Method for in-situ measurement of the surface acoustic impedance of a half-space boundary using a single-layer microphone array

Abstract

Method for in-situ measuring sound impedance of half-space boundary surface by single-layer microphone array, comprising: 1. arranging a sound source and a microphone array on one side of the half-space of the boundary for acoustic pressure holographic measurement; 2. establishing a mathematical model of the sound field in the half-space on one side of the boundary; 3. determining the optimal number of expansion terms of the basis function; 4. establishing a mathematical relationship between the holographic measurement acoustic pressure and the acoustic pressure on the boundary surface to reconstruct the acoustic pressure distribution on the boundary surface; 5. establishing a mathematical relationship between the holographic measurement acoustic pressure and the normal particle velocity of the boundary surface medium to reconstruct the normal particle velocity distribution of the boundary particles; 6. calculating the sound impedance rate of the boundary surface by using the reconstructed acoustic pressure and normal particle velocity. The present invention is based on near-field acoustic holography combined with in-situ acquisition of near-field acoustic pressure information of the physical boundary by a microphone array, realizing in-situ measurement and calculation of the sound impedance of the boundary surface, so that it is no longer necessary to rely on standard impedance measurement equipment and measurement environment to implement the measurement of the sound impedance of the boundary material sample.

Description

Technical Field:

[0001] The present invention relates to a method for in-situ collecting holographic sound pressure in the near field of a half-space boundary by using a single-layer microphone array, reconstructing and calculating acoustic quantities on the boundary surface based on near-field acoustic holography and virtual source principle, and further obtaining the surface acoustic impedance of the boundary surface, belonging to the technical fields of acoustic in-situ measurement, holographic measurement, sound field imaging, and near-field acoustic holography. Background Art:

[0002] Accurately obtaining acoustic characteristic parameters such as the surface acoustic impedance of the physical boundary of the sound field is a prerequisite for correctly controlling and utilizing the sound field and sound source nearby. The impedance tube method and reverberation chamber method are standard methods for measuring the acoustic impedance of small and large-sized material samples, and their implementation processes require special acoustic measurement equipment and standard acoustic environments, and the measurement results cannot accurately reflect the acoustic characteristics and acoustic parameters of the measured material in the actual application environment.

[0003] Collecting holographic sound pressure in the near field of the half-space boundary by using a microphone array, reconstructing and calculating acoustic quantities of the sound field based on near-field acoustic holography and virtual source principle, and further obtaining the surface acoustic impedance of the boundary surface is an effective method for in-situ measuring the surface acoustic impedance of the boundary surface in the actual engineering environment.

[0004] For the methods for measuring the surface acoustic impedance of the boundary surface based on Fourier acoustics method, statistically optimal near-field acoustic holography, and equivalent source method, it is necessary to use a double-layer planar microphone array or a spherical microphone array to collect holographic sound pressure; for the measurement method based on the inverse boundary element method, it is necessary to arrange two layers of microphone arrays surrounding the sound source and the boundary surface respectively. In other words, these methods either require more microphone arrays, such as a double-layer microphone array; or require a microphone array with a special geometric shape, such as a spherical microphone array. Summary of the Invention:

[0005] The present invention overcomes the limitations of the above-mentioned methods for in-situ measuring the surface acoustic impedance of the boundary surface, and proposes a method for in-situ measuring the surface acoustic impedance of the boundary surface that only requires a single-layer microphone array.

[0006] At the center of the sound source and its mirror image point with respect to the boundary surface, a superposition of a group of spherical wave basis functions is used to respectively represent the sound field radiated by the sound source and the boundary reflected sound field, establish a mathematical model of the half-space sound field in the near field of the boundary, construct a transfer function between the sound pressure at the half-space field point, the sound pressure on the boundary surface, and the normal particle velocity of the boundary fluid medium, and use the sound pressure distribution collected by the single-layer microphone array to reconstruct the sound pressure and normal velocity distribution on the boundary surface.

[0007] According to the reconstructed sound pressure and normal velocity distribution on the boundary surface, the present invention calculates the surface acoustic impedance of the boundary surface, and can further calculate other parameters characterizing the acoustic characteristics of the boundary, such as the reflection coefficient and absorption coefficient.

[0008] The boundary surface investigated in the present invention is a plane. By adjusting the azimuth of the sound source, the incident angle of the sound wave is changed, and then the acoustic impedance of the boundary surface under different incident angle conditions is calculated.

[0009] The method for in-situ measuring the acoustic impedance of the boundary surface of a half-space by using a single-layer microphone array in the present invention includes the following contents:

[0010] S1. Arrange a sound source and a single-layer microphone array on one side of the boundary in the half-space for acoustic pressure holographic measurement;

[0011] Arrange a sound source in the half-space, and denote the center of the sound source as O 1 ; in the near field of the boundary surface, arrange a single-layer planar microphone array parallel to the boundary surface, and the distance between the array surface and the boundary is h a ; denote the projection of the center of the array surface on the boundary as point O, and define the angle between the line connecting point O and the sound source center O 1 and the normal of the boundary at point O as the incident angle θ of the sound wave inc ; after the arrangement is completed, start the sound source to emit sound waves, and the single-layer microphone array collects the holographic acoustic pressure; after the collection is completed, turn off the sound source and adjust the position of the sound source to change the incident angle θ of the sound wave inc ; repeat the holographic acoustic pressure collection to obtain the holographic acoustic pressure under different incident angle θ inc conditions;

[0012] When the fluid medium is a water medium, the sound source and the microphone array are replaced with a sound source and a hydrophone array in the water medium;

[0013] S2. Establish a mathematical model of the sound field in the half-space on one side of the boundary;

[0014] Taking point O as the coordinate origin and the plane where the boundary is located as the x-y coordinate plane, establish a global coordinate system; denote the mirror image point of O 1 with respect to the boundary as O 2 , and establish local coordinate systems with O 1 and O 2 as the coordinate origins respectively. Denote the coordinates of the half-space field point x in the two local coordinate systems as x 1 ≡ (r 1 , θ 1 , φ 1 ) and x 2 ≡ (r 2 , θ 2 , φ 2 ); for a steady-state sound field, in the two local coordinate systems, the acoustic pressure responses of the sound source radiation and the boundary reflection at this field point are respectively expressed by the linear superposition of a set of spherical wave functions, and their expressions are:

[0015]

[0016] and

[0017]

[0018] where, ψ 1,j (x 1 ; ω) and ψ 2,j (x 2 ; ω) are spherical wave basis functions with O 1 and O 2 as the coordinate origins respectively; c 1,j (ω) and c 2,j (ω) are the expansion coefficients of two groups of basis functions respectively; ω is the acoustic angular frequency; j is the expansion term ordinal number of the basis function; J is the number of expansion terms of the basis function; in the spherical coordinate system, the expression of ψ j is:

[0019]

[0020] where, is the spherical Hankel function of the first kind, k = ω / c is the acoustic wave number, and c is the sound speed; is the 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 truncation value of n;

[0021] The sound pressure p half (x; ω) at the field point x is the linear superposition of the sound source radiation and the boundary reflection, and can be expressed as:

[0022]

[0023] S3. Using the holographic measurement values of some measurement points as the input, reconstruct the sound pressure values of the remaining measurement points, and determine the optimal number of expansion terms of the basis function with the principle of minimizing the sound pressure reconstruction error;

[0024] Record the sound pressure measurement point coordinates of the array as M is the number of sound pressure measurement points; according to equation (4), a set of sound pressure values collected by the array can be expressed in the following matrix form:

[0025]

[0026] where, the spherical wave function expansion term matrix is:

[0027]

[0028] The coefficient vector {C(ω)} 2J×1 is:

[0029]

[0030] where the superscript T represents the transpose of a vector;

[0031] According to the way of taking points at intervals, the sound pressure measurement points are divided into two groups. The coordinates of the first group of measurement points are denoted as The coordinates of the second group of measurement points are denoted as where and respectively represent rounding up and rounding down; according to Equation (5), establish the mathematical relationship between the sound pressure reconstruction value of the second group of measurement points and the sound pressure measurement value of the first group of measurement points:

[0032]

[0033] where is the vector composed of the sound pressure reconstruction values of the second group of measurement points, is the transfer matrix from the sound pressure measurement value of the first group of measurement points to the sound pressure reconstruction value of the second group of measurement points:

[0034]

[0035] where the superscript represents the pseudoinverse of a matrix:

[0036]

[0037] where the superscript H represents the conjugate transpose of a matrix;

[0038] Set the upper limit of the number of expansion terms J of the basis function to J max , that is, 1 ≤ J ≤ J max ; for any J within this range, use Equations (8) to (10) to reconstruct the sound pressure value of the second group of measurement points and calculate the relative error between the sound pressure reconstruction value and the measurement value of the second group of measurement points:

[0039]

[0040] where ||·|| 2 is the vector 2-norm; traverse all J from 1 to J max , and determine the number of expansion terms corresponding to the minimum value of ε as the optimal number of expansion terms J opt ;

[0041] S4. Establish the mathematical relationship between the holographic measurement sound pressure and the boundary surface sound pressure, and reconstruct the boundary surface sound pressure;

[0042] Set the number of expansion terms of the basis function to J opt , then Equation (5) is transformed into the following form:

[0043]

[0044] According to Equation (12), establish the mathematical relationship between the holographic measurement sound pressure and the boundary surface sound pressure, then the sound pressure on the boundary surface can be reconstructed and calculated by the following formula:

[0045]

[0046] where, is the coordinate of the reconstruction point on the boundary surface, s = 1, 2, …, S, and S is the number of reconstruction points, is the transfer matrix from the holographic measurement sound pressure to the boundary surface sound pressure:

[0047]

[0048] where, is the matrix composed of the expansion terms of two sets of spherical wave functions at the s-th reconstruction point , and the arrangement form of the matrix elements can be seen in Equation (6);

[0049] S5. Establish the mathematical relationship between the holographic measurement sound pressure and the normal particle velocity of the fluid medium on the boundary surface, and reconstruct the normal particle velocity of the boundary particles;

[0050] The sound pressure p half (x; ω) at the field point x and the particle velocity v half (x; ω) satisfy the Euler equation:

[0051]

[0052] where, ρ 0 is the density of the fluid medium, is the gradient operator, According to Equation (12) and Equation (15), establish the mathematical relationship between the holographic measurement sound pressure and the normal particle velocity of the fluid medium on the boundary surface, and the normal particle velocity of the boundary surface can be reconstructed and calculated by the following formula:

[0053]

[0054] where, is the transfer matrix from the holographic measurement sound pressure to the normal particle velocity of the boundary surface:

[0055]

[0056] where, n is the unit normal vector of the boundary surface at the reconstruction point ;

[0057] S6. Calculate the specific acoustic impedance of the boundary surface;

[0058] The specific acoustic impedance of the boundary surface is defined as the boundary surface sound pressure phalf (x; ω) and the normal particle velocity v nhalf The ratio of (x; ω); calculating the surface acoustic impedance rate at each reconstructed point by using a reconstructed set of sound pressure and normal particle velocity, and taking the average value to obtain the boundary surface acoustic impedance rate as:

[0059]

[0060] Advantages of the present invention:

[0061] 1. Based on near-field acoustic holography and in-situ acquisition of near-field sound pressure information of the physical boundary by a microphone array, the present invention realizes in-situ measurement and calculation of the boundary surface acoustic impedance, thus no longer relying on standard impedance measurement equipment and measurement environment to measure the acoustic impedance of the boundary material sample. At the same time, the boundary surface acoustic impedance obtained by the present invention is more in line with the acoustic characteristics of the boundary material in the actual engineering application environment.

[0062] 2. The present invention uses a single-layer microphone array to collect holographic sound pressure information. Compared with other measurement methods using a double-layer microphone array or a spherical microphone array, it reduces the difficulty of the design, processing, on-site layout and installation of the microphone array for in-situ holographic sound pressure measurement. Description of the drawings:

[0063] Figure 1 Schematic diagram of the arrangement of the sound source and the microphone array in the half-space;

[0064] Figure 2 Schematic diagram of the grouping of measurement points when determining the optimal number of expansion terms of the spherical wave basis function;

[0065] Figure 3 Comparison between the calculated value and the theoretical value of the boundary surface acoustic impedance rate. Specific implementation manner:

[0066] The following specifically describes the implementation manner of the present invention in conjunction with the drawings.

[0067] The implementation of the method for in-situ measurement of the boundary surface acoustic impedance of the half-space by the single-layer microphone array of the present invention is carried out according to the following steps:

[0068] Step 1, arranging a sound source and a single-layer microphone array on one side of the half-space of the boundary for sound pressure holographic measurement.

[0069] As Figure 1 shown, arranging a sound source in the half-space, and denoting the center of the sound source as O 1 . In the near-field of the boundary surface, arranging a single-layer planar microphone array parallel to the boundary surface, and the distance between the array surface and the boundary is h a . Denoting the projection of the center of the array surface on the boundary as point O, and denoting point O and the center of the sound source O 1The angle between the connection line and the boundary normal at point O is defined as the acoustic wave incident angle θ. inc After the arrangement is completed, start the sound source to emit acoustic waves, and the single-layer microphone array collects the holographic sound pressure. After the collection is completed, turn off the sound source and adjust the position of the sound source to change the acoustic wave incident angle θ. inc Repeat the holographic sound pressure collection to obtain the holographic sound pressure under different incident angles θ. inc Condition.

[0070] When the fluid medium is water, the sound source and the microphone array are replaced with the sound source and the hydrophone array in water.

[0071] Step 2, establish a mathematical model of the sound field in the half-space on one side of the boundary.

[0072] As Figure 1 Shown, with point O as the coordinate origin and the plane where the boundary is located as the x-y coordinate plane, establish a global coordinate system. Denote the mirror image point of O 1 About the boundary as O 2 , and establish local coordinate systems with O 1 And O 2 As the coordinate origin respectively, and denote the coordinates of the half-space field point x in the two local coordinate systems as x 1 ≡(r 1 ,θ 1 ,φ 1 ) and x 2 ≡(r 2 ,θ 2 ,φ 2 ). For the steady-state sound field, in the two local coordinate systems, the sound pressure responses of the sound source radiation and the boundary reflection at this field point are expressed by the linear superposition of a set of spherical wave functions respectively, and their expressions are:

[0073]

[0074] And

[0075]

[0076] Among them, ψ 1,j (x 1 ; ω) and ψ 2,j (x 2 ; ω) are the spherical wave basis functions with O 1 And O 2 As the coordinate origin respectively; c 1,j (ω) and c 2,j (ω) are the expansion coefficients of the two groups of basis function terms respectively; ω is the acoustic wave angular frequency; j is the order of the basis function expansion term; J is the number of basis function expansion terms. In the spherical coordinate system, the expression of ψ j Is:

[0077]

[0078] wherein, is the first kind of spherical Hankel function, k = ω / c is the acoustic wave number, and c is the sound speed; is the spherical harmonic function. In equations (1) to (3), the integers n, l, and j satisfy the relationship j = n 2 + n + l + 1, wherein, -n ≤ l ≤ n, 0 ≤ n ≤ N, and N is the truncation value of n.

[0079] The sound pressure p half (x; ω) at the field point x is the linear superposition of the sound source radiation and the boundary reflection, and can be expressed as:

[0080]

[0081] Step 3: Using the holographic measurement values of some measurement points as the input, reconstruct the sound pressure values of the remaining measurement points, and determine the optimal number of basis function expansion terms based on the principle of minimizing the sound pressure reconstruction error.

[0082] Denote the sound pressure measurement point coordinates of the array as M is the number of sound pressure measurement points. According to equation (4), a set of sound pressure values collected by the array can be expressed in the following matrix form:

[0083]

[0084] wherein, the spherical wave function expansion term matrix is:

[0085]

[0086] The coefficient vector {C(ω)} 2J×1 is:

[0087]

[0088] wherein, the superscript T represents the transpose of the vector.

[0089] As Figure 2 shown, in the way of taking points at every other point, divide the sound pressure measurement points into two groups. Denote the coordinates of the first group of measurement points as Denote the coordinates of the second group of measurement points as wherein, and respectively represent rounding up and rounding down. According to equation (5), establish the mathematical relationship between the sound pressure reconstruction value of the second group of measurement points and the sound pressure measurement value of the first group of measurement points:

[0090]

[0091] Among them, is a vector composed of the sound pressure reconstruction values of the second group of measurement points, is the transfer matrix from the sound pressure measurement values of the first group of measurement points to the sound pressure reconstruction values of the second group of measurement points:

[0092]

[0093] Among them, the superscript indicates the pseudo-inverse of the matrix:

[0094]

[0095] Among them, the superscript H represents the conjugate transpose of the matrix;

[0096] Set the upper limit of the number of expansion terms J of the basis function to J max , that is, 1 ≤ J ≤ J max . For any J within this range, use Eqs. (8) to (10) to reconstruct the sound pressure values of the second group of measurement points, and calculate the relative error between the sound pressure reconstruction values and the measurement values of the second group of measurement points:

[0097]

[0098] Among them, ||·|| 2 is the vector 2-norm. Traverse all J from 1 to J max , and determine the number of expansion terms corresponding to the minimum value of ε as the optimal number of expansion terms J opt .

[0099] Step 4, establish the mathematical relationship between the holographic measurement sound pressure and the boundary surface sound pressure, and reconstruct the boundary surface sound pressure.

[0100] Set the number of expansion terms of the basis function to J opt , then Eq. (5) is transformed into the following form:

[0101]

[0102] According to Eq. (12), establish the mathematical relationship between the holographic measurement sound pressure and the boundary surface sound pressure, then the sound pressure on the boundary surface can be reconstructed and calculated by the following formula:

[0103]

[0104] Among them, are the reconstructed point coordinates on the boundary surface, s = 1, 2,..., S, S is the number of reconstructed points, is the transfer matrix from the holographic measurement sound pressure to the boundary surface sound pressure:

[0105]

[0106] Among them, is the matrix composed of the expansion terms of two sets of spherical wave functions at the s-th reconstruction point The arrangement form of the matrix elements can be seen in Equation (6).

[0107] Step 5: Establish the mathematical relationship between the holographic measurement sound pressure and the normal velocity of the fluid medium particles on the boundary surface, and reconstruct the normal velocity of the boundary particles.

[0108] The sound pressure p half (x; ω) at the field point x and the particle velocity v half (x; ω) satisfy the Euler equation:

[0109]

[0110] Among them, ρ 0 is the density of the fluid medium, is the gradient operator, According to Equation (12) and Equation (15), establish the mathematical relationship between the holographic measurement sound pressure and the normal velocity of the fluid medium particles on the boundary surface. The normal velocity of the particles on the boundary surface can be reconstructed and calculated by the following formula:

[0111]

[0112] Among them, is the transfer matrix from the holographic measurement sound pressure to the normal velocity of the particles on the boundary surface:

[0113]

[0114] Among them, n is the unit normal vector of the boundary surface at the reconstruction point

[0115] Step 6: Calculate the surface acoustic impedance rate of the boundary surface.

[0116] The surface acoustic impedance rate of the boundary surface is defined as the ratio of the sound pressure p half (x; ω) on the boundary surface and the normal velocity v nhalf (x; ω) of the particles. Use a set of reconstructed sound pressures and normal velocities to calculate the surface acoustic impedance rate at each reconstruction point, and take the average value to obtain the surface acoustic impedance rate of the boundary surface as:

[0117]

[0118] Example: Use a pulsating sphere as the sound source to perform numerical simulation calculations on the half-space sound field on one side of the boundary. In the Figure 1 shown global coordinate system, the boundary coordinate is z = 0, and its surface acoustic impedance rate satisfies the acoustic impedance model:

[0119] Z 0 ​= 0.436(1 + i)(σ e / f) 0.5 + 19.48iα e / f (19)

[0120] where σ e is the effective flow resistivity of the boundary, taking 38 kPa·s / m -2 ; α e is the reduction rate of the boundary porosity with the boundary depth, taking 15 m -1 ; f is the acoustic wave frequency.

[0121] The surface of the single-layer microphone array is parallel to the boundary, its geometric center is located on the z-axis, and the distance to the boundary is h a = 0.3 m; the aperture of the array is 0.15 m × 0.15 m, and 6 × 6 sound pressure measurement points are evenly distributed on it. The distance between adjacent measurement points is 0.03 m. For the schematic diagram of the measurement point distribution, see Figure 2 . The coordinates of the pulsating sphere center are set as At this time, the acoustic wave incident angle is θ inc = 0°. The radius of the pulsating sphere is a = 0.05 m, and the radial vibration velocity V 0 of the surface particles is 0.01 m / s. The density of the air medium is ρ 0 = 1.29 kg / m 3 , and the speed of sound in the air is c = 343 m / s. To simulate the influence of the measurement error of the microphone, Gaussian white noise with a signal-to-noise ratio of 30 dB is added to the measured value.

[0122] Using the method of the present invention, first, the sound pressure on the boundary surface and the distribution of the particle normal vibration velocity are reconstructed by using the sound pressure measurement values of the microphone array, and then the acoustic impedance rate of the boundary surface is calculated. The frequency range under investigation is f = 1000 Hz to 5000 Hz. The comparison between the calculated value and the theoretical value of the acoustic impedance rate of the boundary surface under different frequency conditions is as Figure 3 shown.

[0123] Observation Figure 3 finds that when the acoustic wave incident angle is θ inc = 0°, the acoustic impedance rate of the boundary surface calculated by the method of the present invention under different frequency conditions is consistent with its theoretical value. When the sound source position is adjusted and the acoustic wave incident angle takes other values in the range of θ inc = 0° to 90°, the method of the present invention can also calculate the acoustic impedance rate consistent with the theoretical value. The results show that the method for in-situ measuring the acoustic impedance of the half-space boundary surface by the single-layer microphone array of the present invention can accurately obtain the acoustic impedance of the boundary surface by in-situ collecting holographic sound pressure in the near field of the boundary.

[0124] The content described in the embodiments of this specification is only one of the cases of the implementation forms of the inventive concept. The protection scope of the present invention includes but is not limited to the specific forms and parameters stated in the embodiments, and also includes equivalent technical means that can be conceived by those skilled in the art based on the inventive concept of the present invention.

Claims

1. Method for in-situ measuring the surface acoustic impedance of a half-space boundary by using a single-layer microphone array, Characterized in that: It includes the following steps: S1. Arrange a sound source and a single-layer microphone array on one side of the half-space of the boundary, and perform acoustic pressure holographic measurement; A sound source is arranged in a half - space, and the center of the sound source is denoted as O 1 ; In the near - field of the boundary surface, a single - layer planar microphone array is arranged parallel to the boundary surface, and the distance between the array plane and the boundary is h a ; Denote the projection of the center of the array plane on the boundary as point O, and define the angle between the line connecting point O and the center O of the sound source 1 and the normal of the boundary at point O as the sound - wave incident angle θ inc ; After the arrangement is completed, start the sound source to emit sound waves, and the single - layer microphone array collects the holographic sound pressure; after the collection is completed, turn off the sound source and adjust the position of the sound source to change the sound - wave incident angle θ inc ; Repeat the collection of the holographic sound pressure to obtain the holographic sound pressure under different incident angles θ inc ; S2. Establish a mathematical model of the sound field in the half-space on one side of the boundary; Taking point O as the coordinate origin and the plane where the boundary lies as the x-y coordinate plane, a global coordinate system is established; the 1 mirror point of O with respect to the boundary is denoted as O 2 . Local coordinate systems are established with O 1 and O 2 as the coordinate origins respectively. The coordinates of the half-space field point x in the two local coordinate systems are denoted as x 1 ≡(r 1 , θ 1 , φ 1 ) and x 2 ≡(r 2 , θ 2 , φ 2 ). For the steady-state sound field, in the two local coordinate systems, the acoustic pressure responses of the sound source radiation and the boundary reflection at this field point are expressed as the linear superposition of a set of spherical wave functions respectively, and their expressions are: And Among them, ψ 1,j (x 1 ; ω) and ψ 2,j (x 2 ; ω) are spherical wave basis functions with O 1 and O 2 as the coordinate origins respectively; c 1,j (ω) and c 2,j (ω) are the expansion coefficients of the two groups of basis functions respectively; ω is the acoustic angular frequency; j is the order number of the basis function expansion term; J is the number of basis function expansion terms; in the spherical coordinate system, the expression of ψ j is: Among them, is the first kind of spherical Hankel function, k = ω / c is the acoustic wave number, and c is the speed of sound; is the 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 truncation value of n; The sound pressure p in the half - space at the field point x half (x; ω) is the linear superposition of the sound source radiation and the boundary reflection, and can be expressed as: S3. Use the holographic measurement values of some measurement points as inputs, reconstruct the acoustic pressure values of the remaining measurement points, and determine the optimal number of terms of the basis function expansion with the principle of minimizing the acoustic pressure reconstruction error; Denote the sound pressure measurement point coordinates of the array as m = 1, 2, ..., M, where M is the number of sound pressure measurement points; according to Equation (4), a set of sound pressure values collected by the array can be expressed in the following matrix form: Among them, the spherical wave function expansion term matrix is as follows: Coefficient vector {C(ω)} 2J×1 is as follows: Wherein, the superscript T represents the transpose of a vector; According to the method of taking points at intervals, the sound pressure measurement points are divided into two groups. The coordinates of the first group of measurement points are denoted as m′ = 1, 2, ..., M′, The coordinates of the second group of measurement points are denoted as m″ = 1, 2, ..., M″, where and respectively represent rounding up and rounding down; according to Equation (5), the mathematical relationship between the sound pressure reconstruction value of the second group of measurement points and the sound pressure measurement value of the first group of measurement points is established: Among them, is a vector composed of the sound pressure reconstruction values of the second group of measurement points, is the transfer matrix from the sound pressure measurement values of the first group of measurement points to the sound pressure reconstruction values of the second group of measurement points: Among them, the superscript represents the pseudo-inverse of a matrix: Wherein, the superscript H represents the conjugate transpose of a matrix; Set the upper limit of the number of expansion terms J of the basis function to be J max , that is, 1 ≤ J ≤ J max ; for any J within this range, use equations (8) to (10) to reconstruct the sound pressure values of the second group of measurement points, and calculate the relative error between the reconstructed sound pressure values and the measured values of the second group of measurement points: where, ||·|| 2 is the vector 2-norm; traversing all J from 1 to J max to determine the optimal number of expansion terms J as the number of expansion terms corresponding to the minimum value of ε opt ; S4. Establish a mathematical relationship between the holographic measurement acoustic pressure and the boundary surface acoustic pressure, and reconstruct the boundary surface acoustic pressure; Set the number of expansion terms of the basis function to J opt , then Equation (5) is transformed into the following form: According to Equation (12), establish a mathematical relationship between the holographic measurement acoustic pressure and the boundary surface acoustic pressure, then the acoustic pressure on the boundary surface can be reconstructed and calculated by the following formula: Among them, are the reconstructed point coordinates of the boundary surface, s = 1, 2, …, S, where S is the number of reconstructed points, is the transfer matrix from the holographic measurement sound pressure to the boundary surface sound pressure: Among them, is a matrix composed of the expansion terms of two sets of spherical wave functions at the \(s\)-th reconstruction point The arrangement form of the matrix elements can be seen in Equation (6); S5. Establish a mathematical relationship between the holographic measurement acoustic pressure and the normal particle velocity of the fluid medium on the boundary surface, and reconstruct the normal particle velocity of the boundary; Sound pressure p at field point x half (x; ω) and particle velocity v half (x; ω) satisfy the Euler equation: where ρ 0 is the density of the fluid medium, is the gradient operator, According to Equations (12) and (15), a mathematical relationship between the holographic measurement sound pressure and the normal particle velocity of the fluid medium on the boundary surface is established. The normal particle velocity on the boundary surface can be reconstructed and calculated by the following formula: Among them, is the transfer matrix for holographic measurement of the sound pressure to the normal particle velocity on the boundary surface: where n is the unit normal vector of the boundary surface at the reconstruction point ; S6. Calculate the surface acoustic impedance rate of the boundary; The specific acoustic impedance rate of the boundary surface is defined as the ratio of the acoustic pressure p half (x; ω) and the normal particle velocity v nhalf (x; ω); the specific acoustic impedance rate at each reconstructed point is calculated using a reconstructed set of acoustic pressures and normal velocities, and the average value is taken to obtain the specific acoustic impedance rate of the boundary surface as follows: 。 2. The method for in-situ measuring the surface acoustic impedance of a half-space boundary by using a single-layer microphone array according to claim 1, Characterized in that: The sound source and the microphone array described in step S1 are applicable to the generation of sound waves and the acquisition of acoustic pressure in an air medium. When the half-space fluid medium is a water medium, they are correspondingly replaced with a sound source and a hydrophone array in the water medium for the generation of sound waves and the acquisition of acoustic pressure in the water medium, as well as the measurement and calculation of the surface acoustic impedance of the boundary.

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