Statistically optimal near-field acoustic holography method based on non-uniform sampling

Abstract

The application discloses a statistical optimal near-field acoustic holography method based on non-uniform sampling, relates to the technical field of near-field acoustic holography, and overcomes the problems of large error, high cost and low precision of the existing statistical optimal near-field acoustic holography method based on uniform sampling. The method comprises the following steps: step one, non-uniform sampling of a holographic surface; step two, non-uniform sampling in the wave number domain based on the sampling in the step one; and step three, selection of a regularization parameter by means of the L curve method based on the sampling in the step two, so as to realize the statistical optimal near-field acoustic holography method based on non-uniform sampling. The distribution of sampling points of the holographic surface and the wave number domain is set by means of the non-uniform sampling mode, compared with the case of uniform sampling, the method can improve the reconstruction precision, reduce the cost and time of measurement, effectively reduce the number of measurement points and the matrix dimension while ensuring the reconstruction precision, and the sampling method is simple and easy to set, and therefore, the method is more suitable for practical engineering applications.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of near-field acoustic holography, and particularly relates to a statistical optimal near-field acoustic holography method based on non-uniform sampling. BACKGROUND

[0002] As a noise source identification and positioning technology, near-field acoustic holography has a high spatial resolution. In practical applications, in order to enhance the resolution, the distance between measurement points needs to be reduced. Generally, small distance means an increase in the number of sampling points, i.e. the number of microphone array elements. In addition, near-field acoustic holography requires that the size of the measurement surface must be greater than the size of the measured sound source, so the measurement aperture is usually large. The underwater environment is complex and changeable, and too many underwater microphone array elements will produce errors, which affects the accuracy of sound source reconstruction of near-field acoustic holography and increases the measurement cost.

[0003] Statistical optimal near-field acoustic holography, as a local near-field acoustic holography technology, has attracted wide attention in underwater sound source identification and other aspects. This technology is not limited by the size of the sound source and overcomes the wraparound error and window effect caused by traditional acoustic holography. The holographic surface of statistical optimal near-field acoustic holography can be set with irregular sampling points. When the holographic surface is non-uniformly sampled, the selection of the wave number vector of the statistical optimal near-field acoustic holography is closely related to the regularization parameter. Non-uniform sampling is not limited by the sampling frequency, can resist aliasing, and has high resolution. Therefore, the sampling points and wave number vector of the holographic surface can be set by non-uniform sampling to improve the reconstruction accuracy and reduce the cost and time of underwater measurement. SUMMARY

[0004] In order to solve the problems in the prior art, the present application provides a statistical optimal near-field acoustic holography method based on non-uniform sampling, which overcomes the problems of large error, high cost and low accuracy of the existing statistical optimal near-field acoustic holography method with uniform sampling.

[0005] The technical solution adopted by the present application to solve the technical problems is as follows:

[0006] A statistical optimal near-field acoustic holography method based on non-uniform sampling, the method comprising the following steps:

[0007] Step one: non-uniform sampling of the holographic surface;

[0008] Step two: non-uniform sampling in the wave number domain based on the sampling of step one;

[0009] Step three: selecting the regularization parameter by the L curve method based on the sampling of step two, to realize the statistical optimal near-field acoustic holography method based on non-uniform sampling.

[0010] Preferably, in step one, a power function y=x 2The points on the holographic surface are used as the interval points for non-uniform sampling.

[0011] Preferably, step one includes the following steps:

[0012] Step A: Given an initial value y = 0.01, define the power function y = x. 2 The function value ranges y∈[0.01, y max The independent variable takes values ​​in the range x∈[0,1,x] max ];

[0013] Step B: Let the independent variable x be divided into (N-1) / 2 equal parts, and the power function y = x 2 The function value corresponds to (N-1) / 2 sampling points on the positive half-axis, and similarly, there are (N-1) / 2 sampling points on the negative half-axis. The N sampling points obtained by combining the sampling points and the 0 point are the corresponding microphone positions.

[0014] Preferably, in step two: starting from the lowest-order wavenumber vector, the power function y = x is applied. 2 Increasing the sampling interval results in a total order of M for the final discrete wavenumber vector.

[0015] Preferably, the sampling interval includes all propagating waves and evanescent waves.

[0016] Preferably, step two includes the following steps:

[0017] Step 1: Apply a power function y = x to both propagating waves and evanescent waves. 2 The sampling interval is divided into grids, and k is used for grid division. x and k y Discrete selection is performed; since k x and k y The value of is symmetric about the origin, and the interval is [-k]. max k max There are 2n-1 sampling points, so in the interval [0, k max Given n sampling points and an initial value, determine the power function y = x. 2 The function value ranges from [π / Lx, k] max The corresponding range of values ​​for the independent variable is...

[0018]

[0019] Step 2: Divide the range of the independent variable into n-1 equal parts, and then use the power function y = x 2The sampling values of the corresponding wave number vectors are obtained, n-1 wave number vectors on the positive half axis are obtained, and n-1 wave number vectors on the negative half axis are obtained in the same way, and finally, the n-1 sampling values on the negative half axis, 0 and the n-1 sampling values on the positive half axis are combined to obtain 2n-1 sampling points; k x and k y There are 2n-1 sampling points in each direction, and finally, M grid points are obtained, that is, M=(2n-1) 2 Wave number vectors.

[0020] The beneficial effects of the present application are:

[0021] The reconstruction accuracy of statistical optimal near-field acoustic holography is affected by main parameters. At present, the three parameters that affect the reconstruction accuracy most are wave number vectors, measurement surface sampling points and regularization parameters. In most studies, the holographic measurement surface and the wave number vectors are uniformly sampled. Non-uniform sampling can break through the limitation of the sampling theorem and avoid aliasing effect, so the reconstruction results of uniform sampling and non-uniform sampling of the holographic surface are compared, and the non-uniform sampling of the holographic surface has higher reconstruction accuracy.

[0022] According to the principle of near-field acoustic holography, the energy in the sound field is mainly concentrated near the main analysis wave number. Therefore, when selecting the wave number vectors, more wave number vectors need to be selected near the main analysis wave number, and fewer wave number vectors need to be selected in other regions. Such selection can effectively obtain the main energy in the sound field, ensure the reconstruction accuracy of the sound field, effectively reduce the dimension of the sound field reconstruction matrix, and thus reduce the sound field reconstruction time. Since the evanescent wave energy decays exponentially with the propagation distance, in order to realize that the sampling interval increases with the increase of the wave number when sampling the evanescent wave component, more wave number vectors are selected near the small wave number, and fewer wave number vectors are selected in other regions.

[0023] The present application provides a near-field acoustic holography method based on non-uniform sampling. The distribution of the holographic surface sampling points and the wave number domain is set by the non-uniform sampling method, which can improve the reconstruction accuracy and reduce the cost and time of measurement compared with uniform sampling, effectively reduce the number of measurement points and the dimension of the matrix while ensuring the reconstruction accuracy, and the sampling method is simple and easy to set, so it is more suitable for practical engineering applications. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 It is a holographic surface non-uniform sampling interval point diagram of the present application;

[0025] Figure 2 It is a holographic surface non-uniform sampling reconstruction sound pressure diagram of example 1;

[0026] Figure 3 It is a holographic surface non-uniform sampling and uniform sampling reconstruction error comparison diagram under different frequencies of example 2;

[0027] Figure 4 This is a schematic diagram comparing the reconstruction errors of two sampling scenarios at different frequencies in Example 3;

[0028] Figure 5 This is a schematic diagram comparing the reconstruction errors of different wavenumber domains when using non-uniform sampling of the holographic surface in Example 4.

[0029] Figure 6 This is a schematic diagram of the absolute error of sound pressure reconstruction by uniform sampling in the wavenumber domain of a holographic surface, as shown in Example 5.

[0030] Figure 7 This is a schematic diagram of the absolute error of sound pressure reconstruction by holographic surface uniform sampling and wavenumber domain non-uniform sampling in Example 5;

[0031] Figure 8 This is a schematic diagram of the absolute error of sound pressure reconstruction by uniform sampling in the wavenumber domain using non-uniform sampling of the holographic surface in Example 5.

[0032] Figure 9 This is a schematic diagram of the absolute error of sound pressure reconstruction in the wavenumber domain using non-uniform sampling of the holographic surface, as shown in Example 5. Detailed Implementation

[0033] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0034] like Figure 1 The diagram shows a schematic of non-uniform sampling on a holographic surface. A statistically optimal near-field acoustic holography method based on non-uniform sampling is presented, comprising the following steps:

[0035] Step 1: Non-uniform sampling of the holographic surface was performed. Under the condition of non-uniform sampling of the holographic surface, a power function y = x was selected. 2 As the sampling interval, the power function y = x 2 Given an initial value of 0.01m, define the power function y = x. 2 The function value ranges y∈[0.01, y max The corresponding independent variable takes values ​​in the range x∈[0.1, x...]. max ].

[0036] Divide the range of the independent variable into N equal parts, and then use the power function y = x 2 Find the corresponding microphone position. This will yield the power function y = x. 2 (N-1) / 2 sampled values ​​on the positive half-axis can be obtained similarly on the negative half-axis. Finally, the (N-1) / 2 negative half-axis sampled values, 0, and (N-1) / 2 positive half-axis sampled values ​​are combined to obtain N sampled points.

[0037] Step 2: Based on the non-uniform sampling of the holographic surface, perform non-uniform sampling in the wavenumber domain, starting from the lowest-order wavenumber vector and following the power function y = x. 2 Increasing the sampling interval (to include all propagating and evanescent waves) results in a final discrete wavenumber vector with a total order of M. A power function y = x is uniformly applied to both propagating and evanescent wave components. 2 The sampling interval is divided into grids. Both propagating and evanescent wave components use y = x. 2 The sampling interval is divided into grids, and k is used for grid division. x and k y Discrete selection is performed. Within the interval [0, k]... max Given n sampling points and an initial value, determine the power function y = x. 2 The function value ranges from [π / Lx, k] max The corresponding range of values ​​for the independent variable is...

[0038] Divide the range of the independent variable into 2n-1 equal parts, and then use the power function y = x 2 The corresponding wavenumber vector sampling values ​​are obtained, resulting in n-1 wavenumber vectors on the positive half-axis. Similarly, n-1 wavenumber vectors on the negative half-axis can be obtained. Finally, the n-1 negative half-axis sampling values, 0, and n-1 positive half-axis sampling values ​​are combined to obtain 2n-1 sampling points. x and k y There are 2n-1 sampling points in each direction, and finally M grid points are obtained, that is, the M-order wavenumber vector is obtained.

[0039] Step 3: By combining the non-uniform sampling of the first two steps with the L-curve method to reasonably select regularization parameters, the reconstruction accuracy and stability are improved. The sound pressure reconstruction error is used to evaluate the quality of the reconstruction algorithm; the expression for calculating the reconstruction error is:

[0040]

[0041] In the formula, M represents the total number of calculation points. and represents the theoretical and reconstructed sound pressure values ​​at the i-th calculation point, respectively.

[0042] Example 1:

[0043] When the point source is located at the center of the holographic surface, the radius of the point source is r = 0.001 m, the vibration velocity is v0 = 0.08 m / s, and the sound source frequency is 1500 Hz. The acoustic medium is water with a density of ρ = 1000 kg / m³. 3, the sound wave propagates in water at a speed of 1500 m / s. When the holographic surface is uniformly sampled, the reconstruction surface and the holographic surface are both square planes and adopt the same grid division, and when the holographic surface is non-uniformly sampled, the reconstruction surface still adopts uniform grid division. The holographic surface is 0.4 m away from the source surface, and the reconstruction surface is 0.3 m away from the source surface. The holographic surface is 2 m*2 m. Figure 2 For the reconstructed sound pressure of the non-uniformly sampled holographic surface, the simulation calculation by the MATLAB software shows that the reconstruction error of the non-uniform sampling is 4.53%, so the reconstructed sound pressure of the non-uniformly sampled holographic surface has high precision.

[0044] Example 2

[0045] When the point source is located at the center of the holographic surface, the radius of the point sound source is r=0.001 m, and the vibration speed v0=0.08 m / s. The sound medium is water, and the density is p=1000 kg / m 3 , the sound wave propagates in water at a speed of 1500 m / s. When the holographic surface is uniformly sampled, the reconstruction surface and the holographic surface are both square planes and adopt the same grid division, and when the holographic surface is non-uniformly sampled, the reconstruction surface still adopts uniform grid division. The holographic surface is 0.4 m away from the source surface, and the reconstruction surface is 0.3 m away from the source surface. The holographic surface is 2 m*2 m, and the MATLAB software is used to simulate and calculate the case that the sampling points on the holographic surface are 13*13. Figure 3 The reconstruction error comparison diagram of the uniformly sampled and non-uniformly sampled holographic surfaces under different frequencies is shown in FIG. 2. Figure 3 It can be seen from FIG. 2 that the reconstruction error of the non-uniformly sampled holographic surface is almost smaller than that of the uniformly sampled holographic surface under different frequencies, so the reconstruction precision of the non-uniformly sampled holographic surface is better than that of the uniformly sampled holographic surface.

[0046] Example 3

[0047] According to Example 2, the reconstruction errors of the uniformly sampled holographic surface with sampling points of 11*11 and the non-uniformly sampled holographic surface with sampling points of 21*21 are compared. The other conditions are kept unchanged, Figure 4 The reconstruction error comparison diagram of the two cases under different frequencies is shown in FIG. 3. Figure 4 It can be seen from FIG. 3 that the reconstruction error of the non-uniformly sampled holographic surface with sampling points of 11*11 is basically smaller than that of the uniformly sampled holographic surface with sampling points of 21*21 at each frequency. The MATLAB software is used for simulation and calculation, and the simulation running time of the holographic surface with sampling points of 21*21 is 135.43 s, while the simulation running time of the holographic surface with sampling points of 11*11 is 6.56 s. Therefore, the non-uniform sampling method can reduce the number of measurement points under the premise of ensuring the reconstruction precision, so the method solves the problems of measurement time and cost in practice.

[0048] Example 4

[0049] When the point source is located at the center of the holographic surface, the radius of the point sound source is r = 0.001 m, and the vibration speed is v0 = 0.08 m / s. The acoustic medium is water, the density is p = 1000 kg / m 3 , and the sound wave propagates in water at a speed of 1500 m / s. The distance between the holographic surface and the sound source surface is 0.4 m, the distance between the reconstruction surface and the sound source surface is 0.3 m, and the holographic surface and the reconstruction surface are both 2 m*2 m. The holographic surface is simulated by MATLAB software when the sampling points are 21*21. Figure 5 Figure 8 is a comparison diagram of reconstruction errors of different wave number domains when the holographic surface is non-uniformly sampled. As can be seen from Figure 5 , the reconstruction errors of wave number domain non-uniform sampling at different frequencies are almost less than those of wave number domain uniform sampling, so the reconstruction accuracy of wave number domain non-uniform sampling is better than that of wave number domain uniform sampling.

[0050] Example 5:

[0051] Keeping other simulation conditions unchanged, when the number of sampling points is 11*11 and the frequency is 1500 Hz, the three-dimensional effect of the absolute error of the reconstructed sound pressure and the theoretical sound pressure is shown in Figures 6-9 .Comparing Figure 6 , 7 , 8 and 9, the absolute error of the sound pressure reconstruction value and the theoretical value obtained by MATLAB software simulation calculation is less than 0.5 Pa, and the absolute error of the holographic surface non-uniform sampling is less than that of the holographic surface uniform sampling, and the absolute error of the wave number domain non-uniform sampling is less than that of the wave number domain uniform sampling under the same holographic surface sampling, especially in the middle area, the reconstructed sound pressure value is obviously improved, so the near-field acoustic holography reconstruction accuracy of non-uniform sampling is higher.

Claims

1. A statistically optimal near-field acoustic holography method based on non-uniform sampling, characterized in that, The method comprises the following steps: Step one: non-uniform sampling of the holographic surface; in the step one, the points on the power function y=x 2 are selected as the interval points of the non-uniform sampling of the holographic surface; Step two: performing non-uniform sampling in wave number domain based on the sampling in step one; In the second step, the power function y=x is used to start from the lowest order wave number vector 2 The sampling interval is increased, and the total order of the resulting discrete wave number vector is M. The step two comprises the following steps: Step 1: take power function y=x uniformly for propagating wave and evanescent wave 2 , and divide the sampling interval into grid, discretely select k x and k y ; since the value of k x and k y is symmetrical about the origin, there are 2n-1 sampling points in the interval [-k max , k max ], so there are n sampling points in the interval [0, k max ], given an initial value, determine the function value range [π / Lx, k 2 ] of the power function y=x max , and the corresponding independent variable value range is ; Step 2: divide the range of the independent variable into n-1 equal parts, and then pass through the power function y=x 2 The sampling values of the corresponding wave vectors are obtained, n-1 wave vectors on the positive half axis are obtained, and n-1 wave vectors on the negative half axis are obtained in the same way. Finally, the n-1 sampling values on the negative half axis, 0 and the n-1 sampling values on the positive half axis are combined to obtain 2n-1 sampling points; k x and k y There are 2n-1 sampling points in each direction, and finally M grid points are obtained, that is, M=(2n-1) 2 order wave vectors; Step three: selecting a regularization parameter by means of L curve method based on the sampling in step two, and realizing a statistical optimal near-field acoustic holography method based on non-uniform sampling.

2. The statistically optimal near-field acoustic holography method based on non-uniform sampling according to claim 1, wherein, The step one comprises the following steps: Step A: Given an initial value y = 0.01, set the power function y = x 2 The function value range y ∈ [0.01, y max ], the argument value range x ∈ [0.1, x max ]; Step B: Let the independent variable x be divided into (N-1) / 2, the function value of the power function y=x 2 corresponds to (N-1) / 2 sampling points on the positive half-axis, and similarly there are (N-1) / 2 sampling points on the negative half-axis. Combining the sampling points with the 0 point gives N sampling points, which correspond to the microphone positions.

3. The statistically optimal near-field acoustic holography method based on non-uniform sampling according to claim 1, wherein, The sampling interval comprises all propagating waves and evanescent waves.

Images