CN114630260B - Method for reconstructing sound field in semi-space uniform flow - Google Patents
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Abstract
The invention discloses a sound field reconstruction method in a semi-space uniform flow, which comprises the following four steps: 1. converting the problem of sound field reconstruction in the semi-space uniform flow into the problem of multi-source sound field reconstruction in the free space uniform flow; 2. arranging equivalent sources at the actual sound source and the mirror image sound source respectively, and using a plurality of equivalent sources to equivalent the actual sound source and the mirror image sound source; selecting a holographic measurement surface in the near field of an actual sound source; 3. constructing a mathematical model of a multi-sound source radiation sound field in uniform flow; calculating all equivalent source strengths containing convection effects according to the holographic surface sound pressure; 4. and extracting equivalent source intensity corresponding to the actual sound source, determining the position of a reconstruction surface, and carrying out sound field reconstruction by using the extracted equivalent source and NAH in the free space uniform flow. The invention can remove the influence of half-space reflected sound, fully consider the flow effect generated by medium flow, and realize the identification of sound source in half-space uniform flow and the accurate reconstruction of sound field.
Description
Technical Field
The invention belongs to the field of noise source identification methods, and particularly relates to a reconstruction method of a sound field in a semi-space uniform flow.
Background
In order to solve the problems of reconstruction of sound fields in moving media and sound source identification, for example, for the case of test pieces, fans, wind generators, etc. in acoustic wind tunnels, near-field acoustic holography (Nearfield acoustic holography, NAH) in flowing media has been developed in recent years. Meanwhile, NAH in the flowing medium is also suitable for the identification of a mobile sound source and the sound field reconstruction thereof, such as vehicles such as running automobiles and high-speed rails, and only the sound pressure measuring array is fixed on the sound source to keep synchronous motion. Therefore, NAH in the flowing medium is a technical method with wider application prospect. However, the NAHs in the streaming media currently developed all assume free space without reflective surfaces.
However, in practical problems, many half-space situations exist, for example, sound sources such as automobiles and high-speed rails are affected by ground reflection, and an acoustic wind tunnel test in a semi-anechoic chamber is also affected by ground reflection, so that larger errors can occur in sound field reconstruction by using the NAH in the existing flowing medium.
In practice, there is a half-space problem in static media, and a half-space NAH in static media has been developed to solve the problems of ground reflection, but the technology is not suitable for the identification of sound sources or moving sound sources in flowing media and the reconstruction of sound fields thereof because the flow effect is not considered. Meanwhile, the existing half-space NAH method in the static medium is conceptually complex, for example, the configuration scheme of an equivalent source is complicated or acoustic impedance information of a reflecting surface needs to be known.
Therefore, the existing technical scheme has the following defects or drawbacks: (1) NAH in the flowing medium is limited to free space, and cannot be suitable for half-space sound field reconstruction and sound source identification; (2) The half-space NAH in the static medium does not consider the flow effect, cannot be suitable for the identification of sound sources or moving sound sources in the flow medium and the sound field reconstruction thereof, and has a relatively complex implementation.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a sound field reconstruction method in a half-space uniform flow, which can solve the problem of half-space reflection, is applicable to the condition of medium flow or sound source movement, and has the characteristics of simple scheme implementation and operation.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
a sound field reconstruction method in a semi-space uniform flow comprises the following steps:
step 1): the problem of sound field reconstruction in semi-space uniform flow is equivalently processed: on one hand, the actual sound source is symmetrically mirrored about the reflecting 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 reflecting surface in the half space to obtain mirrored uniform flow, and a mirrored sound source is converted into a flow field environment identical to the actual sound source;
step 2): arranging equivalent sources at the actual sound source and the mirror image sound source respectively, and using a plurality of equivalent sources to equivalent the actual sound source and the mirror image sound source; selecting a holographic measurement surface in the near field of an actual sound source;
step 3): constructing a mathematical model of a multi-sound source radiation sound field in uniform flow; calculating all equivalent source strengths containing convection effects according to the holographic surface sound pressure;
step 4): and extracting equivalent source intensity corresponding to the actual sound source, determining the position of a reconstruction surface, and reconstructing the sound field by using the extracted equivalent source and NAH in the free space uniform flow, so as to obtain a reconstruction result of the sound field generated by the actual sound source, which eliminates the half-space influence and considers the convection effect.
Further, the step 1) includes the following steps:
step 1.1): the method comprises the steps of symmetrically mirroring a potential actual sound source about a reflecting surface in a half space to obtain a mirrored sound source and space distribution information thereof, and regarding reflected sound as mirror sound source radiation to generate, so that a half space sound field reconstruction problem is converted into a free space multi-source sound field reconstruction problem;
step 1.2): considering that the reflected sound is also influenced by the flow effect, the actual uniform flow is symmetrically mirrored about the reflecting surface in the half space to obtain a mirrored uniform flow, the flow speed and the flow direction of the mirrored uniform flow are the same as those of the actual uniform flow, and the reflected sound is influenced by the flow medium, so that the mirrored sound source is regarded as being influenced by the flow medium.
Further, the step 2) includes the following steps:
step 2.1): according to the basic idea of an equivalent source method, namely, a sound field radiated by a sound source with any shape can be approximated by superposition of sound fields radiated by a series of equivalent sources with different source intensities, the equivalent sources are respectively arranged at an actual sound source and a mirror image sound source, a plurality of equivalent sources are used for equivalent of the actual sound source and the mirror image sound source, and an equivalent source arrangement scheme is carried out according to a conventional NAH based on the equivalent source method;
step 2.2): selecting a holographic measurement surface in the near field of an actual sound source, carrying out equidistant grid division on the holographic surface, and ensuring that the number of grid points of the holographic surface is larger than or equal to the sum of the numbers of equivalent sources corresponding to the actual sound source and the mirror image sound source so as to ensure the uniqueness of the equivalent source strength solution;
further, the step 3) includes the following steps:
step 3.1): a mathematical model of a multi-sound source radiation sound field in uniform flow is constructed, and the relationship between holographic sound pressure and equivalent source intensity in a flowing medium is obtained, wherein the specific process is as follows:
establishing a Cartesian rectangular coordinate system, assuming that the reflecting surface is located in an x-o-y plane in a half space, and the medium flows along a positive x direction parallel to the reflecting surface, wherein the flow speed is expressed by Mach number M, the sound pressure at any grid point r= (x, y, z) on the holographic surface in the half space uniform flow can be regarded as superposition of radiation sound pressures in the free space uniform flow corresponding to an equivalent source of an actual sound source and a mirror image sound source, and the expression is as follows:
wherein q (r l ) The first equivalent source intensity, q, representing the actual sound source m (r j ) The j-th equivalent source intensity is the mirror image 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 image sound source, and l=j is recommended; g (r, r) l ) The free space convection transfer function from the first equivalent source to the field point r of the actual sound source is expressed as follows:
where i is an imaginary unit, ρ is air density, c is sound velocity, and k is wave number;
g m (r，r j ) Free space convection transfer function from the jth equivalent source to the field point r of the mirror sound source, expressed as a function of g (r, r l ) The expression of (3) is similar, and the subscript "l" in the formulas (2), (3) and (4) is replaced by the subscript "m".
Since the hologram surface is equally divided into a plurality of grid points as sound pressure sampling points, the hologram surface sound pressure is written into a matrix form according to (1):
wherein G and G m The transfer functions g (r, r l ) And g m (r，r j ) The sound pressure transmission matrix is formed, P is a sound pressure vector containing convection effect on the holographic surface, Q and Q m Respectively by the source strength q (r l ) And q m (r j ) The upper label "T" of the composed vector represents the matrix transpose; the formula (5) is a mathematical model of the multi-sound source radiation sound field in uniform flow, and the convection effect is considered in the sound pressure transmission matrix, so that the transmission relation of the sound field in the flowing medium can be accurately described;
step 3.2): all equivalent source strengths containing convection effects are calculated according to the holographic surface sound pressure, and the specific process is as follows:
vectors containing all equivalent source intensities can be obtained according to equation (5):
the superscript "+" in the equation represents the generalized inverse of the matrix. Due to the inverse matrixIs usually of a pathological nature and the holographic sound pressure data inevitably contains noise, thus in calculating the equivalent sourceWhen the source is strong, regularization treatment is needed to restrain the problem of noise amplification in the solving process, and a Tikhonov regularization method is adopted here, the formula (6) is as follows:
in the formula, the superscript 'H' represents the conjugate transpose of the matrix, E is the identity matrix, lambda is the regularization parameter, and the automatic selection can be carried out by a generalized cross validation (Generalized Cross Validation, GCV) method;
further, the step 4) includes the following steps:
step 4.1): extracting equivalent source intensity corresponding to an actual sound source: from equation (7) a vector containing all equivalent source intensities has been calculatedAt the same time, according to the formula (5), the vector is composed of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound source m Composition, thus can be from->Extracting a source intensity vector Q;
step 4.2): after obtaining a source intensity vector Q corresponding to an actual sound source, reconstructing a sound field by utilizing the partial equivalent source and NAH in the free space uniform stream, selecting the position of a reconstruction surface, performing equidistant grid division on the reconstruction surface, wherein the number of grid points can be determined according to the requirement, and any grid point on the reconstruction surfaceThe calculation expression of the sound pressure is:
in the middle ofFor the first equivalent source of the actual sound source to the reconstruction point +.>A free space convection transfer function at which the expression is:
wherein,
since the reconstruction surface is divided into a plurality of grid points as reconstruction points, sound pressures of all reconstruction points on the reconstruction surface are written into a matrix form according to (8):
P s ＝G s Q (12)
p in the formula s To reconstruct the sound pressure vector containing convection effect on the surface, G s Is made up of free space convection transfer functionA sound pressure transmission matrix is formed; as can be seen from the formula (12), the sound pressure of the reconstruction plane depends on the equivalent source intensity vector Q corresponding to the actual sound source and is irrelevant to the equivalent source corresponding to the mirror image sound source, so that the sound pressure of the reconstruction plane does not contain reflected sound, the sound field generated by the actual sound source is accurately reconstructed, and the identification of the actual sound source can be realized according to the sound pressure of the reconstruction plane.
Compared with the prior art, the sound field reconstruction method in the semi-space uniform flow can remove the influence of the semi-space reflected sound, fully consider the flow effect generated by the medium flow, and realize the identification of the sound source in the semi-space uniform flow and the accurate reconstruction of the sound field. The method is simple in concept, and the equivalent source configuration scheme can be performed according to a conventional equivalent source method; meanwhile, acoustic impedance information of the half-space reflecting surface is not needed, so that the method is suitable for half-space sound field reconstruction with any acoustic characteristic boundary. The method can be applied to the sound source identification and the sound field reconstruction of the flowing medium such as an acoustic wind tunnel test or wind power generation equipment, and can also be applied to the sound source identification and the sound field reconstruction of vehicles such as automobiles or high-speed rails, thereby providing important basis and guidance for the vibration reduction and noise reduction and low-noise design of the products. In particular, if the medium flow velocity is set to m=0 in the above step, the present invention can be also applied to sound source identification in static medium half space and sound field reconstruction thereof.
Drawings
Fig. 1 is a schematic diagram of sound field reconstruction geometry in a semi-spatially uniform stream according to an embodiment of the present invention.
Fig. 2 shows the result of reconstructing the sound pressure on the reconstruction surface at the flow velocity of mach 0.3 in embodiment 1 of the present invention: (a) theoretical sound pressure; (b) the method reconstructs the sound pressure; (c) reconstructing sound pressure by the NAH in the free-space flow medium; (d) reconstructing the sound pressure in the static medium from the half-space NAH.
Fig. 3 is a comparison of the reconstructed sound pressure and the theoretical sound pressure at a flow rate of mach 0.5 in embodiment 2 of the present invention: (a) theoretical sound pressure; (b) the method reconstructs the sound pressure; (c) reconstructing sound pressure by the NAH in the free-space flow medium; (d) reconstructing the sound pressure in the static medium from the half-space NAH.
Fig. 4 is a comparison of the reconstructed sound pressure and the theoretical sound pressure in the case of the flow rate mach 0 in embodiment 3 of the present invention: (a) theoretical sound pressure; (b) the method reconstructs the sound pressure; (c) reconstructing sound pressure by the NAH in the free-space flow medium; (d) reconstructing the sound pressure in the static medium from the half-space NAH.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments.
A sound field reconstruction method in a semi-space uniform flow is shown in figure 1 in a geometric schematic diagram, and comprises the following steps:
step 1): the problem of sound field reconstruction in semi-space uniform flow is equivalently processed: on one hand, the actual sound source is symmetrically mirrored about the reflecting surface in the half space to obtain the space distribution of the mirrored sound source, and the reflected sound is regarded as being generated by the mirrored sound source, so that the problem of half space sound field reconstruction is converted into the problem of free space multi-source sound field reconstruction; on the other hand, the actual uniform flow is symmetrically mirrored about the reflecting surface in the half space to obtain a mirrored uniform flow, the flow speed and the flow direction of the mirrored uniform flow are the same as those of the actual uniform flow, and the influence of the flowing medium on the reflected sound is regarded as the influence of the flowing medium on the mirrored sound source; the method comprises the following specific steps:
step 1.1): the method comprises the steps of symmetrically mirroring an actual sound source about a reflecting surface in a half space to obtain a mirrored sound source and space distribution information of the mirrored sound source, and taking reflected sound as mirror sound source radiation to generate so as to convert a half space sound field reconstruction problem into a free space multi-source sound field reconstruction problem;
step 1.2): considering that the reflected sound is also influenced by the flow effect, the actual uniform flow is symmetrically mirrored about the reflecting surface in the half space to obtain a mirrored uniform flow, the flow speed and the flow direction of the mirrored uniform flow are the same as those of the actual uniform flow, and the reflected sound is influenced by the flow medium, so that the mirrored sound source is regarded as being influenced by the flow medium.
Step 2): arranging equivalent sources at the actual sound source and the mirror image sound source respectively, and using a plurality of equivalent sources to equivalent the actual sound source and the mirror image sound source; selecting a holographic measurement surface in the near field of an actual sound source, carrying out equidistant grid division on the holographic surface, and ensuring that the number of grid points of the holographic surface is larger than or equal to the sum of the numbers of equivalent sources corresponding to the actual sound source and the mirror image sound source so as to ensure the uniqueness of the equivalent source strength solution; the method comprises the following specific steps:
step 2.1): according to the basic idea of the equivalent source method, i.e. the sound field radiated by a sound source of arbitrary shape can be approximated by the superposition of a series of sound fields radiated by equivalent sources with different source intensities, the equivalent sources are arranged in the actual sound source and the mirror image sound source, respectively, for example using source intensity q= [ Q ] 1 ，q 2 ，…，q l ，…，q L ]Equivalent source of (a) to equivalent actual soundSource, use source strength Q m ＝[q 1 ，q 2 ，…，q j ，…，q J ]Equivalent source arrangement scheme is carried out according to a conventional NAH based on an equivalent source method, an equivalent source surface can be determined according to the shape of a sound source surface and can be closed or non-closed, for example, when the sound source surface is a plane, the equivalent source surface can be in a plane shape;
step 2.2): selecting a holographic measurement surface in the near field of an actual sound source, carrying out equidistant grid division on the holographic surface, and ensuring that the number of grid points of the holographic surface is larger than or equal to the sum of the numbers of equivalent sources corresponding to the actual sound source and the mirror image sound source so as to ensure the uniqueness of the equivalent source strength solution;
step 3): constructing a mathematical model of a multi-sound source radiation sound field in uniform flow; calculating all equivalent source strengths containing convection effects according to the holographic surface sound pressure; the method comprises the following specific steps:
step 3.1): constructing a mathematical model of a multi-sound source radiation sound field in uniform flow to obtain the relationship between holographic sound pressure and equivalent source intensity in a flowing medium, wherein the expression of a matrix form is as follows
Wherein G and G m The transfer functions g (r, r l ) And g m The sound pressure transmission matrix formed by (r, rj), P is a sound pressure vector containing convection effect on the holographic surface, and the superscript 'T' represents matrix transposition; g (r, r) l ) The free space convection transfer function from the first equivalent source to the field point r of the actual sound source is expressed as follows:
where i is an imaginary unit, ρ is air density, c is sound velocity, and k is wave number;
g m (r，r j ) Free space convection transfer function from the jth equivalent source to the field point r of the mirror sound source, expressed as a function of g (r, r l ) The expression of (3) is similar, and the subscript "l" in the formulas (2), (3) and (4) is replaced by the subscript "m".
Step 3.2): calculating all equivalent source strengths containing convection effects according to the holographic surface sound pressure; in the solving process, in order to restrain the problem of measurement noise amplification, the source strength solution after the Tikhonov regularization method is adopted is as follows
In the formula, the superscript 'H' represents conjugate transpose of the matrix, the superscript '++' represents generalized inverse operation of the matrix, E is an identity matrix, lambda is a regularization parameter, and the generalized cross validation (Generalized Cross Validation, GCV) method can be used for automatic selection.
Step 4): extracting equivalent source intensity corresponding to an actual sound source, determining a reconstruction surface position, and performing sound field reconstruction by using the extracted equivalent source and NAH in free space uniform flow, so as to obtain a reconstruction result of a sound field generated by the actual sound source, which eliminates half-space influence and considers convection effect; the method comprises the following specific steps:
step 4.1): extracting equivalent source intensity corresponding to an actual sound source: from equation (7) a vector containing all equivalent source intensities has been calculatedAt the same time, according to the formula (5), the vector is composed of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound source m Composition, thus can be from->Extracting a source intensity vector Q;
step 4.2): after obtaining the source intensity vector Q corresponding to the actual sound source, sound field reconstruction is performed using the partially equivalent source and the NAH in the free space uniform stream. And selecting the position of the reconstruction surface, carrying out equidistant grid division on the reconstruction surface, and determining the grid points according to the needs. The matrix form of the reconstruction surface sound pressure calculation expression is as follows:
P s ＝G s Q (12)
p in the formula s To reconstruct the sound pressure vector containing convection effect on the surface, G s Is made up of free space convection transfer functionAnd a sound pressure transmission matrix is formed. />For the first equivalent source of the actual sound source to the reconstruction point +.>A free space convection transfer function at which the expression is:
wherein,
the result P obtained s I.e. the reconstructed sound pressure without reflected sound effects and taking into account flow effects. The method of the invention can not need the acoustic impedance information of the half-space reflecting surfaceThe method is suitable for reconstructing the half-space sound field with any acoustic characteristic boundary. In consideration of the analytic solution of the sound field when the reflecting surface is a rigid surface, the method verification is facilitated, and the following examples are described with the rigid surface and further described by simulation verification performed in examples 1 to 3.
Example 1
Taking a composite sound source consisting 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 at z=0, and the flow rate is set to be 0.3 mach and is close to the cruising speed of a high-speed rail.
Step 1.1): the method comprises the steps of symmetrically mirroring an actual sound source about a reflecting surface in a half space to obtain a mirrored sound source and space distribution information of the mirrored sound source, and taking reflected sound as mirror sound source radiation to generate so as to convert a half space sound field reconstruction problem into a free space multi-source sound field reconstruction problem;
step 1.2): considering that the reflected sound is also influenced by the flow effect, the actual uniform flow is symmetrically mirrored about the reflecting surface in the half space to obtain a mirrored uniform flow, the flow speed direction of the mirrored uniform flow is the same as that of the actual uniform flow, the flow speed is also Mach 0.3, and the influence of the reflected sound by the flow medium is further regarded as the influence of the mirrored sound source by the flow medium.
Step 2.1): equivalent sources are respectively arranged at an actual sound source and a mirror image sound source, and the source intensity is Q= [ Q ] 1 ，q 2 ，…，q l ，…，q L ]Equivalent source of (2) to equivalent actual sound source using source strength Q m ＝[q 1 ，q 2 ，…，q j ，…，q J ]Equivalent source arrangement scheme is carried out according to a conventional NAH based on an equivalent source method: in this embodiment, the sound source surface is a plane, and the equivalent source surface is also arranged in a plane shape, where l=j=144, that is, equivalent sources corresponding to an actual sound source and a mirror image sound source are respectively arranged on grid points of 12×12, and the distance between the equivalent source surface and the sound source surface is 0.05m;
step 2.2): selecting a holographic measurement surface y=0.1m in the near field of an actual sound source, carrying out equidistant dispersion on the holographic surface in the x and z directions, taking the interval as 0.05m to form 24 multiplied by 12 grid points, wherein the number of the grid points of the holographic surface is equal to the sum of the numbers of equivalent sources corresponding to the actual sound source and the mirror image sound source, and guaranteeing the uniqueness of the source strength of the equivalent sources;
step 3.1): a mathematical model of a multi-sound source radiation sound field in uniform flow is constructed, the relation between holographic sound pressure and equivalent source intensity in a flowing medium is obtained, and the expression of a matrix form is as follows:
wherein G and G m The transfer functions g (r, r l ) And g m (r，r l ) The dimension of the sound pressure transmission matrix is 144 multiplied by 144; p is a sound pressure vector containing convection effect on the holographic surface, and the dimension is 144 multiplied by 1; the superscript "T" denotes a matrix transpose; g (r, r) l ) The free space convection transfer function from the first equivalent source to the field point r of the actual sound source is expressed as follows:
wherein,
g m (r，r j ) Free space convection transfer function from the jth equivalent source to the field point r of the mirror sound source, expressed as a function of g (r, r l ) The expression of (3) is similar, and the subscript "l" in the formulas (2), (3) and (4) is replaced by the subscript "m".
Step 3.2): calculating all equivalent source strengths containing convection effects according to the holographic surface sound pressure; in the embodiment, in order to simulate the actual measurement environment, gaussian white noise with a signal-to-noise ratio of 30dB is added into holographic sound pressure data; in the solving process, in order to restrain the problem of measurement noise amplification, the source strength after the Tikhonov regularization method is adopted is as follows:
in the formula, the superscript 'H' represents conjugate transpose of the matrix, the superscript '++' represents generalized inverse operation of the matrix, E is an identity matrix, lambda is a regularization parameter, and the generalized cross validation (Generalized Cross Validation, GCV) method can be used for automatic selection. Here, what is obtainedIs 288 x 1;
step 4.1): extracting equivalent source intensity corresponding to an actual sound source: from equation (7) a vector containing all equivalent source intensities has been calculatedAt the same time, according to the formula (5), the vector is composed of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound source m Composition, thus can be from->Extracting a source intensity vector Q, wherein the dimension of the vector is 144 multiplied by 1;
step 4.2): after obtaining the source intensity vector Q corresponding to the actual sound source, sound field reconstruction is performed using the partially equivalent source and the NAH in the free space uniform stream. The position of the selected reconstruction surface is y=0.03m, the reconstruction surface is subjected to equidistant grid division, and the number of grid points is 12×12. The matrix form of the reconstruction surface sound pressure calculation expression is as follows:
P s ＝G s Q (12)
p in the formula s To reconstruct the sound pressure vector containing convection effect on the surface, G s Is made up of free space convection transfer functionAnd a sound pressure transmission matrix is formed. />For the first equivalent source of the actual sound source to the reconstruction point +.>A free space convection transfer function at which the expression is:
wherein,
the resulting vector P with dimension 144X 1 s I.e. the reconstructed sound pressure without reflected sound effects and taking into account flow effects. This sound pressure vector may be further rearranged into a matrix form of dimension 12 x 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 by the method, a corresponding sound pressure distribution diagram can be drawn, and compared with the sound pressure distribution diagram reconstructed by using the NAH in the existing free space flow medium and the half-space NAH in the static medium, as shown in figure 2, in order to better explain the effectiveness of the method. It can be seen that the reconstructed sound pressure (as in fig. 2 (b)) of the method is better matched with the theoretical sound pressure distribution (as in fig. 2 (a)), while the reconstructed sound pressure (as in fig. 2 (c)) of the NAH in the existing free-space flow medium has larger difference from the theoretical sound pressure distribution, and obvious reflected sound appears at the bottom of the figure, that is, at the position close to the reflecting surface. The sound pressure distribution reconstructed using the half-space NAH in the static medium, as in fig. 2 (d), is quite different from the theoretical sound pressure distribution, since the flow effect is not taken into account. In addition, the reconstruction result using the method can distinguish two monopole sound sources, while the reconstruction result using the other two technical methods cannot distinguish. For quantitative comparative analysis, a reconstruction error is defined, and the expression is calculated as:
where N represents the number of points on the reconstruction surface, pr i Represents the theoretical sound pressure value of a field point, ps i Representing the field point reconstruction sound pressure value. The reconstruction error of the method is 9.87 percent through calculation. The reconstruction error of the NAH in the existing free-space flow medium is 36.03%. The half-space NAH reconstruction error in the static medium exceeds 100%. Therefore, the reconstruction error is smaller by using the method, and the sound field reconstruction in the uniform half-space flow can be realized more accurately.
Example 2
This example examined the effectiveness of the method at other flow rates, set at Mach 0.5, other parameters were the same as those set in example 1, and the procedure was the same as in example 1 and the same computational expression was used. The theoretical sound pressure on the reconstruction plane and the reconstruction of the sound pressure spatial distribution using the present method are also compared to sound pressure distributions reconstructed using the existing NAH in free-space flow media and half-space NAH in static media, such as shown in fig. 3. It can be seen that the reconstructed sound pressure (fig. 3 (b)) of the method is better matched with the theoretical sound pressure distribution (fig. 3 (a)). The difference between the NAH reconstructed sound pressure (as shown in fig. 3 (c)) and the theoretical sound pressure distribution in the existing free space flowing medium is large, and the NAH reconstructed sound pressure is influenced by obvious reflected sound. The sound pressure distribution reconstructed using the half-space NAH in the static medium (as in fig. 3 (d)) is quite different from the theoretical sound pressure distribution. In addition, the reconstruction result using the method can distinguish two monopole sound sources, while the reconstruction result using the other two technical methods cannot distinguish. The reconstruction error of the method is 9.61% by calculating the error by using the formula (13). The reconstruction error of the NAH in the existing free-space flow medium is 56.36%. The half-space NAH reconstruction error in the static medium exceeds 100%. Therefore, the reconstruction error is smaller by using the method, and the sound field reconstruction in the uniform half-space flow can be realized more accurately.
Example 3
In particular, the method is also suitable for reconstructing the half-space sound field in static media when the flow speed is set to Mach 0. In this embodiment, other parameters except for the flow rate are the same as those of embodiment 1, the steps are the same as those of embodiment 1 and the calculation expressions are used. The theoretical sound pressure on the reconstruction plane and the reconstruction of the sound pressure spatial distribution using the present method are also compared to sound pressure distributions reconstructed using the existing NAH in free-space flow media and half-space NAH in static media, such as shown in fig. 4. It can be seen that the reconstructed sound pressure (fig. 4 (b)) of the present method is well matched with the theoretical sound pressure distribution (fig. 4 (a)). The difference between the sound pressure of the reconstruction of the NAH (as shown in fig. 4 (c)) in the existing free space flow medium and the theoretical sound pressure distribution is large, and the reconstruction of the NAH is interfered by reflected sound. The sound pressure distribution reconstructed using the half-space NAH in the static medium (as in fig. 4 (d)) is better in agreement with the theoretical sound pressure. Furthermore, two monopole sound sources can be distinguished using the method and the reconstruction of the half-space NAH in the static medium. Whereas reconstruction results using other methods do not allow a good identification of the monopole at the bottom of the picture (i.e. near the reflecting surface). The reconstruction error of the method is 7.67% after quantitative calculation of the error. The reconstruction error of the NAH in the existing free-space flow medium is 32.62%. The half-space NAH reconstruction error in the static medium is 7.67%. Therefore, the method and the half-space NAH in the static medium can reconstruct the sound field more accurately, and the reconstruction errors are the same, because the method is equivalent to the half-space NAH in the static medium when the flow speed is mach 0.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art, who is within the scope of the present invention, should make equivalent substitutions or modifications according to the technical scheme of the present invention and the inventive concept thereof, and should be covered by the scope of the present invention.
Claims (2)
1. A sound field reconstruction method in a semi-space uniform flow is characterized in that: the method comprises the following steps:
step 1): the problem of sound field reconstruction in semi-space uniform flow is equivalently processed: on one hand, the actual sound source is symmetrically mirrored about the reflecting 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 reflecting surface in the half space to obtain mirrored uniform flow, and a mirrored sound source is converted into a flow field environment identical to the actual sound source;
step 2): arranging equivalent sources at the actual sound source and the mirror image sound source respectively, and using a plurality of equivalent sources to equivalent the actual sound source and the mirror image sound source; selecting a holographic measurement surface in the near field of an actual sound source;
step 3): constructing a mathematical model of a multi-sound source radiation sound field in uniform flow; calculating all equivalent source strengths containing convection effects according to the holographic surface sound pressure;
step 4): extracting equivalent source intensity corresponding to an actual sound source, determining a reconstruction surface position, and performing sound field reconstruction by using the extracted equivalent source and NAH in free space uniform flow, so as to obtain a reconstruction result of a sound field generated by the actual sound source, which eliminates half-space influence and considers convection effect;
the step 1) comprises the following steps:
step 1.1): the method comprises the steps of symmetrically mirroring a potential actual sound source about a reflecting surface in a half space to obtain a mirrored sound source and space distribution information thereof, and regarding reflected sound as mirror sound source radiation to generate, so that a half space sound field reconstruction problem is converted into a free space multi-source sound field reconstruction problem;
step 1.2): considering that the reflected sound is also influenced by the flow effect, the actual uniform flow is symmetrically mirrored about the reflecting surface in the half space to obtain mirrored uniform flow, the flow speed and the flow direction of the mirrored uniform flow are the same as those of the actual uniform flow, and the reflected sound is influenced by the flow medium and is regarded as the mirrored sound source is influenced by the flow medium;
the step 2) comprises the following steps:
step 2.1): according to the basic idea of an equivalent source method, namely, a sound field radiated by a sound source with any shape can be approximated by superposition of sound fields radiated by a series of equivalent sources with different source intensities, the equivalent sources are respectively arranged at an actual sound source and a mirror image sound source, a plurality of equivalent sources are used for equivalent of the actual sound source and the mirror image sound source, and an equivalent source arrangement scheme is carried out according to a conventional NAH based on the equivalent source method;
step 2.2): and selecting a holographic measurement surface in the near field of the actual sound source, carrying out equidistant grid division on the holographic surface, and ensuring that the grid point number of the holographic surface is larger than or equal to the sum of the quantity of equivalent sources corresponding to the actual sound source and the mirror image sound source so as to ensure the uniqueness of the equivalent source strength solution.
Said step 3) comprises the steps of:
step 3.1): a mathematical model of a multi-sound source radiation sound field in uniform flow is constructed, and the relationship between holographic sound pressure and equivalent source intensity in a flowing medium is obtained, wherein the specific process is as follows:
establishing a Cartesian rectangular coordinate system, assuming that the reflecting surface is located in an x-o-y plane in a half space, and the medium flows along a positive x direction parallel to the reflecting surface, wherein the flow speed is expressed by Mach number M, the sound pressure at any grid point r= (x, y, z) on the holographic surface in the half space uniform flow can be regarded as superposition of radiation sound pressures in the free space uniform flow corresponding to an equivalent source of an actual sound source and a mirror image sound source, and the expression is as follows:
wherein q (r l ) The first equivalent source intensity, q, representing the actual sound source m (r j ) The j equivalent source intensity of the mirror image 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 image sound source, and l=j is recommended; g (r, r) l ) The free space convection transfer function from the first equivalent source to the field point r of the actual sound source is expressed as follows:
where i is an imaginary unit, ρ is air density, c is sound velocity, and k is wave number;
g m (r，r j ) Free space convection transfer function from the jth equivalent source to the field point r of the mirror sound source, expressed as a function of g (r, r l ) The expression of (2) is similar, and the subscript "l" in the formulas (2), (3) and (4) is replaced by the subscript "m";
since the hologram surface is equally divided into a plurality of grid points as sound pressure sampling points, the hologram surface sound pressure is written into a matrix form according to (1):
wherein G and G m The transfer functions g (r, r l ) And g m (r，r j ) The sound pressure transmission matrix is formed, P is a sound pressure vector containing convection effect on the holographic surface, Q and Q m Respectively by the source strength q (r l ) And q m (r j ) The upper label "T" of the composed vector represents the matrix transpose; the formula (5) is a mathematical model of the multi-sound source radiation sound field in uniform flow, and the convection effect is considered in the sound pressure transmission matrix, so that the transmission relation of the sound field in the flowing medium can be accurately described;
step 3.2): all equivalent source strengths containing convection effects are calculated according to the holographic surface sound pressure, and the specific process is as follows:
vectors containing all equivalent source intensities can be obtained according to equation (5):
the superscript "+" in the formula represents the generalized inverse operation of the matrix; due to the inverse matrixIn general, the holographic sound pressure data has pathological properties and inevitably contains noise, so regularization processing is needed to be adopted when the equivalent source is calculated to be strong so as to inhibit the problem of noise amplification in the solving process, and a Tikhonov regularization method is adopted here, the formula (6) is:
in the formula, the superscript "H" represents the conjugate transpose of the matrix, E is the identity matrix, lambda is the regularization parameter, and the automatic selection can be performed by a generalized cross validation (Generalized Cross Validation, GCV) method.
2. A method of sound field reconstruction in a semi-spatially uniform stream according to claim 1, characterized by: said step 4) comprises the steps of:
step 4.1): extracting equivalent source intensity corresponding to an actual sound source: from equation (7) a vector containing all equivalent source intensities has been calculatedAt the same time, according to the formula (5), the vector is composed of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound source m Composition, thus can be from->Extracting a source intensity vector Q;
step 4.2): after obtaining the source intensity vector Q corresponding to the actual sound source, the partial equivalent source and free space are utilizedReconstructing a sound field by NAH in the uniform flow, selecting the position of a reconstruction surface, equally dividing grids on the reconstruction surface, determining the grid number according to the need, and selecting any grid point on the reconstruction surfaceThe calculation expression of the sound pressure is:
in the middle ofFor the first equivalent source of the actual sound source to the reconstruction point +.>A free space convection transfer function at which the expression is:
wherein,
since the reconstruction surface is divided into a plurality of grid points as reconstruction points, sound pressures of all reconstruction points on the reconstruction surface are written into a matrix form according to (8):
P s ＝G s Q (12)
p in the formula s To reconstruct the sound pressure vector containing convection effect on the surface, G s Is made up of free space convection transfer functionA sound pressure transmission matrix is formed; as can be seen from the formula (12), the sound pressure of the reconstruction plane depends on the equivalent source intensity vector Q corresponding to the actual sound source and is irrelevant to the equivalent source corresponding to the mirror image sound source, so that the sound pressure of the reconstruction plane does not contain reflected sound, the sound field generated by the actual sound source is accurately reconstructed, and the identification of the actual sound source can be realized according to the sound pressure of the reconstruction plane.
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