CN114630260A - Half-space uniform flow middle sound field reconstruction method - Google Patents
Half-space uniform flow middle sound field reconstruction method Download PDFInfo
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Abstract
The invention discloses a sound field reconstruction method in a half-space uniform flow, which comprises the following four steps: 1. converting the sound field reconstruction problem in the semi-space uniform flow into a multi-source sound field reconstruction problem in the free space uniform flow; 2. respectively arranging equivalent sources at the actual sound source and the mirror image sound source, and using a plurality of equivalent sources to equivalent the actual sound source and the mirror image sound source; selecting a holographic measuring 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 intensities including convection effect according to the sound pressure of the holographic surface; 4. and extracting the 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 the NAH in the free space uniform flow. The invention can not only remove the influence of the half-space reflected sound, but also fully consider the flow effect generated by the medium flow, thereby realizing the identification of the sound source in the half-space uniform flow and the accurate reconstruction of the 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 half-space uniform flow.
Background
In order to solve the problems of sound field reconstruction and sound source identification in moving media, such as test pieces in acoustic wind tunnels, fans, wind generators, etc., near field acoustic holography (NAH) in flowing media has been developed in recent years. Meanwhile, the NAH in the flowing medium is also suitable for identification of a mobile sound source and reconstruction of a sound field of the mobile sound source, such as vehicles driving on automobiles, high-speed rails and the like, and at the moment, the sound pressure measurement array is only required to be fixed on the sound source to keep synchronous motion. Therefore, the NAH in the flowing medium is a technical method with wider application prospect. However, the NAH in the currently developed flowing media assumes free space without reflecting 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 acoustic wind tunnel tests in a semi-anechoic chamber are also affected by ground reflection, so that great errors occur if NAH in the existing flowing medium is used for sound field reconstruction.
Actually, there is a half-space problem in a static medium, and a half-space NAH in a static medium has been developed to solve the problems of ground reflection, etc., but this technique cannot be applied to the identification of a sound source or a moving sound source in a flowing medium and the sound field reconstruction thereof because the flow effect is not considered. Meanwhile, the existing half-space NAH method in the static medium is conceptually complicated, for example, the configuration scheme of the equivalent source is complicated or the acoustic impedance information of the reflecting surface needs to be known.
Therefore, the prior art solutions have the following disadvantages or drawbacks: (1) NAH in a flowing medium is limited to a free space and cannot be applied to half-space sound field reconstruction and source identification; (2) the half-space NAH in the static medium does not consider the flow effect, and is not suitable for the identification of the sound source or the mobile sound source in the flow medium and the sound field reconstruction thereof, and the implementation is complicated.
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, so that the method can solve the problem of half-space reflection, is suitable for the condition of medium flow or sound source movement, and has the characteristics of scheme implementation and simple operation.
In order to achieve the purpose, the invention adopts the following technical scheme:
a sound field reconstruction method in a half-space uniform flow comprises the following steps:
step 1): performing equivalent treatment on the sound field reconstruction problem in the half-space uniform flow: on one hand, an actual sound source is symmetrically mirrored about a reflecting surface in a 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 mirrored symmetrically about the reflecting surface in the half space to obtain a mirror uniform flow, and the mirror sound source is converted into the flow field environment same as the actual sound source;
step 2): respectively arranging equivalent sources at the actual sound source and the mirror image sound source, and using a plurality of equivalent sources to be equivalent to the actual sound source and the mirror image sound source; selecting a holographic measuring surface in the near field of an actual sound source;
and step 3): constructing a mathematical model of a multi-sound-source radiation sound field in uniform flow; calculating all equivalent source intensities including convection effect according to the sound pressure of the holographic surface;
step 4): extracting the equivalent source intensity corresponding to the actual sound source, determining the position of a reconstruction surface, and performing sound field reconstruction by using the extracted equivalent source and the NAH in the free space uniform flow so as to obtain a reconstruction result of the sound field generated by the actual sound source with half-space influence eliminated and convection effect considered.
Further, the step 1) comprises the following steps:
step 1.1): the method comprises the following steps of symmetrically mirroring a potential actual sound source about a reflecting surface in a half space to obtain a mirror image sound source and spatial distribution information thereof, regarding a reflected sound as mirror image sound source radiation generation, and further converting 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 mirrored symmetrically about the reflecting surface in the half space to obtain the mirror image uniform flow, the flow velocity and the direction of the mirror image 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 mirror image sound source.
Further, 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 strengths, equivalent sources are respectively arranged at an actual sound source and a mirror image sound source, a plurality of equivalent sources are used for equivalence 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 measuring surface in the near field of an actual sound source, carrying out equidistant gridding division on the holographic surface, and ensuring that the number of the grid points of the holographic surface is more than or equal to the sum of the number of equivalent sources corresponding to the actual sound source and a mirror image sound source so as to ensure the uniqueness of the forced solution of the equivalent source;
further, the step 3) comprises the following steps:
step 3.1): a mathematical model of a multi-sound-source radiation sound field in uniform flow is constructed to obtain the relation between holographic sound pressure and equivalent source intensity in a flowing medium, and the specific process is as follows:
establishing a Cartesian rectangular coordinate system, assuming that a reflecting surface in a half space is located on an x-o-y plane, a medium flows along a positive x direction parallel to the reflecting surface, the flow speed is expressed by Mach number M, and then sound pressure at any grid point r ═ x, y and z on a holographic surface in the half space uniform stream can be regarded as superposition of radiation sound pressure in a free space uniform stream corresponding to an equivalent source of an actual sound source and a mirror image sound source, wherein the expression is as follows:
in the formula, q (r)l) The l equivalent source intensity, q, representing the actual sound sourcem(rj) The jth equivalent source intensity, which is a mirror image 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, and L is preferably taken to be J; g (r, r)l) The free space convection transfer function of the ith equivalent source of the actual sound source to the field point r is expressed as follows:
wherein i is an imaginary number unit, ρ is air density, c is sound velocity, and k is wave number;
gm(r，rj) The free space convection transfer function of the jth equivalent source of the mirror image sound source to the field point r, the expression of which is equal to g (r, r)l) The expressions in (2), (3) and (4) are similar, and only the subscript "l" needs to be replaced by the subscript "m".
Because the holographic surface is equidistantly divided into a plurality of grid points as sound pressure sampling points, the sound pressure of the holographic surface is written into a matrix form according to the formula (1):
in the formula G and GmAre the transfer functions g (r, r) convected from free spacel) And gm(r，rj) The sound pressure transmission matrix is formed, P is a sound pressure vector containing convection effect on a holographic surface, Q and QmAre respectively the intensity of the source q (r)l) And q ism(rj) The formed vector is marked with a T to represent matrix transposition; the formula (5) is a mathematical model of a multi-sound-source radiation sound field in uniform flow, and the convection effect is considered in the sound pressure transfer matrix, so that the transfer relationship of the sound field in a flowing medium can be accurately described;
step 3.2): calculating all equivalent source intensities including convection effect according to holographic surface sound pressure, and the specific process is as follows:
a vector containing all equivalent source strengths can be obtained according to equation (5):
in the formula, the superscript "+" indicates the generalized inverse operation of the matrix. Due to the inverse matrix
Generally, the method has a pathological property, and the holographic sound pressure data inevitably contains noise, so that regularization processing needs to be adopted when the equivalent source intensity is calculated to suppress the problem of noise amplification in the solution process, where a Tikhonov regularization method is adopted, and then the formula (6) is as follows:
in the formula, the superscript "H" represents the conjugate transpose of the matrix, E is the identity matrix, λ is the regularization parameter, and can be automatically selected by a Generalized Cross Validation (GCV) method;
further, the step 4) comprises the following steps:
step 4.1): extracting equivalent source intensities corresponding to actual sound sources: from equation (7), a vector containing all equivalent source intensities has been calculated
Meanwhile, as can be seen from equation (5), the vector consists of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound sourcemIs thus made up of
Extracting a source intensity vector Q;
step 4.2): after obtaining the source intensity vector Q corresponding to the actual sound source, the equivalent source and the NAH in the free space uniform flow are utilized to reconstruct the sound field, the position of the reconstruction surface is selected, and the equidistant net is carried out on the reconstruction surfaceDividing grids, determining the number of grid points according to the requirement, and reconstructing any grid point on the surface
The computational expression of acoustic pressure is:
in the formula
Is the l equivalent source of the actual sound source to the reconstruction point
The free space convection transfer function of (1) is expressed as:
wherein,
since the reconstruction surface is divided into a plurality of grid points as reconstruction points, the sound pressures of all the reconstruction points on the reconstruction surface are written into a matrix form according to the formula (8):
Ps＝GsQ (12)
in the formula PsFor sound pressure vectors containing convection effects on the reconstruction plane, GsIs a convection transfer function from free space
A sound pressure transmission matrix is formed; as can be seen from equation (12), weight isThe plane-building sound pressure depends on the equivalent source strong vector Q corresponding to the actual sound source and is unrelated to the equivalent source corresponding to the mirror image sound source, so that the plane-building sound pressure does not contain reflected sound, a sound field generated by the actual sound source is accurately reconstructed, and the actual sound source can be identified according to the plane-building sound pressure.
Compared with the prior art, the method for reconstructing the sound field in the semi-space uniform flow can not only remove the influence of semi-space reflected sound, but also fully consider the flow effect generated by medium flow, and can realize the identification of the sound source in the semi-space uniform flow and the accurate reconstruction of the sound field. The method has simple concept, and the equivalent source configuration scheme can be carried out according to a conventional equivalent source method; meanwhile, acoustic impedance information of a 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 invention can be applied to sound source identification and sound field reconstruction in flowing media such as acoustic wind tunnel test or wind power generation equipment, and can also be applied to sound source identification and sound field reconstruction of vehicles such as automobiles or high-speed rails, and further provides important basis and guidance for 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 steps, the present invention can also be applied to sound source identification in a static medium half space and sound field reconstruction thereof.
Drawings
Fig. 1 is a geometrical diagram illustrating sound field reconstruction in a half-space uniform flow according to an embodiment of the present invention.
FIG. 2 shows the sound pressure reconstruction on the reconstruction surface at a flow velocity of Mach 0.3 in example 1 of the present invention: (a) theoretical sound pressure; (b) the method reconstructs sound pressure; (c) NAH reconstruction sound pressure in free space flowing medium; (d) half-space NAH in static medium reconstructs the sound pressure.
Fig. 3 is a comparison of the reconstructed sound pressure and the theoretical sound pressure at a flow velocity of mach 0.5 in example 2 of the present invention: (a) theoretical sound pressure; (b) the method reconstructs sound pressure; (c) NAH reconstruction sound pressure in free space flowing medium; (d) half-space NAH in static medium reconstructs the sound pressure.
Fig. 4 is a comparison of the reconstructed sound pressure and the theoretical sound pressure at mach 0 flow velocity in example 3 of the present invention: (a) theoretical sound pressure; (b) the method reconstructs sound pressure; (c) NAH reconstruction sound pressure in free space flowing medium; (d) half-space NAH in static media reconstructs the sound pressure.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
A method for reconstructing a sound field in a half-space uniform flow, a geometric schematic diagram of which is shown in fig. 1, comprising the following steps:
step 1): carrying out equivalent treatment on the sound field reconstruction problem in the half-space uniform flow: on one hand, an actual sound source is symmetrically mirrored about a reflecting surface in a half space to obtain the spatial distribution of a mirror image sound source, reflected sound is regarded as generated by the mirror image sound source, and then 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 mirrored symmetrically about the reflecting surface in the half space to obtain a mirrored uniform flow, the flow velocity and 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 that an actual sound source is symmetrically mirrored about a reflecting surface in a half space to obtain a mirror image sound source and spatial distribution information of the mirror image sound source, reflected sound is regarded as mirror image sound source radiation generation, and then the 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 mirrored symmetrically about the reflecting surface in the half space to obtain the mirror image uniform flow, the flow velocity and the direction of the mirror image 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 mirror image sound source.
Step 2): respectively arranging equivalent sources at the actual sound source and the mirror image sound source, and using a plurality of equivalent sources to equivalent the actual sound source and the mirror image sound source; selecting a holographic measuring surface in the near field of an actual sound source, carrying out equidistant gridding division on the holographic surface, and ensuring that the number of the grid points of the holographic surface is more than or equal to the sum of the number of equivalent sources corresponding to the actual sound source and a mirror image sound source so as to ensure the uniqueness of the forced solution of the equivalent source; 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 the sound fields radiated by a series of equivalent sources with different source intensities, the equivalent sources are respectively arranged at the actual sound source and the mirror image sound source, for example, using a source intensity of Q ═ Q1，q2，…，ql，…，qL]Is equivalent to the actual sound source, and the source strength is Qm＝[q1，q2，…，qj，…，qJ]The equivalent source of (2) is equivalent to a mirror image sound source, the equivalent source arrangement scheme is performed according to a conventional NAH based on an equivalent source method, an equivalent source surface can be determined according to the shape of the 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 a plane shape;
step 2.2): selecting a holographic measuring surface in the near field of an actual sound source, carrying out equidistant gridding division on the holographic surface, and ensuring that the number of the grid points of the holographic surface is more than or equal to the sum of the number of equivalent sources corresponding to the actual sound source and a mirror image sound source so as to ensure the uniqueness of the forced solution of the equivalent source;
step 3): constructing a mathematical model of a multi-sound-source radiation sound field in uniform flow; calculating all equivalent source intensities including convection effect according to the sound pressure of the holographic surface; 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 relation between holographic sound pressure and equivalent source intensity in a flowing medium, wherein the expression of a matrix form is
In the formula G and GmAre respectively free space convection transfer functions g (r, r)l) And gm(r, rj), P is a sound pressure vector including a convection effect on a hologram plane, and the superscript "T" representsPerforming matrix transposition; g (r, r)l) The free space convection transfer function of the ith equivalent source of the actual sound source to the field point r is expressed as follows:
wherein i is an imaginary number unit, ρ is air density, c is sound velocity, and k is wave number;
gm(r，rj) The free space convection transfer function of the jth equivalent source of the mirror image sound source to the field point r, the expression of which is equal to g (r, r)l) The expressions in (2), (3) and (4) are similar, and only the subscript "l" needs to be replaced by the subscript "m".
Step 3.2): calculating all equivalent source intensities including convection effect according to the sound pressure of the holographic surface; in the solving process, in order to inhibit the problem of measurement noise amplification, the source strong solution after the Tikhonov regularization method is adopted 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 automatically selected by the Generalized Cross Validation (GCV) method.
Step 4): extracting equivalent source intensity corresponding to an actual sound source, determining the position of a reconstruction surface, and performing sound field reconstruction by using the extracted equivalent source and NAH in free space uniform flow to further obtain a reconstruction result of a sound field generated by the actual sound source, wherein the half-space influence is eliminated and the convection effect is considered; the method comprises the following specific steps:
step 4.1): extracting equivalent source intensities corresponding to actual sound sources: from equation (7), a vector containing all equivalent source intensities has been calculated
Meanwhile, as can be seen from equation (5), the vector consists of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound sourcemIs thus made up of
Extracting a source intensity vector Q;
step 4.2): after obtaining the source intensity vector Q corresponding to the actual sound source, the sound field reconstruction is carried out by using the part of equivalent sources and NAH in the free space uniform flow. The position of the reconstruction surface is selected, equidistant grid division is carried out on the reconstruction surface, and the number of grid points can be determined according to the requirement. The matrix form of the reconstruction surface sound pressure calculation expression is as follows:
Ps＝GsQ (12)
in the formula PsFor sound pressure vectors containing convection effects on the reconstruction plane, GsIs a convection transfer function from free space
And forming a sound pressure transmission matrix.
Is the l equivalent source of the actual sound source to the reconstruction point
The free space convection transfer function of (b) is expressed as:
wherein,
obtained result PsI.e. a reconstructed sound pressure that does not contain reflected sound effects and takes into account flow effects. The method of the invention does not need the acoustic impedance information of the half-space reflecting surface, so the method can be suitable for the reconstruction of the half-space sound field with any acoustic characteristic boundary. Considering that the sound field has an analytic solution when the reflection surface is a rigid surface, which is convenient for method verification, the following embodiments are described with respect to the rigid surface, and simulation verification is performed through embodiments 1 to 3, which are further described.
Example 1
Taking a composite sound source composed of two monopoles in a uniform flow as an example, the sound source frequency is 2000Hz, a half-space boundary surface is a rigid surface located at a position where z is equal to 0, and the flow speed is set to be 0.3 mach close to the cruising speed of a high-speed rail.
Step 1.1): the method comprises the steps that an actual sound source is symmetrically mirrored about a reflecting surface in a half space to obtain a mirror image sound source and spatial distribution information of the mirror image sound source, reflected sound is regarded as mirror image sound source radiation generation, and then the 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 mirrored symmetrically about the reflecting surface in the half space to obtain the mirror image uniform flow, the flow velocity direction of the mirror image uniform flow is the same as that of the actual uniform flow, and the flow velocity is also Mach 0.3, so that the reflected sound is influenced by the flow medium and is regarded as that the mirror image sound source is influenced by the flow medium.
Step 2.1): equivalent sources are respectively arranged at the actual sound source and the mirror image sound source, and the source strength is Q ═ Q1，q2，…，ql，…，qL]Is equivalent to the actual sound source, and the source strength is Qm＝[q1，q2，…，qj，…，qJ]The equivalent source placement scheme is performed according to the conventional NAH based on the equivalent source law: in the present embodiment, the sound source plane is a plane, and the equivalent source plane is also arranged in a planar shape, where L is J is 144, that is, equivalent sources corresponding to the actual sound source and the mirror sound source are respectively arranged on 12 × 12 grid points, and the equivalent source plane is 0.05m from the sound source plane;
step 2.2): selecting a holographic measuring surface y of 0.1m in the near field of an actual sound source, equidistantly dispersing the holographic surface in the x and z directions at intervals of 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 number of equivalent sources corresponding to the actual sound source and a mirror image sound source, and the uniqueness of the strong solution of the equivalent source can be ensured;
step 3.1): constructing a mathematical model of a multi-sound-source radiation sound field in uniform flow to obtain the relation between holographic sound pressure and equivalent source intensity in a flowing medium, wherein the expression of a matrix form is as follows:
in the formula G and GmAre the transfer functions g (r, r) convected from free spacel) And gm(r，rl) The dimensionality of the formed sound pressure transfer matrix is 144 multiplied by 144; p is a sound pressure vector containing a convection effect on the holographic surface, and the dimension is 144 multiplied by 1; the superscript "T" denotes matrix transposition; g (r, r)l) The free space convection transfer function of the ith equivalent source of the actual sound source to the field point r is expressed as follows:
wherein,
gm(r，rj) The free space convection transfer function of the jth equivalent source of the mirror image sound source to the field point r, the expression of which is equal to g (r, r)l) The expressions in (2), (3) and (4) are similar, and only the subscript "l" needs to be replaced by the subscript "m".
Step 3.2): calculating all equivalent source intensities including convection effect according to the sound pressure of the holographic surface; in the embodiment, in order to simulate an 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 inhibit the problem of measurement noise amplification, the source strong solution after the Tikhonov regularization method is adopted is as follows:
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 automatically selected by the Generalized Cross Validation (GCV) method. Here, the obtained
Has a dimension of 288 × 1;
step 4.1): extracting equivalent source intensities corresponding to actual sound sources: from equation (7), a vector containing all equivalent source intensities has been calculated
Meanwhile, as can be seen from equation (5), the vector consists of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound sourcemIs thus made up of
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, the sound field reconstruction is carried out by using the part of equivalent sources and NAH in the free space uniform flow. And selecting the position of the reconstruction surface as y being 0.03m, and carrying out equidistant grid division on the reconstruction surface, wherein the number of grid points is 12 multiplied by 12. The matrix form of the reconstruction surface sound pressure calculation expression is as follows:
Ps＝GsQ (12)
in the formula PsFor sound pressure vectors containing convection effects on the reconstruction plane, GsIs a convection transfer function from free space
And forming a sound pressure transmission matrix.
Is the l equivalent source of the actual sound source to the reconstruction point
The free space convection transfer function of (1) is expressed as:
wherein,
resulting vector P with dimension 144X 1sI.e. a reconstructed sound pressure that does not contain reflected sound effects and takes into account flow effects. This sound pressure vector can be further rearranged in a matrix form having a dimension of 12 × 12 so as to correspond to the reconstruction point 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 shown in fig. 2, in order to better explain the effectiveness of the method, the sound pressure distribution reconstructed by using the NAH in the existing free space flowing medium and the half-space NAH in the static medium is also given for comparison. It can be seen that the reconstructed sound pressure (fig. 2(b)) of the method is better matched with the theoretical sound pressure distribution (fig. 2(a)), while the NAH reconstructed sound pressure (fig. 2(c)) in the existing free space flowing medium is more different from the theoretical sound pressure distribution, and obvious reflected sound appears at the bottom of the figure, namely at a position close to the reflecting surface. The sound pressure distribution reconstructed using the half-space NAH in static media, 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 results using the method can distinguish two monopole sound sources, while the reconstruction results using the other two technical methods cannot distinguish. For quantitative comparative analysis, a reconstruction error is defined, and the computational expression is:
in the formula, N represents the number of points on the reconstruction plane, priRepresenting the theoretical sound pressure value of the field point, psiRepresenting the field point reconstructed sound pressure value. The reconstruction error of the method is calculated to be 9.87%. The NAH reconstruction error in the existing free-space flow medium is 36.03%. The half-space NAH reconstruction error in static media exceeds 100%. Therefore, the reconstruction error is small by using the method, and the sound field reconstruction in the semi-space uniform flow can be realized accurately.
Example 2
This example examines the effectiveness of the method at other flow rates, and sets the flow rate to mach 0.5, and the other parameters are the same as the parameter settings of example 1, and the implementation steps are the same as example 1 and the calculation expressions used are the same. The theoretical sound pressure at the reconstruction plane and the reconstruction of the spatial distribution of sound pressures using the present method are also given in comparison to the sound pressure distribution reconstructed here using NAH in the existing free-space flowing medium and half-space NAH in the static medium, such as shown in fig. 3. It can be seen that the reconstructed sound pressure of the method (fig. 3(b)) fits well to the theoretical sound pressure distribution (fig. 3 (a)). The NAH reconstructed sound pressure (as shown in fig. 3(c)) in the existing free space flowing medium has a large difference from the theoretical sound pressure distribution, and is influenced by obvious reflected sound. The sound pressure distribution reconstructed using the half-space NAH in the static medium (see fig. 3(d)) is quite different from the theoretical sound pressure distribution. In addition, the reconstruction results using the method can distinguish two monopole sound sources, while the reconstruction results using the other two technical methods cannot distinguish. The error calculated by the formula (13) can be used to obtain the reconstruction error of the method of 9.61%. The NAH reconstruction error in the existing free-space flow medium is 56.36%. The half-space NAH reconstruction error in static media exceeds 100%. Therefore, the reconstruction error is small by using the method, and the sound field reconstruction in the semi-space uniform flow can be realized accurately.
Example 3
In particular, the method is also suitable for half-space sound field reconstruction in a static medium when the flow velocity is set to be 0 Mach. In this example, the parameters other than the flow rate were set to be the same as those in example 1, the procedure was carried out to be the same as in example 1, and the calculation expression used was the same. Reconstruction of the spatial distribution of sound pressures from theoretical sound pressures on the surface and using the method a comparison is given of the sound pressure distribution reconstructed here using NAH in the existing free-space flowing medium and half-space NAH in the static medium, such as shown in fig. 4. It can be seen that the reconstructed sound pressure of the method (fig. 4(b)) fits well to the theoretical sound pressure distribution (fig. 4 (a)). The NAH reconstructed sound pressure in the existing free space flowing medium (as shown in fig. 4(c)) has a large difference from the theoretical sound pressure distribution, and is interfered by reflected sound. The sound pressure distribution reconstructed using the half-space NAH in the static medium (see fig. 4(d)) fits well with the theoretical sound pressure. In addition, two monopole sound sources can be distinguished by using the method and the reconstruction result of the half-space NAH in the static medium. While the reconstruction results using other methods do not identify the monopole well at the bottom of the picture (i.e., near the reflecting surface). Through quantitative calculation of errors, the reconstruction error of the method is 7.67%. The NAH reconstruction error in the existing free-space flow medium is 32.62%. The half-space NAH reconstruction error in static media 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 velocity is Mach 0.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered to be within the technical scope of the present invention, and the technical solutions and the inventive concepts thereof according to the present invention should be equivalent or changed within the scope of the present invention.
Claims (5)
1. A sound field reconstruction method in a half-space uniform flow is characterized in that: the method comprises the following steps:
step 1): performing equivalent treatment on the sound field reconstruction problem in the half-space uniform flow: on one hand, the actual sound source is symmetrically mirrored about a reflecting surface in a 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 mirrored symmetrically about the reflecting surface in the half space to obtain a mirror uniform flow, and the mirror sound source is converted into the flow field environment same as the actual sound source;
step 2): respectively arranging equivalent sources at the actual sound source and the mirror image sound source, and using a plurality of equivalent sources to equivalent the actual sound source and the mirror image sound source; selecting a holographic measuring surface in the near field of an actual sound source;
and step 3): constructing a mathematical model of a multi-sound-source radiation sound field in uniform flow; calculating all equivalent source intensities including convection effect according to the sound pressure of the holographic surface;
step 4): and extracting equivalent source intensity corresponding to an actual sound source, determining the position of a reconstruction plane, and performing sound field reconstruction by using the extracted equivalent source and the NAH in the free space uniform flow to further obtain a reconstruction result of the sound field generated by the actual sound source, wherein the half space influence is eliminated and the convection effect is considered.
2. The method for reconstructing sound field in semi-space uniform flow according to claim 1, wherein: the step 1) comprises the following steps:
step 1.1): the method comprises the following steps of symmetrically mirroring a potential actual sound source about a reflecting surface in a half space to obtain a mirror image sound source and spatial distribution information thereof, regarding a reflected sound as mirror image sound source radiation generation, and further converting 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 mirrored symmetrically about the reflecting surface in the half space to obtain the mirror image uniform flow, the flow velocity and the direction of the mirror image 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 mirror image sound source.
3. The method for reconstructing sound field in semi-space uniform flow according to claim 1, wherein: 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 strengths, equivalent sources are respectively arranged at an actual sound source and a mirror image sound source, a plurality of equivalent sources are used for equivalence 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 measuring surface in the near field of the actual sound source, carrying out equidistant gridding division on the holographic surface, and ensuring that the number of the grid points of the holographic surface is more than or equal to the sum of the number of the equivalent sources corresponding to the actual sound source and the mirror image sound source so as to ensure the uniqueness of the forced solution of the equivalent source.
4. The method for reconstructing sound field in semi-space uniform flow according to claim 1, wherein: the step 3) comprises the following steps:
step 3.1): a mathematical model of a multi-sound-source radiation sound field in uniform flow is constructed to obtain the relation between holographic sound pressure and equivalent source intensity in a flowing medium, and the specific process is as follows:
establishing a Cartesian rectangular coordinate system, assuming that a reflecting surface in a half space is located on an x-o-y plane, a medium flows along a positive x direction parallel to the reflecting surface, the flow speed is expressed by Mach number M, and then sound pressure at any grid point r ═ x, y and z on a holographic surface in the half space uniform stream can be regarded as superposition of radiation sound pressure in a free space uniform stream corresponding to an equivalent source of an actual sound source and a mirror image sound source, wherein the expression is as follows:
in the formula, q (r)l) The l-th equivalent source intensity, q, representing the actual sound sourcem(rj) The jth 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 sound source, and L is preferably taken to be J; g (r, r)l) The free space convection transfer function of the ith equivalent source of the actual sound source to the field point r is expressed as follows:
wherein,
gm(r，rj) The free space convection transfer function of the jth equivalent source of the mirror image sound source to the field point r, the expression of which is equal to g (r, r)l) The expressions are similar, and only the subscript l in the formulas (2), (3) and (4) needs to be replaced by the subscript m;
because the holographic surface is equidistantly divided into a plurality of grid points as sound pressure sampling points, the sound pressure of the holographic surface is written into a matrix form according to the formula (1):
in the formula G and GmAre the transfer functions g (r, r) convected from free spacel) And gm(r，rj) The sound pressure transmission matrix is formed, P is a sound pressure vector containing convection effect on a holographic surface, Q and QmAre respectively the intensity of the source q (r)l) And q ism(rj) The formed vector is marked with a T to represent matrix transposition; the formula (5) is a mathematical model of a multi-sound-source radiation sound field in uniform flow, and the transmission relation of the sound field in a flowing medium can be accurately described due to the convection effect in the sound pressure transmission matrix;
step 3.2): calculating all equivalent source intensities including convection effect according to holographic surface sound pressure, and the specific process is as follows:
a vector containing all equivalent source strengths can be obtained according to equation (5):
in the formula, the superscript "+" represents the generalized inverse operation of the matrix; due to the inverse matrix
Generally, the method has a pathological property, and the holographic sound pressure data inevitably contains noise, so that regularization processing needs to be adopted when the equivalent source intensity is calculated to suppress the problem of noise amplification in the solution process, where a Tikhonov regularization method is adopted, and then the formula (6) is as follows:
in the formula, the superscript "H" represents the conjugate transpose of the matrix, E is the identity matrix, λ is the regularization parameter, and can be automatically selected by a Generalized Cross Validation (GCV) method.
5. The method for reconstructing sound field in semi-space uniform flow according to claim 4, wherein: the step 4) comprises the following steps:
step 4.1): extracting equivalent source intensities corresponding to actual sound sources: from equation (7), a vector containing all equivalent source intensities has been calculated
Meanwhile, as can be seen from equation (5), the vector consists of a source intensity vector Q corresponding to the actual sound source and a source intensity vector Q corresponding to the mirror image sound sourcemIs thus made up of
Extracting a source intensity vector Q;
step 4.2): after obtaining the source strength vector Q corresponding to the actual sound source, utilizing the equivalent source and NAH in the free space uniform flow to reconstruct the sound field, selecting the position of the reconstruction surface, carrying out equidistant grid division on the reconstruction surface, determining the number of grid points according to the requirement, and determining any grid point on the reconstruction surface
The computational expression of acoustic pressure is:
in the formula
Is the l equivalent source of the actual sound source to the reconstruction point
The free space convection transfer function of (1) is expressed as:
wherein,
since the reconstruction surface is divided into a plurality of grid points as reconstruction points, the sound pressures of all the reconstruction points on the reconstruction surface are written into a matrix form according to the formula (8):
Ps＝GsQ (12)
in the formula PsFor sound pressure vectors containing convection effects on the reconstruction plane, GsIs a convection transfer function from free space
A sound pressure transmission matrix is formed; it can be seen from the formula (12) that the reconstruction plane sound pressure depends on the equivalent source intensity vector Q corresponding to the actual sound source, and is independent of the equivalent source corresponding to the mirror image sound source, so that the reconstruction plane sound pressure does not include reflected sound, the sound field generated by the actual sound source is accurately reconstructed, and further, the identification of the actual sound source can be realized according to the reconstruction plane sound pressure.
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