A jet transient sound field reconstruction method based on equivalent sources and convolutional network

Abstract

The application provides a jet transient sound field reconstruction method based on an equivalent source and a convolution network, comprising the following steps: arranging a three-dimensional orthogonal array and an arc-shaped array in a jet sound field, synchronously collecting measurement data, including sound pressure data and coordinate data; in the interpolation time-domain equivalent source part, arranging a plurality of equivalent sound sources near the jet sound field, solving time-domain equivalent source strength by using coefficient regularization, and then reconstructing the jet sound field by using an interpolation processing mode; in the time-domain convolution network part, constructing a sound propagation function training network of the jet sound field, and fusing the reconstruction data of the interpolation time-domain equivalent source and the measurement data of the arc-shaped array into a training set of the network; taking the sound pressure data of the reconstruction point obtained by the interpolation time-domain equivalent source and the sound pressure data of the arc-shaped array as output verification parts of the time-domain convolution network, and obtaining the sound pressure data, the coordinate data and the radiation sound field of the reconstruction point by iterative updating of the time-domain convolution network. The application realizes high-precision reconstruction of a time-varying radiation sound field of jet noise.

Description

Technical Field

[0001] This invention relates to the field of ultrasonic jet acoustic field reconstruction and visualization technology, and in particular to a jet transient acoustic field reconstruction method based on equivalent source and convolutional network. Background Technology

[0002] In recent years, research on launch vehicles has gradually emerged. Due to their significant advantage in effectively sending artificial Earth satellites, space stations, and space probes into predetermined orbits, they have attracted considerable attention. The development and production of high-performance rockets will undoubtedly greatly enhance a nation's defense and military capabilities. Their takeoff speed can reach Mach 2.5, and the jet temperature can reach 2000–3000 K. The high-intensity jet noise generated by the engine will subject the launch vehicle body and onboard equipment to unevenly distributed load excitation, leading to nonlinear vibration responses in the structure and causing a series of dynamic problems. In addition, it will also cause noise pollution to the environment around the rocket launch site. Therefore, scholars both domestically and internationally have conducted a series of studies on the identification and reconstruction of jet noise during the rocket's takeoff phase under high-temperature and high-velocity environments.

[0003] Internationally, institutions such as the University of California, NASA laboratories, and Georgia Institute of Technology have used conventional beamforming techniques to locate jet noise sources at different Mach numbers, demonstrating that the distribution of jet noise sources varies with Mach number and jet exit conditions. The U.S. Air Force Research Laboratory applied time-domain beamforming to locate aircraft jet noise sources, utilizing the correlation between adjacent microphones. Delft University of Technology in the Netherlands discussed noise field reconstruction methods, showing that the main idea of ​​beamforming methods is to process data collected from multiple microphones, but the location and amplitude of the sound source are often unknown, and the original algorithms have evolved to assume monopole source characteristics. These original methods have been found to perform poorly in reconstructing directional noise sources.

[0004] Jet noise is composed of multiple partially correlated noise sources superimposed. Conventional beamforming algorithms have limited resolution and sidelobe suppression capabilities, leading to the generation of false sound sources. To address this issue, many researchers have applied improved algorithms to jet noise identification. Brigham Young University analyzed the correlation of jet noise using a method combining generalized inverse and cross-spectral beamforming. The results showed that downstream noise sources have stronger coherence and amplitude than upstream noise sources. This method significantly reduced the influence of sidelobes, but it could not remove the interference of sound source directivity. Perm State Research and Technology University in Russia compared the localization effects of three methods—time-delay beamforming, cross-spectral beamforming, and deconvolutional sound source imaging (DAMAS)—on jet noise. They found that time-delay beamforming is affected by microphone self-noise, resulting in sidelobe interference in the localization results. The DAMAS method cannot be used for the localization of coherent sound sources, while the cross-spectral beamforming algorithm can eliminate self-noise interference and can be used to analyze coherent sound sources. Therefore, this method has a relatively better effect on jet noise localization. Sackley University analyzed jet noise correlation sources using the DAMAS-C method, demonstrating its ability to locate highly directional correlation noise sources. However, the method suffers from non-convergence and significant computational overhead. Georgia Institute of Technology investigated the limitations of beamforming in locating jet noise sources, finding that array beam patterns lack sufficient resolution for low-frequency sources, making it impossible to distinguish between the peak and center locations of the sound source intensity distribution. To address this, some researchers have introduced acoustic holography to analyze jet noise. Purdue University used local acoustic holography to analyze subsonic jet noise, revealing that jet noise is composed of many uncorrelated sound sources. Brigham Young University applied near-field acoustic holography based on multi-source statistical optimization to jet noise imaging analysis, using it in 2016 and 2021 to analyze jet noise sources on the F-22A and F-35 aircraft, respectively. Analysis showed that this method can accurately reconstruct low-frequency jet sound fields within the applicable region of holographic measurement, but it is not suitable for mid-to-high frequency bands.

[0005] In China, the University of Science and Technology Beijing proposed an aerodynamic noise source localization method based on Amiet-IMACS, obtaining highly spatially recognizable localization cloud maps of aerodynamic noise sources in material components. Results show that this method effectively corrects localization errors in airflow environments, expanding the application scope of IMACS in various environments. The Beijing Institute of Strength and Environment analyzed jet noise during engine testing using a time-domain delay summation method, creating jet noise images at various moments, including engine model ignition, stable jet injection, servo actuation, and engine model shutdown. Analysis shows that the jet noise source has relatively high energy in the low-frequency range, with the sound source mainly distributed downstream of the nozzle; in the high-frequency range, the sound source is mainly distributed near the nozzle. However, the spatial resolution of this method is limited, and the accuracy of sound field amplitude reconstruction needs improvement.

[0006] In summary, while domestic and international scholars have conducted extensive analysis and research on the identification of jet noise sources, several issues remain: Firstly, domestic scholars have done very little work on jet noise field reconstruction, while international scholars have only conducted reconstruction studies in the frequency domain. Research on time-varying jet noise field reconstruction is almost nonexistent, and frequency domain sound field reconstruction methods based on steady-state signals cannot reconstruct the time-varying sound field of jets. Secondly, traditional sound field transmission models are based on ideal assumptions, making accurate reconstruction of time-varying sound field amplitudes difficult. Therefore, proposing a method suitable for time-varying jet sound field reconstruction has significant theoretical and engineering implications. Summary of the Invention

[0007] To address the shortcomings of the existing technologies, the present invention aims to provide a jet transient sound field reconstruction method based on equivalent sources and convolutional networks. This method combines the principles of interpolation time-domain equivalent sources and time-domain convolutional networks to achieve jet sound field reconstruction based on sound pressure measurement. It has the advantages of convenient implementation, applicability to time-varying jet field reconstruction, good computational stability, and high reconstruction accuracy.

[0008] To address the aforementioned technical problems, embodiments of the present invention provide the following solutions:

[0009] A method for reconstructing the transient acoustic field of a jet based on an equivalent source and a convolutional network includes the following steps:

[0010] S1. Arrange a three-dimensional orthogonal array consisting of two orthogonal measurement surfaces and an arc-shaped array in the jet sound field, and simultaneously collect measurement data from the three-dimensional orthogonal array and the arc-shaped array; the measurement data includes sound pressure data and coordinate data;

[0011] S2. In the interpolation time-domain equivalent source part, multiple equivalent sound sources are arranged near the jet sound field. Then, the time-domain equivalent source strength is solved by coefficient regularization. After that, the jet sound field is reconstructed by interpolation using the solved equivalent source strength.

[0012] S3. In the temporal convolutional network part, a training network for the sound propagation function of the jet sound field is constructed, which is the temporal convolutional network. The sound pressure data and coordinate data of the three-dimensional orthogonal array, the coordinate data of the reconstructed points and the coordinate data of the arc array are used as inputs to the temporal convolutional network. The training set of the temporal convolutional network integrates the sound pressure data of the reconstructed points and the sound pressure data of the arc array.

[0013] S4. The sound pressure data of the reconstructed points obtained from the interpolated time-domain equivalent source and the sound pressure data measured by the arc array are used as the output verification part of the time-domain convolutional network. Through iterative updates of the time-domain convolutional network, the sound pressure data, coordinate data and radiated sound field of the reconstructed points are obtained for the input measurement data to be analyzed.

[0014] Preferably, in step S1, two orthogonal microphone arrays and an arc-shaped microphone array are arranged in the jet sound field, wherein the measurement surfaces of the two orthogonal microphone arrays are two Archimedean spiral arrays; the aperture of the measurement surface is 1 m, and the distance between adjacent measurement points is less than half the wavelength of the analysis frequency; multi-channel synchronous acquisition of the microphone array is completed using a data acquisition system based on the NI-PXIe bus, with a sampling frequency of 204800 Hz; the jet sound field being measured can be a non-steady-state sound field or a steady-state sound field.

[0015] Preferably, in step S2, the equivalent source strength in the time domain is solved, and the jet sound field is reconstructed using the solved equivalent source strength through interpolation. The specific calculation process is as follows:

[0016] After discretizing the sound source time τ, the sound pressure p at any measurement point at any time t can be approximately expressed as:

[0017]

[0018] Where i is the i-th measurement time, j is the j-th sound source time, and p Hm (t i ) represents the m-th measuring point on the measuring surface at t i Sound pressure at any moment R is the source strength of the nth equivalent source at the jth time step; Hmn Φ is the distance between the nth equivalent source and the mth measuring point. j (τ j Let be the Lagrange linear interpolation function, and N be the number of equivalent source strengths. The above equation can be written in matrix form as follows:

[0019]

[0020] In the formula, S is the sound pressure sequence at the i-th measurement time on the measurement surface. j It is all N equivalent sources on the equivalent source surface at τ j The source strength column vector at time t, It is t i The sound pressure and τ at all M measuring points at time t j The transfer matrix between all N equivalent sources at any given time;

[0021] The source strength is solved using sparse regularization. The sparse regularization process is as follows:

[0022]

[0023] In the formula, θ is the regularization parameter, used to balance the relationship between the two objectives, that is, to control the model to be relatively simple while minimizing the training error; ||·||2 is the L2 norm; ||·||1 is the L1 norm; ε is a parameter related to the noise level, ε=||Q||1, and the formula for Q is: λ 2 The regularization parameter corresponding to Tikhonov regularization can be selected using methods such as the fixed parameter method, L-curve method, generalized cross-validation, and golden section method. The superscript T denotes the conjugate transpose, and I represents the identity matrix. t can be calculated using the obtained source strength. i Reconstructing sound pressure on the surface at all times

[0024]

[0025] In the formula, It is t i The sound pressure and τ on the reconstructed surface at all times j The transfer matrix between N equivalent sources at time t.

[0026] Preferably, in step S3, the first layer of the temporal convolutional network is the input layer, the input vector X1 is the sound pressure data, coordinate data and reconstructed point coordinate data of the interpolated temporal equivalent source of the first measurement surface, and the input vector X2 is the sound pressure data, coordinate data and coordinate data of the arc array in the sound field of the second measurement surface.

[0027] The second and third layers are residual temporal convolutional layers, each containing two ordinary convolutions and two temporal convolutions. The temporal convolutions use different dilation coefficients to extract the short- and long-term temporal features of temporal sound pressure, which can meet the needs of modeling temporal correlation mapping relationships. The two convolutional layers and the temporal convolutions can meet the needs of nonlinear and non-stationary modeling. The residual structure accelerates network convergence and alleviates the gradient vanishing problem caused by the increase of network depth.

[0028] H 11 =(ω c1 *X1+b c1 )+ReLU(ω t1 *X1+b t1 )

[0029] H 12 =(ω c2 *X2+b c2 )+ReLU(ω t2 *X2+b t2 )

[0030] H 21 =(ω c3 *X1+b c3 )+ReLU(ω t3 *X1+bt3 )

[0031] H 22 =(ω c4 *X2+b c4 )+ReLU(ω t4 *X2+b t4 )

[0032] Where, ω c1 ω c2 ω c3 and ω c4 For convolution weights, ω t1 ω t2 ω t3 and ω t4 b represents the temporal convolution weights. c1 b c2 b c3 and b c4 For convolution bias, b t1 b t2 b t3 and b t4 For temporal convolution bias, ReLU is the activation function, and H is the value of the convolution. 11 H represents the output of the first convolution of the input signal X1. 12 H represents the output of the second convolution of the input signal X2. 21 H represents the output of the second convolution of the input signal X1. 22 This represents the output of the second convolution of the input signal X2, where * is the convolution operator;

[0033] The fourth layer is the attention layer. Since the measurement data of the arc array in the jet sound field is obtained directly by sensors, in order to fuse the sound pressure data of the reconstruction points and the sound pressure data of the arc array and improve the network prediction accuracy, it is necessary to increase the weight of the data model parameters, and thus introduce an attention mechanism:

[0034] Q1=ω q1 *H 21 Q2=ω q2 *H 22

[0035] K1=ω k1 *H 21 K2=ω k2 *H 22

[0036] V1=ω v1 *H 21 V2=ω v2 *H 22

[0037]

[0038] Where, ω q1 ω k1 ω v1 ω q2 ω k2 and ω v2 For attention weights, d k1 and d k2 Let K be one dimension, softmax be the normalization exponential function, and H be the value of K. 31 For the output of the input signal X1 in the attention layer, H 31 For the output of the input signal X2 in the attention layer, Q1, Q2, K1, K2, V1, and V2 are the results of convolving the output signal of the residual temporal convolution layer, respectively.

[0039] Layer 5 is the splicing layer, which concatenates the two outputs of the attention layer to obtain the splicing layer output value H4:

[0040] H4 = concatenate(H 31 +H 32 )

[0041] Where concatenate is the concatenation function;

[0042] The 6th layer is a fully connected layer, which yields the final output value Y:

[0043] Y = ω y *H4+b y

[0044] Wherein, filter ω y Let b be the weight vector. y For bias;

[0045] The training set output Y1 represents the sound pressure data at the reconstructed points, and Y2 represents the sound pressure data measured by the arc array. The model uses root mean square error as the objective function and updates the model parameters using the Adam optimization algorithm. After obtaining the trained jet sound field sound propagation function training network, the radiated sound field Y3 of the noise source can be reconstructed using the sound pressure data and coordinate data of the three-dimensional orthogonal array measurement surface to be reconstructed, as well as the coordinate data X3 of the reconstructed points. Then, the particle velocity vector field can be obtained using the sound pressure difference.

[0046]

[0047] Where ω is the angular frequency and ρ is the air density. Know Let Δx, Δy, and Δz be the unit vectors in the x, y, and z directions, respectively; let Y3′ be the sound pressure value after displacement in the x, y, and z directions; and let A be an imaginary number.

[0048] Preferably, in step S4, the sound propagation function established based on the temporal convolutional network is introduced into the interpolation temporal equivalent source method. The three-dimensional orthogonal array measurement data is used as input, and the arc array measurement data is used as output verification value. Finally, the jet transient sound field reconstruction characterization of the reconstruction space is realized.

[0049] On the other hand, an electronic device is provided, comprising a processor and a memory, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the above-described jet transient sound field reconstruction method based on equivalent sources and convolutional networks.

[0050] On the other hand, a computer-readable storage medium is provided, wherein at least one instruction is stored in the storage medium, the at least one instruction being loaded and executed by a processor to implement the above-described jet transient sound field reconstruction method based on equivalent sources and convolutional networks.

[0051] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following:

[0052] (1) This invention can reconstruct the time-varying sound field of jet noise by introducing the interpolation time-domain equivalent source into the reconstruction of the sound field of supersonic jet, thus solving the limitation of traditional methods that cannot be applied to the reconstruction of time-varying jet fields based on the free field propagation assumption.

[0053] (2) This invention uses a time-domain convolutional network to fuse reconstructed data based on time-domain equivalent sources and measurement data of an arc array. It uses a data-driven modeling method to establish a sound propagation model under the jet noise field, which solves the problems of poor interpretability of the traditional ideal steady-state free field sound propagation function for the jet noise propagation process and ill-posedness of sound field inverse inversion. Finally, it realizes high-precision reconstruction of the time-varying radiation sound field of jet noise and can characterize the flow characteristics of sound energy. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 This is a flowchart of a jet transient sound field reconstruction method based on equivalent sources and convolutional networks provided in an embodiment of the present invention;

[0056] Figure 2 This is a schematic diagram of the three-dimensional orthogonal array and arc array arrangement used for jet noise measurement in an embodiment of the present invention;

[0057] Figure 3 This is a schematic diagram of the temporal convolutional network used for jet noise reconstruction in an embodiment of the present invention.

[0058] As shown in the figure, specific structures and devices are marked in the figure to clearly illustrate the structure of the embodiments of the present invention. However, this is only for illustrative purposes and is not intended to limit the present invention to the specific structure, device and environment. According to specific needs, those skilled in the art can adjust or modify these devices and environments, and such adjustments or modifications are still included in the protection scope of the present invention. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0060] Embodiments of the present invention provide a method for reconstructing the transient acoustic field of a jet based on an equivalent source and a convolutional network. Figure 1 This is the overall flowchart of the method, which includes the following steps:

[0061] S1. Arrange a three-dimensional orthogonal array consisting of two orthogonal measurement surfaces and an arc array in the jet sound field (or jet noise field, jet transient sound field, supersonic jet radiation sound field, hereinafter referred to as jet sound field), and simultaneously collect measurement data of the three-dimensional orthogonal array and the arc array; the measurement data includes sound pressure data (or time-series sound pressure data) and coordinate data.

[0062] In step S1, two orthogonal microphone arrays and an arc-shaped microphone array are arranged in the jet sound field. The measuring surfaces of the two orthogonal microphone arrays are two Archimedean spiral arrays, such as... Figure 2 As shown. The aperture of the measuring surface is 1 m, and the distance between adjacent measuring points is less than half the wavelength of the analysis frequency. Multi-channel synchronous acquisition of the microphone array is completed using a data acquisition system based on the NI-PXIe bus, with a sampling frequency of 204800 Hz. The measured jet sound field can be a non-steady-state sound field or a steady-state sound field.

[0063] S2. In the interpolation time-domain equivalent source part, multiple equivalent sound sources are arranged near the jet sound field. Then, the time-domain equivalent source strength is solved using coefficient regularization. After that, the jet sound field is reconstructed using the solved equivalent source strength through interpolation.

[0064] In step S2, the equivalent source strength in the time domain is solved, and the jet sound field is reconstructed using the solved equivalent source strength through interpolation. The specific calculation process is as follows:

[0065] After discretizing the sound source time τ, the sound pressure p at any measurement point at any time t can be approximately expressed as:

[0066]

[0067] Where i is the i-th measurement time, j is the j-th sound source time, and p Hm (t i ) represents the m-th measuring point on the measuring surface at t i Sound pressure at any moment R is the source strength of the nth equivalent source at the jth time step; Hmn Φ is the distance between the nth equivalent source and the mth measuring point. j (τ j Let be the Lagrange linear interpolation function, and N be the number of equivalent source strengths. The above equation can be written in matrix form as follows:

[0068]

[0069] In the formula, S is the sound pressure sequence at the i-th measurement time on the measurement surface. j It is all N equivalent sources on the equivalent source surface at τ j The source strength column vector at time t, It is t i The sound pressure and τ at all M measuring points at time t j The transfer matrix between all N equivalent sources at any given time.

[0070] Since the number of equivalent sources is greater than the number of microphones, ill-posed problems easily arise during the source strength calculation process. Furthermore, the calculation error of the source strength at each time step accumulates to the next time step, ultimately causing the sound field reconstruction to fail. To address these issues, a sparse regularization method is used to solve for accurate source strength, while constraints are applied to the source strength at each step to prevent divergence in the source strength calculation.

[0071] The source strength is solved using sparse regularization. The sparse regularization process is as follows:

[0072]

[0073] In the formula, θ is the regularization parameter, used to balance the relationship between the two objectives, that is, to control the model to be relatively simple while minimizing the training error; ||·||2 is the L2 norm; ||·||1 is the L1 norm; ε is a parameter related to the noise level, ε=||Q||1, and the formula for Q is: λ 2 The regularization parameter corresponding to Tikhonov regularization can be selected using methods such as the fixed parameter method, L-curve method, generalized cross-validation, and golden section method. The superscript T denotes the conjugate transpose, and I represents the identity matrix. t can be calculated using the obtained source strength. i Reconstructing sound pressure on the surface at all times

[0074]

[0075] In the formula, It is t i The sound pressure and τ on the reconstructed surface at all times j The transfer matrix between N equivalent sources at time t.

[0076] S3. In the temporal convolutional network part, a training network for the sound propagation function of the jet sound field is constructed, which is the temporal convolutional network. The sound pressure data and coordinate data of the three-dimensional orthogonal array, the coordinate data of the reconstructed points and the coordinate data of the arc array are used as inputs to the temporal convolutional network. The training set of the temporal convolutional network integrates the sound pressure data of the reconstructed points and the sound pressure data of the arc array.

[0077] The sound propagation function in step S3 is based on the free-field sound propagation assumption, which requires the sound field to be a free-field environment and that there is no energy flow in or out between the equivalent source and the measurement surface. However, the ideal sound propagation function is difficult to characterize the real propagation state between the jet noise source and the transient radiated sound field. Therefore, the time-domain convolutional network method in step S3 is needed to establish the sound propagation function of the jet noise field.

[0078] like Figure 3 As shown, the temporal convolutional network consists of 6 layers: an input layer, two residual temporal convolutional layers, an attention layer, a concatenation layer, and a fully connected layer.

[0079] The first layer of the temporal convolutional network is the input layer. The input vector X1 is the sound pressure data, coordinate data and reconstructed point coordinate data of the interpolated temporal equivalent source of the first measurement surface, and the input vector X2 is the sound pressure data, coordinate data and coordinate data of the arc array in the sound field of the second measurement surface.

[0080] The second and third layers are residual temporal convolutional layers, each containing two ordinary convolutions and two temporal convolutions. The temporal convolutions use different dilation coefficients to extract the short- and long-term temporal features of temporal sound pressure, which can meet the needs of modeling temporal correlation mapping relationships. The two convolutional layers and the temporal convolutions can meet the needs of nonlinear and non-stationary modeling. The residual structure accelerates network convergence and alleviates the gradient vanishing problem caused by the increase of network depth.

[0081] H 11 =(ω c1 *X1+b c1 )+ReLU(ω r1 *X1+b t1 )

[0082] H 12 =(ω c2 *X2+b c2 )+ReLU(ω r2 *X2+b t2 )

[0083] H 21 =(ω c3 *X1+b c3 )+ReLU(ω t3 *X1+b t3 )

[0084] H 22 =(ω c4 *X2+b c4 )+ReLU(ω t4 *X2+b t4 )

[0085] Where, ω c1 ω c2 ω c3 and ω c4 For convolution weights, (ω) t1 ω t2 ω t3 and ω t4 b represents the temporal convolution weights. c1 b c2 b c3 and b c4 For convolution bias, b t1 b t2 b t3 and b t4 For temporal convolution bias, ReLU is the activation function, and H is the value of the convolution. 11 H represents the output of the first convolution of the input signal X1. 12 H represents the output of the second convolution of the input signal X2. 21 H represents the output of the second convolution of the input signal X1.22 This represents the output of the second convolution of the input signal X2, where * is the convolution operator;

[0086] The fourth layer is the attention layer. Since the measurement data of the arc array in the jet sound field is obtained directly by sensors, in order to fuse the sound pressure data of the reconstruction points and the sound pressure data of the arc array and improve the network prediction accuracy, it is necessary to increase the weight of the data model parameters, and thus introduce an attention mechanism:

[0087] Q1=ω q1 *H 21 Q2=ω q2 *H 22

[0088] K1=ω k1 *H 21 K2=ω k2 *H 22

[0089] V1=ω v1 *H 21 V2=ω v2 *H 22

[0090]

[0091] Where, ω q1 ω k1 ω v1 ω q2 ω k2 and ω v2 For attention weights, d k1 and d k2 Let K be one dimension, softmax be the normalization exponential function, and H be the value of K. 31 For the output of the input signal X1 in the attention layer, H 31 For the output of the input signal X2 in the attention layer, Q1, Q2, K1, K2, V1, and V2 are the results of convolving the output signal of the residual temporal convolution layer, respectively.

[0092] Layer 5 is the splicing layer, which concatenates the two outputs of the attention layer to obtain the splicing layer output value H4:

[0093] H4 = concatenate(H 31 +H 32 )

[0094] Where concatenate is the concatenation function;

[0095] The 6th layer is a fully connected layer, which yields the final output value Y:

[0096] Y = ωy *H4+b y

[0097] Wherein, filter ω y Let b be the weight vector. y For bias;

[0098] The training set output Y1 represents the sound pressure data at the reconstructed points, and Y2 represents the sound pressure data measured by the arc array. The model uses root mean square error as the objective function and updates the model parameters using the Adam optimization algorithm. After obtaining the trained jet sound field sound propagation function training network, the radiated sound field Y3 of the noise source can be reconstructed using the sound pressure data and coordinate data of the three-dimensional orthogonal array measurement surface to be reconstructed, as well as the coordinate data X3 of the reconstructed points. Then, the particle velocity vector field can be obtained using the sound pressure difference.

[0099]

[0100] Where ω is the angular frequency and ρ is the air density. and Let Δx, Δy, and Δz be the unit vectors in the x, y, and z directions, respectively; let Y3′ be the sound pressure value after displacement in the x, y, and z directions; and let A be an imaginary number.

[0101] S4. The sound pressure data of the reconstructed points obtained from the interpolated time-domain equivalent source and the sound pressure data measured by the arc array are used as the output verification part of the time-domain convolutional network. Through iterative updates of the time-domain convolutional network, the sound pressure data, coordinate data and radiated sound field of the reconstructed points are obtained for the input measurement data to be analyzed.

[0102] In step S4, the sound propagation function established based on the temporal convolutional network is introduced into the interpolation temporal equivalent source method. The three-dimensional orthogonal array measurement data is used as input, and the arc array measurement data is used as output verification value. Finally, the jet transient sound field reconstruction characterization of the reconstruction space is realized.

[0103] The specific implementation process of this invention is as follows:

[0104] (1) In the radiating sound field of the supersonic jet, two orthogonal microphone arrays and an arc microphone array are arranged. The measurement surface is an Archimedean spiral array composed of two 28-channel microphones and an 8-channel arc microphone array. The aperture of the measurement surface is 1 m. The distance between adjacent measurement points is less than half the wavelength of the analysis frequency. Multi-channel synchronous acquisition of the microphone array is completed using a data acquisition system based on the NI-PXIe bus. The sampling frequency is 204800 Hz. The sound field under test can be a non-steady-state sound field or a steady-state sound field.

[0105] (2) In the process of reconstructing the sound field of the radiative jet from the equivalent source strength, after discretizing the sound source time τ, the sound pressure p at any measurement point at any time t is approximately expressed as:

[0106]

[0107] Where i is the i-th measurement time, j is the j-th sound source time, and p Hm (t i ) represents the m-th measuring point on the measuring surface at t i The sound pressure at any moment R represents the source strength of the nth equivalent source at the jth time step. Hmn Φ is the distance between the nth equivalent source and the mth measuring point. j (τ j Let be the Lagrange linear interpolation function, and N be the number of equivalent source strengths. The above equation can be written in matrix form as follows:

[0108]

[0109] In the formula, S is the sound pressure sequence at the i-th measurement time on the measurement surface. j It is all N equivalent sources on the equivalent source surface at τ j The source strength column vector at time t, It is t i The sound pressure and τ at all M measuring points at time t j The transfer matrix between all N equivalent sources at each time step is given. Since the number of equivalent sources is greater than the number of sensors, ill-posed problems easily arise during the source strength calculation. Furthermore, the calculation error of the source strength at each time step accumulates to the next time step, ultimately causing the sound field reconstruction to fail. To solve these problems, a sparse regularization method is used to solve for accurate source strength, while constraints are applied to the source strength at each step to prevent divergence in the source strength calculation. The sparse regularization process is as follows:

[0110]

[0111] In the formula, θ is the regularization parameter, used to balance the relationship between the two objectives, that is, to control the model to be relatively simple while minimizing the training error; ||·||2 is the L2 norm; ||·||1 is the L1 norm; ε is a parameter related to the noise level, ε=||Q||1, and the formula for Q is: λ 2 Let T be the regularization parameter corresponding to Tikhonov regularization. Selection methods include the fixed parameter method, L-curve method, generalized cross-validation, and golden section method. The superscript T denotes the conjugate transpose, and I is the identity matrix. t can be calculated using the obtained source strength. i Constantly reconstructing the sound pressure on the surface

[0112]

[0113] In the formula, It is t i The sound pressure and τ on the reconstructed surface at all times j The transfer matrix between N equivalent sources at time t.

[0114] (3) The sound propagation function is based on the assumption of free-field sound propagation, which requires the sound field to be a free-field environment and that there is no energy flow in or out between the equivalent source and the measurement surface. However, the ideal sound propagation function is difficult to characterize the real propagation state between the jet noise source and the transient radiated sound field. Therefore, it is necessary to use the method of time-domain convolutional network to establish the sound propagation function of the jet noise field. The specific calculation process is as follows:

[0115] The first layer of the network is the input layer. The input vector X1 is the sound pressure time series data, coordinate data and reconstruction point coordinates of the time-domain equivalent source of the measurement surface. The input vector X2 is the sound pressure time series data, coordinate data and coordinates of the arc array in the sound field of the measurement surface.

[0116] The second and third layers are residual temporal convolutional layers, each containing two ordinary convolutions and two temporal convolutions. The temporal convolutions use different dilation coefficients to extract short- and long-term temporal features of temporal sound pressure, satisfying the need for modeling temporal correlation mappings. The two convolutional layers and temporal convolutions satisfy the needs for nonlinear and non-stationary modeling. The residual structure accelerates network convergence and alleviates the gradient vanishing problem caused by increased network depth.

[0117] H 11 =(ω c1 *X1+b c1 )+ReLU(ω t1 *X1+b t1 )

[0118] H 12 =(ω c2 *X2+b c2 )+ReLU(ω t2 *X2+b t2 )

[0119] H 21 =(ω c3 *X1+b c3 )+ReLU(ω t3 *X1+b t3 )

[0120] H 22 =(ω c4 *X2+b c4 )+ReLU(ω t4 *X2+bt4 )

[0121] Where, ω c1 ω c2 ω c3 and ω c4 For convolution weights, ω t1 ω t2 ω t3 and ω t4 b represents the temporal convolution weights. c1 b c2 b c3 and b c4 For convolution bias, b t1 b t2 b t3 and b t4 For temporal convolution bias, ReLU is the activation function, and H is the value of the convolution. 11 H represents the output of the first convolution of the input signal X1. 12 H represents the output of the second convolution of the input signal X2. 21 H represents the output of the second convolution of the input signal X1. 22 This represents the output of the second convolution of the input signal X2, where * is the convolution operator.

[0122] The fourth layer is the attention layer. Since the data of the arc array in the sound field is obtained directly by sensors, in order to fuse the reconstructed data of the temporal equivalent source and the measurement data of the arc array and improve the network prediction accuracy, it is necessary to increase the weight of the data model parameters, and thus introduce an attention mechanism:

[0123] Q1=ω q1 *H 21 Q2=ω q2 *H22

[0124] K1=ω k1 *H 21 K2=ω k2 *H 22

[0125] V1=ω v1 *H 21 V2=ω v2 *H 22

[0126]

[0127] Where, ω q1 ω k1 ω v1 ω q2 ω k2 and ω v2 For attention weights, dk1 and d k2 Let K be one dimension, softmax be the normalization exponential function, and H be the value of K. 31 For the output of the input signal X1 in the attention layer, H 31 For the output of the input signal X2 in the attention layer, Q1, Q2, K1, K2, V1, and V2 are the results of convolving the output signal of the residual temporal convolution layer, respectively.

[0128] Layer 5 is the splicing layer, which concatenates the two outputs of the attention layer to obtain the splicing layer output value H4:

[0129] H4 = concatenate(H 31 +H 32 )

[0130] Here, concatenate is the concatenation function.

[0131] The 6th layer is a fully connected layer, which yields the final output value Y:

[0132] Y = ω y *H4+b y

[0133] Wherein, filter ω y Let b be the weight vector. y For bias.

[0134] The training set outputs Y1, representing the temporal sound pressure at the reconstruction point, and Y2, representing the temporal sound pressure measured by the arc array. The model uses root mean square error as the objective function and updates the model parameters using the Adam optimization algorithm. Once the trained jet noise field sound propagation model is obtained, the radiated sound field Y3 of the noise source can be reconstructed using the temporal sound pressure and coordinates of the three-dimensional array measurement surface to be reconstructed, as well as the coordinates X3 of the reconstruction point. Then, the particle velocity vector field can be obtained using the sound pressure difference.

[0135]

[0136] Where ω is the angular frequency and ρ is the air density. and Let be the unit vectors in the x, y, and z directions, respectively; Δx, Δy, and Δz be the displacements in the x, y, and z directions, respectively; Y3′ be the sound pressure value after displacement in the x, y, and z directions; and A be an imaginary number.

[0137] (4) The acoustic propagation function based on the time-domain convolutional network is introduced into the interpolation time-domain equivalent source method. The three-dimensional orthogonal array measurement data is used as input and the arc array is used as the output verification value. Finally, the jet transient sound field reconstruction characterization of the reconstruction space is realized.

[0138] This invention enables the reconstruction of the time-varying sound field of jet noise by introducing an interpolated time-domain equivalent source into the reconstruction of the sound field of supersonic jets, thus overcoming the limitation of traditional methods that cannot be applied to the reconstruction of time-varying jet fields based on the free-field propagation assumption.

[0139] This invention uses a time-domain convolutional network to fuse reconstructed data based on time-domain equivalent sources and measurement data from an arc array. It then uses a data-driven modeling method to establish a sound propagation model under a jet noise field. This solves the problems of poor interpretability of the traditional ideal steady-state free-field sound propagation function for the jet noise propagation process and ill-posedness of sound field inverse inversion. Ultimately, it achieves high-precision reconstruction of the time-varying radiated sound field of jet noise and can characterize the flow characteristics of sound energy.

[0140] Embodiments of the present invention also provide an electronic device, which may vary considerably due to different configurations or performance. It may include one or more central processing units (CPUs) and one or more memories, wherein the memory stores at least one instruction, which is loaded and executed by the processor to implement the steps of the jet transient acoustic field reconstruction method based on equivalent sources and convolutional networks described above.

[0141] In an exemplary embodiment, a computer-readable storage medium is also provided, such as a memory including instructions that can be executed by a processor in a terminal to complete the jet transient sound field reconstruction method based on equivalent sources and convolutional networks. For example, the computer-readable storage medium may be a ROM, random access memory (RAM), CD-ROM, magnetic tape, floppy disk, or optical data storage device.

[0142] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0143] The use of terms such as "an embodiment," "an embodiment," "an exemplary embodiment," and "some embodiments" in the specification indicates that the described embodiment may include a specific feature, structure, or characteristic, but not every embodiment necessarily includes that specific feature, structure, or characteristic. Furthermore, when a specific feature, structure, or characteristic is described in connection with an embodiment, implementing such a feature, structure, or characteristic in conjunction with other embodiments (whether explicitly described or not) should be within the knowledge of those skilled in the art.

[0144] This invention encompasses any substitutions, modifications, equivalent methods, and solutions made within the spirit and scope of this invention. To provide the public with a thorough understanding of this invention, specific details are described in detail in the following preferred embodiments; however, those skilled in the art will fully understand the invention even without these details. Furthermore, to avoid unnecessary misunderstanding of the essence of this invention, well-known methods, processes, procedures, components, and circuits are not described in detail.

[0145] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc.

[0146] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for reconstructing the transient sound field of a jet based on an equivalent source and a convolutional network, characterized in that, Includes the following steps: S1. Arrange a three-dimensional orthogonal array consisting of two orthogonal measurement surfaces and an arc-shaped array in the jet sound field, and simultaneously collect measurement data from the three-dimensional orthogonal array and the arc-shaped array; the measurement data includes sound pressure data and coordinate data; S2. In the interpolation time-domain equivalent source part, multiple equivalent sound sources are arranged near the jet sound field. Then, the time-domain equivalent source strength is solved by coefficient regularization. After that, the jet sound field is reconstructed by interpolation using the solved equivalent source strength. S3. In the temporal convolutional network part, a training network for the sound propagation function of the jet sound field is constructed, which is the temporal convolutional network. The sound pressure data and coordinate data of the three-dimensional orthogonal array, the coordinate data of the reconstructed points and the coordinate data of the arc array are used as inputs to the temporal convolutional network. The training set of the temporal convolutional network integrates the sound pressure data of the reconstructed points and the sound pressure data of the arc array. S4. The sound pressure data of the reconstructed points obtained from the interpolated time-domain equivalent source and the sound pressure data measured by the arc array are used as the output verification part of the time-domain convolutional network. Through iterative updates of the time-domain convolutional network, the sound pressure data, coordinate data and radiated sound field of the reconstructed points are obtained for the input measurement data to be analyzed.

2. The jet transient sound field reconstruction method based on equivalent source and convolutional network according to claim 1, characterized in that, In step S1, two orthogonal microphone arrays and an arc-shaped microphone array are arranged in the jet sound field. The measurement surfaces of the two orthogonal microphone arrays are two Archimedean spiral arrays. The aperture of the measurement surface is 1 m, and the distance between adjacent measurement points is less than half the wavelength of the analysis frequency. Multi-channel synchronous acquisition of the microphone array is completed using a data acquisition system based on the NI-PXIe bus, with a sampling frequency of 204800 Hz. The jet sound field being measured can be a non-steady-state sound field or a steady-state sound field.

3. The jet transient sound field reconstruction method based on equivalent source and convolutional network according to claim 1, characterized in that, In step S2, the equivalent source strength in the time domain is solved, and the jet sound field is reconstructed using the solved equivalent source strength through interpolation. The specific calculation process is as follows: After discretizing the sound source time τ, the sound pressure p at any measurement point at any time t can be approximately expressed as: Where i is the i-th measurement time, j is the j-th sound source time, and p Hm (t i ) represents the m-th measuring point on the measuring surface at t i The sound pressure at any moment R is the source strength of the nth equivalent source at the jth time step; Hmn Φ is the distance between the nth equivalent source and the mth measuring point. j (τ j Let be the Lagrange linear interpolation function, and N be the number of equivalent source strengths. The above equation can be written in matrix form as follows: In the formula, S is the sound pressure sequence at the i-th measurement time on the measurement surface. j It is all N equivalent sources on the equivalent source surface at τ j The source strength column vector at time t, It is t i The sound pressure and τ at all M measuring points at time t j The transfer matrix between all N equivalent sources at any given time; The source strength is solved using sparse regularization. The sparse regularization process is as follows: In the formula, θ is the regularization parameter, used to balance the relationship between the two objectives, that is, to control the model to be relatively simple while minimizing the training error; ||·||2 is the L2 norm; ||·||1 is the L1 norm; ε is a parameter related to the noise level, ε=||Q||1, and the formula for Q is: λ 2 The regularization parameter corresponding to Tikhonov regularization can be selected using methods such as the fixed parameter method, L-curve method, generalized cross-validation, and golden section method. The superscript T denotes the conjugate transpose, and I represents the identity matrix. t can be calculated using the obtained source strength. i Constantly reconstructing the sound pressure on the surface In the formula, It is t i The sound pressure and τ on the reconstructed surface at all times j The transfer matrix between N equivalent sources at time t.

4. The jet transient sound field reconstruction method based on equivalent source and convolutional network according to claim 1, characterized in that, In step S3, the first layer of the temporal convolutional network is the input layer. The input vector X1 is the sound pressure data, coordinate data and reconstructed point coordinate data of the interpolated temporal equivalent source of the first measurement surface, and the input vector X2 is the sound pressure data, coordinate data and coordinate data of the arc array in the sound field of the second measurement surface. The second and third layers are residual temporal convolutional layers, each containing two ordinary convolutions and two temporal convolutions. The temporal convolutions use different dilation coefficients to extract the short- and long-term temporal features of temporal sound pressure, which can meet the needs of modeling temporal correlation mapping relationships. The two convolutional layers and the temporal convolutions can meet the needs of nonlinear and non-stationary modeling. The residual structure accelerates network convergence and alleviates the gradient vanishing problem caused by the increase of network depth. H 11 =(ω c1 *X1+b c1 )+ReLU(ω t1 *X1+b t1 ) H 12 =(ω c2 *X2+b c2 )+ReLU(ω t2 *X2+b t2 ) H 21 =(ω c3 *X1+b c3 )+ReLU(ω t3 *X1+b t3 ) H 22 =(ω c4 *X2+b c4 )+ReLU(ω t4 *X2+b t4 ) Where, ω c1 ω c2 ω c3 and ω c4 ω represents the convolution weights. t1 ω t2 ω t3 and ω t4 b represents the temporal convolution weights. c1 b c2 b c3 and b c4 For convolution bias, b t1 b t2 b t3 and b t4 For temporal convolution bias, ReLU is the activation function, and H is the value of the convolution. 11 H represents the output of the first convolution of the input signal X1. 12 H represents the output of the second convolution of the input signal X2. 21 H represents the output of the second convolution of the input signal X1. 22 This represents the output of the second convolution of the input signal X2, where * is the convolution operator; The fourth layer is the attention layer. Since the measurement data of the arc array in the jet sound field is obtained directly by sensors, in order to fuse the sound pressure data of the reconstruction points and the sound pressure data of the arc array and improve the network prediction accuracy, it is necessary to increase the weight of the data model parameters, and thus introduce an attention mechanism: Q1=ω q1 *H 21 ,Q2=ω q2 *H 22 K1=ω k1 *H 21 ,K2=ω k2 *H 22 V1=ω v1 *H 21 ,V2=ω v2 *H 22 Where, ω q1 ω k1 ω v1 ω q2 ω k2 and ω v2 For attention weights, d k1 and d k2 Let K be one dimension, softmax be the normalization exponential function, and H be the value of K. 31 For the output of the input signal X1 in the attention layer, H 31 For the output of the input signal X2 in the attention layer, Q1, Q2, K1, K2, V1, and V2 are the results of convolving the output signal of the residual temporal convolution layer, respectively. Layer 5 is the splicing layer, which concatenates the two outputs of the attention layer to obtain the splicing layer output value H4: H4=concatenate(H 31 +H 32 ) Where concatenate is the concatenation function; The 6th layer is a fully connected layer, which yields the final output value Y: Y=ω y *H4+b y Wherein, filter ω y Let b be the weight vector. y For bias; The training set output Y1 represents the sound pressure data at the reconstructed points, and Y2 represents the sound pressure data measured by the arc array. The model uses root mean square error as the objective function and updates the model parameters using the Adam optimization algorithm. After obtaining the trained jet sound field sound propagation function training network, the radiated sound field Y3 of the noise source can be reconstructed using the sound pressure data and coordinate data of the three-dimensional orthogonal array measurement surface to be reconstructed, as well as the coordinate data X3 of the reconstructed points. Then, the particle velocity vector field can be obtained using the sound pressure difference. Where ω is the angular frequency and ρ is the air density. surface Let Δx, Δy, and Δz be the unit vectors in the x, y, and z directions, respectively; let Y3′ be the sound pressure value after displacement in the x, y, and z directions, respectively; and let A be an imaginary number.

5. The jet transient sound field reconstruction method based on equivalent source and convolutional network according to claim 1, characterized in that, In step S4, the sound propagation function established based on the temporal convolutional network is introduced into the interpolation temporal equivalent source method. The three-dimensional orthogonal array measurement data is used as input, and the arc array measurement data is used as output verification value. Finally, the jet transient sound field reconstruction characterization of the reconstruction space is realized.

6. An electronic device, characterized in that, The electronic device includes a processor and a memory, the memory storing at least one instruction, which is loaded and executed by the processor to implement the jet transient sound field reconstruction method based on equivalent sources and convolutional networks as described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, The storage medium stores at least one instruction, which is loaded and executed by a processor to implement the jet transient acoustic field reconstruction method based on equivalent sources and convolutional networks as described in any one of claims 1-5.

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