A dynamic mirrored boundary acoustic holographic testing device and method

Abstract

This invention discloses a dynamic mirrored boundary acoustic holographic testing device and method, belonging to the field of near-field acoustic holographic testing technology. It includes a translational track, with a first driving mechanism on one side and a testing mechanism on the other. The first driving mechanism is connected to a first base, and a second driving mechanism is mounted on the first base and connected to the second base. The top of the second base is connected to a rigid plate. This invention employs the aforementioned dynamic mirrored boundary acoustic holographic testing device and method, increasing the amount of test information and improving the accuracy of sound field reconstruction without increasing the number of sensors. The combination of fixed measurement points and rigid boundary movement increases the sound pressure data from a single movement of the rigid surface, increasing the total number of sensors and reducing measurement time compared to point-by-point sensor movement. It relies on a small number of fixed sound pressure sensors and a controllable rigid boundary, reducing the difficulty of multi-sensor synchronization and calibration. It utilizes the mirror principle to introduce an adjustable mirror source point, which is not limited by holographic aperture requirements.

Description

Technical Field

[0001] This invention relates to the field of near-field acoustic holography testing technology, and in particular to a dynamic mirror boundary acoustic holography testing device and method. Background Technology

[0002] Acoustic holography, as an important means of sound source identification and sound field reconstruction, has significant value in noise localization, vibration analysis, and acoustic imaging. Although near-field acoustic holography (NAH) theoretically outperforms other methods in terms of accuracy due to its near-field measurement characteristics, achieving high-precision sound field reconstruction is costly. Depending on the algorithm, NAH can be divided into branches based on Fourier transform (FFT), boundary element method (BEM), and equivalent source method (ESM), but these methods are all constrained by two major limitations: insufficient number of measurement points and limited measurement aperture. For example, Fourier transform-based NAH requires the distance between measurement points to be less than half the wavelength of the highest frequency sound wave (Nyquist criterion), but in practical engineering, the measurement point density is often difficult to meet due to limitations in sensor cost and deployment difficulty, leading to loss of high-frequency sound field information or aliasing errors. Furthermore, the physical size of the measurement aperture directly limits the spatial resolution. To alleviate these problems, researchers often use regularization methods (such as Tikhonov regularization) to solve the underdetermined inverse problem or introduce sparse sampling strategies to reduce the number of measurement points. However, these improvement schemes often fall into a trade-off between computational efficiency and accuracy: regularization requires manual adjustment of the penalty factor, excessive regularization can lead to the loss of sound field details, and sparse sampling may cause distortion in low-frequency sound field reconstruction due to missing information. Although dynamic NAH technology based on measurement point scanning can expand the aperture by moving the sensor, it introduces Doppler effect errors and sensor positioning deviations. Summary of the Invention

[0003] The purpose of this invention is to provide a dynamic mirrored boundary acoustic holographic testing device and method, which increases the amount of test information and improves the accuracy of sound field reconstruction without increasing the number of sensors; the fixed measurement point combined with rigid boundary movement increases the sound pressure data of the entire sensor by moving the rigid surface once, reducing the measurement time compared to moving the sensors point by point; it relies on a small number of fixed sound pressure sensors and a controllable rigid boundary, reducing the difficulty of multi-sensor synchronization and calibration; and it utilizes the mirror principle to introduce an adjustable mirror source point, which is not limited by the holographic aperture requirements.

[0004] To achieve the above objectives, the present invention provides a dynamic mirrored boundary acoustic holographic testing device, including a translation track, a first driving mechanism on one side of the translation track, a testing mechanism on the other side, the first driving mechanism being connected to a first base, a second driving mechanism being installed on the first base, the second driving mechanism being connected to the second base, and the top of the second base being connected to a rigid plate.

[0005] Preferably, the first drive mechanism includes a first motor, which is mounted on one side of the translation track, connected to a lead screw, and the bottom of the first base is connected to the lead screw.

[0006] Preferably, the second drive mechanism includes a second motor, which is mounted on the first base and connected to a rotating component, which is connected to the second base.

[0007] Preferably, the bottom of the first base is provided with sliders at both ends, and the translation track is provided with grooves that cooperate with the sliders.

[0008] This invention provides a dynamic mirrored boundary acoustic holographic testing method, specifically including the following steps:

[0009] S1. Determine the number of equivalent sources of the vibrating structure and the position between the sound source surface and the holographic measurement surface;

[0010] S2. Set and adjust the translation and rotation angle of the rigid surface to obtain the position coordinates of the sound source and the mirror source;

[0011] S3. Determine the number and position coordinates of the sound pressure sensors on the holographic measurement surface, and calculate the distance between the sound source point and the mirror source point and the measurement point;

[0012] S4. Perform sound pressure measurement at the measurement points determined in S3;

[0013] S5. Adjust the translation and rotation angle of the rigid surface individually or in combination to obtain the adjusted mirror source position coordinates. Repeat S3 and S4 to obtain the measurement results. Take multiple measurements until the sound pressure and source strength vector acoustic transfer matrix of the holographic surface measurement are full rank or the condition number of the acoustic transfer matrix changes little after the test.

[0014] S6. Using the measurement results obtained in S4, calculate the source intensity vector of the sound source by combining the least squares method or the regularization method.

[0015] Preferably, in S2, the origin of the coordinate system is set on the sound source surface, then the coordinates of the sound source point i in the rectangular coordinate system can be expressed as (x si ,y si ,z si When the rigid surface is parallel to the oyz surface and the distance between it and the origin o in the x-direction is D, the coordinates of the mirror source point can be expressed as (2D-x). si ,y si ,z si When the rigid surface is rotated by an angle θ around the (D,0) axis, the formula for determining the position coordinates of the mirror source is as follows:

[0016] (2Dcos 2 θ-x si cos2θ+y si sin2θ,(x si-D)sin2θ+y si cos2θ,z si );

[0017] Preferably, in S3, based on the distance between the sound source point and the measurement point and the position of the mirror source determined in S1 and S2, the sound source point (x) can be obtained as shown below. si ,y si ,z si ) and measurement point (x) hj ,y hj ,z hj The distance r between ) ij and mirror source point (x' si ,y' si ,z' si ) and measurement point (x) hj ,y hj ,z hj The distance r between ) ij ',

[0018]

[0019] Preferably, in S5, when the number of measurement points is P, the number of sound source points is M, and P < M, N×P sound pressure data are generated after N measurements, which are represented by the following formula:

[0020] (G+G')q=p;

[0021] Where G is the transfer matrix between the sound source and the sound pressure at the measurement point, G' is the transfer matrix between the mirror source and the sound pressure at the measurement point, q is the source intensity vector, and p is the sound pressure vector;

[0022] Alternatively, the relationship between sound pressure and sound source intensity can be directly established based on the sound pressure difference measured with or without rigid boundaries:

[0023] G'q=p 刚性 -p 自由场 ;

[0024] Where, p 刚性 For the sound pressure measurement results with dynamic rigid boundaries, p 自由场 The sound pressure test results at the measuring point are without dynamic boundaries.

[0025] The matrix elements G of the transfer matrix G between the sound source and the sound pressure at the measurement point ij It can be represented as:

[0026]

[0027] Where j is the imaginary part, c is the speed of sound, ρ is the density of the sound propagation medium, k is the wave number, k = 2πf / c, and f is the frequency;

[0028] The matrix elements G' of the transfer matrix between the mirror source point and the measurement point sound pressure are G' and G'. i ' j It can be represented as:

[0029]

[0030] Preferably, the source intensity vector q calculated by the least squares method in S6 is:

[0031]

[0032] The source intensity vector q calculated by the Tikhonov regularization method is:

[0033]

[0034] After obtaining the source intensity vector q, the sound pressure information at any position in the sound field is reconstructed by p = Gq, thus completing the sound field reconstruction.

[0035] Therefore, the present invention employs the above-mentioned dynamic mirror boundary acoustic holographic testing device and method, which has the following beneficial effects:

[0036] (1) Without increasing the number of sensors, the amount of test information increases, thus improving the accuracy of sound field reconstruction;

[0037] (2) Fixed measuring points combined with rigid boundary motion, the sound pressure data of a single movement of the rigid surface increases the total number of sensors, which reduces the measurement time compared to moving the sensors point by point.

[0038] (3) Relying on a small number of fixed sound pressure sensors and controllable rigid boundaries reduces the difficulty of multi-sensor synchronization and calibration;

[0039] (4) The mirror principle is used to introduce a position-adjustable mirror source point, which is not limited by the holographic aperture requirement.

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0041] Figure 1 This is a three-dimensional structural schematic diagram of a dynamic mirrored boundary acoustic holographic testing device according to the present invention;

[0042] Figure 2 This is a schematic diagram of the sound field superposition after rigid surface translation in the dynamic mirror boundary acoustic holographic testing method of the present invention;

[0043] Figure 3 This is a schematic diagram of the sound field superposition after rigid surface rotation in the dynamic mirror boundary acoustic holographic testing method of the present invention;

[0044] Figure 4The results show a comparison of the sound field reconstruction accuracy between the dynamic mirror boundary acoustic holography test method and the Tikhonov regularized equivalent source acoustic holography method.

[0045] Figure Labels

[0046] 1. Translation track; 2. Testing mechanism; 3. First motor; 4. Lead screw; 5. First base; 6. Slider; 7. Slide groove; 8. Second motor; 9. Rotating assembly; 10. Second base; 11. Rigid plate. Detailed Implementation

[0047] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0048] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0049] Example 1

[0050] like Figure 1 As shown, this invention provides a dynamic mirrored boundary acoustic holographic testing device, including a translational track 1. A first driving mechanism is provided on one side of the translational track 1, and the first driving mechanism is connected to a first base 5. The first driving mechanism can drive the first base 5 to slide along the translational track 1. The first driving mechanism includes a first motor 3, which is installed on one side of the translational track 1 and provides power to the first driving mechanism. The first motor 3 is connected to a lead screw 4, and the bottom of the first base 5 is connected to the lead screw 4. The bottom of the first base 5 is provided with a threaded hole that mates with the lead screw 4. The first motor 3 can drive the lead screw 4 to rotate, and the rotation of the lead screw 4 can cause the first base 5 to move along the lead screw 4. Slider 6 is provided at both ends of the bottom of the first base 5, and a sliding groove 7 that mates with the slider 6 is provided on the translational track 1. When the first base 5 moves along the lead screw 4, it can drive the slider 6 to slide along the sliding groove 7, thereby keeping the first base 5 stable. A testing mechanism 2 is provided on the other side of the translational track 1. A sound pressure sensor is installed on the testing mechanism 2. The sound pressure sensor, as a sensitive element, can convert the sound pressure changes in the sound field into electrical signals, thereby obtaining the sound pressure information in the sound field.

[0051] A second drive mechanism is mounted on the first base 5 and connected to the second base 10. The top of the second base 10 is connected to a rigid plate 11. The second drive mechanism can drive the second base 10 to rotate, thereby causing the rigid plate 11 to rotate. The second drive mechanism includes a second motor 8, which provides power to the second drive mechanism. The second motor 8 is mounted on the first base 5, and the first base 5 provides support for the second motor 8. The second motor 8 is connected to a rotating assembly 9, which is connected to the second base 10. The second motor 8 can drive the second base 10 to rotate through the rotating assembly 9.

[0052] This invention provides a dynamic mirrored boundary acoustic holographic testing method, specifically including the following steps:

[0053] S1. Determine the number of equivalent sources of the vibrating structure and the position between the sound source surface and the holographic measurement surface;

[0054] S2. Set and adjust the translation and rotation angle of the rigid surface to obtain the position coordinates of the sound source and the mirror source;

[0055] If the origin of the coordinate system is set on the surface of the sound source, then the coordinates of the sound source point i in the rectangular coordinate system can be expressed as (x... si ,y si ,z si When the rigid surface is parallel to the oyz surface and the distance between it and the origin o in the x-direction is D, the coordinates of the mirror source point can be expressed as (2D-x). si ,y si ,z si When the rigid surface is rotated by an angle θ around the (D,0) axis, the formula for determining the position coordinates of the mirror source is as follows:

[0056] (2Dcos 2 θ-x si cos2θ+y si sin2θ,(x si -D)sin2θ+y si cos2θ,z si );

[0057] S3. Determine the number and position coordinates of the sound pressure sensors on the holographic measurement surface, and calculate the distance between the sound source point and the mirror source point and the measurement point;

[0058] Based on the distance between the sound source point and the measurement point determined by S1 and S2, and the location of the mirror source, the sound source point (x) can be obtained as shown below. si ,y si ,z si ) and measurement point (x) hj ,y hj ,z hj The distance r between )ij and mirror source point (x' si ,y' si ,z' si ) and measurement point (x) hj ,y hj ,z hj The distance r between ) ij ',

[0059]

[0060] S4. Perform sound pressure measurement at the measurement points determined in S3;

[0061] S5, such as Figure 2 and Figure 3 As shown, adjust the translation and rotation angle of the rigid surface individually or in combination to obtain the adjusted mirror source position coordinates. Repeat S3 and S4 to obtain the measurement results. Perform multiple measurements until the sound pressure and source strength vector acoustic transfer matrix of the holographic surface measurement are at full rank or the condition number of the acoustic transfer matrix changes little after the test.

[0062] When the number of measurement points is P, the number of sound source points is M, and P < M, N measurements will generate N×P sound pressure data points, which can be represented by the following formula:

[0063] (G+G')q=p;

[0064] Where G is the transfer matrix between the sound source and the sound pressure at the measurement point, G' is the transfer matrix between the mirror source and the sound pressure at the measurement point, q is the source intensity vector, and p is the sound pressure vector;

[0065] Alternatively, the relationship between sound pressure and sound source intensity can be directly established based on the sound pressure difference measured with or without rigid boundaries:

[0066] G'q=p 刚性 -p 自由场 ;

[0067] Where, p 刚性 For the sound pressure measurement results with dynamic rigid boundaries, p 自由场 The sound pressure test results at the measuring point are without dynamic boundaries.

[0068] The matrix elements G of the transfer matrix G between the sound source and the sound pressure at the measurement point ij It can be represented as:

[0069]

[0070] Where j is the imaginary part, c is the speed of sound, ρ is the density of the sound propagation medium, k is the wave number, k = 2πf / c, and f is the frequency;

[0071] The matrix elements G' of the transfer matrix between the mirror source point and the measurement point sound pressure are G' and G'.i ' j It can be represented as:

[0072]

[0073] Here, G' represents the ideal rigid surface. In actual use, G' can be adjusted based on measured or simulated results to accommodate imperfect conditions such as boundary sound diffraction caused by a rigid surface of finite size and surface sound absorption caused by factors like wall impedance. After each adjustment of the rigid surface position, r... ij The change causes a nonlinear change in G, so the newly generated equation is linearly independent of the original equation.

[0074] S6. Using the measurement results obtained in S4, calculate the source intensity vector by combining the least squares method or the regularization method.

[0075] The source intensity vector q calculated by the least squares method is:

[0076]

[0077] The source intensity vector q calculated by the Tikhonov regularization method is:

[0078]

[0079] After obtaining the source intensity vector q, the sound pressure information at any position in the sound field is reconstructed by p = Gq, thus completing the sound field reconstruction.

[0080] Comparing the sound field reconstruction accuracy of the dynamic mirror boundary acoustic holography test method and the Tikhonov regularized equivalent source acoustic holography method, such as... Figure 4 As shown, the acoustic reconstruction error of the dynamic rigid surface acoustic holography method and the Tikhonov regularized equivalent source acoustic holography method varies with frequency. The acoustic reconstruction error of the dynamic rigid surface acoustic holography method remains relatively stable across the entire frequency range, consistently maintaining a low level with minor fluctuations around 2%, indicating that this method is less affected by frequency changes and exhibits relatively stable acoustic reconstruction accuracy. The acoustic reconstruction error of the Tikhonov regularized equivalent source acoustic holography method shows a significant upward trend as the frequency gradually increases from 200Hz to 2000Hz, rising from approximately 8.5% to nearly 17%, indicating that the acoustic reconstruction accuracy of this method is significantly affected by frequency, with the reconstruction error increasing substantially at higher frequencies. Within the tested frequency range, the acoustic reconstruction accuracy of the dynamic mirror boundary acoustic holography method is significantly better than that of the Tikhonov regularized equivalent source acoustic holography method, especially in the high-frequency region, where the advantages of the dynamic rigid surface acoustic holography are more pronounced, while the Tikhonov regularized method experiences a substantial increase in reconstruction error at high frequencies.

[0081] Therefore, the present invention employs the aforementioned dynamic mirror boundary acoustic holographic testing device and method, which increases the amount of test information and improves the accuracy of sound field reconstruction without increasing the number of sensors; the fixed measurement point combined with rigid boundary movement increases the sound pressure data of a single movement of the rigid surface by the total number of sensors, reducing the measurement time compared to moving the sensors point by point; it relies on a small number of fixed sound pressure sensors and a controllable rigid boundary, reducing the difficulty of multi-sensor synchronization and calibration; and it utilizes the mirror principle to introduce a position-adjustable mirror source point, which is not limited by the holographic aperture requirements.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A dynamic mirror boundary acoustic holographic testing method performed by a dynamic mirror boundary acoustic holographic testing device, wherein the dynamic mirror boundary acoustic holographic testing device includes a translation track, a first driving mechanism is provided on one side of the translation track, a testing mechanism is provided on the other side of the translation track, the first driving mechanism is connected to a first base, a second driving mechanism is installed on the first base, the second driving mechanism is connected to a second base, and the top of the second base is connected to a rigid plate. The first drive mechanism includes a first motor, which is mounted on one side of the translation track and connected to a lead screw. The bottom of the first base is also connected to the lead screw. The second drive mechanism includes a second motor, which is mounted on the first base and connected to a rotating component, which is also connected to the second base. The first base has sliders at both ends of its bottom, and the translation track has grooves that cooperate with the sliders; Its features are: The dynamic mirror boundary acoustic holographic testing method specifically includes the following steps: S1. Determine the number of equivalent sources of the vibrating structure and the position between the sound source surface and the holographic measurement surface; S2. Set and adjust the translation and rotation angle of the rigid surface to obtain the position coordinates of the sound source and the mirror source; S3. Determine the number and position coordinates of the sound pressure sensors on the holographic measurement surface, and calculate the distance between the sound source point and the mirror source point and the measurement point; S4. Perform sound pressure measurement at the measurement points determined in S3; S5. Adjust the translation and rotation angle of the rigid surface individually or in combination to obtain the adjusted mirror source position coordinates. Repeat S3 and S4 to obtain the measurement results. Take multiple measurements until the sound pressure and source strength vector acoustic transfer matrix of the holographic surface measurement are full rank or the condition number of the acoustic transfer matrix changes little after the test. S6. Using the measurement results obtained in S4, calculate the source intensity vector of the sound source by combining the least squares method or the regularization method.

2. The dynamic mirror boundary acoustic holographic testing method performed by the dynamic mirror boundary acoustic holographic testing device according to claim 1, characterized in that: In S2, the origin of the coordinate system is set on the surface of the sound source, then the sound source point... The coordinates in a rectangular coordinate system can be expressed as: When the rigid surface is parallel to the oyz surface, the distance between it and the origin o in the x-direction is... Then the coordinates of the mirror source point can be expressed as When the rigid surface is around Axis rotation angle The formula for determining the coordinates of the mirror source is as follows: 。 3. The dynamic mirror boundary acoustic holographic testing method performed by the dynamic mirror boundary acoustic holographic testing device according to claim 2, characterized in that: Based on the distance between the sound source point and the measurement point, and the location of the mirror source determined in S1 and S2, the sound source point can be obtained as shown below in S3. With measurement point Distance between and mirror source With measurement point Distance between , ； 。 4. The dynamic mirror boundary acoustic holographic testing method performed by the dynamic mirror boundary acoustic holographic testing device according to claim 3, characterized in that: In S5, when the number of measurement points is The number of sound source points is ,and When, after N measurements, the following is generated The sound pressure data are used to construct the following formula: ； in, This is the transfer matrix between the sound source and the sound pressure at the measurement point. This is the transfer matrix between the sound pressure at the mirror source point and the measurement point. The source intensity vector is the sound source vector. This is the sound pressure vector; Alternatively, the relationship between sound pressure and sound source intensity can be directly established based on the sound pressure difference measured with or without rigid boundaries: ； in, The sound pressure measurement results are for the presence of dynamic rigid boundaries. The sound pressure test results at the measuring point are without dynamic boundaries. The transfer matrix between the sound source and the sound pressure at the measurement point matrix elements It can be represented as: ； in, The virtual part, For the speed of sound, For the density of the sound propagation medium, For wave number, , For frequency; Transfer matrix between the sound pressure at the mirror source and the measurement point matrix elements It can be represented as: 。 5. The dynamic mirror boundary acoustic holographic testing method performed by the dynamic mirror boundary acoustic holographic testing device according to claim 4, characterized in that: The source intensity vector calculated by the least squares method in S6 for: ； The source intensity vector calculated using the Tikhonov regularization method for: ； Obtaining the source intensity vector After that, by Reconstruct the sound pressure information at any location within the sound field to complete the sound field reconstruction.

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