CN114630260B - A sound field reconstruction method in half-space uniform flow - Google Patents

Abstract

The invention discloses a sound field reconstruction method in a half-space uniform flow, which includes the following four steps: 1. Convert the sound field reconstruction problem in a half-space uniform flow into a multi-source sound field reconstruction problem in a free-space uniform flow; 2. In actual sound Equivalent sources are arranged at the source and mirror sound source respectively, and several equivalent sources are used to equate the actual sound source and mirror sound source; a holographic measurement surface is selected in the near field of the actual sound source; 3. Construct multiple sound source radiation in uniform flow Sound field mathematical model; calculate all equivalent source strengths including convection effects based on the sound pressure of the holographic surface; 4. Extract the equivalent source intensity corresponding to the actual sound source, and determine the position of the reconstructed surface, using the extracted equivalent source and Sound field reconstruction by NAH in free space uniform flow. The invention can not only remove the influence of half-space reflected sound, but also fully consider the flow effect caused by the flow of media, and realize the identification of sound sources and the accurate reconstruction of the sound field in the uniform flow of half-space.

Description

A sound field reconstruction method in half-space uniform flow

Technical field

The invention belongs to the field of noise source identification methods, and specifically relates to a method for reconstructing the sound field in a half-space uniform flow.

Background technique

In order to solve the problems of sound field reconstruction and sound source identification in moving media, such as test pieces, wind turbines and wind turbines in acoustic wind tunnels, nearfield acoustic holography (NAH) in flowing media has been developed in recent years. ). At the same time, NAH in flowing media is also suitable for the identification of moving sound sources and the reconstruction of their sound fields, such as moving cars and high-speed trains. In this case, the sound pressure measurement array only needs to be fixed on the sound source to maintain synchronous movement. Therefore, NAH in flowing media is a technical method with broad application prospects. However, the NAH in the flow media that has been developed so far assumes that it is in free space without reflecting surfaces.

However, there are many half-space situations in actual problems. For example, sound sources such as cars and high-speed trains will be affected by ground reflections. Acoustic wind tunnel tests in semi-anechoic chambers will also be affected by ground reflections. At this time, if you use the existing flow There will be a large error in the sound field reconstruction of NAH in the medium.

In fact, half-space problems also exist in static media, and half-space NAH in static media has been developed to solve problems such as ground reflection. However, this technology does not consider the flow effect and cannot be applied to sound sources or sound sources in flowing media. Identification of moving sound sources and their sound field reconstruction. At the same time, the existing half-space NAH method in static media is conceptually complex. For example, the equivalent source configuration scheme is cumbersome or the acoustic impedance information of the reflecting surface needs to be known.

Therefore, the existing technical solutions have the following shortcomings or defects: (1) NAH in flowing media is limited to free space and cannot be applied to half-space sound field reconstruction and sound source identification; (2) Half-space NAH in static media does not consider the flow effect , cannot be applied to the identification of sound sources or moving sound sources in flowing media and their sound field reconstruction, and the implementation scheme is relatively complex.

Contents of the invention

The purpose of the present invention is to overcome the above-mentioned shortcomings of the prior art and propose a sound field reconstruction method in a half-space uniform flow, so that the method can not only solve the half-space reflection problem, but also be applicable to situations where the medium flows or the sound source moves, and It has the characteristics of simple implementation and operation.

In order to achieve the above objects, the present invention adopts the following technical solutions:

A sound field reconstruction method in half-space uniform flow, including the following steps:

Step 1): Equivalent processing of the sound field reconstruction problem in half-space uniform flow: on the one hand, the actual sound source is mirrored symmetrically about the reflection surface in the half-space, and the half-space sound field reconstruction problem is converted into a free-space multi-source sound field reconstruction problem; On the other hand, the actual uniform flow is symmetrically mirrored about the reflection surface in the half space to obtain the mirrored uniform flow, and the mirrored sound source is converted into the same flow field environment as the actual sound source;

Step 2): Arrange equivalent sources at the actual sound source and the mirror image sound source respectively, and use several equivalent sources to equate the actual sound source and the mirror image sound source; select a holographic measurement surface in the near field of the actual sound source;

Step 3): Construct a mathematical model of the radiation sound field of multiple sound sources in uniform flow; calculate all equivalent source strengths including convection effects based on the holographic surface sound pressure;

Step 4): Extract the equivalent source intensity corresponding to the actual sound source, and determine the position of the reconstruction surface. Use the extracted equivalent source and the NAH in the free space uniform flow to reconstruct the sound field, and then eliminate the half-space effect and consider Reconstruction of the sound field produced by an actual sound source due to convection effects.

Further, the step 1) includes the following steps:

Step 1.1): Mirror the potential actual sound source symmetrically about the reflection surface in the half space, obtain the mirror sound source and its spatial distribution information, treat the reflected sound as the radiation of the mirror sound source, and then convert the half space sound field reconstruction problem into Free space multi-source sound field reconstruction problem;

Step 1.2): Considering that the reflected sound is also affected by the flow effect, the actual uniform flow is symmetrically mirrored about the reflective surface in the half space to obtain the mirrored uniform flow, whose flow speed and direction are the same as the actual uniform flow, and then the reflected sound is affected by The influence of flowing media is considered as the image sound source is affected by the flowing media.

Further, the step 2) includes the following steps:

Step 2.1): According to the basic idea of the equivalent source method, that is, the sound field radiated by an arbitrary-shaped sound source can be approximated by the superposition of the sound fields radiated by a series of equivalent sources with different source strengths. In the actual sound source and the mirror sound source Equivalent sources are arranged separately at different places, and several equivalent sources are used to equate actual sound sources and mirror sound sources. The equivalent source layout plan is carried out according to the conventional NAH based on the equivalent source method;

Step 2.2): Select the holographic measurement surface in the near field of the actual sound source, divide the holographic surface into equidistant grids, and ensure that the number of holographic surface grid points is greater than or equal to the number of equivalent sources corresponding to the actual sound source and the mirror sound source. and, to ensure the uniqueness of the equivalent source strong solution;

Further, the step 3) includes the following steps:

Step 3.1): Construct a mathematical model of the radiation sound field of multiple sound sources in uniform flow, and obtain the relationship between the holographic sound pressure and the equivalent source intensity in the flowing medium. The specific process is as follows:

Establish a Cartesian rectangular coordinate system. Assume that the reflective surface in the half space is located on the x-o-y plane, the medium flows along the positive x direction parallel to the reflective surface, and the flow speed is represented by the Mach number M. Then any grid on the holographic surface of the uniform flow in the half space The sound pressure at point r = (x, y, z) can be regarded as the superposition of sound pressure radiated by the equivalent source corresponding to the actual sound source and the mirror sound source in the uniform flow in free space, and its expression is:

In the formula, q(r _l ) represents the l-th equivalent source intensity of the actual sound source, and q _m (r _j ) is the j-th equivalent source intensity of the mirror sound source. L is the number of equivalent sources corresponding to the actual sound source, J is the number of equivalent sources corresponding to the mirror sound source, it is recommended to take L=J; g(r,r _l ) is the lth equivalent source of the actual sound source The expression of the free space convection transfer function to the field point r is:

Among them, i is the imaginary unit, ρ is the air density, c is the speed of sound, and k is the wave number;

g _m (r, r _j ) is the free space convection transfer function from the jth equivalent source of the mirror sound source to the field point r. Its expression is similar to the expression of g (r, r _l ). You only need to change the formula Just replace the subscript "l" with the subscript "m" in (2), (3) and (4).

Since the holographic surface is equally divided into multiple grid points as sound pressure sampling points, the sound pressure of the holographic surface is written in matrix form according to equation (1):

In the formula, G and G _m are the sound pressure transfer matrices composed of the free space convection transfer functions g(r, r _l ) and g _m (r, r _j ) respectively, and P is the sound pressure vector containing the convection effect on the holographic surface, Q and Q _m are vectors composed of source strengths q(r _l ) and q _m (r _j ) respectively, and the superscript "T" represents the matrix transpose; Formula (5) is the radiation sound field of multiple sound sources in uniform flow Mathematical model, since the convection effect is considered in the sound pressure transfer matrix, it can accurately describe the transfer relationship of the sound field in the flowing medium;

Step 3.2): Calculate all equivalent source strengths including convection effects based on the sound pressure of the holographic surface. The specific process is as follows:

According to formula (5), the vector containing all equivalent source strengths can be obtained:

The superscript "+" in the formula represents the generalized inverse operation of the matrix. Since the inverse matrix It usually has pathological properties, and holographic sound pressure data inevitably contains noise. Therefore, regularization processing needs to be used when calculating the equivalent source intensity to suppress the problem of noise amplification during the solution process. The Tikhonov regularization method is used here, then (6 ) formula is:

In the formula, the superscript "H" represents the conjugate transpose of the matrix, E is the identity matrix, and λ is the regularization parameter, which can be automatically selected by the Generalized Cross Validation (GCV) method;

Further, the step 4) includes the following steps:

Step 4.1): Extract the equivalent source intensity corresponding to the actual sound source: the vector containing all equivalent source intensities has been calculated from formula (7) At the same time, according to formula (5), it can be seen that this vector consists of the source intensity vector Q corresponding to the actual sound source and the source intensity vector Q _m corresponding to the mirror sound source, so it can be obtained from/> Extract the source strength vector Q from

Step 4.2): After obtaining the source intensity vector Q corresponding to the actual sound source, use this part of the equivalent source and the NAH in the free space uniform flow to reconstruct the sound field, select the position of the reconstruction surface, and perform an equidistant grid on the reconstruction surface Division, the number of grid points can be determined as needed, any grid point on the reconstructed surface The calculation expression of sound pressure is:

in the formula is the l-th equivalent source of the actual sound source to the reconstruction point/> The free space convection transfer function at , its expression is:

in,

Since the reconstruction surface is divided into multiple grid points as reconstruction points, the sound pressure of all reconstruction points on the reconstruction surface is written in matrix form according to equation (8):

P _s = G _s Q (12)

In the formula, P _s is the sound pressure vector containing the convection effect on the reconstructed surface, and G _s is the free space convection transfer function. The sound pressure transfer matrix composed of The surface sound pressure does not include reflected sound, and the sound field generated by the actual sound source is accurately reconstructed, and the actual sound source can be identified based on the reconstructed surface sound pressure.

Compared with the existing technology, the sound field reconstruction method in a half-space uniform flow of the present invention can not only remove the influence of half-space reflected sound, but also fully consider the flow effect caused by the medium flow, and can achieve a half-space uniform flow. Identification of sound sources and accurate reconstruction of sound fields. The concept of this method is simple, and the equivalent source configuration scheme can be carried out according to the conventional equivalent source method; at the same time, it does not require the acoustic impedance information of the half-space reflection surface, so it is suitable for the reconstruction of the half-space sound field with arbitrary acoustic property boundaries. The results of the present invention can be applied to sound source identification and sound field reconstruction in flowing media such as acoustic wind tunnel testing or wind power generation equipment, and can also be applied to sound source identification and sound field reconstruction of transportation vehicles such as cars or high-speed trains. This provides important basis and guidance for the vibration and noise reduction and low-noise design of such products. In particular, if the medium flow velocity is set to M=0 in the above steps, the present invention can also be applied to sound source identification and sound field reconstruction in a static medium half space.

Description of the drawings

Figure 1 is a geometric schematic diagram of sound field reconstruction in a half-space uniform flow according to an embodiment of the present invention.

Figure 2 shows the results of sound pressure reconstruction on the reconstruction surface when the flow velocity is Mach 0.3 in Embodiment 1 of the present invention: (a) theoretical sound pressure; (b) sound pressure reconstructed by this method; (c) sound pressure reconstruction by NAH in free space flowing medium Pressure; (d) Half-space NAH reconstructed sound pressure in static medium.

Figure 3 is a comparison of the reconstructed sound pressure and the theoretical sound pressure in Embodiment 2 of the present invention when the flow rate is Mach 0.5: (a) Theoretical sound pressure; (b) The sound pressure reconstructed by this method; (c) NAH in the free space flowing medium Reconstructed sound pressure; (d) Reconstructed sound pressure with half-space NAH in static medium.

Figure 4 is a comparison of the reconstructed sound pressure and the theoretical sound pressure in Embodiment 3 of the present invention when the flow rate is Mach 0: (a) Theoretical sound pressure; (b) The sound pressure reconstructed by this method; (c) NAH in the free space flowing medium Reconstructed sound pressure; (d) Reconstructed sound pressure with half-space NAH in static medium.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all the embodiments.

A sound field reconstruction method in a half-space uniform flow, whose geometric diagram is shown in Figure 1, including the following steps:

Step 1): Equivalent treatment of the problem of sound field reconstruction in uniform flow in half space: on the one hand, the actual sound source is symmetrically mirrored about the reflection surface in the half space to obtain the spatial distribution of the mirror sound source, and the reflected sound is regarded as the mirror sound source generated, and then convert the half-space sound field reconstruction problem into a free-space multi-source sound field reconstruction problem; on the other hand, the actual uniform flow is symmetrically mirrored about the reflection surface in the half-space, and the mirrored uniform flow is obtained, and its flow velocity and direction are consistent with the actual The uniform flow is the same, and the influence of the reflected sound by the flowing medium is regarded as the influence of the mirror sound source by the flowing medium; the specific steps are:

Step 1.1): Mirror the actual sound source symmetrically about the reflection surface in the half space, obtain the mirror sound source and its spatial distribution information, treat the reflected sound as radiation from the mirror sound source, and then convert the half-space sound field reconstruction problem into the free space Multi-source sound field reconstruction problem;

Step 1.2): Considering that the reflected sound is also affected by the flow effect, the actual uniform flow is symmetrically mirrored about the reflective surface in the half space to obtain the mirrored uniform flow, whose flow speed and direction are the same as the actual uniform flow, and then the reflected sound is affected by The influence of flowing media is considered as the image sound source is affected by the flowing media.

Step 2): Arrange equivalent sources at the actual sound source and the mirror image sound source respectively, and use several equivalent sources to equivalent the actual sound source and the mirror image sound source; select the holographic measurement surface in the near field of the actual sound source, and measure the holographic surface Carry out equidistant grid division and ensure that the number of holographic surface grid points is greater than or equal to the sum of the number of equivalent sources corresponding to the actual sound source and the mirror sound source to ensure the uniqueness of the strong solution of the equivalent source source; the specific steps are:

Step 2.1): According to the basic idea of the equivalent source method, that is, the sound field radiated by an arbitrary-shaped sound source can be approximated by the superposition of the sound fields radiated by a series of equivalent sources with different source strengths. In the actual sound source and the mirror sound source Arrange equivalent sources respectively at each location. For example, use an equivalent source with a source strength of Q = [q ₁ , q ₂ ,..., q _l ,..., q _L ] to equivalent the actual sound source, and use a source with a source strength of Q _m =[ q ₁ , q ₂ ,…, q _j ,…, q _J ] to equivalent mirror sound sources. The equivalent source layout plan is carried out according to the conventional NAH based on the equivalent source method. The equivalent source surface can be Determined according to the shape of the sound source surface, it can be closed or non-closed. For example, when the sound source surface is a plane, the equivalent source surface can be a plane shape;

Step 2.2): Select the holographic measurement surface in the near field of the actual sound source, divide the holographic surface into equidistant grids, and ensure that the number of holographic surface grid points is greater than or equal to the number of equivalent sources corresponding to the actual sound source and the mirror sound source. and, to ensure the uniqueness of the equivalent source strong solution;

Step 3): Construct a mathematical model of the radiation sound field of multiple sound sources in uniform flow; calculate all equivalent source strengths including convection effects based on the holographic surface sound pressure; the specific steps are:

Step 3.1): Construct a mathematical model of the radiation sound field of multiple sound sources in uniform flow, and obtain the relationship between the holographic sound pressure and the equivalent source intensity in the flowing medium. The expression in matrix form is:

In the formula, G and G _m are the sound pressure transfer matrices composed of the free space convection transfer functions g (r, r _l ) and g _m (r, rj) respectively, and P is the sound pressure vector containing the convection effect on the holographic surface. The mark "T" indicates matrix transposition; g(r,r _l ) is the free space convection transfer function from the lth equivalent source of the actual sound source to the field point r, and its expression is:

Among them, i is the imaginary unit, ρ is the air density, c is the speed of sound, and k is the wave number;

g _m (r, r _j ) is the free space convection transfer function from the jth equivalent source of the mirror sound source to the field point r. Its expression is similar to the expression of g (r, r _l ). You only need to change the formula Just replace the subscript "l" with the subscript "m" in (2), (3) and (4).

Step 3.2): Calculate all equivalent source strengths including convection effects based on the sound pressure of the holographic surface; during the solution process, in order to suppress the problem of measurement noise amplification, the source strength solution after using the Tikhonov regularization method is

In the formula, the superscript "H" represents the conjugate transpose of the matrix, the superscript "+" represents the generalized inverse operation of the matrix, E is the identity matrix, and λ is the regularization parameter, which can be calculated by Generalized Cross Validation (GCV) method for automatic selection.

Step 4): Extract the equivalent source intensity corresponding to the actual sound source, and determine the position of the reconstruction surface. Use the extracted equivalent source and the NAH in the free space uniform flow to reconstruct the sound field, and then eliminate the half-space effect and consider Reconstruction results of the sound field generated by the actual sound source due to convection effect; the specific steps are:

Step 4.1): Extract the equivalent source intensity corresponding to the actual sound source: the vector containing all equivalent source intensities has been calculated from formula (7) At the same time, according to formula (5), it can be seen that this vector consists of the source intensity vector Q corresponding to the actual sound source and the source intensity vector Q _m corresponding to the mirror sound source, so it can be obtained from/> Extract the source strength vector Q from

Step 4.2): After obtaining the source intensity vector Q corresponding to the actual sound source, use this part of the equivalent source and the NAH in the free space uniform flow to reconstruct the sound field. Select the location of the reconstruction surface and divide the reconstruction surface into equidistant grids. The number of grid points can be determined as needed. The matrix form of the calculated expression of the reconstructed surface sound pressure is:

P _s = G _s Q (12)

In the formula, P _s is the sound pressure vector containing the convection effect on the reconstructed surface, and G _s is the free space convection transfer function. The sound pressure transfer matrix composed of. /> is the l-th equivalent source of the actual sound source to the reconstruction point/> The free space convection transfer function at , its expression is:

in,

The obtained result P _s is the reconstructed sound pressure that does not include the influence of reflected sound and takes into account the flow effect. Since the method of the present invention does not require the acoustic impedance information of the half-space reflecting surface, it can be applied to the reconstruction of the half-space sound field with arbitrary acoustic property boundaries. Considering that there is an analytical solution to the sound field when the reflecting surface is a rigid surface, which facilitates method verification, the following examples use a rigid surface to illustrate, and simulation verification is performed through Examples 1 to 3 for further explanation.

Example 1

Taking a composite sound source composed of two monopoles in a uniform flow as an example, the sound source frequency is 2000Hz, the half-space boundary surface is a rigid surface located at z=0, and the flow speed is set to Mach 0.3, which is similar to the cruising speed of a high-speed rail. near.

Step 1.1): Mirror the actual sound source symmetrically about the reflection surface in the half space, obtain the mirror sound source and its spatial distribution information, treat the reflected sound as radiation from the mirror sound source, and then convert the half-space sound field reconstruction problem into the free space Multi-source sound field reconstruction problem;

Step 1.2): Considering that the reflected sound is also affected by the flow effect, mirror the actual uniform flow symmetrically about the reflective surface in the half space to obtain the mirror uniform flow. Its flow speed direction is the same as the actual uniform flow, and the flow speed is also Mach 0.3. Furthermore, the influence of reflected sound by the flowing medium is regarded as the influence of the mirror sound source by the flowing medium.

Step 2.1): Arrange equivalent sources at the actual sound source and the mirror sound source respectively, and use equivalent sources with source strengths of Q = [q ₁ , q ₂ ,..., q _l ,..., q _L ] to equivalent to the actual sound source. For sound sources, use equivalent sources with source strengths of Q _m = [q ₁ , q ₂ ,..., q _j ,..., q _J ] to equivalent mirror sound sources. The equivalent source layout plan is based on the conventional equivalent source It is carried out based on the NAH method: in this embodiment, the sound source surface is a plane, and the equivalent source surface is also arranged in a planar shape. Here, L=J=144 is taken, that is, the equivalent sources corresponding to the actual sound source and the mirror sound source are arranged respectively. On a 12×12 grid point, the equivalent source surface distance from the sound source surface is 0.05m;

Step 2.2): Select the holographic measurement surface y = 0.1m in the actual sound source near field, and disperse the holographic surface equidistantly in the x and z directions with an interval of 0.05m to form 24×12 grid points. The number of surface grid points is equal to the sum of the number of equivalent sources corresponding to the actual sound source and the mirror sound source, which can ensure the uniqueness of the strong solution of the equivalent source;

Step 3.1): Construct a mathematical model of the radiation sound field of multiple sound sources in uniform flow, and obtain the relationship between the holographic sound pressure and the equivalent source intensity in the flowing medium. The expression in matrix form is:

In the formula, G and G _m are the sound pressure transfer matrices composed of the free space convection transfer function g (r, r _l ) and g _m (r, r _l ) respectively, with dimensions of 144 × 144; P is the holographic surface The sound pressure vector including the convection effect has a dimension of 144×1; the superscript "T" indicates the matrix transpose; g(r, r _l ) is the free space from the lth equivalent source of the actual sound source to the field point r The convection transfer function, its expression is:

in,

g _m (r, r _j ) is the free space convection transfer function from the jth equivalent source of the mirror sound source to the field point r. Its expression is similar to the expression of g (r, r _l ). You only need to change the formula Just replace the subscript "l" with the subscript "m" in (2), (3) and (4).

Step 3.2): Calculate all equivalent source strengths including convection effects based on the holographic surface sound pressure; in this embodiment, in order to simulate the actual measurement environment, Gaussian white noise with a signal-to-noise ratio of 30dB is added to the holographic sound pressure data; in During the solution process, in order to suppress the problem of measurement noise amplification, the source strength solution after using the Tikhonov regularization method is:

In the formula, the superscript "H" represents the conjugate transpose of the matrix, the superscript "+" represents the generalized inverse operation of the matrix, E is the identity matrix, and λ is the regularization parameter, which can be calculated by Generalized Cross Validation (GCV) method for automatic selection. Here, get The dimension is 288×1;

Step 4.1): Extract the equivalent source intensity corresponding to the actual sound source: the vector containing all equivalent source intensities has been calculated from formula (7) At the same time, according to formula (5), it can be seen that this vector consists of the source intensity vector Q corresponding to the actual sound source and the source intensity vector Q _m corresponding to the mirror sound source, so it can be obtained from/> The source strength vector Q is extracted from , and the dimension of this vector is 144×1;

Step 4.2): After obtaining the source intensity vector Q corresponding to the actual sound source, use this part of the equivalent source and the NAH in the free space uniform flow to reconstruct the sound field. The position of the selected reconstruction surface is y=0.03m, and the reconstruction surface is divided into equidistant grids with a number of grid points of 12×12. The matrix form of the calculated expression of the reconstructed surface sound pressure is:

P _s = G _s Q (12)

In the formula, P _s is the sound pressure vector containing the convection effect on the reconstructed surface, and G _s is the free space convection transfer function. The sound pressure transfer matrix composed of. /> is the l-th equivalent source of the actual sound source to the reconstruction point/> The free space convection transfer function at , its expression is:

in,

The resulting vector P _s with a dimension of 144×1 is the reconstructed sound pressure that does not include the influence of reflected sound and takes into account the flow effect. This sound pressure vector can be further rearranged into a matrix form with a dimension of 12×12, so as to correspond to the reconstruction points in spatial order.

According to the theoretical sound pressure matrix on the reconstruction surface and the sound pressure matrix reconstructed using this method, the corresponding sound pressure distribution map can be drawn. The comparison is shown in Figure 2. In order to better illustrate the effectiveness of this method, the current sound pressure matrix will be used. The reconstructed sound pressure distributions of NAH in some free-space flowing media and half-space NAH in static media are also given for comparison. It can be seen that the sound pressure reconstructed by this method (Figure 2(b)) is in good agreement with the theoretical sound pressure distribution (Figure 2(a)), while the sound pressure reconstructed by NAH in the existing free space flowing medium (Figure 2(a)) 2(c)) is quite different from the theoretical sound pressure distribution. There is obvious reflected sound at the bottom of the figure, that is, close to the reflecting surface. The sound pressure distribution reconstructed using half-space NAH in static media (as shown in Figure 2(d)) is completely different from the theoretical sound pressure distribution because the flow effect is not considered. In addition, the reconstruction results using this method can distinguish two monopole sound sources, while the reconstruction results using the other two technical methods cannot distinguish them. In order to conduct quantitative comparative analysis, the reconstruction error is defined, and the calculation expression is:

In the formula, N represents the number of points on the reconstructed surface, pr _i represents the theoretical sound pressure value of the field point, and ps _i represents the reconstructed sound pressure value of the field point. After calculation, the reconstruction error of this method is 9.87%. The NAH reconstruction error in existing free space flow media is 36.03%. Half-space NAH reconstruction error exceeds 100% in static media. Therefore, the reconstruction error using this method is small, and more accurate sound field reconstruction in half-space uniform flow can be achieved.

Example 2

This embodiment examines the effectiveness of this method at other flow rates. The flow rate is set to Mach 0.5. Other parameters are set the same as those in Example 1. The implementation steps are the same as those in Example 1 and the calculation expressions used are the same. The comparison of the theoretical sound pressure on the reconstructed surface and the spatial distribution of the sound pressure reconstructed using this method is shown in Figure 3. Here, the sound pressure distribution reconstructed using the existing NAH in the free space flowing medium and the half-space NAH in the static medium are also given for comparison. . It can be seen that the sound pressure reconstructed by this method (Figure 3(b)) agrees well with the theoretical sound pressure distribution (Figure 3(a)). The reconstructed sound pressure of NAH in the existing free space flowing medium (as shown in Figure 3(c)) is quite different from the theoretical sound pressure distribution, and is affected by obvious reflected sound. The sound pressure distribution reconstructed using half-space NAH in static media (as shown in Figure 3(d)) is completely different from the theoretical sound pressure distribution. In addition, the reconstruction results using this method can distinguish two monopole sound sources, while the reconstruction results using the other two technical methods cannot distinguish them. Using formula (13) to calculate the error, the reconstruction error of this method is 9.61%. The NAH reconstruction error in existing free space flow media is 56.36%. Half-space NAH reconstruction error exceeds 100% in static media. Therefore, the reconstruction error using this method is small, and more accurate sound field reconstruction in half-space uniform flow can be achieved.

Example 3

In particular, this method is also suitable for half-space sound field reconstruction in static media when the flow velocity is set to Mach 0. In this embodiment, except for the flow rate, other parameter settings are the same as those in Embodiment 1, the implementation steps are the same as those in Embodiment 1, and the calculation expressions used are the same. The comparison of the theoretical sound pressure on the reconstructed surface and the spatial distribution of the sound pressure reconstructed using this method is shown in Figure 4. Here, the sound pressure distribution reconstructed using the existing NAH in the free space flowing medium and the half-space NAH in the static medium are also given for comparison. . It can be seen that the sound pressure reconstructed by this method (Figure 4(b)) agrees well with the theoretical sound pressure distribution (Figure 4(a)). The NAH reconstructed sound pressure in the existing free space flowing medium (as shown in Figure 4(c)) is quite different from the theoretical sound pressure distribution, and is interfered by reflected sound. The sound pressure distribution reconstructed using half-space NAH in static media (as shown in Figure 4(d)) is in good agreement with the theoretical sound pressure. In addition, two monopole sound sources can be resolved using this method and the reconstruction results of half-space NAH in static media. The reconstruction results using other methods cannot better identify the monopole at the bottom of the image (that is, close to the reflecting surface). After quantitatively calculating the error, the reconstruction error of this method is 7.67%. The NAH reconstruction error in existing free space flow media is 32.62%. The half-space NAH reconstruction error in static media is 7.67%. Therefore, both this method and half-space NAH in static media can reconstruct the sound field more accurately, and the reconstruction error is the same. This is because when the flow velocity is Mach 0, this method is equivalent to half-space NAH in static media.

The above are only preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person familiar with the technical field can, within the technical scope disclosed in the present invention, implement the technical solutions of the present invention. Equivalent substitutions or changes of the inventive concept thereof shall be included in the protection scope of the present invention.

Claims (2)

1. A sound field reconstruction method in half-space uniform flow, which is characterized by: including the following steps: Step 1): Equivalent processing of the sound field reconstruction problem in half-space uniform flow: on the one hand, the actual sound source is mirrored symmetrically about the reflection surface in the half-space, and the half-space sound field reconstruction problem is converted into a free-space multi-source sound field reconstruction problem; On the other hand, the actual uniform flow is symmetrically mirrored about the reflection surface in the half space to obtain the mirrored uniform flow, and the mirrored sound source is converted into the same flow field environment as the actual sound source; Step 2): Arrange equivalent sources at the actual sound source and the mirror image sound source respectively, and use several equivalent sources to equate the actual sound source and the mirror image sound source; select a holographic measurement surface in the near field of the actual sound source; Step 3): Construct a mathematical model of the radiation sound field of multiple sound sources in uniform flow; calculate all equivalent source strengths including convection effects based on the holographic surface sound pressure; Step 4): Extract the equivalent source intensity corresponding to the actual sound source, and determine the position of the reconstruction surface. Use the extracted equivalent source and the NAH in the free space uniform flow to reconstruct the sound field, and then eliminate the half-space effect and consider Reconstruction results of the sound field produced by the actual sound source due to convection effects; Described step 1) includes the following steps: Step 1.1): Mirror the potential actual sound source symmetrically about the reflection surface in the half space, obtain the mirror sound source and its spatial distribution information, treat the reflected sound as the radiation of the mirror sound source, and then convert the half space sound field reconstruction problem into Free space multi-source sound field reconstruction problem; Step 1.2): Considering that the reflected sound is also affected by the flow effect, the actual uniform flow is symmetrically mirrored about the reflective surface in the half space to obtain the mirrored uniform flow, whose flow speed and direction are the same as the actual uniform flow, and then the reflected sound is affected by The influence of the flowing medium is regarded as the image sound source being affected by the flowing medium; Described step 2) includes the following steps: Step 2.1): According to the basic idea of the equivalent source method, that is, the sound field radiated by an arbitrary-shaped sound source can be approximated by the superposition of the sound fields radiated by a series of equivalent sources with different source strengths. In the actual sound source and the mirror sound source Equivalent sources are arranged separately at different places, and several equivalent sources are used to equate actual sound sources and mirror sound sources. The equivalent source layout plan is carried out according to the conventional NAH based on the equivalent source method; Step 2.2): Select the holographic measurement surface in the near field of the actual sound source, divide the holographic surface into equidistant grids, and ensure that the number of holographic surface grid points is greater than or equal to the number of equivalent sources corresponding to the actual sound source and the mirror sound source. and, to ensure the uniqueness of the equivalent source strong solution. Described step 3) includes the following steps: Step 3.1): Construct a mathematical model of the radiation sound field of multiple sound sources in uniform flow, and obtain the relationship between the holographic sound pressure and the equivalent source intensity in the flowing medium. The specific process is as follows: Establish a Cartesian rectangular coordinate system. Assume that the reflective surface in the half space is located on the x-o-y plane, the medium flows along the positive x direction parallel to the reflective surface, and the flow speed is represented by the Mach number M. Then any grid on the holographic surface of the uniform flow in the half space The sound pressure at point r = (x, y, z) can be regarded as the superposition of sound pressure radiated by the equivalent source corresponding to the actual sound source and the mirror sound source in the uniform flow in free space, and its expression is: In the formula, q (r _l ) represents the l-th equivalent source intensity of the actual sound source, q _m (r _j ) is the j-th equivalent source intensity of the mirror sound source; L is the equivalent source intensity corresponding to the actual sound source. The number of sources, J is the number of equivalent sources corresponding to the mirror sound source, it is recommended to take L=J; g(r,r _l ) is the free space convection transfer function from the lth equivalent source of the actual sound source to the field point r , its expression is: Among them, i is the imaginary unit, ρ is the air density, c is the speed of sound, and k is the wave number; g _m (r, r _j ) is the free space convection transfer function from the jth equivalent source of the mirror sound source to the field point r. Its expression is similar to the expression of g (r, r _l ). You only need to change the formula Just replace the subscript "l" with the subscript "m" in (2), (3) and (4); Since the holographic surface is equally divided into multiple grid points as sound pressure sampling points, the sound pressure of the holographic surface is written in matrix form according to equation (1): In the formula, G and G _m are the sound pressure transfer matrices composed of the free space convection transfer functions g(r, r _l ) and g _m (r, r _j ) respectively, and P is the sound pressure vector containing the convection effect on the holographic surface, Q and Q _m are vectors composed of source strengths q(r _l ) and q _m (r _j ) respectively, and the superscript "T" represents the matrix transpose; Formula (5) is the radiation sound field of multiple sound sources in uniform flow Mathematical model, since the convection effect is considered in the sound pressure transfer matrix, it can accurately describe the transfer relationship of the sound field in the flowing medium; Step 3.2): Calculate all equivalent source strengths including convection effects based on the sound pressure of the holographic surface. The specific process is as follows: According to formula (5), the vector containing all equivalent source strengths can be obtained: The superscript "+" in the formula represents the generalized inverse operation of the matrix; since the inverse matrix It usually has pathological properties, and holographic sound pressure data inevitably contains noise. Therefore, regularization processing needs to be used when calculating the equivalent source intensity to suppress the problem of noise amplification during the solution process. The Tikhonov regularization method is used here, then (6 ) formula is: In the formula, the superscript "H" represents the conjugate transpose of the matrix, E is the identity matrix, and λ is the regularization parameter, which can be automatically selected by the Generalized Cross Validation (GCV) method. 2. A sound field reconstruction method in a half-space uniform flow according to claim 1, characterized in that: the step 4) includes the following steps: Step 4.1): Extract the equivalent source intensity corresponding to the actual sound source: the vector containing all equivalent source intensities has been calculated from formula (7) At the same time, according to formula (5), it can be seen that this vector consists of the source intensity vector Q corresponding to the actual sound source and the source intensity vector Q _m corresponding to the mirror sound source, so it can be obtained from/> Extract the source strength vector Q from Step 4.2): After obtaining the source intensity vector Q corresponding to the actual sound source, use this part of the equivalent source and the NAH in the free space uniform flow to reconstruct the sound field, select the position of the reconstruction surface, and perform an equidistant grid on the reconstruction surface Division, the number of grid points can be determined as needed, any grid point on the reconstructed surface The calculation expression of sound pressure is: in the formula is the l-th equivalent source of the actual sound source to the reconstruction point/> The free space convection transfer function at , its expression is: in, Since the reconstruction surface is divided into multiple grid points as reconstruction points, the sound pressure of all reconstruction points on the reconstruction surface is written in matrix form according to equation (8): P _s = G _s Q (12) In the formula, P _s is the sound pressure vector containing the convection effect on the reconstructed surface, and G _s is the free space convection transfer function. The sound pressure transfer matrix composed of The surface sound pressure does not include reflected sound, and the sound field generated by the actual sound source is accurately reconstructed, and the actual sound source can be identified based on the reconstructed surface sound pressure.