Method for measuring acoustic impedance on surface of material in situ by embedded microphone array

Abstract

The invention provides a method for measuring acoustic impedance of a material surface in situ by using an embedded microphone array. The method comprises the following steps: arranging a rectangular microphone array on the surface of a material to be measured; the microphones are divided into two groups; setting a sound wave incidence angle, arranging a sound source in a half space on one side of the surface of the material based on the sound wave incidence angle, and collecting sound pressure through two groups of microphones; respectively describing a sound source radiation sound field and a boundary reflection sound field by using two groups of spherical wave primary functions; on the basis of the two groups of spherical wave primary functions, a mass point vibration velocity component in a unit normal vector direction is obtained, and the mass point normal vibration velocity at the first group of microphones is reconstructed by using sound pressure distribution collected by the two groups of microphones; and based on the material surface sound pressure and the mass point normal vibration velocity collected by the first group of microphones, calculating the acoustic impedance rate at the first group of microphones, and averaging to obtain the surface acoustic impedance rate of the to-be-measured material. Influence of sound scattering of components on a sound field is avoided, and sound pressure measurement precision is improved.

Description

Technical Field

[0001] The invention relates to the technical field of acoustic impedance measurement, and in particular to a method for in-situ measuring the acoustic impedance of a material surface using an embedded microphone array. Background Art

[0002] The acoustic impedance of a material surface is an important physical quantity that characterizes the acoustic properties of the material. The classic methods for measuring acoustic impedance are the impedance tube method and the reverberation chamber method, and their implementation requires standard acoustic equipment and environmental conditions. In actual engineering environments, the sound pressure distribution is collected using a microphone array, and the boundary acoustic quantity distribution is calculated based on near-field acoustic holographic reconstruction to obtain the boundary acoustic impedance, which can realize in-situ measurement of the acoustic impedance of the material surface.

[0003] The in-situ measurement method of acoustic impedance in the prior art requires that a microphone array be arranged in the half-space on one side of the boundary to collect the sound pressure distribution, and then the boundary sound pressure and particle normal velocity distribution are calculated based on near-field acoustic holographic reconstruction. Depending on the near-field acoustic holography method adopted, the arranged microphone array can be a double-layer planar array, a double-layer closed surface array, a single-layer spherical array, a single-layer planar array, etc. Regardless of the complexity of the array structure, the presence of components such as array brackets and cables will affect the half-space sound field distribution, thereby affecting the sound pressure measurement and the reconstruction calculation results of the acoustic quantity, and ultimately affecting the calculation results of the acoustic impedance. Summary of the invention

[0004] The present invention proposes a method for in-situ measuring the acoustic impedance of a material surface using an embedded microphone array, so as to solve the technical problem that the existing acoustic impedance measurement method has inaccurate measurement due to the influence of components such as array brackets and cables on the sound field distribution.

[0005] In order to solve the above technical problems, the present invention provides a method for in-situ measuring the surface acoustic impedance of a material using an embedded microphone array, comprising the following steps:

[0006] Step S1: evenly arranging a rectangular microphone array on the surface of the material to be tested; dividing the microphones into two groups, the sum of the row and column numbers of the first group is an even number, and the sum of the row and column numbers of the second group is an odd number;

[0007] The measuring points of the first group of microphones are flush with the surface of the material to be tested, and the measuring points of the second group of microphones are higher than the surface of the material to be tested;

[0008] Step S2: setting the incident angle of the sound wave, arranging a sound source in the half space on one side of the surface of the material based on the incident angle of the sound wave, and collecting sound pressure through the two groups of microphones;

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

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

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

[0012] Preferably, the measurement apertures of the microphones arranged in a rectangular array are larger than half of the wavelength of the sound waves 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 waves emitted by the sound source in step S2.

[0014] Preferably, the distance at which the microphone exceeds the surface of the material to be measured is greater than one tenth of the wavelength of the sound waves emitted by the sound source.

[0015] Preferably, step S3 comprises:

[0016] Step S31: Establish a global coordinate system with the center of the microphone array as the coordinate origin O and the plane where the boundary of the material to be tested is located as the xy coordinate plane; record the mirror 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 record 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, a set of spherical wave functions are linearly superposed to describe the sound pressure response of the sound source radiation and the boundary reflection at the field point x.

[0018] Preferably, the expression of 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 coordinate origins respectively; c 1,j (ω) and c 2,j (ω) are the coefficients of 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 terms; J is the number of basis function expansion terms; (r1, θ1, φ1) and (r2, θ2, φ2) represent the spherical coordinates of the field points in the two local coordinate systems respectively; is the first kind of spherical Hankel function; k = ω / c is the acoustic wave number, c is the speed of sound; is a spherical harmonic function; integers n, l and j satisfy the relationship j = n 2 +n+l+1, where -n≤l≤n, 0≤n≤N, and N is the cutoff value of n.

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

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

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

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

[0025]

[0026] Where ρ0 is the density of the fluid medium; Represents the direction of the unit normal vector.

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

[0028] Step S421: mark the global coordinates of all microphones on the rectangular array as x m , m = 1, 2, ..., M, M is the number of microphones, and its coordinates in the two local coordinate systems are denoted by x 1,m and x 2,m ; The sound pressure value collected by the array It is expressed in the following matrix form:

[0029]

[0030] Step S422: For the coefficient vector {c(ω)} 2J×1 Solve, get

[0031]

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

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

[0034]

[0035] In the formula, x m′ are the global coordinates of the first set of measurement points, Indicates rounding up.

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

[0037]

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

[0039] 1) The present 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 the material, thereby realizing in-situ acquisition of the surface acoustic impedance in an actual engineering environment without relying on an impedance measuring instrument.

[0040] 2) The microphone array used in the present invention is placed in the material in an inlaid manner, which avoids the influence of sound scattering of components such as the array bracket 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) The present invention utilizes an embedded microphone array to directly collect the sound pressure information on the material surface. It only needs to reconstruct the normal particle velocity, and no longer needs to reconstruct the sound pressure on the material surface. This can avoid the error introduced by sound pressure reconstruction and improve the accuracy and efficiency of acoustic impedance calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic diagram of a method flow chart of an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of the three-dimensional structure of the arrangement of the microphone array, the sound source and the material to be measured according to an embodiment of the present invention;

[0044] Figure 3 A schematic diagram of a two-dimensional structure for establishing a global coordinate system and two local coordinate systems according to an embodiment of the present invention;

[0045] Figure 4 It is a schematic projection diagram of the distribution of measurement points of the microphone array according to an embodiment of the present invention on the xy plane;

[0046] Figure 5 Schematic diagram of a curve showing a relative error between a calculated value and a true value of the surface acoustic impedance of a material according to an embodiment of the present invention as a function of the incident angle of a sound wave. DETAILED DESCRIPTION

[0047] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0048] Example 1

[0049] like Figure 1 As shown, an embodiment of the present invention provides a method for in-situ measuring the surface acoustic impedance of a material 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. According to the microphone size parameters, a through hole is punched at the microphone embedding position. The microphones are embedded in the holes one by one, and the tail cable extends from the other end of the through hole to connect with the data acquisition system.

[0052] The microphones are divided into two groups according to the method of selecting points at intervals. Specifically, Figure 2 As shown, the sum of the row and column numbers of the first group is an even number, and the sum of the row and column numbers of the second group is an odd number; the measurement points of the first group of microphones are flush with the surface of the material to be tested, and the measurement points of the second group of microphones are higher than the surface of the material to be tested, and can collect the half-space sound pressure on one side of the material surface.

[0053] Step S2: setting the incident angle of the sound wave, arranging a sound source in the half space on one side of the material surface based on the incident angle of the sound wave, and collecting sound pressure through two groups of microphones.

[0054] Specifically, Figure 2 As shown, the sound source is arranged in the half space on one side of the material surface, and the center of the sound source is recorded as O1. The geometric center of the area covered by the projection of all measurement points on the material surface is recorded as O, and 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, recorded as θ inc The sound source is started to emit sound waves, and the microphone array collects the sound pressure and obtains the incident angle θ of the sound wave. inc Sound pressure data under the condition. Turn off the sound source and adjust the sound source position to change the sound wave incident angle θ inc Repeat the above sound pressure collection process to obtain different incident angles θ inc The sound pressure data under these conditions can be used to calculate the different incident angles θ through subsequent steps. inc Acoustic impedance under .

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

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

[0057]

[0058] Among them, ψ 1,j (x1;ω) and ψ 2,j (x2; ω) are the spherical wave basis functions with O1 and O2 as the coordinate origins respectively; c 1,j (ω) and c 2,j (ω) are 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 terms in the basis function expansion term. In the spherical coordinate system, the expression of the spherical wave basis function is:

[0059]

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

[0061] Step S4: Based on the two groups of spherical wave basis functions, the particle velocity component in the direction of the unit normal vector is obtained, and the normal velocity of the particle at the first group of microphones is reconstructed using the sound pressure distribution collected by the two groups of microphones.

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

[0063]

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

[0065]

[0066] Where ρ0 is the density of the fluid medium, is the gradient operator, According to equations (4) and (5), we can get that at the field point x, under the unit normal vector The particle velocity component in the direction is:

[0067]

[0068] Step S5: Based on the material surface sound pressure and particle normal vibration velocity collected by the first group of microphones, the acoustic impedance at the first group of microphones is calculated, and the surface acoustic impedance of the material to be tested is obtained by taking the average value.

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

[0070]

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

[0072]

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

[0074]

[0075] Where superscript T represents the transpose of the vector; solving the coefficient vector, we get:

[0076]

[0077] Among them, the superscript Represents the pseudo-inverse of the matrix; then use equation (6) to reconstruct the normal velocity of the particle at the first set of measurement points on the material surface:

[0078]

[0079] Among them, x m′ are the global coordinates of the first set of measurement points, Indicates rounding up.

[0080] Then, the acoustic impedance of the first group of measurement points is calculated by using the material surface acoustic pressure directly collected from the first group of measurement points and the normal vibration velocity of the particles at the first group of measurement points reconstructed by formula (11). The material surface acoustic impedance is obtained by taking the average value:

[0081]

[0082] Example 2

[0083] This embodiment Figure 3 In the global coordinate system shown, the measurement is performed using the method of Example 1, and the coordinates of the boundary and the material surface are z = 0. Assume that the wavelength of the sound wave under consideration is λ = 0.23 m, and the frequency is f = 1500 Hz. A hole is punched near the center of the material surface according to the size of the microphone. By way of example, the following is an explanation of the calculation of this embodiment using the arrangement parameters of one of the microphones, but it is not intended to be a limitation of this embodiment.

[0084] The number of through holes is selected as 6×6, and the spacing between adjacent through holes is 0.03m. The geometric center O of the through hole coverage area is the origin of the global coordinate system. The microphones are embedded in the through holes in an inlay manner, and the microphones are divided into two groups by taking points at intervals. The measurement points of the first group of microphones are flush with the material surface, and the measurement points of the second group of microphones are 0.03m above the material surface. The projections of the positions of the two groups of measurement points on the xy plane are shown in Figure 4 .

[0085] A pulsating ball sound source is arranged in the half space on one side of the material surface, the distance between its center O1 and O is 2m, and the incident angle of the sound wave is θ inc The sound source is driven to generate sound, the microphone array collects the sound pressure, and the sound source is turned off. Adjust the position of the sound source to change the incident angle of the sound wave θ inc , collect the sound pressure under different incident angles. After the collection is completed, the normal vibration velocity of the air medium particles at the first set of measurement points is reconstructed according to the sound field reconstruction algorithm. Finally, the surface acoustic impedance of the material is calculated using the sound pressure measurement values ​​and the reconstructed values ​​of the normal vibration velocity of the particles at the first set of measurement points.

[0086] The calculation results of numerical simulation are given below to verify the calculation accuracy of acoustic impedance. Assume that the radius of the pulsating ball sound source is a = 0.05m, the radial vibration velocity of the surface particle V0 = 0.01m / s, and the air medium density ρ0 = 1.20kg / m 3 , sound velocity v = 343m / s. Assume that 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] Among them, σ e is the effective flow resistivity of the material, taking 38kPa sm -2 ; α e is the rate of decrease of material porosity with material depth, taking 15m -1 ; f is the sound wave frequency; the relationship between the acoustic impedance ratio 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 by analytical formulas. To simulate the influence of microphone measurement error, Gaussian white noise with a signal-to-noise ratio of 30dB is added to the measured sound pressure.

[0090] When the frequency f = 1500 Hz, the true value of the acoustic impedance ratio is Z = 903.25 + 983.43i obtained by formula (13). inc = 0°, the calculated value of the boundary acoustic impedance is Z cal =868.82+974.10i, the calculated value is consistent with the true value. When the frequency is f=1500Hz, different incident angles θ inc The acoustic impedance calculation result under the condition of cal The relative error ε between the true value Z is:

[0091]

[0092] ε varies with the incident angle θ inc The change curve of Figure 5 shown.

[0093] observe Figure 5 It is found that the relative error of the calculated acoustic impedance ratio under different incident angles obtained by the method of the present invention is less than 8%, indicating that the calculated acoustic impedance ratio is very close to the true value and has high calculation accuracy. The results show that the method of the present invention for in-situ measurement of the acoustic impedance of the material surface by the embedded microphone array can accurately obtain the material surface acoustic impedance ratio by directly collecting the sound pressure distribution on the material surface and reconstructing and calculating the normal velocity distribution of the surface particles.

[0094] Example 3

[0095] Based on Example 1, in order to further increase the rationality of data collection, this example considers the spatial sampling problem related to wavelength, and determines the parameters such as the microphone array measurement aperture and the spacing between adjacent microphones according to the acoustic wavelength λ under investigation. The lower limit of the measurement aperture in each dimension is The upper limit of microphone spacing is The second set of microphone measurement points is at least

[0096] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. Only the preferred embodiments of the present invention are expressed. The description is more specific and detailed, but it cannot be understood as limiting the scope of the present invention. As long as there is no contradiction in the combination of these technical features, they should be considered as within the scope of this specification.

[0097] It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these modifications and improvements all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A method for in-situ measurement of surface acoustic impedance of a material using an embedded microphone array, characterized in that: The following steps are involved: Step S1: evenly arranging a rectangular microphone array on the surface of the material to be tested; Divide the microphones into two groups, wherein the sum of the row and column numbers of the first group is an even number, and the sum of the row and column numbers of the second group is an odd number; The measuring points of the first group of microphones are flush with the surface of the material to be tested, and the measuring points of the second group of microphones are higher than the surface of the material to be tested; Step S2: setting the incident angle of the sound wave, arranging a sound source in the half space on one side of the surface of the material based on the incident angle of the sound wave, and collecting sound pressure through the two groups of microphones; Step S3: using two sets of spherical wave basis functions to describe the sound source radiation and boundary reflection sound field respectively; Step S4: based on the two groups of spherical wave basis functions, obtain the particle velocity component in the direction of the unit normal vector, and reconstruct the particle normal velocity at the first group of microphones using the sound pressure distribution collected by the two groups of microphones; Step S5: based on the material surface sound pressure and the normal vibration velocity of the particle collected by the first group of microphones, the acoustic impedance at the first group of microphones is calculated, and the surface acoustic impedance of the material to be tested is obtained 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 measurement apertures of the microphones arranged in a rectangular array are larger than half of the wavelength of the sound waves 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 waves 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 at which the microphone exceeds the surface of the material to be measured 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 coordinate origin O and the plane where the boundary of the material to be tested is located as the xy coordinate plane; record the mirror 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 record 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, a set of spherical wave functions are linearly superposed to describe the sound pressure response of the sound source radiation and the boundary reflection at the field point x.

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 of 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 coordinate origins respectively; c 1,j (ω) and c 2,j (ω) are the coefficients of the expansion terms of two groups of basis functions; 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; is the first kind of spherical Hankel function; k = ω / c is the acoustic wave number, c is the speed of sound; is a spherical harmonic function; integers n, l and j satisfy the relationship j = n 2 +n+l+1, where -n≤l≤n, 0≤n≤N, and N is the cutoff value of 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 component in the direction of the unit normal vector includes: Step S411: The half-space sound pressure p at the field point x is half (x; ω) represents the linear superposition of the sound source radiation and the boundary reflection; Step S412: Using the relationship between the half-space sound pressure and the particle velocity of the fluid medium to satisfy the condition of the Euler equation, the particle velocity component in the direction of the unit normal vector 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 direction of the unit normal vector The expression is: Where ρ0 is the density of the fluid medium; Represents 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 of reconstructing the normal velocity of the particle at the first group of microphones by using the sound pressure distribution collected by the two groups of microphones includes: Step S421: mark the global coordinates of all microphones on the rectangular array as x m , m = 1, 2, ..., M, M is the number of microphones, and its coordinates in the two local coordinate systems are denoted by x 1,m and x 2,m ; The sound pressure value collected by the array It is expressed in the following matrix form: Step S422: For the coefficient vector {c(ω)} 2J×1 Solve, get In the formula, the superscript T represents the transpose of the vector; the superscript represents the pseudo-inverse of a matrix; Step S423: Reconstruct the normal velocity of the particles at the first set of measurement points on the material surface: In the formula, x m′ are the global coordinates of the first set of measurement points, Indicates rounding up.

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

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