Acoustic impedance in-situ measurement method based on reflection coefficient mean value optimization

Abstract

The invention provides an acoustic impedance in-situ measurement method based on reflection coefficient mean value optimization, which comprises the following steps: arranging a tested sound source in a semi-open space containing a reflection boundary, arranging a microphone array near the tested sound source to form a holographic sound pressure measurement surface, and arranging a reference microphone near the boundary; starting a tested sound source, and collecting sound pressure superposed by sound source radiation and boundary reflection through the microphone array and the reference microphone; describing a half-space sound pressure field by linear superposition of a half-space spherical wave basis function, taking a reflection coefficient corresponding to a geometric center of a holographic sound pressure measurement surface as a reflection coefficient mean value, replacing the reflection coefficient of each array point, and establishing a mathematical model of the half-space sound pressure field; traversing all values in a value range of a reflection coefficient mean value, solving a primary function coefficient, reconstructing the sound pressure at the reference microphone, and determining an optimal reflection coefficient mean value by taking the minimum relative error between the reconstructed sound pressure and the measured sound pressure as a criterion; and calculating the boundary acoustic impedance rate according to the optimal reflection coefficient mean value.

Description

Technical Field

[0001] This invention relates to the field of acoustic impedance measurement technology, and specifically to an in-situ acoustic impedance measurement method based on optimizing the mean value of the reflection coefficient. Background Technology

[0002] Surface acoustic impedance is an important physical quantity characterizing the acoustic properties of materials, and it has wide applications in architectural acoustics, noise control, and underwater acoustic engineering. In semi-open space acoustic test fields with reflective boundaries, the implementation of sound source direct radiation field reconstruction algorithms usually requires the prior acquisition of boundary acoustic impedance as a known parameter, making accurate measurement of boundary acoustic impedance a prerequisite for related testing techniques.

[0003] Currently, methods for measuring the surface acoustic impedance of materials mainly fall into three categories: impedance tube method, reverberation chamber method, and in-situ measurement method. Impedance tube and reverberation chamber methods rely on standard acoustic equipment or specific measurement environments to measure the acoustic impedance of material samples. While offering high accuracy, these methods require the material to be prepared into samples of specific sizes and sent to a laboratory, making it difficult to reflect the acoustic performance of the material under actual installation conditions. In-situ measurement methods, on the other hand, involve setting up a standard sound source at the site of the object being measured and calculating the surface acoustic impedance of the material using the sound pressure measurement values ​​at the field point. Compared to impedance tube or reverberation chamber methods, this approach is more efficient and easier to implement in specific engineering applications.

[0004] However, existing in-situ methods for measuring acoustic impedance on material surfaces have significant limitations. These methods typically require an additional standard sound source as an excitation source in a half-space on one side of the material surface boundary, and a specially distributed array of microphones near the boundary to collect sound pressure distribution. The boundary sound pressure and particle velocity distribution are then calculated based on near-field acoustic holographic reconstruction in a non-free field, followed by further calculation of the boundary acoustic impedance. This process not only increases the complexity of the testing equipment but also reduces the efficiency of the test. Summary of the Invention

[0005] This invention proposes an in-situ acoustic impedance measurement method based on mean reflection coefficient optimization. This method addresses the need to pre-obtain the boundary acoustic impedance as a parameter for reconstructing the direct radiation field of a sound source in a semi-open space with a reflective boundary. The method utilizes the sound pressure distribution collected by the existing sound source and microphone array in the test field to solve for the reflection coefficient and boundary acoustic impedance, eliminating the need for additional standard sound sources and specifically distributed microphone arrays in the test field for sound field reconstruction and acoustic impedance calculation. This improves the efficiency of boundary acoustic impedance measurement and direct radiation field reconstruction in a semi-open space with a reflective boundary.

[0006] To address the aforementioned technical problems, this invention provides an in-situ acoustic impedance measurement method based on mean reflection coefficient optimization, comprising the following steps: Step S1: Arrange the test sound source in a semi-open space containing a reflective boundary, arrange a microphone array near the test sound source to form a holographic sound pressure measurement surface, and arrange a reference microphone near the boundary. Step S2: Activate the test sound source and collect the sound pressure of the superposition of sound source radiation and boundary reflection through the microphone array and the reference microphone; Step S3: The sound pressure field of the half-space is described by the linear superposition of the basis functions of the half-space spherical wave. The reflection coefficient corresponding to the geometric center of the holographic sound pressure measurement surface is used as the mean of the reflection coefficient to replace the reflection coefficient of each array point, and a mathematical model of the sound pressure field of the half-space is established. Step S4: Iterate through all values ​​within the range of the mean reflection coefficient, solve for the basis function coefficients, reconstruct the sound pressure at the reference microphone, and determine the optimal mean reflection coefficient based on minimizing the relative error between the reconstructed sound pressure and the measured sound pressure. Step S5: Calculate the boundary acoustic impedance ratio based on the mean value of the optimal reflection coefficient.

[0007] Preferably, the geometric centers of the reference microphone, the holographic sound pressure measurement surface, and the geometric center of the test sound source are collinear with respect to the boundary.

[0008] Preferably, the geometry of the holographic sound pressure measurement surface is conformal to the geometry of the test sound source surface.

[0009] Preferably, the measuring aperture of the microphone array is not less than 1.2 times the surface area of ​​the tested sound source.

[0010] Preferably, the spacing between adjacent microphones in the microphone array is less than one-sixth of the sound wave wavelength.

[0011] Preferably, the distance between the reference microphone and the boundary is one-quarter of the sound wave wavelength.

[0012] Preferably, in step S3, the average reflection coefficient Satisfy constraints ,in This indicates taking the modulus of a complex number.

[0013] Preferably, in step S4, the average reflection coefficient is expressed as: in, Represents the real part of a complex number. Represents the imaginary part of a complex number. The imaginary unit; with For the horizontal axis, Establish a rectangular coordinate system for the vertical axis, divide the grid into a circle with the origin as the center and a radius of 1, and solve for the mean value of the optimal reflection coefficient by traversing the grid nodes.

[0014] Preferably, in step S4, the number of terms in the expansion of the half-space spherical wave basis function is set. The range of values ​​is ,in The maximum number of expansion terms is set within the specified range. For each expansion term, all possible values ​​of the mean reflection coefficient are iterated over. After solving the basis function coefficients, the sound pressure at the reference microphone is reconstructed, and the relative error is calculated.

[0015] Preferably, in step S5, the boundary acoustic impedance ratio Calculate using the following formula: in, The mean of the optimal reflection coefficient. The polar coordinates of the geometric center of the holographic sound pressure measurement surface in a local coordinate system with the mirror point of the geometric center of the test sound source about the boundary as the origin.

[0016] The beneficial effects of the present invention include at least the following: First, this invention enables in-situ measurement of the acoustic impedance of a material surface without the need for specialized measuring instruments or special measurement conditions. Traditional methods rely on specialized equipment such as impedance tubes or reverberation chambers, while this invention performs measurements directly in the actual engineering application environment, eliminating the need to send material samples to a laboratory, and thus accurately reflecting the acoustic performance of the material under actual installation conditions.

[0017] Second, this invention fully utilizes the sound pressure information obtained from the existing test sound source and microphone array in a semi-open space sound source radiation test field, and calculates the boundary acoustic impedance ratio through a mean reflection coefficient optimization algorithm. Compared with existing in-situ measurement methods, this invention does not require additional standard sound sources as excitation sources, nor does it require specially designed microphone arrays with specific distributions to implement sound field reconstruction, significantly simplifying the test implementation process.

[0018] Third, by introducing a strategy of approximating the mean of the reflection coefficient and minimizing the error of the reference microphone, this invention significantly improves measurement efficiency while ensuring measurement accuracy, thus meeting the accuracy requirements of engineering applications. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the method flow according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the arrangement of the microphone array and the reference microphone in an embodiment of the present invention. Figure 3This is a schematic diagram illustrating the geometric relationship between two local coordinate systems relative to the global coordinate system in an embodiment of the present invention. Figure 4 This is a schematic diagram of the arrangement of the microphone array, reference microphone, and board sound source according to an embodiment of the present invention. Detailed Implementation

[0020] 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.

[0021] like Figure 1 As shown, this embodiment of the invention provides an in-situ acoustic impedance measurement method based on mean reflection coefficient optimization, comprising the following steps: Step S1: Arrange the test sound source in a semi-open space containing a reflective boundary, arrange a microphone array near the test sound source to form a holographic sound pressure measurement surface, and arrange a reference microphone near the boundary.

[0022] like Figure 2 As shown, the test sound source is first placed in a semi-open space sound source radiation test field containing a reflective boundary. At this point, the boundary acoustic impedance of the semi-open space is unknown, which is the target quantity to be measured in this invention. A microphone array is arranged near the test sound source, forming a holographic sound pressure measurement surface to collect spatial distribution information of the sound source radiation field. Simultaneously, a reference microphone is placed near the boundary. This reference microphone provides an independent sound pressure measurement point for calculating reconstruction errors in the subsequent optimization algorithm.

[0023] The geometric arrangement of the measurement system needs to meet specific constraints. In this embodiment of the invention, the geometric centers of the reference microphone, the holographic sound pressure measurement surface, and the mirror image of the geometric center of the test sound source about the boundary should remain collinear. This geometric relationship ensures that the reflection coefficient at the reference microphone is equal to the reflection coefficient at the geometric center of the measurement surface, providing a theoretical basis for subsequent optimization of the mean reflection coefficient.

[0024] To ensure the integrity and validity of the measurement data, the arrangement of the microphone array must also consider spatial sampling issues related to the sound wave wavelength. The geometry of the holographic sound pressure measurement surface should be conformal to the geometry of the tested sound source surface to uniformly capture the spatial distribution characteristics of the direct radiation field of the tested sound source surface. The measurement aperture of the microphone array should not be less than 1.2 times the area of ​​the tested sound source surface; this setting ensures that the array can fully acquire the spatial distribution of the direct radiation field of the tested sound source surface. The spacing between adjacent microphones in the microphone array should be less than the sound wave wavelength. One-sixth, that is, the spacing is less than one-sixth. This is to meet the requirements of the spatial sampling theorem and improve the spatial resolution of the acquired sound field information. The distance between the reference microphone and the boundary should preferably be set to one-quarter of the sound wave wavelength, that is, approximately [missing information]. This position can effectively distinguish the contributions of incident and reflected waves, and improve the sensitivity of reflection coefficient optimization.

[0025] Step S2: Start the test sound source and collect the sound pressure of the superposition of sound source radiation and boundary reflection through the microphone array and reference microphone.

[0026] After the measurement system setup is completed, the test sound source is activated to emit sound waves. The sound waves emitted by the source propagate in a semi-open space. Part of the sound waves directly reach the microphone array to form a direct sound field, while the other part is reflected by the boundary and then reaches the microphone array to form a reflected sound field. The sound pressure signals collected by the microphone array and the reference microphone are the result of the superposition of the direct radiation field of the sound source and the boundary reflection field.

[0027] During data acquisition, the position coordinates of each microphone and its corresponding complex sound pressure value need to be recorded. The sound pressure data from each measuring point of the microphone array will be used to establish a mathematical model of the sound pressure field in the half-space and solve for the basis function coefficients, while the sound pressure data of the reference microphone will serve as a reference benchmark for the optimization algorithm.

[0028] Step S3: The sound pressure field of the half-space is described by the linear superposition of the basis functions of the half-space spherical wave. The reflection coefficient corresponding to the geometric center of the holographic sound pressure measurement surface is used as the mean of the reflection coefficient to replace the reflection coefficient of each array point, and a mathematical model of the sound pressure field of the half-space is established.

[0029] To describe the sound pressure field distribution in a semi-open space containing reflecting boundaries, this invention employs a linear superposition of the basis functions of a half-space spherical wave to establish a mathematical model. For example... Figure 3 As shown, with the geometric center of the sound source The projection of the boundary of the surface of the material under test is taken as the origin of the coordinate system. Taking the plane containing the boundary as - Establish a global coordinate system in the coordinate plane. Denote the mirror image of the geometric center of the sound source about the boundary as... And translate the global coordinate system to respectively and Establish two local coordinate systems. For any point in half-space... The coordinates in the two local coordinate systems are denoted as follows: and They are related to global coordinates The relationship between them can be represented as: ; ; In the formula, From the geometric center of the sound source to - Distance between planes, for A unit vector in direction.

[0030] In the global coordinate system, sound source radiation and boundary reflection occur at a half-space field point. sound pressure response It can be described by a linear superposition of a set of half-space spherical wave basis functions: ; In the formula, For the basis functions of the half-space spherical wave, These are the corresponding basis function coefficients. The angular frequency of the sound wave Let the ordinal number be the expansion term of the basis function. This represents the total number of terms in the basis function expansion.

[0031] The basis function of a half-space spherical wave consists of two parts: centered on the sound source... The spherical wave basis function at the origin represents the contribution of the direct field, with the mirror point as the reference point. The product of the spherical wave basis function at the origin and the reflection coefficient represents the contribution of the reflected field. Its expression is: ; Among them, with and The spherical wave basis functions with the origin as the coordinate point are defined as follows: ; ; In the formula, and These represent the spherical coordinates of the field point in the two local coordinate systems, respectively. For the first kind of spherical Hankel function, For sound wave number, For the speed of sound, It is a spherical harmonic function. Integer. , and Satisfying the relation ,in , , for The cutoff value.

[0032] Sound pressure reflection coefficient Related to boundary acoustic properties, its expression is: ; In the formula, The angle of incidence of the sound wave. The normalized boundary acoustic admittance is the reciprocal of the boundary acoustic impedance. The magnitude of the reflection coefficient satisfies the constraint condition: ; In the formula, This indicates taking the modulus of a complex number.

[0033] Since the reflection coefficient varies with the incident angle, the reflection coefficient at each measuring point of the microphone array is not strictly the same. In this embodiment of the invention, the mean reflection coefficient is approximated: the geometric center of the holographic sound pressure measurement surface is used as the reference point. Corresponding reflection coefficient As the mean of the reflection coefficient This is used to approximate the reflection coefficient at each array point. Based on the geometric arrangement requirements in step S1, the reference microphone is used... Reflectance coefficient and They are equal. After approximating with the mean of the reflection coefficients, the basis function of the half-space spherical wave can be simplified to: ; In this embodiment, the average reflection coefficient is... Abbreviated as It should satisfy the constraints. .

[0034] Step S4: Iterate through all values ​​within the range of the mean reflection coefficient, solve for the basis function coefficients, reconstruct the sound pressure at the reference microphone, and determine the optimal mean reflection coefficient based on minimizing the relative error between the reconstructed sound pressure and the measured sound pressure.

[0035] Based on the mathematical model established in step S3, this step uses a traversal optimization algorithm to determine the optimal mean reflection coefficient. The sound pressure collected at each measuring point of the microphone array can be expressed in the following matrix form: ; In the formula, This is a column vector composed of half-space sound pressure measurements. It is a column vector consisting of the basis function coefficients of the half-space spherical wave. The coordinates of the measuring point are... , The number of measurement points on the array. It is a matrix composed of the expansion terms of the half-space spherical wave basis functions at each measuring point.

[0036] mean reflectance For a complex number, it can be represented as: ; In the formula, Represents the real part of a complex number. Represents the imaginary part of a complex number. It is the imaginary unit. Because... ,by For the horizontal axis, If a rectangular coordinate system is established with the vertical axis as the coordinate axis, then All possible values ​​should fall within a circle centered at the origin with a radius of 1. This region within the circle is discretized using a specific meshing method, and the value corresponding to any mesh node... This is the mean of the possible optimal reflectance coefficient. , This represents the total number of nodes.

[0037] The optimization calculation is performed according to the following process: Set the number of terms in the expansion of the half-space spherical wave basis function. The range of values ​​is ,in This is the maximum number of expanded items. The number of expanded items is then set sequentially within this range. For each expansion term, iterate through all possible values ​​of the mean reflection coefficient. For a given and First, solve for the basis function coefficients: ; In the formula, The pseudo-inverse of a matrix is ​​expressed by the following formula: ; In the formula, This represents the conjugate transpose of a matrix.

[0038] After obtaining the basis function coefficients, the reference microphone The reconstructed sound pressure value of the half-space at that location can be calculated by the following formula: ; Let the number of terms in the expansion of the basis functions of the half-space spherical wave be... ,Will The value is assigned to the basis function of the spherical wave in the half-space, and the process is iterated through all... The corresponding sound pressure reconstruction value is obtained. .

[0039] Let the number of terms be expanded Repeat the above reconstruction calculation process; repeat this cycle until the number of expanded terms is completed. Reconstruction calculation at time; calculation of the relative error between the reconstructed sound pressure value and the measured value: ; The optimal value is determined by minimizing the reconstruction error, and this value is used as the mean value of the reflection coefficient.

[0040] Step S5: Calculate the boundary acoustic impedance ratio based on the mean value of the optimal reflection coefficient.

[0041] Based on the geometric center coordinates of the holographic sound pressure measurement surface and the geometric relationship between the sound source center and the material boundary, the mean value of the optimal reflection coefficient obtained in step S4 is used. Boundary acoustic impedance Calculate using the following formula: In the formula, Geometric center of the holographic sound pressure measurement surface In The polar coordinates in the local coordinate system with the origin as the point.

[0042] The effectiveness of the method of the present invention is verified through a specific numerical simulation example below. Figure 4 As shown, the test sound source is assumed to be a square plate with a side length of 0.10m, with the source surface parallel to the material surface and 0.25m from the boundary. The investigated sound wave frequency is 1700Hz, and the air medium density is 1.20kg / m³. 3 When the speed of sound is 343 m / s, the corresponding wavelength of the sound wave is 0.20 m.

[0043] A square array of 36 microphones (6×6=36) is arranged on one side of the sound source surface. The array's measuring aperture is 0.15m×0.15m, which meets the requirement of being no less than 1.2 times the area of ​​the sound source surface. The array is 0.05m away from the sound source surface. The geometric center coordinates of the square holographic sound pressure measurement surface formed by the array are... Place a reference microphone near the boundary, at coordinates [coordinates missing]. The distance from the boundary is approximately one-quarter of the wavelength.

[0044] The test sound source is activated, and the sound pressure, a superposition of source radiation and boundary reflection, is collected through the microphone. The half-space sound pressure field measured by the microphone array is described using the linear superposition of the basis functions of the half-space spherical wave. Under the array parameter settings, the geometric center of the holographic measurement surface... The corresponding angle of incidence of the sound wave is The reflection coefficient corresponding to the geometric center of the measurement surface. As the mean of the reflection coefficient By approximating the reflection coefficients at all array points, a mathematical model of the approximate half-space sound pressure field is obtained. The maximum number of expansion terms for the basis functions is set to... Let the number of terms expanded be... At that time, iterate through all values ​​within the range of the mean reflection coefficient, solve for the basis function coefficients, reconstruct the sound pressure at the reference microphone, and calculate the relative error. Then, let the number of expansion terms be... Repeat the above solution process, calculating the relative error, until the number of expanded terms is [number missing]. The optimal calculation is performed. The optimal value of the mean reflection coefficient is determined based on minimizing the reconstruction error. The acoustic impedance is calculated using the obtained optimal mean reflection coefficient, according to the geometric relationship between the geometric center coordinates of the holographic measurement surface, the sound source center, and the material boundary.

[0045] The numerical simulation results are presented below to verify the accuracy of the calculated acoustic impedance. The frequency is assumed to be... When the surface acoustic impedance of the material is _____, The Young's modulus of the plate structure is Poisson's ratio is Thickness is The density is Apply a force of size to the geometric center of the plate. The simple harmonic excitation force is used to calculate the radiated sound pressure field of the sound source in the half-space using relevant analytical formulas. This yields the sound pressure measurement value of the microphone. The influence of microphone measurement error is simulated, and a signal-to-noise ratio of [value missing] is added to the measured sound pressure. Gaussian white noise.

[0046] To quantify the accuracy of acoustic impedance calculation, the calculated acoustic impedance value is defined. Compared with the true value relative error between for: ; Simulation results show that when the number of expanded terms is When, relative error Get the minimum value At this point, the average reflection coefficient obtained by selection is The calculated acoustic impedance value is The relative error between it and its true value is .

[0047] The results show that the in-situ acoustic impedance measurement method based on mean reflection coefficient optimization of the present invention can obtain the acoustic impedance of the material surface more accurately by directly utilizing the existing sound source and holographic measurement surface arrangement in the test field, combining the sound pressure information of a single field point with the reference microphone, and using the optimization algorithm of the mean reflection coefficient of the array measurement points.

[0048] 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.

[0049] 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. An acoustic impedance in-situ measurement method based on reflection coefficient mean value optimization, characterized in that, The method comprises the following steps: Step S1: arranging a test sound source in a semi-open space with a reflecting boundary, arranging a microphone array near the test sound source to form a holographic sound pressure measurement surface, and arranging a reference microphone near the boundary; Step S2: starting the test sound source, and collecting sound pressure of superposition of sound source radiation and boundary reflection through the microphone array and the reference microphone; Step S3: describing a half-space sound pressure field by linear superposition of half-space spherical wave basis functions, taking a reflection coefficient mean value corresponding to a geometric center of the holographic sound pressure measurement surface as a reflection coefficient, replacing reflection coefficients of each array point, and establishing a mathematical model of the half-space sound pressure field; Step S4: traversing all values in a value range of the reflection coefficient mean value, solving basis function coefficients, reconstructing sound pressure at the reference microphone, and taking a relative error between the reconstructed sound pressure and the measured sound pressure as a criterion to determine an optimal reflection coefficient mean value; Step S5: calculating a boundary acoustic impedance ratio according to the optimal reflection coefficient mean value. 2.The acoustic impedance in-situ measurement method based on the reflection coefficient mean value optimization of claim 1, wherein: The reference microphone, a geometric center of the holographic sound pressure measurement surface, and a mirror image point of a geometric center of the test sound source about the boundary are collinear. 3.The acoustic impedance in-situ measurement method based on the reflection coefficient mean value optimization of claim 1, wherein: A geometric shape of the holographic sound pressure measurement surface is conformal to a geometric shape of a surface of the test sound source. 4.The acoustic impedance in-situ measurement method based on the reflection coefficient mean value optimization of claim 1, wherein: A measurement aperture of the microphone array is not less than 1.2 times of an area of the surface of the test sound source.

5. The method of claim 1, wherein: A distance between adjacent microphones in the microphone array is less than one sixth of a wavelength of a sound wave.

6. The method of claim 1, wherein: A distance between the reference microphone and the boundary is one fourth of the wavelength of the sound wave.

7. The method of claim 1, wherein: In step S3, the reflection coefficient mean satisfying the constraint where denotes complex modulo. 8.The acoustic impedance in-situ measurement method based on the reflection coefficient mean value optimization of claim 7, wherein: In step S4, the reflection coefficient mean value is represented as: wherein, represents the real part of a complex number, represents the imaginary part of a complex number, is the imaginary unit; in establishes a rectangular coordinate system with the abscissa, establishes a rectangular coordinate system with the abscissa, establishes a rectangular coordinate system with the abscissa, 9.The acoustic impedance in-situ measurement method based on the optimization of the mean value of reflection coefficient according to claim 1, characterized in that: In step S4, the number of half-space spherical wave basis function expansion terms is set The value range of is , wherein is the maximum value of the number of expansion terms; within the value range, the number of expansion terms is set in sequence, all possible values of the mean value of the reflection coefficient are traversed for each number of expansion terms, the sound pressure at the reference microphone is reconstructed after solving the basis function coefficients, and the relative error is calculated.

10. The acoustic impedance in-situ measurement method based on the optimization of the mean value of reflection coefficient according to claim 1, characterized in that: In step S5, the boundary acoustic impedance ratio is calculated according to the following equation: wherein, is the optimal reflection coefficient mean, is the polar angular coordinate of the holographic sound pressure measurement surface geometric center in the local coordinate system with the mirror point of the subject sound source geometric center with respect to the boundary as the origin.

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