An equivalent source sound field positioning method and system based on sparse sound intensity measurement

Abstract

The present application belongs to the field of sound field reconstruction and sound source identification technology, and discloses an equivalent source sound field positioning method and system based on sparse sound intensity measurement, which acquires the complex sound pressure and complex particle velocity at the measurement point on the holographic surface through a vector sensor array, and calculates the measured sound intensity vector; constructs a sound intensity transfer matrix based on the equivalent source method, establishes a linear measurement equation between the measured sound intensity vector and the equivalent source intensity vector; by using the spatial sparsity of the equivalent source intensity, the solving of the equivalent source intensity vector is converted into an L1 norm sparse optimization problem, and a convex optimization algorithm is used to solve it to obtain the optimal equivalent source intensity vector; based on the optimal equivalent source intensity vector, the acoustic quantity at any point in the target sound field is reconstructed by combining the free field Green function. The present application uses the active component of the sound intensity vector to suppress non-related noise, improves the ill-conditioned inversion by combining the compressive sensing theory, and can realize high robustness and high precision sound source positioning and sound field reconstruction without reference microphones.

Description

Technical Field

[0001] This invention belongs to the field of sound field reconstruction and sound source identification technology, and particularly relates to an equivalent source sound field localization method and system based on sparse sound intensity measurement. Background Technology

[0002] In the fields of industrial noise diagnostics and underwater acoustics, accurate simulation of sound fields and precise localization of sound sources have always been key research focuses. The equivalent source method, as a numerical solution for solving the radiated or scattered sound field of a target, is based on the core principle that the sound field generated by a target of any shape can be represented by the superposition of sound fields generated by several equivalent source intensities on a virtual surface. This method effectively avoids the singular integral calculation problem faced by other methods when dealing with complex targets, demonstrating significant advantages in near-field acoustic holography research.

[0003] The equivalent source method can achieve sound source localization with fewer measurement points. Existing equivalent source methods mostly rely on measuring sound pressure or particle velocity on a holographic surface for sound source localization. Traditional systems often require a large number of measurement points. Furthermore, in industrial noise measurement applications, if the number of channels is insufficient, additional reference microphones are needed to use scanning methods to obtain a larger number of measurement points. This not only increases measurement costs and computational complexity but also places extremely high demands on measurement equipment and computing resources. Simultaneously, in complex sound field environments with background noise or incoherent sound sources, sound pressure-based inversion methods are susceptible to noise interference, exacerbating ill-conditioned problems and reducing reconstruction accuracy. Sound intensity vectors, on the other hand, can directly indicate the direction of sound energy flow and have a natural ability to suppress unrelated noise. They can also perform sound source localization without reference microphones. However, currently, there is a lack of a systematic technical solution that combines sparse sound intensity measurement with the equivalent source method to achieve efficient and robust sound field reconstruction.

[0004] The theoretical basis of sound intensity measurement can be traced back to the concept of sound energy flow proposed by Olson in 1932. However, due to limitations in early electronic technology and sensor performance, it was not put into practical use until the late 1970s. Early mainstream PP probes (dual pressure microphones) approximate particle velocity through finite difference, which suffers from phase mismatch, finite difference error, and low-frequency limitations in strong reactive fields. In the 1990s, the Dutch company Microflown developed the PU probe (pressure-velocity combination) based on a hot-wire particle velocity sensor (U-probe), achieving direct measurement of particle velocity and significantly improving measurement accuracy and applicability in high reverberation, near-field, and broadband sound sources.

[0005] However, the core bottleneck of PU probes lies in the lack of a standard reference sensor for u-probes, leading to calibration difficulties. Simultaneously, industrial broadband and incoherent sound sources often cannot provide reference signals, and traditional NAH (near-field acoustic holography) requires synchronous sampling or a reference microphone, limiting its field applications. To address this, in 1988, Loyau et al. proposed Broadband Acoustic Holography Based on Sound Intensity Measurement (BAHIM), which reconstructs the complex sound pressure phase on the holographic surface through secondary pressure and tangential sound intensity components, requiring no reference signal and suitable for broadband industrial noise sources. Subsequent developments include 3D PU probes, field separation techniques combining NAH and sound intensity, and NAH calibration methods based on the Equivalent Source Method (ESM), further solving problems such as interference source separation and calibration of unknown acoustic impedance fields.

[0006] Internationally, sound intensity measurement technology has matured and achieved commercial application. Companies such as Microflown have launched PU probes, 3D USP probes, and array systems covering 20 Hz to 14 kHz, supporting real-time sound intensity vector visualization, in-situ sound power measurement, and noise source localization. These technologies are widely used in noise diagnosis of automotive, aviation, marine, and industrial equipment. BAHIM and its extensions (such as 3D-BAHIM) have proven effective in handling broadband, incoherent, and complex sound fields with interference sources. Related research has been concentrated in journals such as J. Acoust. Soc. Am. and Acta Acustica. In recent years, research has shifted its focus to high-frequency / high-temperature environmental probes, calibration methods combined with laser / particle image velocimetry (PIV), and volumetric sound intensity vector imaging technology, driving the evolution from single-point measurement to full-field reconstruction.

[0007] In recent years, driven by the demands of noise pollution control, precision manufacturing, and the development of high-end equipment, teams led by Zhang Yongbin and Bi Chuanxing at Hefei University of Technology have made systematic progress in NAH calibration of particle velocity sensors, 3D-BAHIM extension, and sound field separation technology. They have solved the challenges of u-probe calibration under unknown acoustic impedance fields and the problem of interference source separation. Related findings have been published in journals such as Acta Acustica united with Acustica and J. Acoust. Soc. Am. Other universities and research institutions are also conducting research on sound intensity probe optimization, broadband holographic reconstruction, and engineering applications (such as bridge / ship noise and industrial equipment diagnosis), forming a preliminary system from theoretical modeling to field testing. However, breakthroughs in core sensor technology and broadband phase reconstruction algorithms are urgently needed.

[0008] Sound intensity measurement technology overcomes the limitations of traditional methods, providing an efficient, reference-free measurement means for broadband, incoherent, and complex industrial sound sources. Furthermore, it supports in-situ measurement of noise source noise (NAH), sound power, and noise source visualization, thus promoting noise control and product acoustic optimization. Research addressing the difficulties in calibrating existing u-probes and the need for reference signals in industrial measurements can provide new methods for industrial noise measurement, with broad engineering application prospects.

[0009] Therefore, how to utilize the physical advantages of sound intensity vectors, combine them with compressed sensing theory to reduce the number of measurement points, improve inversion stability, and construct a complete sound field reconstruction system is a technical problem that urgently needs to be solved in this field.

[0010] Traditional equivalent source methods typically require simultaneous measurement of sound field information on a plane or cylindrical surface. This necessitates a large number of microphones and data acquisition channels, leading to high costs. A common solution is to use data from a fixed-position microphone as a reference signal, then employ a small array of microphones to acquire data across the entire surface using a scanning method. This method is inefficient and susceptible to non-uniform, uncorrelated noise in construction environments, affecting measurement accuracy and potentially causing localization failures. Furthermore, traditional sound pressure methods suffer from severe ill-conditioned problems when determining the equivalent source strength, resulting in poor localization and reconstruction stability.

[0011] In summary, although existing technologies have made some progress in the field of sound source localization, they still face many challenges in practical engineering applications. Therefore, how to utilize the suppression characteristics of sound intensity vectors on uncorrelated noise, combined with compressed sensing theory to significantly reduce the number of measurement points, improve inversion ill-conditioning, and construct a complete equivalent source sound field reconstruction system are technical problems that urgently need to be solved in this field. Summary of the Invention

[0012] The purpose of this invention is to provide an equivalent source sound field localization method and system based on sparse sound intensity measurement to solve the above-mentioned technical problems.

[0013] To address the aforementioned technical problems, the present invention provides a specific technical solution for an equivalent source sound field localization method and system based on sparse sound intensity measurement, as follows:

[0014] A method for locating an equivalent source sound field based on sparse sound intensity measurement includes the following steps: Step 1: Collect complex sound pressure and complex particle velocity at the measurement point on the holographic surface using a vector sensor array, and calculate the measured sound intensity vector; Step 2: Construct a sound intensity transfer matrix based on the equivalent source method, and establish a linear measurement equation between the measured sound intensity vector and the equivalent source intensity vector; Step 3: Utilize the spatial sparsity of the equivalent source intensity to transform the solution of the equivalent source intensity vector into an L1 norm sparse optimization problem, and use a convex optimization algorithm to solve it to obtain the optimal equivalent source intensity vector; Step 4: Based on the optimal equivalent source intensity vector, combine it with the free-field Green's function to reconstruct the acoustic quantities at any point in the target sound field.

[0015] Furthermore, step 1 includes the following steps:

[0016] Step 1.1: Arrange a vector sensor array in a uniform or non-uniform grid within the near-field radiation region of the sound source;

[0017] Step 1.2: Sample the array to obtain the time-domain sound pressure and vibration velocity signals at each measurement point, and convert them into frequency-domain complex sound pressure and complex particle vibration velocity through Fourier transform;

[0018] Step 1.3: Calculate the x-component of the sound intensity vector at the m-th measurement point.

[0019] Furthermore, step 2 includes the following steps:

[0020] Step 2.1: Arrange equivalent sources: Arrange equivalent source surfaces inside or near the surface of the target sound source, and place N virtual monopole sources;

[0021] Step 2.2: Establish the sound pressure transfer matrix between the complex sound pressure level and the equivalent source intensity;

[0022] Step 2.3: Establish the velocity transfer matrix between the complex particle velocity and the equivalent source intensity, then substitute both into the sound intensity calculation formula and rearrange to obtain the sound intensity transfer matrix.

[0023] Step 2.4: Establish a linear equation: The measured sound intensity vector is equal to the sound intensity transfer matrix multiplied by the square of the equivalent source intensity vector.

[0024] Furthermore, the objective of solving the L1 norm sparse optimization problem in step 3 is to find the equivalent source intensity vector with the minimum L1 norm, provided that the error between the measured sound intensity vector and the theoretical sound intensity vector reconstructed from the equivalent source intensity vector does not exceed a preset noise tolerance.

[0025] Furthermore, the preset noise tolerance is determined by the measured signal-to-noise ratio. Specifically, when the noise standard deviation can be estimated, the preset noise tolerance is taken as the square root of the number of measurement points multiplied by the noise standard deviation; when the noise level cannot be accurately estimated, the ten-fold cross-validation criterion is used to determine it.

[0026] Furthermore, the convex optimization algorithm described in step 3 adopts either the convex optimization method based on the CVX toolbox or the minimum absolute shrinkage and selection operator algorithm; wherein, the convex optimization method based on the CVX toolbox transforms the L1 norm sparse optimization problem into a second-order cone programming form and then calls the underlying solver to solve it.

[0027] Furthermore, in step 4, the acoustic quantities at any point in the reconstructed target sound field include the square of the sound pressure amplitude or the sound intensity amplitude. Specifically, the optimal equivalent source strength vector is superimposed with the free field Green's function at the reconstruction point to obtain the complex sound pressure and complex particle velocity at the reconstruction point, and then the sound intensity amplitude at that point is calculated.

[0028] This invention also discloses an equivalent source sound field localization system based on sparse sound intensity measurement, used to execute the method described above, comprising: a sound intensity acquisition module, used to acquire complex sound pressure and complex particle velocity at measurement points on a holographic surface through a vector sensor array, and calculate the measured sound intensity vector; an equivalent source model construction module, used to construct a sound intensity transfer matrix based on the equivalent source method, and establish a linear measurement equation between the measured sound intensity vector and the equivalent source intensity vector; a compressed sensing solution module, used to utilize the spatial sparsity of the equivalent source intensity to transform the solution of the equivalent source intensity vector into an L1 norm sparse optimization problem, and use a convex optimization algorithm to solve it to obtain the optimal equivalent source intensity vector; and a sound field reconstruction module, used to reconstruct the acoustic quantities at any point in the target sound field based on the optimal equivalent source intensity vector and combined with the free-field Green's function.

[0029] The equivalent source sound field localization method and system based on sparse sound intensity measurement of the present invention has the following advantages:

[0030] (1) This invention utilizes the physical advantages of sound intensity vectors to directly construct a linear measurement model through sound intensity vectors. The active component of sound intensity has a natural ability to suppress uncorrelated noise between measurement channels, making the inversion results more robust in noisy environments and significantly improving the system's anti-interference ability in complex sound field environments.

[0031] (2) This invention fully utilizes the sparsity of actual sound sources in the spatial domain and, combined with compressed sensing theory, transforms the solution of equivalent source strength into an L1 norm sparse optimization problem. Compared with traditional methods, this invention significantly reduces the number of measurement points required, thereby reducing data acquisition costs and computational resource requirements while ensuring high-resolution sound source localization and sound field reconstruction accuracy.

[0032] (3) The equation system constructed by the inversion method based on sound intensity measurement has a better condition number, which can effectively avoid the serious ill-conditioning problem in the traditional sound pressure method, improve the numerical stability of the inversion process, and provide a reliable technical solution for broadband, incoherent industrial sound source localization and visualization in engineering applications.

[0033] (4) The inversion method based on sound intensity measurement can achieve measurement of any surface without the need for a reference microphone, which can effectively avoid the problem that the scanning method must have a reference signal, improve the stability of engineering measurement, and provide a reliable technical solution for broadband, incoherent industrial sound source localization and visualization in engineering applications. Attached Figure Description

[0034] Figure 1 This is a system block diagram of the sound field reconstruction system based on sparse sound intensity measurement proposed in this invention.

[0035] Figure 2 This is a schematic diagram of the source intensity amplitude reconstructed based on the sparse sound intensity measurement method proposed in this invention.

[0036] Figure 3 This is a schematic diagram of the sound intensity amplitude on the reconstructed surface based on the sparse sound intensity measurement method proposed in this invention. Detailed Implementation

[0037] To better understand the purpose, structure, and function of this invention, the following detailed description of an equivalent source sound field localization method and system based on sparse sound intensity measurement is provided in conjunction with the accompanying drawings.

[0038] Sound intensity, as a vector, possesses the following unique advantages: Sound intensity is a sound energy flux density vector, directly pointing in the direction of sound energy propagation, thus possessing directional information. This helps to more accurately locate and identify sound sources, especially in environments with multiple sound sources or reflections. The active (real) component of sound intensity has a natural ability to suppress unrelated noise (such as electrical noise and unrelated background noise) between measurement channels, because the sound intensity contribution of unrelated noise is zero. This makes the inversion results more robust in noisy environments. Sound intensity-based inversion methods directly utilize the sound intensity vector, resulting in a better condition number in the constructed equation system, sometimes avoiding serious ill-conditioned problems in traditional sound pressure methods and improving inversion stability. Therefore, this invention uses direct sound intensity measurement for sparse reconstruction to locate sound sources. Figure 1 As shown, the present invention provides an equivalent source sound field localization method based on sparse sound intensity measurement, comprising the following steps:

[0039] Step 1: Sound intensity acquisition: The complex sound pressure and complex particle velocity at the measurement point on the holographic surface are acquired by a vector sensor array, and the measured sound intensity vector is calculated.

[0040] Step 1.1: Arrange a vector sensor array in a uniform or non-uniform grid within the near-field radiation region of the sound source;

[0041] Step 1.2: Sample the array to obtain the time-domain sound pressure and vibration velocity signals at each measurement point, and convert them into frequency-domain complex sound pressure signals via Fourier transform. and the vibration velocity of complex particles (Taking the x-direction as an example, but not limited to this).

[0042] Step 1.3: The x-component of the sound intensity vector at the m-th measurement point. The calculation is as follows:

[0043] (1)

[0044] The superscript H indicates conjugate. This formula reflects the active component of sound intensity and has a natural ability to suppress unrelated noise.

[0045] Step 2: Construct an equivalent source model based on source intensity measurement: Based on the equivalent source method, construct the sound intensity transfer matrix and establish a linear measurement equation between the measured sound intensity vector and the equivalent source intensity vector.

[0046] Step 2.1: Arrange equivalent sources: Arrange equivalent source surfaces inside or near the surface of the target sound source, and place N virtual monopole sources.

[0047] Step 2.2: Define the transfer matrix:

[0048] Complex sound pressure at the m-th measurement point With equivalent source strength The relationship is:

[0049] (2)

[0050] in, This represents the source strength of the nth equivalent source. This represents the sound pressure transfer matrix between the m-th measurement point and the n-th equivalent source. R is the distance between the m-th measurement point and the n-th equivalent source, i is the imaginary unit, and k is the wave number;

[0051] The total sound pressure at measurement point m is a linear superposition of the sound pressures produced by all N equivalent sources. Similarly, the vibration velocity at the m-th measurement point is... The particle velocity at this point in a certain direction (such as the x-direction) is also a linear superposition of the equivalent sources at that point. Therefore, the complex particle velocity at the m-th measurement point is... With equivalent source strength The relationship is:

[0052] (3) Among them, This represents the velocity transfer matrix between the m-th measurement point and the n-th equivalent source. In the formula, Angular velocity, The density is the medium.

[0053] Step 2.3: Construct the sound intensity transfer matrix: Substitute equations (2) and (3) above into the sound intensity calculation formula (1), and rearrange them into a linear form to obtain the sound intensity transfer matrix. The elements are

[0054] (4)

[0055] Step 2.4: Establish a linear equation: Therefore, the vector formed by the sound intensity of all M measurement points on the holographic surface... The square of the equivalent source strength vector The following linear relationship is established between them:

[0056] (5)

[0057] in, For measuring the sound intensity vector in M×1 dimensions, For the sound intensity transfer matrix, .

[0058] Step 3: Compressed sensing solves the inverse problem: Utilizing the spatial sparsity of the equivalent source strength, the solution of the equivalent source strength vector is transformed into an L1 norm sparse optimization problem, and a convex optimization algorithm is used to solve it.

[0059] Sparsity analysis: In a real sound field, the number of truly significant equivalent sources is far less than the total number of virtual sources, i.e. It exhibits spatial sparsity.

[0060] Problem transformation: Solving ill-conditioned linear equations The problem is transformed into a problem of minimizing the L1 norm, and the cost function for solving it is:

[0061] (6)

[0062] in, This is a regularization parameter that controls the balance between the sparsity of the solution and the accuracy of data fitting; its value is determined by the measurement signal-to-noise ratio. Specifically, , where M is the amount of measurement data (number of array elements). The noise standard deviation is estimated by collecting ambient noise data when there is no noise source. σ n ≈0.1 Pa. When the noise level cannot be accurately estimated, the optimal value can be determined using the ten-fold cross-validation criterion. value.

[0063] Solution Algorithm: A convex optimization algorithm (such as the convex optimization method based on the CVX toolbox, the minimum absolute shrinkage and selection operator LASSO) is used to solve the above optimization problem to obtain the square of the optimal equivalent source strength vector. .

[0064] By utilizing the sparsity of the equivalent source strength, the originally difficult-to-solve underdetermined ill-conditioned problem is transformed into finding a solution with the minimum L1 norm under certain noise constraints through formula (6), thereby improving the robustness and accuracy of the underdetermined problem.

[0065] The specific implementation process of the convex optimization method based on the CVX toolbox is as follows:

[0066] 1. Variable definition: complex variables , containing variables to be optimized (Square of the equivalent source strong vector) and the total number of equivalent sources.

[0067] 2. The objective function is:

[0068] in, Variables to be optimized The L1 norm of the sound source is automatically minimized by CVX by taking advantage of the sparsity of the sound source (i.e., most of the equivalent source strength is zero or close to zero), and tends to output a solution containing only a few non-zero elements.

[0069] 3. Constraints

[0070] in, Calculate the L2 norm of the residual vector, which requires that the solution be obtained from the given information. The calculated reconstructed sound intensity and the measured sound intensity The error between them does not exceed the preset noise tolerance. This ensures that the inversion results physically match the measurement data, avoiding overfitting.

[0071] 4. Solution Results and Post-processing

[0072] CVX automatically recognizes this as a convex optimization problem with an L1 norm objective, transforms it into a second-order cone programming (SOCP) form, and then calls the underlying solver (such as SeDuMi or SDPT3) to solve it. After the solution is completed, the variables... The value is assigned to the optimal solution. The optimal objective function value (i.e. the minimized L1 norm value) is stored in cvx_optval.

[0073] Step 4: Sound Field Reconstruction: Based on the Squared Vector of Optimal Equivalent Source Strength By combining the free-field Green's function, the acoustic quantities at any point in the target sound field are reconstructed.

[0074] Step 4.1: Determine the reconstruction point: Select the reconstruction surface of the sound field to be reconstructed, such as the surface of the sound source or any plane in space.

[0075] In a free field, the Green's function only includes direct waves; the table of Green's functions for the free field of sound pressure on the reconstructed surface is defined. , representing the sound pressure transfer matrix between the m-th measurement point and the n-th equivalent source on the reconstructed surface, and the vibration velocity free-field Green's function table. , representing the velocity transfer matrix between the m-th measurement point and the n-th equivalent source on the reconstructed surface. To reconstruct the measurement points on the surface Distance to the sound source;

[0076] Step 4.2: Calculate sound intensity: For the first sound intensity on the reconstructed surface... Each point, its source strength It is composed of the superposition of source strengths contributed by all equivalent sources.

[0077] The process of obtaining the reconstructed sound intensity distribution by combining the free-field Green's function with the optimal equivalent source strength is as follows:

[0078] The square vector of the equivalent source strength of compressed sensing has been obtained. Then the square of the reconstructed sound intensity at a certain point is the sum of the sound intensities produced at that point by all the real equivalent sources. For M measurement points, the real equivalent sources have In the case of the first case, then the second case... Reconstruction sound intensity The formula for calculation is:

[0079] (7)

[0080] in, and These represent the measurement points on the reconstructed surface. The sound pressure and vibration velocity at the point. The square vector of the equivalent source strength The elements in.

[0081] Simplifying equation (7) yields the following:

[0082] (8)

[0083] This method yields the distribution of sound intensity at any point in a real sound field.

[0084] The present invention discloses an equivalent source sound field reconstruction system based on sparse sound intensity measurement, comprising a sound intensity acquisition module, an equivalent source model construction module based on source intensity measurement, a compressed sensing inverse problem solving module, and a sound field reconstruction module.

[0085] The sound intensity acquisition module acquires the complex sound pressure and complex particle velocity at the measurement point on the holographic surface through a vector sensor array, and calculates the measured sound intensity vector.

[0086] The equivalent source model construction module based on source intensity measurement constructs a sound intensity transfer matrix based on the equivalent source method and establishes a linear measurement equation between the measured sound intensity vector and the equivalent source intensity vector.

[0087] The compressed sensing inverse problem solving module utilizes the spatial sparsity of equivalent source strengths to transform the solution of the equivalent source strength vector into an L1 norm sparse optimization problem, and uses a convex optimization algorithm to solve it.

[0088] The sound field reconstruction module is based on the square vector of the optimal equivalent source strength. By combining the free-field Green's function, the acoustic quantities at any point in the target sound field are reconstructed.

[0089] The effectiveness of this invention will be verified below using two monopole sound sources as an example.

[0090] 1. Simulation configuration:

[0091] Sound source setup: Two monopole sound sources, located at (-0.05, 0, 0) m and (0.05, 0, 0) m respectively, with a frequency of 1000 Hz.

[0092] Equivalent source surface: coincides with the sound source surface (for simplified verification), with a range of x, y∈[-0.25, 0.25] m, an equivalent source spacing of 0.1 m, and a total of 36 equivalent sources.

[0093] Holographic surface: located on the z=0.15 m plane, with a measurement point spacing of 0.05 m and a range of x, y∈[-0.25, 0.25] m.

[0094] Measurement points (sparse measurement): 64 points are randomly selected from the regular grid of the holographic surface as sound intensity acquisition points.

[0095] Signal-to-noise ratio: To simulate a real environment, 20 dB of Gaussian white noise is added to the acquired sound pressure signal.

[0096] Reconstructed plane: located on the z=0.10 m plane.

[0097] 2. Implementation steps:

[0098] Sound intensity acquisition: Using a sound intensity acquisition module, according to the formula... Calculate the sound intensity value at measurement point m. .

[0099] Model Construction: The intelligent analysis module constructs a sound intensity transfer matrix based on the locations of the equivalent source and the measurement point. .

[0100] Compressed sensing solution: The compressed sensing module uses L1 norm optimization algorithms (such as BPDN) to solve the sparse optimization problem, obtaining... ,in The diagonal is the square of the equivalent source amplitude.

[0101] Sound field reconstruction: The sound field reconstruction module utilizes the solved optimal source strength Using the free-field Green's function, the source intensity at all points on the reconstructed surface is calculated, and the sound field distribution on the reconstructed surface is obtained.

[0102] 3. Result Evaluation:

[0103] Performance metrics: Reconstruction accuracy is evaluated using the relative root mean square error (RMSE).

[0104] (9)

[0105] in, and These are the squares of the reconstructed sound intensity amplitude on the reconstructed surface and the squares of the theoretical sound intensity amplitude, respectively.

[0106] Results: Under sparse measurement (64 points) and 20dB noise conditions, the reconstruction RMSE of the present invention is 11.9%, which is much lower than the 31.9% of the RMSE of the traditional L2 norm minimization method. Moreover, it can clearly identify the positions of the two sound sources, verifying the advantages of high positioning accuracy and strong robustness.

[0107] In summary, this invention directly reconstructs the squared amplitude of sound pressure, vibration velocity, or sound intensity, omitting phase post-processing steps, thus reducing computational complexity and improving reconstruction efficiency, making it suitable for real-time monitoring. The invention employs source intensity amplitude squared regularization constraints to effectively suppress noise amplification, achieving clear imaging results even in low signal-to-noise ratio environments, enhancing noise suppression capabilities. This invention can output the squared amplitude of sound pressure (potential energy distribution) and active sound intensity (energy flow direction), distinguishing between radiating and non-radiating regions, providing precise data for noise control, and better characterizing the radiation characteristics of sound sources. The sound source localization system based on this measurement system does not require a reference signal; combined with a MEMS array and embedded processing unit, it can realize a portable, low-cost near-field acoustic holographic measurement system, broadening engineering application scenarios.

[0108] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of the present invention.

Claims

1. A method for locating an equivalent source sound field based on sparse sound intensity measurement, characterized in that, Includes the following steps: Step 1: Collect the complex sound pressure and complex particle velocity at the measurement point on the holographic surface using a vector sensor array, and calculate the measured sound intensity vector; Step 1.1: Arrange a vector sensor array in a uniform or non-uniform grid within the near-field radiation region of the sound source; Step 1.2: Sample the array to obtain the time-domain sound pressure and vibration velocity signals at each measurement point, and convert them into frequency-domain complex sound pressure signals via Fourier transform. and the vibration velocity of complex particles ; Step 1.3: The x-component of the sound intensity vector at the m-th measurement point. The calculation is as follows: （1） The superscript H indicates conjugate; this formula reflects the active component of sound intensity and has a natural ability to suppress unrelated noise. Step 2: Based on the equivalent source method, construct the sound intensity transfer matrix and establish a linear measurement equation between the measured sound intensity vector and the equivalent source intensity vector; Step 2.1: Arrange equivalent sources: Arrange equivalent source surfaces inside or near the surface of the target sound source, and place N virtual monopole sources; Step 2.2: Establish complex sound pressure levels With equivalent source strength The sound pressure transmission matrix between , Step 2.3: Establish the vibration velocity of the complex mass. With equivalent source strength The vibration velocity transfer matrix between Then, substitute both into the sound intensity calculation formula (1) to obtain the sound intensity transfer matrix; Step 2.4: Establish a linear equation: Therefore, the vector formed by the sound intensity of all M measurement points on the holographic surface... The square of the equivalent source strength vector The following linear relationship is established between them: (5) in, For the sound intensity transfer matrix, ; Step 3: Utilize the spatial sparsity of the equivalent source strength to transform the solution of the equivalent source strength vector into an L1 norm sparse optimization problem, and use a convex optimization algorithm to solve it to obtain the optimal equivalent source strength vector. The objective of solving the L1 norm sparse optimization problem is to find the equivalent source intensity vector with the smallest L1 norm, provided that the error between the measured sound intensity vector and the theoretical sound intensity vector reconstructed from the equivalent source intensity vector does not exceed a preset noise tolerance. Step 4: Based on the optimal equivalent source strength vector, and combined with the free-field Green's function, reconstruct the acoustic quantities at any point in the target sound field; In step 4, the acoustic quantities at any point in the reconstructed target sound field include the square of the sound pressure amplitude or the sound intensity amplitude. Specifically, the optimal equivalent source strength vector is superimposed with the free field Green's function at the reconstruction point to obtain the complex sound pressure and complex particle velocity at the reconstruction point, and then the sound intensity amplitude at that point is calculated.

2. The equivalent source sound field localization method based on sparse sound intensity measurement according to claim 1, characterized in that, The convex optimization algorithm adopts either the convex optimization method based on the CVX toolbox or the minimum absolute shrinkage and selection operator algorithm; wherein, the convex optimization method based on the CVX toolbox transforms the L1 norm sparse optimization problem into a second-order cone programming form and then calls the underlying solver to solve it.

3. An equivalent source sound field localization system based on sparse sound intensity measurement, used to perform the method as described in any one of claims 1-2, characterized in that, include: The sound intensity acquisition module is used to acquire the complex sound pressure and complex particle velocity at the measurement point on the holographic surface through a vector sensor array, and to calculate the measured sound intensity vector. The equivalent source model construction module is used to construct the sound intensity transfer matrix based on the equivalent source method and establish a linear measurement equation between the measured sound intensity vector and the equivalent source intensity vector. The compressed sensing solution module is used to transform the solution of the equivalent source strength vector into an L1 norm sparse optimization problem by taking advantage of the spatial sparsity of the equivalent source strength, and then using a convex optimization algorithm to solve it and obtain the optimal equivalent source strength vector. The sound field reconstruction module is used to reconstruct the acoustic quantities at any point in the target sound field based on the optimal equivalent source strength vector and the free-field Green's function.

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