CN111561991B - Near-field acoustic holography method based on edge filling and Fourier transform - Google Patents
Near-field acoustic holography method based on edge filling and Fourier transform Download PDFInfo
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- CN111561991B CN111561991B CN202010510380.9A CN202010510380A CN111561991B CN 111561991 B CN111561991 B CN 111561991B CN 202010510380 A CN202010510380 A CN 202010510380A CN 111561991 B CN111561991 B CN 111561991B
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Abstract
The invention discloses a near-field acoustic holography method based on edge filling and Fourier transform, which comprises the following steps: arranging a holographic surface H in a near-field radiation area of a sound source, and measuring sound pressure at each measurement grid point; determining the size of a sound source plane, and setting a virtual holographic surface V at the holographic surface H, wherein the area of the virtual holographic surface V is larger than or equal to that of the sound source plane, and the central point of the virtual holographic surface V is coincident with the holographic surface H; filling virtual measurement points into the virtual holographic surface V, and calculating the sound pressure value of each virtual measurement point; determining reconstruction surface S coordinates (x, y, z)S) And the wave number component kx、ky、kzDetermining a transfer function; and (4) reconstructing a sound field according to the sound pressure data of the virtual holographic surface V and the transfer function, and converting the spatial domain convolution into a wave number domain product form. The invention reduces the influence of the coiling error and the edge Gibbs effect on the premise of not increasing the measurement workload and the measurement cost, and obviously improves the reconstruction result under the small holographic aperture.
Description
Technical Field
The invention relates to an acoustic processing technology, in particular to a near-field acoustic holography method based on Fourier transform for a small-aperture holographic surface.
Background
Near-field Acoustic Holography (NAH) is an important sound source identification, positioning and sound field visualization technology, and not only can identify and position a noise source, but also can predict the radiation characteristics of the sound source in a sound field.
Among the near-field acoustic holography technologies, the near-field acoustic holography technology based on Fourier transform has the advantages of high calculation speed, simple theory, easy realization and the like, so the near-field acoustic holography technology is most widely applied to practical engineering. However, due to the influence of a winding error and an edge gibbs effect, the reconstruction effect of the near-field acoustic holography technology based on fourier transform is poor under a small holographic aperture, and in order to obtain higher reconstruction accuracy, the size of the holographic aperture is often required to be at least twice of the area of a sound source, which causes many problems in practical engineering application. On one hand, the measuring surface is large, the number of measuring points is very large, and the measuring workload and the measuring cost are greatly increased; on the other hand, the technology is difficult to be applied to large-size structures such as automobiles, airplanes, submarine shells and the like.
Therefore, the research on how to improve the reconstruction precision of the Fourier transform-based near-field acoustic holography under the small-aperture holographic surface has great significance for practical engineering application.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a near-field acoustic holography method based on edge filling and Fourier transform, and improves the reconstruction accuracy under a small holographic aperture.
In order to achieve the purpose, the invention adopts the following technical scheme:
a near-field acoustic holography method based on edge filling and fourier transform, comprising the steps of:
(1) arranging a holographic surface H in a near-field radiation area of a sound source, wherein the holographic surface H is a square matrix in a sound field generated by the sound source, measuring grid points are distributed on the holographic surface H, and the sound pressure at the measuring grid points is measured;
(2) determining the size of a sound source plane, and setting a virtual holographic surface V at the holographic surface H, wherein the area of the virtual holographic surface V is larger than or equal to that of the sound source plane, and the central point of the virtual holographic surface V is coincident with the holographic surface H;
(3) filling virtual measurement points into the virtual holographic surface V, and calculating the sound pressure value of each virtual measurement point;
(4) determining reconstruction surface S coordinates (x, y, z)S) And the wave number component kx、ky、kzDetermining a transfer function according to the reconstruction surface coordinates and the wave number components;
(5) and (4) reconstructing a sound field according to the sound pressure data of the virtual holographic surface V and the transfer function, and converting the spatial domain convolution into a wave number domain product form.
Further, in the step (3), the number of virtual measurement points is filled in the virtual holographic surface V in a manner that the scanning lines scan line by line, and the specific method is as follows: setting a scan parallel to the x-axisA line for scanning the virtual holographic surface by moving a distance d in the positive direction of the y-axis, and when there are four intersections between the scanning line and the boundaries of the virtual holographic surface V and the holographic surface H, x is respectively set from left to right0，x1，x2，x3At x0And x1Supplementing a virtual measuring point at x every distance d2And x3Supplementing a virtual measuring point every distance d; when the scanning line only has an intersection point with the boundary of the virtual holographic surface V, supplementing a virtual measuring point every distance d between the two intersection points; when the boundaries of the scanning line, the holographic surface H and the virtual holographic surface V have no intersection point, no treatment is carried out; where d is the spacing of the holographic surface measurement grid points.
Further, the step (3) obtains the sound pressure value of each virtual measurement point by using the sound pressure value on the holographic surface H through a berger recurrence method.
Further, the step (3) further comprises: and filtering the sound pressure data of the virtual holographic surface V by using Turkey filtering.
Further, the transfer function in the step (4) is a two-dimensional space Fourier transform G of a Green functionD(kx,kyZ) of the form:
i is the unit of imaginary number and z is the coordinate of the spatial point on the z-axis.
Further, the reconstruction formula in the step (5) is specifically:
in the formula, p (x, y, z)V) Sound pressure value, F, of virtual hologram plane Vx、FyFourier transform of the x, y axes, respectively, zV、zsRespectively, the z-axis coordinates of the virtual holographic surface and the reconstruction surface.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a near-field acoustic holography method based on edge filling and Fourier transform, which reduces the influence of a winding error and an edge Gibbs effect on the premise of not increasing the measurement workload and the measurement cost, and obviously improves the reconstruction result under a small holographic aperture. Compared with the traditional Fourier transform near-field acoustic holography algorithm, the method provided by the invention greatly reduces the requirements on the holographic aperture, and has higher reconstruction precision and application range.
Drawings
FIG. 1 is a flow chart of a near-field acoustic holography method based on edge filling and Fourier transform according to the present invention;
FIG. 2 is a schematic diagram of the process before and after the virtual measurement point is supplemented;
FIG. 3 is a schematic view of the completion of the supplement of the virtual hologram surface according to the present invention;
FIG. 4 is a time domain and frequency domain diagram of the Turkey window of the present invention;
FIG. 5 is a sound pressure reconstruction contrast diagram of a conventional Fourier transform-based near-field acoustic holography algorithm under a small aperture condition;
FIG. 6 is a sound pressure reconstruction contrast diagram under a small holographic aperture condition according to the method of the present invention.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
The invention provides a near-field acoustic holography method based on edge filling and Fourier transform, which has good reconstruction precision for a small-aperture holographic surface. Referring to fig. 1, the method generally comprises an edge filling algorithm and a near-field acoustic holography algorithm based on fourier transform, wherein the edge filling algorithm fills virtual measurement points in an original holographic measurement surface, the algorithm adopts a berger recurrence method to obtain sound pressure values of the virtual measurement points, and edges are smoothed through Turkey filtering, so that a new virtual holographic surface is obtained; and (3) performing convolution conversion on the virtual holographic surface sound pressure data and the space domain of the Green function into a wave number domain product form based on a Fourier transform near-field acoustic holography algorithm to reconstruct the sound field. By utilizing the method provided by the invention, the holographic aperture does not need to be increased to reduce errors, the influence of the winding error and the edge Gibbs effect is reduced on the premise of not increasing the measurement workload and the measurement cost, and the reconstruction precision of the Fourier transform-based near-field acoustic holographic algorithm under the small-aperture holographic surface is obviously improved.
A detailed description of the steps of the near-field acoustic holography method based on edge filling and fourier transform is given below in conjunction with a simulation example.
In step 001, the present embodiment performs numerical simulation by taking 5 point sound sources as an example. The simulated point sound source has a radius of 0.01m, a frequency of 1500Hz, a vibration speed of 2.5m/s, and coordinates (-0.5, -0.5,0) (-0.5,0.5,0) (0,0,0) (0.5,0.5,0) (0.5, -0.5,0) in a spatial rectangular coordinate system. The distances between the hologram surface H and the sound source surface are 0.05m, respectively. The numerical aperture of the holographic surface, that is, the holographic aperture, is 0.5m × 0.5m, and the measurement point pitch is 0.05 m.
And step 002, for each individual point sound source, obtaining a sound pressure simulation theoretical value at the holographic surface H and the reconstruction surface S through the following point sound source radiation formula. And then overlapping the sound pressure to obtain a final theoretical value.
In the formula (I), the compound is shown in the specification,
v0、r0respectively the vibration speed and radius of the point sound source, omega and k respectively the frequency and wave number of the point sound source, i is an imaginary unit, rho0R is the distance from the point source to each point on the holographic or reconstruction surface, which is the density of the air medium. It should be understood that the above steps 001 and 002 are the calculation of the sound pressure in the holographic plane with the simulation example. In the practical application process, a holographic surface H can be arranged in a near-field radiation area of a sound source, the holographic surface H is a square matrix in a sound field generated by the sound source, measuring grid points are distributed on the holographic surface H, and a sensor is used for measuring sound pressure at the measuring grid points.
And step 003, placing a virtual holographic surface V at the position of the holographic surface H, wherein the numerical aperture of the virtual holographic surface is 1.5m multiplied by 1.5 m. In order to obtain a reconstruction value with higher precision, the numerical aperture and the number of measurement points of the reconstruction surface are the same as those of the virtual holographic surface, and the distance between the virtual holographic surface and the sound source surface is 0.03 m. In the example, the area of the sound source surface is 1m multiplied by 1m, the area of the holographic surface is 0.5m multiplied by 0.5m, the area of the sound source surface is obviously larger than that of the holographic surface, and the area of the virtual holographic surface is ensured to be larger than or equal to that of the sound source surface to be detected, so that the effectiveness of the method is verified.
Step 004, supplementing virtual measuring points on the virtual holographic surface V.
The method comprises the following specific steps:
(1) fig. 2 is a schematic diagram of a process of supplementing virtual measurement points, which is a schematic diagram before supplementation and a schematic diagram after one supplementation from left to right, wherein black dots represent original measurement points on the holographic surface H, hollow circles represent supplemented virtual measurement points, and black squares represent intersections of scanning lines with boundaries of the virtual holographic surface V and the holographic surface H. The supplementary method is as follows: a scanning line is arranged parallel to the x-axis, and the virtual holographic surface is scanned by moving a distance d (d is the distance between the measuring points of the holographic surface, and is 0.05m in the embodiment) in the positive direction of the y-axis, which is shown by a dotted line. When the scanning line has four intersections with the boundaries of the virtual holographic surface V and the holographic surface H, x is respectively set from left to right0，x1，x2，x3At x0And x1Supplementing a virtual measurement point for each distance d of the interval. For x2And x3The same process is carried out between the two, and one virtual measuring point is supplemented at every distance d. When the scanning line has an intersection only with the boundary of the virtual hologram plane V, go to (2). When the scanning line has no intersection with the boundaries of the holographic surface H and the virtual holographic surface V, no processing is performed.
(2) When the scanning line has two intersections with the virtual hologram surface V, as shown by x in FIG. 24，x5As shown, two intersection points supplement one virtual measurement point per distance d apart. And finally, replacing the point where the scanning line intersects with the virtual holographic surface with a virtual measuring point. After all the virtual measurement points are set, as shown in fig. 3, the open circles represent the supplementary virtual measurement points, and the black dots represent the original measurement points on the hologram surface H.
And 005, determining the coordinates of the virtual measurement points, and calculating the sound pressure value of each virtual measurement point.
In the method, the sound pressure value of each point on the virtual holographic surface V is reconstructed by utilizing the sound pressure value on the holographic surface H through the principle of the Berger recursion method. To obtain the point measurement values of the entire virtual hologram surface, the virtual measurement values of all rows on the virtual hologram surface are first derived in the positive and negative directions of the x-axis, and then the virtual measurement values of all columns on the virtual hologram surface are derived in the positive and negative directions of the y-axis, the virtual measurement values of the columns including the boundary filling portions that did not exist before. And setting L as the measuring point number of the original holographic surface in the x direction and S as the measuring point number of the virtual holographic surface in the x direction. Assuming that the sound pressure value of a certain line of the original holographic surface is PHrow＝[p(rHrow1)，p(rHrow2)，···，p(rHrowL)]T. The holographic surface is expanded rightwards at first, and the right side sound pressure value is
The sound pressure value on the left side is
The sound pressure value of a certain row on the right side of the holographic surface is as follows:
in the formula, P is the number of the supplementary measuring points in a certain line on the right side of the original holographic surface and is less than or equal to L.
The sound pressure value of the same row on the left side of the holographic surface is as follows:
wherein P is the number of measurement points supplemented to a certain line on the left side of the original holographic surface and is less than or equal to L, aiThe method is a P-order autoregressive parameter obtained by fitting of a Berger algorithm, and the solving process is as follows:
is provided with
And
p-order forward and backward prediction errors, respectively, where,
the reflection coefficient formula is:
order to
ap(p)＝kp
ρp＝(1-|kp|2)ρp-1
The coefficient a can be obtained1(p)＝k1，ρ1＝(1|k1|2)rp(0)。
By
Can obtain the product
And
and bring it into the reflection coefficientK can be obtained from the formula2And by analogy, all the order autoregressive parameters can be obtained until P is equal to P.
The sound pressure value calculated as described above is used as a virtual point on the virtual hologram surface. The virtual measuring point and the original measuring point on the holographic surface jointly form sound pressure data of the virtual holographic surface.
Step 006, filtering the sound pressure data of the virtual holographic surface V by using the Tukey window, thereby improving the problem that the signal-to-noise ratio of the sound pressure signal at the edge of the holographic surface is low.
As shown in fig. 4, the Tukey window is a superposition of a rectangular window and two cosine windows, and is characterized in that the main side lobe ratio of the sampled signal is high, and the side lobes converge quickly. This is used here because the constant part of the window is placed right above the original aperture, while the cosine part covers the area that fills the border. In this way, the spatial window does not affect the acoustic information and leakage is reduced.
Step 007 of determining spatial wavenumber component kx,kyAnd kzThe method comprises the following specific steps:
(1) k in the simulation example of the present invention according to the Nyquist sampling theoremx,kyThe value ranges are defined as follows:
Δ x and Δ y are sampling intervals in the x and y directions, respectively, and are determined by dividing the hologram surface size by the number of measurement points.
(2) Wave number component k in z directionzAccording to kx,kyAnd the sound source frequency k.
Step 008, respectively reconstructing a sound field through a Fourier transform near-field acoustic holography algorithm according to the sound pressure data of the holographic surface H and the sound pressure data of the virtual holographic surface V, and comparing the reconstruction effects of the sound field and the sound field.
Sound field reconstruction is performed according to the sound pressure data of the holographic surface H by a conventional fourier transform-based near-field acoustic holography algorithm, and the reconstruction result is shown in fig. 5, wherein the theoretical sound pressure of the reconstruction surface is calculated in step 002. The reconstruction formula based on the Fourier transform near-field acoustic holography algorithm is specifically as follows:
in the formula, p (x, y, z)H) Sound pressure data, transfer function G, obtained for holographic surface HD(kx,kyZ) is a two-dimensional spatial Fourier transform of the Green function,
Fx、Fyfourier transform of the x, y axes respectively. z is a radical ofV、zsRespectively, the z-axis coordinates of the virtual holographic surface and the reconstruction surface.
The reconstruction is carried out by using the method of the invention, the reconstruction result is shown in figure 6, the concrete steps are consistent with the reconstruction according to the holographic surface H, and only the input holographic surface sound pressure value p (x, y, z)H) Replacing the sound pressure value p (x, y, z) of the virtual holographic surface V after Tukey window filteringV) And the corresponding parameters such as the size of the reconstruction surface are changed. The concrete reconstruction formula is as follows:
as can be seen from fig. 5 and 6, the sound pressure reconstructed by the method of the present invention is substantially consistent with the theoretical sound pressure of the reconstruction surface, and compared with the conventional near-field acoustic holography technique of fourier transform, the reconstruction accuracy is greatly improved.
The components not specified in this embodiment can be implemented by the prior art.
The invention provides a near-field acoustic holography method based on edge filling and Fourier transform, which can be used in the fields of noise level evaluation, mechanical noise control, equipment fault diagnosis, tone quality design, loudspeaker systems, indoor acoustics and the like. For example, the position of the noise source is determined by reconstructing the sound field distribution of the whole three-dimensional space, which has great significance for effectively carrying out noise source control and noise source sound radiation characteristic research. The method greatly reduces the requirement of the traditional Fourier transform-based near-field acoustic holography algorithm on the holographic aperture, and has higher reconstruction precision and application range.
The above description is only a preferred embodiment of the present invention and there are many ways and ways to implement this solution. It should be noted that, for those skilled in the art, without departing from the principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be construed as the protection scope of the present invention.
Claims (4)
1. A near-field acoustic holography method based on edge filling and Fourier transform is characterized by comprising the following steps:
(1) arranging a holographic surface H in a near-field radiation area of a sound source, wherein the holographic surface H is a square matrix in a sound field generated by the sound source, measuring grid points are distributed on the holographic surface H, and the sound pressure at the measuring grid points is measured;
(2) determining the size of a sound source plane, and setting a virtual holographic surface V at the holographic surface H, wherein the area of the virtual holographic surface V is larger than or equal to that of the sound source plane, and the central point of the virtual holographic surface V is coincident with the holographic surface H;
(3) filling virtual measurement points into the virtual holographic surface V in a scanning line-by-line scanning mode, and calculating the sound pressure value of each virtual measurement point, wherein the filling of the virtual measurement points into the virtual holographic surface V in the scanning line-by-line scanning mode comprises the following steps: setting a scanning line parallel to the x-axis, scanning the virtual holographic surface by moving a distance d in the positive direction of the y-axis each time, and scanning the boundary between the scanning line and the virtual holographic surface V and the boundary between the scanning line and the holographic surface HWhen there are four intersections, let x from left to right0，x1，x2，x3At x0And x1Supplementing a virtual measuring point at x every distance d2And x3Supplementing a virtual measuring point every distance d; when the scanning line only has an intersection point with the boundary of the virtual holographic surface V, supplementing a virtual measuring point every distance d between the two intersection points; when the boundaries of the scanning line, the holographic surface H and the virtual holographic surface V have no intersection point, no treatment is carried out; wherein d is the distance between the holographic surface measuring grid points; the sound pressure value of each virtual measurement point is obtained by a Berger recurrence method by utilizing the sound pressure value on the holographic surface H;
(4) determining reconstruction surface S coordinates (x, y, z)S) And the wave number component kx、ky、kzDetermining a transfer function according to the reconstruction surface coordinates and the wave number components;
(5) and (4) reconstructing a sound field according to the sound pressure data of the virtual holographic surface V and the transfer function, and converting the spatial domain convolution into a wave number domain product form.
2. A near-field acoustic holography method based on edge filling and fourier transform as claimed in claim 1 wherein said step (3) further comprises: and filtering the sound pressure data of the virtual holographic surface V by using Turkey filtering.
3. The edge-filling and Fourier-transform-based near-field acoustic holography method according to claim 1, wherein the transfer function in step (4) is a two-dimensional spatial Fourier transform G of a Green's functionD(kx，kyZ) of the form:
i is the unit of imaginary number and z is the coordinate of the spatial point on the z-axis.
4. The near-field acoustic holography method based on edge filling and Fourier transform of claim 3, wherein the reconstruction formula in step (5) is specifically:
in the formula, p (x, y, z)V) Sound pressure value, F, of virtual hologram plane Vx、FyFourier transform of the x, y axes, respectively, zV、zsRespectively, the z-axis coordinates of the virtual holographic surface and the reconstruction surface.
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