CN109764956B - Near-field acoustic holography method based on combinatorial optimization regularization method - Google Patents
Near-field acoustic holography method based on combinatorial optimization regularization method Download PDFInfo
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Abstract
The invention discloses a near-field acoustic holography method based on a combined optimization regularization method, which utilizes sound pressure of each point measured on a holographic surface, adopts a truncated singular value and a standard Tikhonov combined optimization regularization method to inhibit measurement errors of wave number vectors caused by noise and random errors on the basis of a statistical optimal cylindrical near-field acoustic holography theory method, namely, the combined optimization regularization method, utilizes the combined optimization regularization method and a GCV method to obtain a superposition coefficient matrix and the sound pressure of each point measured on the holographic surface, expresses the sound pressure of each point on the surface of a shell structure equipment as linear superposition of conformal measurement surface sound pressure, can obtain a shell structure equipment surface sound field, fully shows the effectiveness of the shell structure in shell radiation noise analysis, is suitable for a cylindrical shell structure, and displays a cylindrical underwater vehicle sound field in a visual mode, therefore, the size and the distribution condition of the radiation sound field can be visually seen, and the method has important theoretical significance and engineering application value.
Description
Technical Field
The invention belongs to the field of mechanical structure acoustic radiation signal processing, and particularly relates to a near-field acoustic holography method based on a combined optimization regularization method.
Background
The underwater vehicle has large endurance, strong maneuverability and strong independent combat capability, but noise waves generated by the underwater vehicle can be transmitted to hundreds of seas in seawater and are easy to be detected locally, and the sound stealth performance of the underwater vehicle is seriously weakened, so that the key for ensuring the safety of the underwater vehicle is to improve the sound stealth performance of the underwater vehicle. At present, the technical problem to be solved firstly is to obtain a radiation sound field of an underwater vehicle so as to realize accurate evaluation on the stealth performance of the underwater vehicle. However, for underwater vehicle hull equipment with a plurality of internal sound sources and complex propagation paths, accurate assessment of the sound stealth performance of the underwater vehicle hull equipment is difficult. At present, the naval strong country generally utilizes an underwater acoustic test field test equipped with a high-precision fixed measurement and analysis system to evaluate the acoustic stealth performance of an underwater vehicle, however, the site selection requirement of the underwater acoustic test field is extremely high, the technology is complex and the cost is high.
Near-field acoustical Holography (NAH) is a very effective noise source identification, positioning and sound field visualization method, and is to obtain enough low-spatial frequency propagation waves and high-spatial frequency evanescent wave components through near-field testing to reconstruct a high-precision holographic image and rich space sound field information, the resolution of which is not limited by analysis wavelength. However, in the conventional NAH, deconvolution operation is realized through spatial two-dimensional fourier transform to obtain reconstructed surface sound pressure, and a window effect and a winding error are caused in a holographic calculation process, so that the test aperture area is required to be at least twice of the sound source area, and for large-size cylindrical shell structure equipment, accurate test meeting the NAH requirement is difficult to realize. The statistical optimal near-field acoustic holography (SONAH) technology directly realizes the reconstruction of a space sound field through the linear superposition of the complex sound pressure of a holographically measured surface, thereby fundamentally avoiding the window effect and the winding error of the traditional NAH and overcoming the strict requirement on the measurement size. However, the domestic scholars have conducted a great deal of theoretical and experimental research on the method, but the research is usually focused on the problem of statistical optimal planar near-field acoustic holography, the cylindrical sound source of the underwater vehicle is less researched, and the problem of acoustic unsuitability is lacked.
Disclosure of Invention
The invention aims to provide a near-field acoustic holography method based on a combined optimization regularization method, so as to overcome the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a near-field acoustic holography method based on a combined optimization regularization method comprises the following steps:
step 1), selecting wave number vectors at unequal intervals on a space wave number plane limited by the maximum wave number;
step 2), the measurement error of the wave number vector caused by noise and random error is inhibited by adopting a truncated singular value and standard Tikhonov combined optimization regularization method for the selected wave number vector;
step 3), utilizing the combination optimization regularization method and the GCV method in the step 2) to obtain a superposition coefficient matrix C (r)S) And on the holographic surfaceMeasured sound pressure p (r) of each pointHn) Expressing sound pressures of all points on the surface of the shell structure equipment as linear superposition of sound pressures of conformal measuring surfaces, namely p (r)S,θ,z)＝C(rS)p(rHn) And the surface sound field of the shell structure equipment can be obtained.
Further, in step 1), selecting each wavenumber vector at unequal intervals on a spatial wavenumber plane defined by the maximum wavenumber:
the optimal cylindrical near-field acoustic holography method comprises the following steps:
the travelling wave of the steady-state acoustic field Helmholtz equation under the cylindrical coordinate system is solved into
Wherein p (r, θ, z) is a sound pressure at an arbitrary point in space, and is defined as einθAnd
is the cylindrical wave function, kzIn the case of the axial wave number,
k is the sound wave number, and n is the circumferential wave number;
in order to determine the unknown number to be determined,
representing a first class Henkel function of order n;
let P be under the cylindrical coordinate systemn(r,n,kz) Is a two-dimensional Fourier transform of p (r, θ, z) of
Giving its inverse Fourier transform as
Let the above formula r be a,
the formula (1), (2), (3) and (4) can be solved:
in the formula, Pn(a,kz) Is a two-dimensional Fourier transform of p (a, theta, z).
Using wave number vector K ═ n, Kz) The determined spatial frequency domain unit cylindrical wave on the cylindrical surface is as follows:
reconstruction of any point r on the surface of the cylindrical shell structure equipmentS＝(rSTheta, z) is KmThe unit cylindrical wave can be formed by all points r on the holographic surfaceHn＝(rH,θn,zn) Wave number vector of KmIs obtained by superposing the unit cylindrical waves, i.e.
In the formula, rHn＝(rH,θn,zn) (N ═ 1,2, …, N) are N sound pressure measurement points on the holographic cylinder, M is the number of elementary cylindrical waves contained in the reconstruction cylinder and the complex sound pressure on the holographic cylinder, and C (r) isS) Is a superposition coefficient matrix;
order to
The linear equation system formed by the M linear equations determined by the above formula is expressed in a matrix form
b＝AC(rS) (9)
Obtaining sound pressure of each point on a reconstruction surface:
in the formula, p (r)Sθ, z) is the sound pressure at each point on the reconstruction plane, p (r)Hn) To measure the sound pressure at each point on the surface.
Further, on the basis of the Nyguist sampling theorem, sampling intervals with different sizes are adopted inside and outside the wavenumber domain radiation circle.
Further, the sampling interval within the wavenumber domain radiating circle is smaller than the sampling interval outside the radiating circle.
Furthermore, wave number vectors are selected in a high wave number area outside the radiation circle according to the maximum sampling interval delta l meeting the sampling theorem, and low wave number areas in the radiation circle are sampled at small intervals
And selecting a wave number vector.
Further, a regularization method of truncated singular value and standard Tikhonov combination optimization is adopted: processing the low spatial frequency component which does not contain noise and corresponds to the larger singular value before the truncation point by adopting a TSVD (sequential quadratic decomposition) method without performing regularization processing; for small singular values after the truncation point, a Tikhonov regularization method is adopted to control the transition method of the small singular values to noise, and meanwhile, high-frequency detail information is kept;
the solution obtained by combined regularization is
Further, the truncation point and regularization parameters are selected using generalized cross validation based on a posteriori criteria:
determining an interception point k by adopting a generalized cross validation method, selecting a regularization parameter lambda in the formula (11), and taking the interception point k as the regularization parameter of a singular value after the regularization treatment of the interception point, wherein the solution obtained by the optimized combined regularization method is as follows:
combining the formulas (8), (9) and (12) to obtain a superposition coefficient matrix C (r)S)。
Further, according to the obtained superposition coefficient matrix C (r)S) And the sound pressure p (r) of each point measured on the hologram surfaceHn) Expressing the sound pressure of each point on the surface of the cylindrical shell structure equipment as the linear superposition of the sound pressure of the conformal measuring surface, namely p (r)S,θ,z)＝C(rS)p(rHn) And obtaining a radiation sound field of the cylindrical shell structure equipment.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention discloses a near-field acoustic holography method based on a combined optimization regularization method, which utilizes the sound pressure p (r) of each point measured on a holographic surfaceHn) On the basis of a statistical optimal cylindrical surface near-field acoustic holography theory method, an improvement method is provided, a truncated singular value and standard Tikhonov combined optimization regularization method is adopted for selected wave number vectors to inhibit measurement errors of the wave number vectors caused by noise and random errors, a combined optimization regularization method is provided, and a superposition coefficient matrix C (r) is obtained by utilizing the combined optimization regularization method and a GCV methodS) And the sound pressure p (r) of each point measured on the hologram surfaceHn) Expressing sound pressures of all points on the surface of the shell structure equipment as linear superposition of sound pressures of conformal measuring surfaces, namely p (r)S,θ,z)＝C(rS)p(rHn) The method has the advantages that the surface sound field of the shell structure equipment can be obtained, the effectiveness of the method in shell radiation noise analysis is fully demonstrated, the method is suitable for the cylindrical shell structure, the shooting sound field of the cylindrical underwater vehicle is displayed in a visual mode, the size and the distribution condition of the radiation sound field can be visually seen, and the method has important theoretical significance and engineering application value.
On the basis of statistics of optimal cylindrical surface near-field acoustic holography and technology, wave number vectors are selected at unequal intervals on a space wave number plane limited by the maximum wave number, so that low-wave-number main energy in a sound field can be effectively acquired, high-wave-number-domain energy can be acquired, the integrity of sound field information acquisition is ensured, and the influence of noise signals on reconstruction accuracy is effectively reduced.
The combined optimization method provided by the invention contains more detail information than TSVD, and meanwhile, Tikhonov regularization retains high-frequency detail information and inhibits the amplification effect of small singular values on noise, so that higher reconstruction precision and stability can be obtained.
Drawings
FIG. 1 is a surface theoretical sound pressure diagram of a cylindrical shell structure;
FIG. 2 is a sound pressure diagram of a cylindrical shell structure surface reconstructed by a conventional method;
FIG. 3 is a sound pressure diagram of the surface of a reconstructed cylindrical shell structure according to the present invention;
fig. 4 is a graph of sound pressure distribution on the 0 bus line according to the present invention and the conventional method;
FIG. 5 is a graph showing the noise suppression effect of the improved near-field acoustic holography method of the present invention;
FIG. 6 is a graph of the noise suppression effect of the improved near-field acoustic holography method of the present invention;
FIG. 7 is an axial distribution plot of reconstructed acoustic pressure according to the method of the present invention;
FIG. 8 is a graph of the reconstruction error of the present invention compared to different prior regularization methods;
FIG. 9 is a graph of reconstruction errors of the present invention with different regularization methods;
FIG. 10 is a graph of the noise suppression effect of the method of the present invention;
fig. 11 is a cylindrical wave number vector diagram.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
as shown in fig. 1 to 10, a near-field acoustic holography method based on a combinatorial-optimization regularization method includes the following steps:
step 1), selecting wave number vectors at unequal intervals on a space wave number plane limited by the maximum wave number: on the basis of Nyguist sampling theorem, sampling intervals with different sizes are adopted inside and outside a wavenumber domain radiation circle, so that reconstruction accuracy is improved; the sampling interval in the wave number domain radiation circle is smaller than the sampling interval outside the radiation circle;
step 2), the measurement error of the wave number vector caused by noise and random error is inhibited by adopting a Truncated Singular Value (TSVD) and standard Tikhonov combined optimization regularization method for the selected wave number vector;
step 3), utilizing the combination optimization regularization method of the step 2) to combine with the GCV method to obtain a superposition coefficient matrix C (r)S) And the sound pressure p (r) of each point measured on the hologram surfaceHn) Expressing sound pressures of all points on the surface of the shell structure equipment as linear superposition of sound pressures of conformal measuring surfaces, namely p (r)S,θ,z)＝C(rS)p(rHn) And the surface sound field of the shell structure equipment can be obtained.
The invention relates to a device for simulating a cylindrical shell structure, which adopts a cylindrical shell with an axial length of 2.0m and a radius of 0.2m as a research object; selecting reasonable measurement parameters by using a measurement surface conformal to the surface of the cylindrical shell structure equipment, and arranging a sound pressure sensor to obtain high-efficiency holographic sound pressure data;
in step 1), selecting wave number vectors at unequal intervals on a space wave number plane defined by the maximum wave number:
the optimal cylindrical near-field acoustic holography method (SOCNAH) procedure is as follows:
the travelling wave of the steady-state acoustic field Helmholtz equation under the cylindrical coordinate system is solved into
Wherein p (r, θ, z) is a sound pressure at an arbitrary point in space, and is defined as einθAnd
is the cylindrical wave function, kzIn the case of the axial wave number,
k is the sound wave number, and n is the circumferential wave number;
in order to determine the unknown number to be determined,
representing a first class Henkel function of order n;
let P be under the cylindrical coordinate systemn(r,n,kz) Is a two-dimensional Fourier transform of p (r, θ, z) of
Giving its inverse Fourier transform as
Let the above formula r be a,
the formula (1), (2), (3) and (4) can be solved:
in the formula, Pn(a,kz) Is a two-dimensional Fourier transform of p (a, theta, z).
Using wave number vector K ═ n, Kz) The determined spatial frequency domain unit cylindrical wave on the cylindrical surface is as follows:
according to the sound field superposition principle, the reconstruction of any point r on the surface of the cylindrical shell structure equipmentS＝(rSTheta, z) is KmThe unit cylindrical wave can be formed by all points r on the holographic surfaceHn＝(rH,θn,zn) Wave number vector of KmIs obtained by superposing the unit cylindrical waves, i.e.
In the formula, rHn＝(rH,θn,zn) (N ═ 1,2, …, N) are N sound pressure measurement points on the holographic cylinder, M is the number of elementary cylindrical waves contained in the reconstruction cylinder and the complex sound pressure on the holographic cylinder, and C (r) isS) Is a superposition coefficient matrix;
order to
The linear equation system formed by the M linear equations determined by the above formula is expressed in a matrix form
b＝AC(rS) (9)
Therefore, it is only necessary to determine the wave number vector K in the formula (7)mThen the coefficient matrix C (r) is superimposedS) The method can uniquely determine (M is more than or equal to N), and further obtain the sound pressure of each point on the reconstruction surface:
in the formula, p (r)Sθ, z) is the sound pressure at each point on the reconstruction plane, p (r)Hn) To measure the sound pressure at each point on the surface, the key to the problem is the M wave number vector KmDetermination of (1);
however, the SOCNAH reconstruction process has ill-posed characteristics, that is, the matrix a is ill-conditioned, the main cause of the generation is the small singular value of the matrix a, in practice, because the attenuation of the high-wave-number evanescent wave is fast, even if the measurement is performed in the near-field range, the measurement error is easily covered, so when the measurement data of the holographic surface contains error signals such as noise, the regularization method is needed to limit the amplification effect of the small singular value on the measurement error; further, in SOCNAH, the singular value distribution of the matrix A corresponds to unit cylindrical waves in a wave number domain interval determined according to the sampling theorem; in the equations (8) and (9), it can be seen that M is not less than N in the matrix a to ensure the uniqueness of the solution, and when M is greater than N, the singular values and the cylindrical waves of each unit are not in one-to-one correspondence; in fact, a larger singular value corresponds to a propagation wave and an evanescent wave with a low wave number, a smaller singular value corresponds to an evanescent wave with a high wave number, and when the matrix A is established, the more the number of terms of the used evanescent wave with a high wave number is, the more the number of small singular values is, the more obvious the amplification effect on the measurement error is; however, if the energy of the high-wave-number evanescent wave in the sound field is completely discarded in the reconstruction process, part of the sound field energy is lost, and the reconstruction accuracy cannot be guaranteed; in view of the above analysis, the present invention improves the method of selecting the array of wavenumber vectors in the spatial wavenumber domain:
on the basis of Nyguist sampling theorem, a small sampling interval is adopted in a wavenumber domain radiation circle, and a large sampling interval is adopted outside the radiation circle, so that the reconstruction precision is improved; as shown in fig. 11, the method selects wave number vectors at unequal intervals on a space wave number plane defined by the maximum wave number, and adopts a small sampling interval in a wave number domain radiation circle and a large sampling interval outside the radiation circle; according to the near-field acoustic holography principle, energy in a sound field is mainly concentrated in low wave number sound waves; therefore, when selecting wave number vectors, the improved method selects the wave number vectors in a high wave number region outside a radiation circle according to the maximum sampling interval delta l meeting the sampling theorem, and selects the wave number vectors in a low wave number region inside the radiation circle at small sampling intervals
Selecting a wave number vector; therefore, the main energy in the sound field can be effectively obtained, the contribution of the high-wavenumber domain energy to the sound field reconstruction can be ensured, the amplification of measurement errors in the reconstruction process is reduced, and the sound field reconstruction precision is ensured.
A regularization method adopting Truncated Singular Value (TSVD) and standard Tikhonov combined optimization: the method treats singular values of different sizes differently, and processes low-space frequency components which do not contain noise and correspond to the larger singular value before the truncation point by a TSVD (sequential differential scanning VD) method without regularization; for small singular values after the truncation point, the small singular values correspond to high spatial frequency components containing noise and play a role in amplifying signals causing errors in measurement such as the noise and the like, so the small singular values need to be processed, but if a method of directly performing truncation in TSVD is adopted, high-frequency detail information is lost, and the reconstruction precision is reduced, so that for the small singular values, a Tikhonov regularization method is adopted, the transition method of the small singular values to the noise is controlled, and meanwhile, the high-frequency detail information is kept;
combining the above analyses, the solution obtained by combinatorial regularization is
Selecting an interception point and a regularization parameter by using Generalized Cross Validation (GCV) based on a posterior criterion;
since the noise level in the sound field cannot usually be determined in practice, empirical formulas are reused
The truncation point cannot be determined, and the SNR is the signal-to-noise ratio; therefore, the GCV method is adopted to determine the truncation point k, and the truncation point k is directly taken as the regularization parameter of the singular value after the regularization processing truncation point for selecting the middle regularization parameter lambda of the latter item in the formula (11), so that only one undetermined parameter in the combined regularization is ensured, and the singular value after the truncation point is not directly zero-assigned, so that the combined regularization contains more detailed information than TSVD, meanwhile, the regularization inhibits the amplification effect of the small singular value on noise, and higher reconstruction accuracy can be obtained.
Based on the above analysis, the solution obtained by the final combination regularization method is
Further, a method for removing measurement errors by using combinatorial optimization regularization is combined with formulas (8), (9) and (12) to obtain a superposition coefficient matrix C (r)S)；
Using the superposition coefficient C (r) obtained in step 3)S) And the sound pressure p (r) of each point measured on the hologram surfaceHn) Expressing the sound pressure of each point on the surface of the cylindrical shell structure equipment as the sound pressure of a conformal measuring surfaceLinear superposition of, i.e. p (r)S,θ,z)＝C(rS)p(rHn) And obtaining a surface sound field of the cylindrical shell structure equipment.
Using a measuring surface conformal to the surface of the cylindrical shell structure equipment, and acquiring holographic sound pressure data outside the structure to be measured according to the measuring distance, the sensor interval and the measuring area, namely acquiring sound pressure p (r) of each point measured on the holographic surfaceHn)；
In order to verify the effectiveness of the reconstruction of the radiation sound field of the cylindrical shell structure equipment, the cylindrical shell structure equipment is simulated by a cylindrical surface with the axial length of 2.0m and the radius of 0.2 m; 60 pulsating ball sound sources are selected in a shell to form a linear array sound source, the distance between pulsating balls is 0.02m, the vibration frequency is f, the distance between microphone array elements for simulation measurement is 0.1m, the holographic measurement size is 2m, the measurement distance is 0.27m, the reconstruction distance (the distance from a measurement surface to a reconstruction surface) is 0.05m, and random noise with the signal-to-noise ratio of 40dB is added to the holographic surface in order to simulate the actual measurement condition. Using a measuring surface conformal to the surface of the cylindrical shell structure equipment, and acquiring holographic sound pressure data outside the structure to be measured according to the measuring parameters; the measurement parameters comprise measurement distance, sensor interval and measurement area; measuring sound field holographic sound pressure data by using a microphone;
random noise with the signal-to-noise ratio of 40 is applied to the holographic measurement surface, and when different sound source frequencies exist, theoretical sound pressure maps of the surface of the cylindrical shell structure, sound pressure maps of the surface of the cylindrical shell structure reconstructed by a traditional method, sound pressure maps of the surface of the cylindrical shell structure reconstructed by the method and sound pressure distribution of the two methods along the axial direction are respectively shown in fig. 1, fig. 2, fig. 3 and fig. 4.
Fig. 5 shows the noise suppression effect of the improved method, and it can be seen that, in the improved method, when the signal-to-noise ratio is reduced from 40dB to 20dB, the relative average error variation of the reconstruction result is small, and when the signal-to-noise ratio is further reduced to 10dB, the reconstruction error is slightly increased, which fully illustrates that the noise suppression effect of the improved method is better.
In fig. 5, the total relative error of reconstruction is mostly below 30% at different frequencies, and is the lowest at 700Hz, but the total relative error is still 24% because the reconstruction accuracy is better when the side length of the measuring surface is greater than 3 times the acoustic wavelength, but the side length of the measuring surface used in the simulation is only less than 2 times the acoustic wavelength. Further, the side length of the measuring surface is increased to 3.2 times of the sound wavelength, the length of the linear array sound source is increased from 1.2m to 2m, and other simulation conditions are unchanged, so that the reconstruction error of the improved method under the condition that Tikhonov regularization is combined with a GCV regularization parameter selection method is shown in FIG. 6, as can be seen from FIG. 6, the total relative error of reconstruction is greatly reduced on different frequency bands, wherein the total relative error of reconstruction is reduced to less than 10% in a low-frequency band, compared with FIGS. 3-8, when the signal-to-noise ratio is 40dB, the total relative error of reconstruction is reduced by at least 10% in a low-frequency band of 200-800 Hz, and particularly, the total relative error of reconstruction is reduced by nearly 20% in 200 Hz. In order to visually see the reconstruction effect of the improved method, fig. 7 shows the degree of coincidence between the reconstruction value of the improved method and the theoretical value, from which it can be seen that the reconstruction value of the improved method and the theoretical value are well coincided at each reconstruction point, and the effectiveness of the improved method is fully verified.
FIGS. 8 and 9 show the total relative error of each regularization method reconstruction at hologram sizes of 1.7 and 3.2 acoustic wavelengths, respectively, with a signal-to-noise ratio of 20 dB. It can be seen that the combinatorial optimization method has better reconstruction performance in the high frequency band. The advantages of the method for reconstructing the high-frequency sound field are shown; in order to further verify the noise suppression effect of the combinatorial optimization method, fig. 10 shows the total relative error of the combinatorial optimization regularization method of the present invention on reconstruction under different signal-to-noise ratios of the measurement surface; under the condition of different signal-to-noise ratios, the total relative error of the reconstruction of the combination method is not changed greatly, particularly in a high frequency band, the reconstruction error of the combination method is smaller, and the method has good inhibition effect on noise.
In the existing near-field acoustic holography technology, the cylindrical sound source of an underwater vehicle is rarely researched, and the problem of acoustic unsuitability is lacked for research. The method provides an improvement method on the basis of the existing statistical optimal near-field acoustic holography technology, provides a combined optimization regularization method on the basis of the improvement method, and effectively improves the reconstruction precision and stability of the surface sound field of the shell structure equipment, thereby providing a theoretical basis for the acoustic stealth performance evaluation of the cylindrical shell structure equipment, and having important theoretical significance and engineering application value.
Claims (8)
1. A near-field acoustic holography method based on a combined optimization regularization method is characterized by comprising the following steps:
step 1), selecting wave number vectors at unequal intervals on a space wave number plane limited by the maximum wave number;
step 2), the measurement error of the wave number vector caused by noise and random error is inhibited by adopting a truncated singular value and standard Tikhonov combined optimization regularization method for the selected wave number vector; specifically, the method comprises the following steps: processing the low spatial frequency component which does not contain noise and corresponds to the larger singular value before the truncation point by adopting a TSVD (sequential quadratic decomposition) method without performing regularization processing; for small singular values after the truncation point, a Tikhonov regularization method is adopted to control the transition method of the small singular values to noise, and meanwhile, high-frequency detail information is kept;
the solution obtained by combined regularization is
Step 3), utilizing the combination optimization regularization method and the GCV method in the step 2) to obtain a superposition coefficient matrix C (r)S) And the sound pressure p (r) of each point measured on the hologram surfaceHn) Expressing sound pressures of all points on the surface of the shell structure equipment as linear superposition of sound pressures of conformal measuring surfaces, namely p (r)S,θ,z)＝C(rS)p(rHn) And the surface sound field of the shell structure equipment can be obtained.
2. The near-field acoustic holography method based on the combinatorial-optimization regularization method according to claim 1,
in step 1), selecting wave number vectors at unequal intervals on a space wave number plane defined by the maximum wave number:
the optimal cylindrical near-field acoustic holography method comprises the following steps:
the travelling wave of the steady-state acoustic field Helmholtz equation under the cylindrical coordinate system is solved into
Wherein p (r, θ, z) is a sound pressure at an arbitrary point in space, and is defined as einθAnd
is the cylindrical wave function, kzIn the case of the axial wave number,
k is the sound wave number, and n is the circumferential wave number;
in order to determine the unknown number to be determined,
representing a first class Henkel function of order n;
let P be under the cylindrical coordinate systemn(r,n,kz) Is a two-dimensional Fourier transform of p (r, θ, z) of
Giving its inverse Fourier transform as
Let the above formula r be a,
the formula (1), (2), (3) and (4) can be solved:
in the formula, Pn(a,kz) Is a two-dimensional Fourier transform of p (a, theta, z);
using wave number vector K ═ n, Kz) The determined spatial frequency domain unit cylindrical wave on the cylindrical surface is as follows:
reconstruction of any point r on the surface of the cylindrical shell structure equipmentS＝(rSTheta, z) is KmThe unit cylindrical wave can be formed by all points r on the holographic surfaceHn＝(rH,θn,zn) Wave number vector of KmIs obtained by superposing the unit cylindrical waves, i.e.
In the formula, rHn＝(rH,θn,zn) (N ═ 1,2, …, N) are N sound pressure measurement points on the holographic cylinder, M is the number of elementary cylindrical waves contained in the reconstruction cylinder and the complex sound pressure on the holographic cylinder, and C (r) isS) Is a superposition coefficient matrix; order to
The linear equation system formed by the M linear equations determined by the above formula is expressed in a matrix form
b＝AC(rS) (9)
Obtaining sound pressure of each point on a reconstruction surface:
wherein p is: (rSθ, z) is the sound pressure at each point on the reconstruction plane, p (r)Hn) To measure the sound pressure at each point on the surface.
3. The near-field acoustic holography method based on the combinatorial-optimization regularization method as claimed in claim 2, wherein based on the Nyguist sampling theorem, sampling intervals with different sizes are adopted inside and outside the wavenumber domain radial circle.
4. The near-field acoustic holography method based on the combinatorial-optimization regularization method as claimed in claim 3, wherein the sampling interval within the radians circle in the wavenumber domain is smaller than the sampling interval outside the radians circle.
5. The near-field acoustic holography method based on the combinatorial optimization regularization method as claimed in claim 4, wherein the wave number vectors are selected according to the maximum sampling interval Δ l satisfying the sampling theorem in the high wave number region outside the radiating circle, and the small sampling interval is selected in the low wave number region inside the radiating circle
And selecting a wave number vector.
6. The near-field acoustic holography method based on the combinatorial-optimization regularization method according to claim 1, wherein the truncation point and the regularization parameter are selected using generalized cross validation based on a posteriori criterion:
determining an interception point k by adopting a generalized cross validation method, selecting a regularization parameter lambda in the formula (11), and taking the interception point k as the regularization parameter of a singular value after the regularization treatment of the interception point, wherein the solution obtained by the optimized combined regularization method is as follows:
combining the formulas (8), (9) and (12) to obtain a superposition coefficient matrix C (r)S)。
7. A near-field acoustic holography method based on a combinatorial-optimization regularization method as claimed in claim 6, characterized in that it is based on the solved superposition coefficient matrix C (r)S) And the sound pressure p (r) of each point measured on the hologram surfaceHn) Expressing the sound pressure of each point on the surface of the cylindrical shell structure equipment as the linear superposition of the sound pressure of the conformal measuring surface, namely p (r)S,θ,z)＝C(rS)p(rHn) And obtaining a radiation sound field of the cylindrical shell structure equipment.
8. The near-field acoustic holography method based on the combinatorial optimization regularization method as claimed in claim 1, wherein the sound pressure p (r) of each point measured on the holography plane is obtained by using a measuring plane conformal to the surface of the cylindrical shell structure equipment according to the measuring distance, the sensor interval and the measuring areaHn)。
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