A near-field acoustic holography-based equivalent noise source reconstruction method

Abstract

This invention discloses an equivalent noise source reconstruction method based on near-field acoustic holography, relating to the field of rail transit noise testing technology. The invention employs a two-stage architecture of offline modeling and calibration followed by online reconstruction: In the offline stage, near-field sound pressure is collected under normal operating conditions using multiple arrays. After Doppler correction, acoustic mode dimensionality reduction modeling, two-dimensional sound source decoupling, and adaptive regularization inversion, a multi-condition equivalent sound source modal coefficient database is constructed. In the online stage, the train trajectory is discretized into quasi-static units. Modal coefficients are quickly obtained through database retrieval and radial basis interpolation, reconstructing the equivalent sound source and extrapolating the global sound field. Finally, the cumulative noise effect and the contribution ratio of various sound sources are quantified. This invention solves the problems of high cost of line closures, severe distortion of moving sound sources, low accuracy of multi-source separation, and poor online computation efficiency in existing technologies. It can be widely applied to low-noise rail transit vehicle design, track vibration reduction and noise reduction retrofitting, and environmental impact assessment of noise along the railway line.

Description

Technical Field

[0001] This invention relates to the fields of rail transit noise testing, sound source identification and sound field reconstruction, and in particular to an equivalent noise source reconstruction method based on near-field acoustic holography. Background Technology

[0002] When a train runs at high speed, it simultaneously generates wheel-rail rolling noise, car body aerodynamic noise, and bridge structure vibration radiation noise. These multiple sound sources overlap in space and their sound fields couple and superimpose with each other. Traditional noise testing and sound source identification technologies have several inherent defects. 1. Single-point / few measurement points cannot distinguish the contribution of sound sources: Conventional noise monitoring along the line only collects the total sound pressure of the mixed sound field, which cannot reverse the equivalent sound source distribution of the train body, wheel rail, and bridge surface. The sound source positioning accuracy is poor, and it is impossible to quantify the noise radiation ratio of the train body, wheel rail, and bridge. It is difficult to support the engineering needs of low-noise train body optimization, track vibration reduction and noise reduction transformation, and environmental impact assessment of noise in residential areas along the line.

[0003] 2. Traditional near-field acoustic holography is difficult to adapt to the Doppler effect of moving trains: Static near-field acoustic holography theory is only applicable to stationary sound sources. The high-speed movement of the train produces significant Doppler frequency shift and time-domain amplitude modulation. Directly acquiring the signal will cause frequency distortion and sound field reconstruction distortion. Existing moving sound source correction schemes only perform simple frequency shift compensation and do not combine quasi-static segmentation of the train trajectory, resulting in large reconstruction errors.

[0004] 3. Strict testing conditions and high engineering costs: Existing high-precision sound source identification tests require closing the line and stopping trains to conduct static excitation or low-speed passage tests, interrupting railway operations, with long testing cycles and high economic costs, and cannot reflect the noise radiation characteristics of trains under real high-speed operating conditions.

[0005] Therefore, there is an urgent need for a method and system for reconstructing equivalent noise sources based on near-field acoustic holography to solve the problems in existing technologies. Summary of the Invention

[0006] The present invention aims to solve at least one of the technical problems existing in the prior art, and proposes an equivalent noise source reconstruction method based on near-field acoustic holography.

[0007] In a first aspect, embodiments of the present invention provide a method for reconstructing an equivalent noise source based on near-field acoustic holography, comprising: S100. A planar microphone array is pre-deployed on the track to form a near-field acoustic holographic measurement surface, and the near-field time-domain sound pressure, bridge vibration acceleration signal and train position and speed trigger signal are collected simultaneously under normal train passage. S200. The time-domain sound pressure is deDopplerized and resampled to eliminate the frequency shift and amplitude modulation of the moving sound source. After transformation to the sound source follower reference frame, the frequency domain holographic sound pressure vector is obtained by Fourier transform. Orthogonal acoustic mode basis functions of vehicle structure vibration mode and spatial harmonic combination are introduced to expand the equivalent source strength into a mode superposition form and establish a two-way mapping matrix equation between holographic surface sound pressure and equivalent sound source mode coefficients. S300 uses variational mode decomposition and cross-spectral matrix orthogonalization to separate three independent sound source components—wheel-rail rolling noise, vehicle aerodynamic noise, and bridge structure radiation noise—from the dual dimensions of frequency domain and spatial coherence. For each component, Tikhonov regularization is used to solve for the equivalent sound source mode coefficients, and adaptive closed-loop verification is performed through back-projection residuals. S400. Using train speed, ambient temperature, bridge structure, and vehicle type as index dimensions, the three types of equivalent sound source modal coefficients obtained under various working conditions are classified and stored to construct a standardized equivalent sound source modal coefficient database. S500. Discretize the continuous motion trajectory of the train crossing the bridge into multiple trajectory units with a fixed spatial step size, extract the vehicle speed and position parameters corresponding to each unit, retrieve the equivalent sound source modal coefficient database, and obtain the corresponding equivalent sound source modal coefficients. S600. Substitute the obtained modal coefficients into the acoustic modal model, reconstruct the intensity distribution on the surface of the sound source in reverse, and extrapolate to calculate the sound pressure and sound intensity at any observation point along the track. S700. Employs sound exposure level quantification to measure the cumulative noise effect of the entire train passage process, calculates the radiation contribution ratio of three types of sound sources, and generates an equivalent sound source cloud map and a three-dimensional sound field rendering model.

[0008] Furthermore, in S100, a planar microphone array is pre-deployed on the track to form a near-field acoustic holographic measurement surface. The near-field acoustic holographic measurement surface includes three planar sub-arrays, of which two vertical sub-arrays are arranged opposite each other on both sides of the track, enclosing the train wheel-rail area and the car body; and one horizontal sub-array is suspended below the bottom plate of the box girder to collect the bridge structure radiated noise.

[0009] Furthermore, in S200, deDoppler resampling is performed on the time-domain sound pressure. The deDoppler resampling is based on the frequency shift formula of the moving sound source, and the frequency shift formula is:

[0010] In the formula, For the observation frequency, Let c be the natural frequency of the sound source, c be the speed of sound, and v be the instantaneous speed of the train. The angle between the line connecting the sound source and the measuring point and the direction of train motion.

[0011] Furthermore, in S200, orthogonal acoustic modal basis functions combining vehicle body structural vibration modes and spatial harmonics are introduced to expand the equivalent source strength into a modal superposition form. The form of the acoustic modal expansion is as follows:

[0012] In the formula, For equivalent source strength, Let n be the basis functions of the acoustic mode. For the corresponding modal coefficients, N is the modal order and is much smaller than the total number of equivalent sound source points; The bidirectional mapping matrix equation is: ,in The modal transfer matrix, The matrix for transferring the Green's function. The modality-source strength mapping matrix is... Let be the vector of modal coefficients to be determined. The measured sound pressure vector is the actual sound pressure vector at the measuring point.

[0013] Furthermore, in S300, the constrained optimization objective of the variational mode decomposition is: ; In the formula, For the k-th eigenmode To correspond to the center frequency, This is the core bandwidth metric used to calculate the estimated bandwidth of the k-th mode. For a first-order partial differential operator in the time domain, The unit impulse function, The kernel function of the Hilbert transform. For the k-th band-limited intrinsic mode component, For complex exponential frequency shift operators, This means that the sum of all K modal components must be exactly equal to the original input signal. .

[0014] Furthermore, in S300, the orthogonalization of the cross-spectral matrix is ​​achieved by performing eigenvalue decomposition on the holographic surface cross-spectral matrix, resulting in the following cross-spectral matrix:

[0015] In the formula, For eigenvalues, These are orthogonal eigenvectors, and incoherent sound sources correspond to different principal eigenvectors, thereby achieving spatial coherence decoupling.

[0016] Furthermore, in S300, the objective functional of Tikhonov regularization is:

[0017] In the formula, The modal transfer matrix, Let be the vector of modal coefficients to be determined. The regularization parameter is determined adaptively by the L-curve method, generalized cross-validation, or the bias principle; the obtained modal coefficients are:

[0018] In the formula, the superscript H indicates the conjugate transpose. It is an identity matrix.

[0019] Furthermore, in S500, the equivalent sound source modal coefficient database is retrieved to obtain the corresponding equivalent sound source modal coefficients. Specific methods include: If a matching condition is found, the corresponding equivalent sound source modal coefficients are read directly; if no matching condition is found, radial basis interpolation is used to fit the modal coefficients of the corresponding condition.

[0020] Furthermore, in S700, the formula for calculating the acoustic exposure level is:

[0021] The A-weighted sound exposure level characterizes the total noise energy exposure level of an entire train throughout its journey from entering to leaving the measurement point. For reference time, For reference sound pressure level, Let A be the weighted sound pressure, and [t1,t2] be the time period during which the train passes. The formula for calculating the proportion of sound source contribution is:

[0022] In the formula, For single-type sound source radiating sound energy, , , These are the radiated sound energy from the wheel-rail, vehicle aerodynamics, and bridge structure sound sources, respectively.

[0023] Secondly, the present invention also discloses an electronic device, comprising: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method.

[0024] This invention discloses an equivalent noise source reconstruction method based on near-field acoustic holography. The invention employs a two-stage architecture: offline modeling and calibration, and online reconstruction application. In the offline stage, near-field sound pressure is collected under normal operating conditions using multiple arrays. After Doppler correction, acoustic mode dimensionality reduction modeling, two-dimensional sound source decoupling, and adaptive regularization inversion, a multi-condition equivalent sound source modal coefficient database is constructed. In the online stage, the train trajectory is discretized into quasi-static units. Modal coefficients are quickly obtained through database retrieval and radial basis interpolation. The equivalent sound source is reconstructed and extrapolated to the global sound field, ultimately quantifying the noise accumulation effect and the contribution ratio of various sound sources. This invention solves the problems of high cost of line closures, severe distortion of moving sound sources, low accuracy of multi-source separation, and poor online computation efficiency in existing technologies. It can be widely applied to low-noise vehicle design for rail transit, track vibration reduction and noise reduction retrofitting, and environmental impact assessment of noise along the railway line.

[0025] Compared with the prior art, the present invention has the following beneficial effects: 1. Realistic testing conditions and low engineering costs. All data can be collected under normal high-speed train operation conditions without closing lines, interrupting operations, or requiring external vibration loading. This ensures that the test data is consistent with real operating conditions while significantly reducing testing time and economic costs.

[0026] 2. Excellent motion source processing and high reconstruction accuracy. Doppler distortion is eliminated through time-based resampling in the time dimension, and continuous motion conditions are adapted through quasi-static trajectory segmentation in the spatial dimension. Combined with acoustic mode expansion incorporating prior knowledge of the vehicle structure, the ill-conditioned problem of the transfer matrix is ​​effectively improved, and the resolution loss caused by the large array distance from the surface under the bounded constraint is compensated, significantly improving the reconstruction accuracy.

[0027] 3. Dual-dimensional decoupling ensures high accuracy in sound source separation. Variational mode decomposition enables frequency domain segmentation, while cross-spectral matrix orthogonalization achieves spatial coherence separation. This dual decoupling mechanism effectively distinguishes between three types of noise: spectral overlap, spatial overlap, and accurately quantifies the contribution ratio of each type of sound source.

[0028] 4. Adaptive closed-loop inversion with strong robustness. Tikhonov regularization combined with adaptive parameter selection, along with residual closed-loop verification, can automatically suppress measurement noise amplification, eliminating the need for repeated manual parameter adjustments and maintaining stable reconstruction accuracy even in complex field environments. Attached Figure Description

[0029] Figure 1 A flowchart illustrating an equivalent noise source reconstruction method based on near-field acoustic holography provided in an embodiment of the present invention; Figure 2 This is a schematic diagram showing the specific location and arrangement of the microphone array provided in an embodiment of the present invention; Figure 3 This is a structural block diagram of an electronic device provided in an embodiment of the present invention. Detailed Implementation

[0030] To enable those skilled in the art to better understand the technical solutions of the present invention, exemplary embodiments of the present invention are described below in conjunction with the accompanying drawings, including various details of the embodiments of the present invention to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of the present invention. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0031] Where there is no conflict, the various embodiments of the present invention and the features thereof may be combined with each other.

[0032] As used herein, the term “and / or” includes any and all combinations of one or more related enumerated entries.

[0033] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used herein, the singular forms “a” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that when the terms “comprising” and / or “made of” are used in this specification, the presence of the stated feature, integral, step, operation, element, and / or component is specified, but the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof is not excluded. Terms such as “connected” or “linked” are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect.

[0034] Unless otherwise specified, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art. It will also be understood that terms such as those defined in commonly used dictionaries should be interpreted as having the meaning consistent with their meaning in the context of the relevant art and the invention, and will not be interpreted as having an idealized or overly formal meaning unless expressly so defined herein.

[0035] In the technical solution of this invention, the collection, storage, use, processing, transmission, provision, and disclosure of user personal information all comply with relevant laws and regulations and do not violate public order and good morals. The use of user data in this technical solution follows relevant national laws and regulations (e.g., the "Information Security Technology - Personal Information Security Specification"). For example: appropriate measures are taken for personal information access control; restrictions are imposed on the display of personal information; the purpose of using personal information does not exceed the scope of direct or reasonable association; and explicit identity targeting is eliminated when using personal information to avoid precisely locating a specific individual.

[0036] To address at least one of the technical problems existing in the aforementioned related technologies, the present invention provides an equivalent noise source reconstruction method based on near-field acoustic holography.

[0037] This implementation discloses an equivalent noise source reconstruction method based on near-field acoustic holography, such as... Figure 1 ,include: S100. A planar microphone array is pre-deployed on the track to form a near-field acoustic holographic measurement surface, and the near-field time-domain sound pressure, bridge vibration acceleration signal and train position speed trigger signal are collected simultaneously under normal train passage.

[0038] In S100 of this implementation, a planar microphone array is pre-deployed on the track to form a near-field acoustic holographic measurement surface. The near-field acoustic holographic measurement surface includes three planar sub-arrays, of which two vertical sub-arrays are arranged opposite each other on both sides of the track, enclosing the train wheel-rail area and the car body; and one horizontal sub-array is suspended below the bottom plate of the box girder to collect the bridge structure radiated noise.

[0039] Specifically, the array measurement point spacing and sampling frequency are first determined based on the train type, body length, and normal operating speed. To avoid spatial wavenumber domain aliasing, the spatial sampling spacing d of the microphone measurement points on the holographic surface must satisfy the spatial Nyquist criterion, i.e., it should not exceed half the wavelength corresponding to the highest analysis frequency, as shown in the following formula: (1)

[0040] In the formula, c is the speed of sound. The highest analysis frequency of interest. Taking the upper limit of the main energy of wheel-rail noise fmax=5kHz and the speed of sound c≈343m / s as an example, we can get d≤c / (2·fmax)≈0.034m; during engineering implementation, the sampling points can be arranged in stages according to the frequency band of interest, with a rough measurement of 0.10~0.20m and a fine measurement of 0.03~0.05m.

[0041] The out-of-plane distance *zh* of the holographic surface should be minimized to capture the evanescent wave component carrying high spatial resolution information. According to angular spectrum theory, the sound pressure along the out-of-plane direction satisfies: (2)

[0042] When kx² + ky² > k², kz is a purely imaginary number, and the corresponding high wavenumber component decays exponentially along the out-of-plane direction. To effectively acquire this component, the out-of-plane distance is generally taken as zh ≈ 0.1–0.5 m. The time sampling frequency satisfies the time Nyquist criterion f_s ≥ 2·f_max, and is typically taken as 12.8–51.2 kHz in engineering. Planar microphone arrays are deployed on both sides of the track and under the bridge, forming a near-field acoustic holographic measurement surface. Vibration accelerometers are simultaneously deployed at key nodes of the bridge, and the train's head and tail times are recorded using photoelectric, magnetic, or GPS triggers to invert the instantaneous train speed v(t) and position x(t). The train travels at high speed throughout the entire journey without the need for track closures or external vibration loading.

[0043] The specific location and arrangement of the microphone array in this embodiment are as follows: Figure 2 As shown, the 32m railway simply supported box girder bridge is a double-track integral box girder with a beam height of approximately 3.05m, a total bridge deck width of approximately 12.0m, a double track spacing of 5.0m, and a box girder bottom plate width of approximately 5.5m. The train running direction is defined as the x-axis, the transverse direction as the y-axis, and the vertical direction as the z-axis. The origin of the coordinate system is taken as the top of the rail near the middle of the span being measured. The near-field acoustic holographic measurement surface is composed of three planar sub-arrays: the first is a near-rail side vertical sub-array, arranged along the inner edge of the bridge deck shield (collision barrier) on the outside of the track under test, with the array face vertical and parallel to the train side wall, facing the car body, and its lateral distance from the centerline of the track under test is about 3.5m (i.e. about 1.8m from the side wall of the car body, located outside the railway construction clearance); the second is a line-to-line side vertical sub-array, arranged in the line-to-line area between the two lines (adjacent lines are closed and shut down during the test), with the array face facing the other side of the train, close to the car body, and lateral distance from the centerline of the track under test is about 2.5m (i.e. about 0.8m from the side wall of the car body), provided that the clearance of the train under test is met; the above two vertical sub-arrays are opposite each other on both sides of the track under test, jointly enveloping the wheel-rail source (near the lower rail top) and the aerodynamic source of the car body (along the full height of the car body) of the moving train. The third element is a horizontal sub-array under the bridge, suspended on a temporary truss erected directly below the bottom plate of the box girder being measured. The array surface is horizontal and parallel to the bottom plate of the box girder, facing the bottom of the girder, and is used to collect the low-frequency sound field radiated by the bridge structure.

[0044] The measurement points of each subarray are arranged hierarchically according to the spatial Nyquist criterion. For the frequency band where the main energy of wheel-rail rolling noise is located (approximately ≤1.7kHz), the measurement point spacing is taken as d=0.10m (corresponding to the spatial cutoff frequency c / (2d)≈1.7kHz); for the high-frequency band where vehicle aerodynamic noise is prominent (upper limit approximately 5kHz), a dense measurement point area with a spacing of d=0.03~0.05m is superimposed in the middle of the array to satisfy d≤c / (2·fmax); for the horizontal subarray under the bridge, since the radiation of the bridge structure of interest is mainly low frequency, the measurement point spacing can be relaxed to 0.20m. Each vertical subarray has an aperture of approximately 0.8m along the length (x-direction) and approximately 3.5m vertically (z-direction), vertically covering the entire car body height from the wheel-rail contact area below the rail top to the top of the car. The continuous coverage along the length is equivalently synthesized by the train's motion through Doppler regression and quasi-static segmentation of the trajectory; therefore, its x-direction physical aperture does not need to cover the entire car. The horizontal subarray under the bridge has an aperture of approximately 5.0m transverse to the bridge (covering the full width of the box girder bottom plate) and approximately 2.0m along the bridge direction. The time sampling frequency is set to fs = 25.6kHz, satisfying fs ≥ 2·fmax. Due to railway construction clearance constraints, the distance between the two vertical sub-arrays and the surface cannot reach the optimal 0.1m range for evanescent waves (approximately 0.8–1.8m in this embodiment). However, the sub-array under the bridge, without motion clearance constraints at the bottom of the beam, can achieve a near-field distance between the surface and the surface of 0.3–0.5m. For the vertical sub-arrays with larger surface clearances due to clearance constraints, the loss in spatial resolution is compensated by the acoustic mode expansion in step two, which incorporates the prior vibration modes of the vehicle structure. In addition, vibration accelerometers are installed at the bottom plate, web plate, and rail fasteners in the middle of the span of the box girder under test to collect structural vibration data to assist in the decoupling and closed-loop verification of the bridge structure's sound source. Photoelectric / magnetic / GPS triggers are installed at both ends of the span under test to record the times when the train head and tail pass over the span to invert the instantaneous train speed v(t) and position x(t).

[0045] S200. The time-domain sound pressure is de-Dopplerized and resampled to eliminate the frequency shift and amplitude modulation of the moving sound source. After transformation to the sound source follower reference frame, the frequency domain holographic sound pressure vector is obtained by Fourier transform. Orthogonal acoustic mode basis functions of vehicle structure vibration mode and spatial harmonic combination are introduced to expand the equivalent source strength into a mode superposition form and establish a two-way mapping matrix equation between holographic surface sound pressure and equivalent sound source mode coefficients.

[0046] Specifically, Doppler distortion correction is first performed: based on the instantaneous vehicle speed and the angle between the sound source and the measurement point, the original time-domain sound pressure is resampled to eliminate Doppler frequency shift and amplitude modulation, and the signal is transformed to the sound source follower reference frame; the holographic surface frequency domain sound pressure vector at each analysis frequency is obtained by Fourier transform. The observed frequency and natural frequency of a moving sound source satisfy the following: (3)

[0047] In the formula, For the observation frequency, Let c be the natural frequency of the sound source, c be the speed of sound, and v be the instantaneous speed of the train. Let θ be the angle between the line connecting the sound source and the measuring point and the direction of train motion. Based on this, the original time-domain sound pressure is resampled using the instantaneous train speed v(t) and the angle θ(t) to eliminate Doppler frequency shift and amplitude modulation. The signal is then transformed to the sound source follower reference frame and subjected to Fourier transform to obtain the holographic surface frequency domain sound pressure vector p(ω) at each analysis frequency ω, whose dimension is equal to the number of array measuring points Nm.

[0048] Then, the train body, wheel-rail area, and bridge surface are discretized into Ns equivalent sound source points. The Green's function for a free-field monopole is: (4)

[0049] In the formula For the free field Green's function, This is the three-dimensional position vector of the field point (receiving point / microphone measuring point). The three-dimensional position vector of the sound source point. The angular frequency of the sound wave. Let be the speed of sound in the medium. The sound pressure at the holographic surface is the superposition of contributions from each equivalent source, and can be written in matrix form: (5)

[0050] In the formula, G is the Nm×Ns transfer matrix, and q is the equivalent source strength vector. Directly treating Ns independent source points as unknowns will lead to severe ill-conditioning. Therefore, a physical prior is introduced, and the surface equivalent source strength is expanded on a set of orthogonal spatial basis functions (acoustic modes) Ψn: (6)

[0051] In the formula a n This refers to the equivalent sound source modal coefficients; the basis function Ψn is taken from the combination of the train body structure vibration mode and the spatial harmonic function of the rail transit scene, reducing the number of unknowns from Ns to N (N is much smaller than Ns), and incorporating the physical characteristics of structural radiation. Substituting the modal expansion into the mapping equation, we obtain the mapping equation between the holographic surface sound pressure and the modal coefficients: (7)

[0052] In the formula, Ψ is the mode-source intensity mapping matrix, H=GΨ is the mode transfer matrix, and a is the vector of mode coefficients to be determined. Thus, a bidirectional mapping is established between the holographic surface sound pressure and the equivalent sound source of the train surface partition: the forward mapping from the source to the holographic surface is p=Ha, and the reverse mapping from the holographic surface to the source is a=H. -1 p.

[0053] S300 employs a combination of variational mode decomposition and cross-spectral matrix orthogonalization to separate three independent sound source components—wheel-rail rolling noise, vehicle aerodynamic noise, and bridge structure radiation noise—from both frequency domain and spatial coherence dimensions. For each component, Tikhonov regularization is used to solve for the equivalent sound source mode coefficients, and adaptive closed-loop verification is performed using the back-projection residuals.

[0054] In this embodiment, the measured mixed sound field contains three types of mechanistic sound sources: wheel-rail rolling noise (broadband, main energy concentrated in the mid-frequency range), vehicle aerodynamic noise (broadband, increases strongly with vehicle speed, high frequency prominent), and bridge structure radiated noise (low frequency, structurally transmitted sound). This invention first decouples the mixed sound field and then inverts it separately, using variational mode decomposition combined with cross-spectral matrix orthogonalization to achieve dual decoupling in the frequency domain and space.

[0055] Specifically, variational mode decomposition is used to decompose the time-domain signal f(t) at each measurement point into K band-limited eigenmodes. (center frequency) Its constrained optimization objective is: (8)

[0056] In the formula, For the k-th eigenmode To correspond to the center frequency, This is the core bandwidth metric used to calculate the estimated bandwidth of the k-th mode. For a first-order partial differential operator in the time domain, The unit impulse function, The kernel function of the Hilbert transform. For the k-th band-limited intrinsic mode component, For complex exponential frequency shift operators, This means that the sum of all K modal components must be exactly equal to the original input signal. .

[0057] Then, spatial coherence decoupling is performed, the holographic surface acoustic pressure cross-spectrum matrix is ​​constructed, and eigenvalue decomposition is performed: (9)

[0058] In the formula, For eigenvalues, As orthogonal eigenvectors, incoherent sound sources correspond to different principal eigenvectors, thus achieving spatial coherence decoupling. Incoherent sound sources correspond to mutually orthogonal principal eigenvectors; by inverting according to the principal eigencomponents, local sound source maps belonging to a single mechanism can be obtained, thereby eliminating multi-source coupling and superposition interference. Variational mode decomposition (frequency dimension) and cross-spectral matrix orthogonalization (spatial coherence dimension) are used together to finally separate three independent equivalent sound source component signals: wheel-rail, vehicle aerodynamics, and bridge structure.

[0059] In this embodiment, for each type of component signal obtained from decoupling, its mapping equation p=Ha is solved to obtain the corresponding equivalent source mode coefficients. Since the transfer matrix H has a large condition number and is ill-conditioned, direct inversion would amplify measurement noise; therefore, Tikhonov regularization is used to construct the objective functional: (10)

[0060] In the formula, the first term is the data fitting term, the second term is the regularization term, and λ is the regularization parameter. The modal transfer matrix, Let be the vector of modal coefficients to be determined. The regularization parameter is determined adaptively by the L-curve method, generalized cross-validation, or the bias principle; letting J(a) be minimized, and solving the normal equation using the conjugate transpose, we obtain: (11)

[0061] In the formula, the superscript H indicates the conjugate transpose. Let be the identity matrix. To avoid manual parameter selection, the regularization parameter λ is adaptively determined by the L-curve method, generalized cross-validation, or the bias principle. The generalized cross-validation criterion is to minimize the following equation: (12)

[0062] Engineering implementation can also be achieved using singular value decomposition H=UΣV H Solve in the form of filter factors: (13)

[0063] In the formula, σi represents singular values, and the filter factor fi suppresses small singular values, thereby suppressing noise amplification.

[0064] After obtaining the modal coefficients through inversion, a closed-loop verification is further performed: the equivalent sound source reconstructed from these modal coefficients is forward-projected onto the holographic surface via the mapping equation, and the residual between the projected sound pressure and the measured sound pressure is used as the reconstruction quality criterion. (14)

[0065] When the residual ε exceeds the set threshold, the regularization parameter λ or the modal order N of the acoustic modal basis function is adjusted and the inversion is performed again to make the selected participants consistent with the measured data, thereby realizing adaptive feedback and process closure.

[0066] S400. Using train speed, ambient temperature, bridge structure, and vehicle type as index dimensions, the three types of equivalent sound source modal coefficients obtained under various working conditions are classified and stored to construct a standardized equivalent sound source modal coefficient database.

[0067] Specifically, using train speed v, ambient temperature T, bridge span or type S, and vehicle type as characteristic parameters, the equivalent sound source modal coefficients obtained from decoupling and inversion under various operating conditions are categorized and stored to establish a standardized equivalent sound source modal coefficient database. Ambient temperature is listed separately as a single dimension because the speed of sound changes with temperature, and the relationship is as follows: (15)

[0068] In the formula, T represents the temperature in Celsius. Temperature changes alter the transfer matrix H via the wavenumber k = ω / c(T), therefore the modal coefficients at the same operating speed are not the same at different temperatures, requiring multidimensional storage. Taking T = 20℃ as an example, c ≈ 331.3 × √(1 + 20 / 273.15) ≈ 343.2 m / s. Each database record is a key-value pair: (v, T, S, type) as the key, and the corresponding equivalent sound source modal coefficients for wheel-rail, vehicle body, and bridge as the values. The selection of index dimensions is based on the criterion of real-time retrieval during the application reconstruction phase, ensuring consistency between the index space and the query space.

[0069] S500. Discretize the continuous motion trajectory of the train crossing the bridge into multiple trajectory units with a fixed spatial step size, extract the vehicle speed and position parameters corresponding to each unit, retrieve the equivalent sound source modal coefficient database, and obtain the corresponding equivalent sound source modal coefficients. In this embodiment S500, the equivalent sound source modal coefficient database is retrieved to obtain the corresponding equivalent sound source modal coefficients. The specific method includes: If a matching condition is found, the corresponding equivalent sound source modal coefficients are read directly; if no matching condition is found, radial basis interpolation is used to fit the modal coefficients of the corresponding condition.

[0070] Specifically, the continuous trajectory of the train crossing the bridge or the observation array is discretized into M trajectory units with a fixed spatial step size Δs. The train speed vm and position xm corresponding to each unit are extracted, and the database is searched using (vm, T, S, type). When no matching condition for the train speed of a given unit exists in the database, radial basis function interpolation is used to fit the modal coefficients among existing samples. (16)

[0071] In the formula, the basis function φ can be Gaussian or multiple quadratic, and the weight coefficients wi are obtained from the known sample fitting equation Φw=a known Solve for the problem. The fixed spatial step size should be small enough so that the train sound source within each trajectory unit can be approximated as stationary, thus allowing the application of a static holographic model. Since the inverse problem has already been solved in the modeling and calibration stage, only interpolation is needed here to obtain the equivalent sound source parameters for the continuous motion process, eliminating the need for repeated solutions. This is the key to the online efficiency of this invention.

[0072] S600. Substitute the obtained modal coefficients into the acoustic modal model, reconstruct the intensity distribution on the surface of the sound source in reverse, and extrapolate to calculate the sound pressure and sound intensity at any observation point along the track. Specifically, the modal coefficients obtained through matching or interpolation are substituted into the acoustic modal model to reconstruct the equivalent noise source intensity distribution in the train body and wheel-rail region; then, the sound pressure is extrapolated for any observation point r along the track. (17)

[0073] This formula is the core formula for sound field extrapolation by combining acoustic mode expansion and Green's function superposition. Its physical meaning is: after superimposing the contributions of all equivalent sound sources according to modes, the total sound pressure at any observation point in space is calculated through the sound wave propagation function.

[0074] in, Location of the observation point The frequency domain complex sound pressure level is given by N, where N is the total number of acoustic modes and n is the order number of the acoustic mode. These are the modal coefficients corresponding to the nth acoustic mode. Let J be the total number of discrete equivalent sound source points, and J be the index of the equivalent sound source point. Let be the spatial position vector of the j-th equivalent sound source point. The value of the nth-order acoustic mode basis function at the j-th equivalent sound source point is given. The basis function is composed of the vehicle body structure mode shape and spatial harmonics, and is used to map the mode coefficients to the source strength of the corresponding source point. Let Green's function be a free-field monopole function describing the sound wave radiated from the j-th equivalent sound source, originating from the source point. The relationship between amplitude attenuation and phase change during propagation to the observation point r.

[0075] In this embodiment, the sound intensity is calculated from the sound pressure and particle velocity: (18)

[0076] This formula is the standard formula for calculating the time-averaged sound intensity in a frequency-domain harmonic sound field, representing the sound energy passing through a unit area per unit time. I represents the time-averaged sound intensity at the observation point, and P is the complex amplitude of the frequency-domain sound pressure at the observation point. It is the conjugate complex number of the particle's velocity and complex amplitude.

[0077] S700. Employs sound exposure level quantification to measure the cumulative noise effect of the entire train passage process, calculates the radiation contribution ratio of three types of sound sources, and generates an equivalent sound source cloud map and a three-dimensional sound field rendering model.

[0078] In this embodiment, to quantify the noise accumulation effect of the train's complete passage, the sound exposure level is used to perform a time integral of the square of the sound pressure during the train's passage period: (19)

[0079] In the formula, T0=1s is the reference time, p0=20μPa is the reference sound pressure, pA is the A-weighted sound pressure, and [t1,t2] is the train passage time. This time integral is essentially the sum of the sound fields reconstructed by each trajectory unit along the train passage time. Finally, the radiation contribution ratio of various sound sources such as wheel-rail, car body, and bridge to the sound field along the line is calculated by extrapolating the three types of decoupled components respectively. (20)

[0080] It generates equivalent sound source cloud maps of the train surface, three-dimensional sound field rendering models along the track, and contribution ratio maps of each sound source, which can directly serve low-noise car body optimization, track noise reduction transformation, and environmental impact assessment of noise along the track.

[0081] This embodiment discloses a method for reconstructing equivalent noise sources in rail transit based on near-field acoustic holography. This embodiment adopts a two-stage architecture of offline modeling and calibration followed by online reconstruction application. In the offline stage, near-field sound pressure is collected under normal operating conditions using multiple arrays. After Doppler correction, acoustic mode dimensionality reduction modeling, two-dimensional sound source decoupling, and adaptive regularization inversion, a multi-condition equivalent sound source modal coefficient database is constructed. In the online stage, the train trajectory is discretized into quasi-static units. Modal coefficients are quickly obtained through database retrieval and radial basis interpolation. The equivalent sound source is reconstructed and extrapolated to the global sound field, ultimately quantifying the noise accumulation effect and the contribution ratio of various sound sources. This invention solves the problems of high cost of line closures, severe distortion of moving sound sources, low accuracy of multi-source separation, and poor online computation efficiency in existing technologies. It can be widely applied to low-noise vehicle design for rail transit, track vibration reduction and noise reduction retrofitting, and environmental impact assessment of noise along the line.

[0082] Based on the same inventive concept, embodiments of the present invention also provide an electronic device. Figure 3 A structural block diagram of an electronic device provided in an embodiment of the present invention. (See diagram below.) Figure 3 As shown, an embodiment of the present invention provides an electronic device including: one or more processors 101, a memory 102, and one or more I / O interfaces 103. The memory 102 stores one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement any of the methods described in the above embodiments; the one or more I / O interfaces 103 are connected between the processor and the memory, configured to enable information interaction between the processor and the memory.

[0083] The processor 101 is a device with data processing capabilities, including but not limited to a central processing unit (CPU); the memory 102 is a device with data storage capabilities, including but not limited to random access memory (RAM, more specifically SDRAM, DDR, etc.), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), and flash memory (FLASH); the I / O interface (read / write interface) 103 is connected between the processor 101 and the memory 102, and can realize information interaction between the processor 101 and the memory 102, including but not limited to a data bus (Bus).

[0084] In some embodiments, the processor 101, memory 102, and I / O interface 103 are interconnected via bus 104, and thus connected to other components of the computing device.

[0085] In some embodiments, the one or more processors 101 include a field-programmable gate array.

[0086] This invention also provides a computer-readable medium. The computer-readable medium stores a computer program, which, when executed by a processor, implements the steps of any of the methods described in the above embodiments. The computer-readable storage medium may be a volatile or non-volatile computer-readable storage medium.

[0087] This invention also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in the processor of an electronic device, the processor in the electronic device executes the above-described method.

[0088] Those skilled in the art will understand that all or some of the steps, systems, and apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software can be distributed on a computer-readable storage medium, which may include computer storage media (or non-transitory media) and communication media (or transient media).

[0089] As is known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable program instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), static random access memory (SRAM), flash memory or other memory technologies, portable compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, it is known to those skilled in the art that communication media typically contain computer-readable program instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0090] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0091] The computer program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing state information from the computer-readable program instructions. This electronic circuitry can execute the computer-readable program instructions to implement various aspects of the invention.

[0092] The computer program product described herein can be implemented specifically through hardware, software, or a combination thereof. In one alternative embodiment, the computer program product is specifically embodied in a computer storage medium; in another alternative embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0093] Various aspects of the present invention are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0094] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0095] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0096] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction, which contains one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0097] Example embodiments have been disclosed herein, and while specific terminology has been used, it is for illustrative purposes only and should be construed as such, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of the invention as set forth in the appended claims.

Claims

1. A method for reconstructing an equivalent noise source based on near-field acoustic holography, characterized in that, include: S100. A planar microphone array is pre-deployed on the track to form a near-field acoustic holographic measurement surface, and the near-field time-domain sound pressure, bridge vibration acceleration signal and train position and speed trigger signal are collected simultaneously under normal train passage. S200. The time-domain sound pressure is deDopplerized and resampled to eliminate the frequency shift and amplitude modulation of the moving sound source. After transformation to the sound source follower reference frame, the frequency domain holographic sound pressure vector is obtained by Fourier transform. Orthogonal acoustic mode basis functions of vehicle structure vibration mode and spatial harmonic combination are introduced to expand the equivalent source strength into a mode superposition form and establish a two-way mapping matrix equation between holographic surface sound pressure and equivalent sound source mode coefficients. S300 uses variational mode decomposition and cross-spectral matrix orthogonalization to separate three independent sound source components—wheel-rail rolling noise, vehicle aerodynamic noise, and bridge structure radiation noise—from the dual dimensions of frequency domain and spatial coherence. For each component, Tikhonov regularization is used to solve for the equivalent sound source mode coefficients, and adaptive closed-loop verification is performed through back-projection residuals. S400. Using train speed, ambient temperature, bridge structure, and vehicle type as index dimensions, the three types of equivalent sound source modal coefficients obtained under various working conditions are classified and stored to construct a standardized equivalent sound source modal coefficient database. S500. Discretize the continuous motion trajectory of the train crossing the bridge into multiple trajectory units with a fixed spatial step size, extract the vehicle speed and position parameters corresponding to each unit, retrieve the equivalent sound source modal coefficient database, and obtain the corresponding equivalent sound source modal coefficients. S600. Substitute the obtained modal coefficients into the acoustic modal model, reconstruct the intensity distribution on the surface of the sound source in reverse, and extrapolate to calculate the sound pressure and sound intensity at any observation point along the track. S700. Employs sound exposure level quantification to measure the cumulative noise effect of the entire train passage process, calculates the radiation contribution ratio of three types of sound sources, and generates an equivalent sound source cloud map and a three-dimensional sound field rendering model.

2. The method according to claim 1, characterized in that, In S100, a planar microphone array is pre-installed on the track to form a near-field acoustic holographic measurement surface. The near-field acoustic holographic measurement surface includes three planar sub-arrays. Two vertical sub-arrays are arranged opposite each other on both sides of the track, enclosing the train wheel-rail area and the car body. A horizontal sub-array is suspended below the bottom plate of the box girder to collect the bridge structure radiated noise.

3. The method according to claim 1, characterized in that, In S200, time-domain sound pressure is subjected to deDoppler-resampled time-base resampling. The deDoppler-resampled time-base resampling is based on the frequency shift formula of the moving sound source. The frequency shift formula is: ； In the formula, For the observation frequency, Let c be the natural frequency of the sound source, c be the speed of sound, and v be the instantaneous speed of the train. The angle between the line connecting the sound source and the measuring point and the direction of train motion.

4. The method according to claim 1, characterized in that, In S200, orthogonal acoustic modal basis functions combining vehicle body structural vibration modes and spatial harmonics are introduced to expand the equivalent source strength into a modal superposition form. The form of the acoustic modal expansion is as follows: ； In the formula, For equivalent source strength, Let n be the basis functions of the acoustic mode. For the corresponding modal coefficients, N is the modal order and is much smaller than the total number of equivalent sound source points; The bidirectional mapping matrix equation is: ,in The modal transfer matrix, The matrix for transferring the Green's function. The modality-source strength mapping matrix is... Let be the vector of modal coefficients to be determined. The measured sound pressure vector is the actual sound pressure vector at the measuring point.

5. The method according to claim 1, characterized in that, In S300, the constrained optimization objective of the variational mode decomposition is: ; In the formula, For the k-th eigenmode To correspond to the center frequency, This is the core bandwidth metric used to calculate the estimated bandwidth of the k-th mode. For a first-order partial differential operator in the time domain, The unit impulse function, The kernel function of the Hilbert transform. For the k-th band-limited intrinsic mode component, For complex exponential frequency shift operators, This means that the sum of all K modal components must be exactly equal to the original input signal. .

6. The method according to claim 1, characterized in that, In S300, cross-spectral matrix orthogonalization is achieved by performing eigenvalue decomposition on the holographic surface cross-spectral matrix, resulting in the cross-spectral matrix as follows: ； In the formula, For eigenvalues, These are orthogonal eigenvectors, and incoherent sound sources correspond to different principal eigenvectors, thereby achieving spatial coherence decoupling.

7. The method according to claim 1, characterized in that, In S300, the objective functional of Tikhonov regularization is: ； In the formula, The modal transfer matrix, Let be the vector of modal coefficients to be determined. The measured sound pressure vector at the measuring point. The regularization parameter is determined adaptively by the L-curve method, generalized cross-validation, or the bias principle; the obtained modal coefficients are: ； In the formula, the superscript H indicates the conjugate transpose. It is an identity matrix.

8. The method according to claim 1, characterized in that, In S500, the equivalent sound source modal coefficient database is retrieved to obtain the corresponding equivalent sound source modal coefficients. Specific methods include: If a matching condition is found, the corresponding equivalent sound source modal coefficients are read directly; if no matching condition is found, radial basis interpolation is used to fit the modal coefficients of the corresponding condition.

9. The method according to claim 1, characterized in that, In S700, the formula for calculating the acoustic exposure level is: ； In the formula, The A-weighted sound exposure level characterizes the total noise energy exposure level of an entire train throughout its journey from entering to leaving the measurement point. For reference time, For reference sound pressure level, Let A be the weighted sound pressure, and [t1,t2] be the time period during which the train passes. The formula for calculating the proportion of sound source contribution is: ； In the formula, For single-type sound source radiating sound energy, , , These are the radiated sound energy from the wheel-rail, vehicle aerodynamics, and bridge structure sound sources, respectively.

10. An electronic device, characterized in that, include: One or more processors; Memory, used to store one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1 to 9.

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