilizes an embedded microphone array to directly collect sound pressure information from the material surface. It only requires reconstruction of the normal particle velocity, without the need to reconstruct the sound pressure on the material surface. This avoids errors introduced by sound pressure reconstruction and improves the accuracy and efficiency of acoustic impedance calculation. Attached Figure Description

[0042] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention;

[0043] Figure 2 This is a three-dimensional structural diagram illustrating the arrangement of the microphone array, sound source, and test material according to an embodiment of the present invention.

[0044] Figure 3 This is a two-dimensional structural diagram illustrating the establishment of the global coordinate system and two local coordinate systems in an embodiment of the present invention.

[0045] Figure 4 This is a schematic diagram of the projection of the measurement points of the microphone array in the xy plane according to an embodiment of the present invention.

[0046] Figure 5 This is a schematic diagram showing the relative error between the calculated and actual values ​​of the acoustic impedance of the material surface in an embodiment of the present invention as a function of the incident angle of the sound wave. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0048] Example 1

[0049] like Figure 1 As shown, this embodiment of the invention provides a method for in-situ measurement of the acoustic impedance of a material surface using an embedded microphone array, comprising the following steps:

[0050] Step S1: Arrange a rectangular microphone array on the surface of the material to be tested.

[0051] Specifically, the embedding position of each microphone is determined near the geometric center of the material surface. Based on the microphone size parameters, through holes are drilled at the microphone embedding positions. Each microphone is then embedded into one of the holes, with the tail cable extending from the other end of the through hole and connected to the data acquisition system.

[0052] The microphones are divided into two groups according to the method of taking points at intervals, specifically, as follows: Figure 2 As shown, the sum of the row and column numbers of the first group is even, and the sum of the row and column numbers of the second group is odd. The measurement point of the microphone in the first group is flush with the surface of the material to be measured, while the measurement point of the microphone in the second group is higher than the surface of the material to be measured, which can collect the sound pressure in the half-space on one side of the material surface.

[0053] Step S2: Set the sound wave incident angle. Based on the sound wave incident angle, arrange the sound source in the half space on one side of the material surface and collect the sound pressure through two sets of microphones.

[0054] Specifically, such as Figure 2 As shown, a sound source is arranged in a half-space on one side of the material surface, and the center of the sound source is denoted as O1. The geometric center of the area covered by the projection of all measurement points onto the material surface is denoted as O. The angle between the line connecting point O and the sound source center O1 and the boundary normal at point O is the sound wave incident angle, denoted as θ. inc The sound source is activated to emit sound waves, and the microphone array collects the sound pressure to obtain the incident angle θ of the sound waves. inc Sound pressure data under the given conditions. The sound source was turned off, and its position was adjusted to change the sound wave incident angle θ. inc Repeat the above sound pressure acquisition process to obtain different incident angles θ. inc The sound pressure data under the given conditions can be used to calculate different incident angles θ in subsequent steps. inc Acoustic impedance under certain conditions.

[0055] Step S3: Use two sets of spherical wave basis functions to describe the sound field of source radiation and boundary reflection, respectively.

[0056] Specifically, such as Figure 3 As shown, a global coordinate system is established with point O as the origin and the plane containing the boundary as the xy coordinate plane. The mirror image of O1 about the boundary is denoted as O2. The global coordinate system is translated to O1 and O2, establishing two local coordinate systems. The coordinates of any point x in the half-space are denoted as x1 and x2 in the two local coordinate systems, respectively. For the steady-state sound field, in each of the two local coordinate systems, the sound pressure response at that point is described by a linear superposition of a set of spherical wave functions, with the expressions as follows:

[0057]

[0058] Where, ψ 1,j (x1; ω) and ψ 2,j (x2; ω) are the spherical wave basis functions with O1 and O2 as the origins, respectively; c 1,j (ω) and c 2,j (ω) represents the coefficients of the two sets of basis function expansions; ω is the angular frequency of the sound wave; j is the ordinal number of the basis function expansion term; J is the number of terms in the basis function expansion term. In spherical coordinates, the expression for the spherical wave basis function is:

[0059]

[0060] in, For the first kind of sphere Hankel function, k = ω / c is the wave number of the sound wave, and c is the speed of sound; It is a spherical harmonic function; in equations (1) to (3), integers n, l, and j satisfy the relation j = n 2 +n+l+1, where -n≤l≤n, 0≤n≤N, and N is the cutoff value for n.

[0061] Step S4: Based on the two sets of spherical wave basis functions, obtain the particle velocity components in the unit normal vector direction, and reconstruct the particle normal velocity at the first set of microphones using the sound pressure distribution collected by the two sets of microphones.

[0062] Specifically, the half-space sound pressure p at field point x half (x; ω) is the linear superposition of sound source radiation and boundary reflection, which can be expressed as:

[0063]

[0064] The sound pressure p at point x half (x; ω) and the vibrational velocity v of the fluid medium particles half The relationship between (x; ω) satisfies the Euler equation:

[0065]

[0066] Where ρ0 is the density of the fluid medium, For gradient operators, According to equations (4) and (5), at the field point x, the unit normal vector... The particle velocity components in the direction are:

[0067]

[0068] Step S5: Based on the surface acoustic pressure and particle normal velocity of the material collected by the first set of microphones, calculate the acoustic impedance at the first set of microphones, and obtain the surface acoustic impedance of the material to be tested by taking the average value.

[0069] Specifically, a mathematical relationship is established between the measured sound pressure value and the normal vibration velocity of the fluid medium particles on the material surface, and the normal vibration velocity of the particles on the material surface is reconstructed. The global coordinates of all measurement points on the array are denoted as x. m m = 1, 2, ..., M, where M is the number of measurement points, and their coordinates in the two local coordinate systems are denoted as x and y respectively. 1,m and x 2,m According to equation (4), the sound pressure value collected by the array It can be represented in the following matrix form:

[0070]

[0071] Among them, the spherical wave function expansion term matrix [ψ] p (x m ;ω)] M×2J for:

[0072]

[0073] Coefficient vector {c(ω)} 2J×1 for:

[0074]

[0075] Where the superscript T denotes the transpose of the vector; solving for the coefficient vector yields:

[0076]

[0077] Among them, superscript The pseudo-inverse of the matrix is ​​represented; then, using equation (6), the normal velocity of the particles at the first set of measurement points on the material surface is reconstructed:

[0078]

[0079] Where, x m′ The global coordinates of the first set of measurement points. This indicates rounding up to the nearest integer.

[0080] Then, using the sound pressure of the material surface directly collected from the first set of measurement points and the normal vibration velocity of the particles at the first set of measurement points reconstructed by equation (11), the acoustic impedance of the first set of measurement points is calculated, and the average value is taken to obtain the acoustic impedance of the material surface:

[0081]

[0082] Example 2

[0083] This embodiment is in Figure 3 In the global coordinate system shown, measurements are performed using the method of Example 1, with the coordinates of the boundary and material surface set to z = 0. It is assumed that the wavelength of the sound wave under investigation is λ = 0.23 m and the frequency is f = 1500 Hz. A through-hole is drilled near the center of the material surface, according to the size of the microphone. Exemplarily, the following calculations are provided using one type of microphone arrangement parameters, but are not intended to limit the scope of this embodiment.

[0084] The number of through-holes is selected as 6×6, with a spacing of 0.03m between adjacent through-holes. The geometric center O of the area covered by the through-holes is the origin of the global coordinate system. Microphones are embedded into the through-holes in a mosaic manner, and the microphones are divided into two groups using a point-by-point sampling method. The measurement points of the first group of microphones are flush with the material surface, while the measurement points of the second group of microphones are 0.03m above the material surface. The projections of the two groups of measurement points onto the xy-plane are shown in the figure. Figure 4 .

[0085] A pulsating spherical sound source is arranged in a half-space on one side of the material surface, with a distance of 2m between its center O1 and O, and an incident angle of θ for the sound wave. inc The sound source is driven to emit sound, the microphone array collects the sound pressure, and the sound source is turned off. The position of the sound source is adjusted to change the incident angle θ of the sound wave. inc Sound pressure was collected under different incident angles. After collection, the normal vibration velocity of air particles at the first set of measurement points was reconstructed using a sound field reconstruction algorithm. Finally, the acoustic impedance of the material surface was calculated using the sound pressure measurements and the reconstructed normal vibration velocity values ​​at the first set of measurement points.

[0086] The numerical simulation results are presented below to verify the accuracy of the acoustic impedance calculation. Assume the radius of the pulsating sphere sound source is a = 0.05 m, the radial vibration velocity of the surface particles is V0 = 0.01 m / s, and the air density is ρ0 = 1.20 kg / m³. 3 The speed of sound, v = 343 m / s. Assume the boundary normalized acoustic impedance Z0 satisfies the model:

[0087] Z0=0.436(1+i)(σ e / f) 0.5 +19.48iα e / f (13)

[0088] Where, σ e The effective flow resistance of the material is taken as 38 kPa sm. -2 ;α e The value represents the rate of decrease in material porosity with material depth, taken as 15m. -1 f is the sound wave frequency; the relationship between the acoustic impedance Z and Z0 satisfies Z = ρ0cZ0.

[0089] The sound pressure distribution in the half-space on one side of the boundary and at the boundary can be calculated using analytical formulas. To simulate the effect of microphone measurement error, Gaussian white noise with a signal-to-noise ratio of 30 dB is added to the measured sound pressure.

[0090] When the frequency f = 1500 Hz, the true acoustic impedance value obtained from equation (13) is Z = 903.25 + 983.43i. Using the method of this invention, when the incident angle θ inc When the angle is 0°, the calculated boundary acoustic impedance is Z. cal =868.82+974.10i, the calculated value agrees well with the actual value. We then examine the different incident angles θ when the frequency is f=1500Hz. inc The acoustic impedance ratio is calculated under the following conditions. The calculated acoustic impedance ratio value Z is defined. cal The relative error ε between the true value Z and the actual value Z is:

[0091]

[0092] ε varies with the incident angle θ inc The change curve is as follows Figure 5 As shown.

[0093] observe Figure 5 It was found that the relative error of the calculated acoustic impedance values ​​under different incident angle conditions obtained by the method of the present invention is less than 8%, indicating that the calculated acoustic impedance values ​​are very close to the true values ​​and the calculation accuracy is high. The results show that the method of in-situ measurement of the acoustic impedance of a material surface using an embedded microphone array of the present invention can accurately obtain the acoustic impedance of the material surface by directly acquiring the sound pressure distribution on the material surface and reconstructing and calculating the normal vibration velocity distribution of the surface particles.

[0094] Example 3

[0095] Based on Example 1, this embodiment, to further enhance the rationality of the collected data, considers the spatial sampling problem related to wavelength. According to the investigated sound wave wavelength λ, parameters such as the microphone array measurement aperture and the spacing between adjacent microphones are determined. The lower limit of the measurement aperture in each dimension is... The upper limit of the microphone spacing is The second set of microphone measurement points extends at least beyond the material surface.

[0096] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described; only preferred embodiments of the present invention are illustrated. The descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. As long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0097] It should be noted that those skilled in the art can make various modifications and improvements without departing from the inventive concept, and these all fall within the scope of protection of this invention. Therefore, the scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for in-situ measurement of the acoustic impedance of a material surface using an embedded microphone array, characterized in that: Includes the following steps: Step S1: Arrange a rectangular microphone array uniformly on the surface of the material to be tested; The microphones are divided into two groups. The sum of the row and column numbers of the first group is even, and the sum of the row and column numbers of the second group is odd. The measurement points of the first set of microphones are flush with the surface of the material to be tested, while the measurement points of the second set of microphones are higher than the surface of the material to be tested. Step S2: Set the sound wave incident angle, and based on the sound wave incident angle, arrange the sound source in the half space on one side of the material surface, and collect the sound pressure through the two sets of microphones; Step S3: Use two sets of spherical wave basis functions to describe the sound field of source radiation and boundary reflection respectively; Step S4: Based on the two sets of spherical wave basis functions, obtain the particle velocity component in the unit normal vector direction, and reconstruct the particle normal velocity at the first set of microphones using the sound pressure distribution collected by the two sets of microphones. Step S5: Based on the material surface acoustic pressure and the normal vibration velocity of the particle collected by the first group of microphones, calculate the acoustic impedance at the first group of microphones, and obtain the surface acoustic impedance of the material to be tested by taking the average value.

2. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 1, characterized in that: The measuring aperture of the microphones arranged in a rectangular array is greater than half the wavelength of the sound wave emitted by the sound source in step S2 in the dimensions of the two sides of the rectangle.

3. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 1, characterized in that: The spacing between the microphones arranged in a rectangular array is less than one-sixth of the wavelength of the sound wave emitted by the sound source in step S2.

4. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 1, characterized in that: The distance of the microphone beyond the surface of the material being tested is greater than one-tenth of the wavelength of the sound wave emitted by the sound source.

5. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 1, characterized in that: Step S3 includes: Step S31: Establish a global coordinate system with the center of the microphone array as the origin O and the plane where the boundary of the material to be measured is located as the xy coordinate plane; denote the mirror image point of the sound source center O1 about the boundary as O2, translate the global coordinate system to O1 and O2, establish two local coordinate systems, and denote the coordinates of any field point x in the half space in the two local coordinate systems as x1 and x2 respectively. Step S32: In two local coordinate systems, the sound pressure response of the source radiation and boundary reflection at the field point x is described by a linear superposition of a set of spherical wave basis functions.

6. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 5, characterized in that: The expression for step S32 is: In the formula, ψ 1,j (x1; ω) and ψ 2,j (x2; ω) are the spherical wave basis functions with O1 and O2 as the origins, respectively; c 1,j (ω) and c 2,j (ω) are the coefficients of the expansion terms of the two sets of basis functions, respectively; ω is the angular frequency of the sound wave; j is the ordinal number of the basis function expansion term; J is the number of terms in the basis function expansion term; (r1,θ1,φ1) and (r2,θ2,φ2) represent the spherical coordinates of the field point in the two local coordinate systems, respectively; For a sphere of the first kind, Hankel function is used; k = ω / c is the wave number of the sound wave, and c is the speed of sound. It is a spherical harmonic function; integers n, l, and j satisfy the relation j = n 2 +n+l+1, where -n≤l≤n, 0≤n≤N, and N is the cutoff value for n.

7. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 6, characterized in that: In step S4, the method for obtaining the particle velocity components in the unit normal vector direction includes: Step S411: Increase the half-space sound pressure p at field point x. half (x;ω) represents the linear superposition of sound source radiation and boundary reflection; Step S412: By utilizing the relationship between the sound pressure in half-space and the particle velocity of the fluid medium to satisfy the conditions of the Euler equation, the particle velocity component in the unit normal vector direction is obtained.

8. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 7, characterized in that: In step S412, the particle velocity component in the unit normal vector direction The expression is: In the formula, ρ0 is the density of the fluid medium; Indicates the direction of the unit normal vector.

9. The method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array according to claim 8, characterized in that: In step S4, the method for reconstructing the normal velocity of the particles at the first set of microphones using the sound pressure distribution collected by the two sets of microphones includes: Step S421: Set the global coordinates of all microphones on the rectangular array to x m m = 1, 2, ..., M, where M is the number of microphones, and their coordinates in the two local coordinate systems are denoted as x and y respectively. 1,m and x 2,m The sound pressure values ​​collected by the array Represented in the following matrix form: Step S422: For the coefficient vector {c(ω)} 2J×1 Solve for the problem, and you will get the following results. In the formula, the superscript T denotes the transpose of the vector; the superscript T... Represents the pseudo-inverse of a matrix; Step S423: Reconstruct the normal vibration velocity of the mass points at the first set of measurement points on the material surface: In the formula, x m′ The global coordinates of the first set of measurement points. This indicates rounding up to the nearest integer.

10. A method for in-situ measurement of the surface acoustic impedance of a material using an embedded microphone array according to claim 9, characterized in that: The expression for the surface acoustic impedance is:

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