Acoustic inversion device for underwater bubble group size distribution based on forward and backscattering

Abstract

An acoustic inversion device for underwater bubble group size distribution based on forward and backscattering belongs to the field of underwater acoustics. The device comprises: a first hydrophone is deployed at x = d1 along the axial direction with a transmitting transducer as the origin x = 0, and a second hydrophone is deployed at x = d1 + d2 along the axial direction; the transmitting transducer transmits a single-frequency pulse acoustic signal at x = 0 into the bubble-containing water medium to be measured, and the hydrophone collects the signal; the incident sound pressure amplitude, the forward scattered sound pressure amplitude, and the backscattered sound pressure amplitude are measured; the transmitting frequency is changed to perform a frequency sweep, and an inversion equation in matrix form is obtained based on the discretized inversion equation of the forward and backscattering joint theory; the inversion equation is subjected to positive and finite constraints; and Tikhonov regularization is introduced into the inversion equation to calculate the bubble group size distribution parameters of the bubble-containing water medium to be measured. The invention is applicable to complex environments, can quickly measure the underwater bubble group size distribution, corrects the error of the ideal inversion model, and solves the problem of accurate measurement of non-resonant bubbles.

Description

Technical Field

[0001] The present invention belongs to the field of underwater acoustic technology and relates to a device for measuring the size distribution of a bubble group, specifically to a device and method for acoustic inversion of the size distribution of an underwater bubble group based on forward and backscattering. Background Art

[0002] The presence of bubbles in ocean water affects the nonlinear interaction of acoustic waves, significantly complicating the study of nonlinear wave theory. Furthermore, it complicates the propagation behavior and evolution of the acoustic field, providing a richer range of possibilities for the utilization of acoustic fields. Therefore, measuring the distribution of bubbles on the sea surface is of vital importance to ocean exploration. When utilizing or mitigating the effects of bubbles, it is also essential to determine the scale distribution parameters of bubbles in liquids.

[0003] In 1991, KW Commander proposed discretizing the first-order Fredholm integral equation for bubble inversion, converting it into a matrix equation and using regularization to obtain a stable solution. This enabled the bubble distribution to be inverted from the measured attenuation coefficient at multiple frequencies, resolving the problem of non-convergence of ill-posed integral equations under small perturbations (Commander, Kerry W., and Robert J. McDonald. "Finite-element solution of the inverse problem in bubble swarm acoustics." The journal of the acousticalsociety of America 89.2 (1991): 592-597.). In 2021, Hou Sen proposed using an iterative method to invert the bubble distribution using modified phase velocity and bubble vibration parameters. He proposed a simplified inversion method to address the problem encountered when data is sparse. The results show that this simplified method can more accurately determine the main parameters of the bubble swarm distribution (Hou Sen, Hu Changqing, Zhao Mei. Research on methods for inverting bubble swarm distribution using acoustic attenuation [J]. Acta Physica Sinica, 2021.). In 2021, Jianghui Li proposed an adaptive single-bubble passive acoustic identification technology, which combines the acoustic characteristics of bubbles, including pulsation time interval, frequency bandwidth and radiation intensity, and uses cross-spectrum to improve the signal-to-noise ratio, thereby reducing the false alarm rate of bubble identification (Jianghui Li, et al. Acoustic and optical determination of bubble size distributions–Quantification of seabed gas emissions[J]. International Journal of Greenhouse Gas Control, 108[2024-02-20].).Acoustic measurements of bubbles have wide-ranging applications. Several studies have focused on the sound scattering properties of ocean bubbles and evaluated the acoustic properties of seawater media containing bubble clouds based on experimental data obtained from sound scattering of bubbles in the upper layer of seawater (Liu, Ruoyun. The effects of bubble scattering on sound propagation in shallow water. Journal of Marine Science and Engineering 2021, 9(12), 1441.)(5Bulanov, Vladimir A. On sound scattering and acoustic properties of the upper layer of the sea with bubble clouds. Journal of Marine Science and Engineering 2022, 10(7), 872.).

[0004] Traditional bubble parameter measurement methods primarily utilize the acoustic attenuation and velocity characteristics of bubbles to invert and determine their distribution. A limitation of these methods is that when the number of bubbles is small, they are significantly affected by the attenuation coefficient of pure water. Without prior knowledge of the pure water attenuation coefficient, measurement errors can be significant. Furthermore, due to the lack of effective means to measure the sound pressure scattered by bubbles, a bubble acoustic inversion device that would best overcome these challenges is currently unavailable. Summary of the Invention

[0005] Based on previous theories, the present invention proposes an acoustic inversion device and method for the size distribution of underwater bubble groups based on forward and backscattering. The device transmits a single-frequency pulse in a sweeping frequency manner, deploys two hydrophones in the acoustic axis direction of the transmitting transducer, measures the incident sound pressure, and the amplitudes of the forward and backscattered sound pressures. Substituting these into the inversion theory of the discretized forward and backscattering joint theory, the inversion equation is obtained in matrix form. Tikhonov regularization is introduced under positive and finite constraints to derive the size distribution parameters of the bubble group in the bubble-containing water medium to be measured. The device is simple to measure and highly applicable, making it suitable for use in complex environments. It can more quickly measure the size distribution of underwater bubble groups, correct the errors of the ideal inversion model, and solve the problem of accurate measurement of non-resonant bubbles.

[0006] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0007] The present invention provides an acoustic inversion device for underwater bubble group size distribution based on forward and backscattering, comprising:

[0008] Signal source, which sends out the required known electrical signal;

[0009] High-frequency power amplifier, converts the electrical signal from the signal source into a high-power electrical signal output;

[0010] Oscilloscope, to monitor the electrical signals output by the signal source and high-frequency amplifier;

[0011] The transmitting transducer converts the electrical signal output by the high-frequency power amplifier into an acoustic signal and outputs it underwater;

[0012] Hydrophones, which convert acoustic signals received in water into electrical signals;

[0013] Collector, which collects the electrical signals received by the hydrophone in real time;

[0014] On the PC side, the electrical signals collected by the collector are stored and displayed;

[0015] Mounting frame, used to fix the device in place.

[0016] Furthermore, with the transmitting transducer as the origin x=0, hydrophone #1 is placed at x=d1 along the axial direction, and hydrophone #2 is placed at x=d1+d2 along the axial direction.

[0017] The method for acoustic inversion of underwater bubble group size distribution based on forward and backscattering provided by the present invention is implemented using the acoustic inversion device for underwater bubble group size distribution based on forward and backscattering according to claim 1 or 2, and includes the following steps:

[0018] (a) The device is deployed and the transmitting transducer emits a signal;

[0019] With the transmitting transducer as the origin x = 0, hydrophone #1 is deployed at x = d1 along the axial direction, and hydrophone #2 is deployed at x = d1 + d2 along the axial direction; the transmitting transducer transmits a single-frequency pulse acoustic signal with a frequency of ω1 into the bubble-containing water medium to be measured at x = 0, and hydrophone #1 and hydrophone #2 simultaneously collect the single-frequency pulse acoustic signal;

[0020] (b) Measure the incident sound pressure amplitude P1(ω1);

[0021] (c) Measure the forward scattered sound pressure amplitude P2(ω1);

[0022] (d) Measure the backscattered sound pressure amplitude P b (ω1);

[0023] (e) Change the transmission frequency to perform frequency sweep, and the frequency sweep range is ω[ω1ω2…ω n ], repeat steps (b)-(d), and obtain the inversion equation in matrix form according to the discretization of the forward and backscattering joint theory;

[0024] (f) Inversion equations under positive and finite constraints;

[0025] (g) Tikhonov regularization is introduced into the inversion equation, and the bubble group size distribution parameters of the bubble-containing water medium to be tested are obtained by calculation.

[0026] Furthermore, in step (b), the waveform of the direct wave signal received by hydrophone #1 is Fourier transformed to read the incident sound pressure amplitude P1(ω1) of the bubble-containing water medium to be measured at the corresponding frequency ω1.

[0027] Furthermore, in step (c), the waveform of the direct wave signal received by the 2# hydrophone is Fourier transformed to read the forward scattered sound pressure amplitude P2(ω1) of the bubble-containing water medium to be measured at the corresponding frequency ω1.

[0028] Furthermore, in step (d), the time delay τ of the single-frequency pulse echo signal emitted in the bubble-containing water medium to be tested is calculated, the backscattered signal waveform received by the 1# hydrophone within the time delay τ is Fourier transformed, and the backscattered sound pressure amplitude P of the bubble-containing water medium to be tested at the corresponding frequency ω1 is read. b (ω1).

[0029] Furthermore, in step (e), for the radius range of the bubble-containing water medium to be measured, R=[R1 R2…R m ], according to the joint theory of forward and backscattering:

[0030] λ(ω)=∫σ s (ω,R)N(R)dR (1)

[0031] in, is the backscattering cross section of a bubble with a radius of R under frequency ω excitation, N(R)=[N1(R1)N2(R2)…N m (R m )] is the number of bubbles with a radius of R, δ is the viscous damping coefficient, and ω0 is the resonance frequency of the bubble with a radius of R.

[0032] Furthermore, the discretization of formula (1) yields the inversion equation in matrix form:

[0033] λ(ω)=σ s (ω,R)N(R) (2)

[0034] Furthermore, in step (f), the inversion equation under the positive constraint and the finite constraint is expressed as follows:

[0035]

[0036] Furthermore, in step (g), Tikhonov regularization is introduced into the inversion equation, and its specific calculation formula is:

[0037]

[0038] Among them, N is the exact solution of the inversion equation, N * is the initial estimate, ε is the regularization parameter, L = tridiag (1, -2, 1) is the tridiagonal matrix; the regularized solution N of the bubble group size distribution parameter of the bubble-containing water medium to be measured is obtained by calculation ε .

[0039] The beneficial effects of the present invention are:

[0040] (1) Compared with the traditional bubble measurement device, the present invention solves the problem of accurate measurement of non-resonant bubbles, broadens the radius coverage of the inversion bubble, and solves the problem that the resonance frequency of small bubbles is too high to be accurately measured.

[0041] (2) In the present invention, the theory combines forward scattering with back scattering, which is more in line with reality than the previous inversion model under ideal conditions and corrects the error of the ideal inversion model.

[0042] (3) In the present invention, inversion can be performed when prior information is scarce, and has high robustness, which can effectively avoid the situation where the physical parameters of the bubble-containing water medium to be measured cannot be obtained a priori and affect the measurement results.

[0043] (4) The present invention is simple to operate and has strong applicability. It is suitable for use in complex environments. The calculation results are accurate, the calculation steps are simple and fast, and it has high experimental value and application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 This is a flow chart of an acoustic inversion method for underwater bubble group size distribution based on forward and backscattering of the present invention.

[0045] Figure 2 This is a structural diagram of an acoustic inversion device for underwater bubble group size distribution based on forward and backscattering according to the present invention.

[0046] Figure 3 Schematic diagram of the hydrophone receiving signal in one cycle.

[0047] Figure 4 is the receiving sound pressure level frequency response curve of the receiving hydrophone.

[0048] Figure 5 This is the bubble inversion result.

[0049] Figure 6This is a comparison chart of the scattering coefficient of the measured bubble group and the scattering coefficient corresponding to the measured results. DETAILED DESCRIPTION

[0050] The device is described in further detail below in conjunction with the accompanying drawings and specific embodiments.

[0051] like Figure 2 As shown, the present invention provides an acoustic inversion device for underwater bubble group size distribution based on forward and backscattering, which specifically includes the following components:

[0052] Signal source, which sends out the required known electrical signal;

[0053] High-frequency power amplifier, converts the electrical signal from the signal source into a high-power electrical signal output;

[0054] Oscilloscope, to monitor the electrical signals output by the signal source and high-frequency amplifier;

[0055] The transmitting transducer converts the electrical signal output by the high-frequency power amplifier into an acoustic signal and outputs it underwater;

[0056] Hydrophones, which convert acoustic signals received in water into electrical signals;

[0057] Collector, which collects the electrical signals received by the hydrophone in real time;

[0058] On the PC side, the electrical signals collected by the collector are stored and displayed;

[0059] Mounting frame, used to fix the device in place.

[0060] like Figure 1 As shown, the present invention provides an acoustic inversion method for underwater bubble group size distribution based on forward and backscattering, and its specific implementation process is as follows:

[0061] (a) The device is deployed and the transmitting transducer emits a signal;

[0062] With the transmitting transducer as the origin x=0, hydrophone #1 is placed at x=d1 along the axial direction, and hydrophone #2 is placed at x=d1+d2 along the axial direction.

[0063] The transmitting transducer transmits a single-frequency pulse sound signal with a frequency of ω1 into the bubble-containing water medium to be measured at x=0, and the 1# hydrophone and the 2# hydrophone simultaneously collect the single-frequency pulse sound signal;

[0064] (b) Perform Fourier transform on the direct wave signal waveform received by hydrophone #1 and read the incident sound pressure amplitude P1(ω1) of the bubble-containing water medium to be measured at the corresponding frequency ω1;

[0065] (c) Perform Fourier transform on the direct wave signal waveform received by hydrophone #2 and read the forward scattered sound pressure amplitude P2(ω1) of the bubble-containing water medium under test at the corresponding frequency ω1;

[0066] (d) Calculate the time delay τ of the single-frequency pulse echo signal transmitted in the bubble-containing water medium to be tested, perform Fourier transform on the backscattered signal waveform received by hydrophone #1 within the time delay τ, and read the backscattered sound pressure amplitude P of the bubble-containing water medium to be tested at the corresponding frequency ω1. b (ω1);

[0067] (e) Change the transmission frequency to perform frequency sweep, and the frequency sweep range is ω[ω1ω2…ω n ], repeat steps (b)-(d), for the radius range of the bubble-containing water medium to be tested R=[R1 R2…R m ], according to the joint theory of forward and backscattering:

[0068] λ(ω)=∫σ s (ω,R)N(R)dR (1)

[0069] in, is the backscattering cross section of a bubble with a radius of R under frequency ω excitation, N(R)=[N1(R1)N2(R2)…N m (R m )] is the number of bubbles with a radius of R, δ is the viscous damping coefficient, and ω0 is the resonance frequency of the bubble with a radius of R.

[0070] Discretization gives the inverse equation in matrix form:

[0071] λ(ω)=σ s (ω,R)N(R) (2)

[0072] (f) Inverse equation under positive and finite constraints:

[0073]

[0074] (g) Tikhonov regularization is introduced into the inversion equation:

[0075]

[0076] Among them, N is the exact solution of the inversion equation, N * is the initial estimate, ε is the regularization parameter, L = tridiag (1, -2, 1) is the tridiagonal matrix; the regularized solution N of the bubble group size distribution parameter of the bubble-containing water medium to be measured is obtained by calculation ε .

[0077] The present invention measures the incident sound pressure and the forward and backscattered sound pressure amplitudes, and uses the forward and backscattered joint theory to invert the bubble size distribution parameters. It has the advantages of simple operation and strong applicability. It is suitable for use in complex environments and can more quickly invert the size distribution of underwater bubble groups.

[0078] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0079] The structure of the field experiment device is as follows Figure 2 As shown, the transmission signal type is CW pulse signal, the signal amplitude is 500mv, the pulse frequency is swept from 53kHz to 143kHz, a total of 91 frequency points, the frequency step is 1kHz, 1#2# two 8103 hydrophones are coaxial with the transmitting transducer, and the data is collected by B&KPULSE collector. The acquisition time is 60s, the sampling rate is 524288Hz, the pulse width is 20ms, the sound speed in water c0=1480m / s, and the water medium density ρ0=998kg / m 3 , the radius of the bubble to be measured R0=(10,10.5,11,…,200)(μm), the gas density inside the bubble ρ g =1.29kg / m 3 , specific heat ratio γ = 1.4, the damping coefficient δ is set according to the Medwin model, and the regularization parameter is selected by the I-curve method.

[0080] The schematic diagram of the hydrophone receiving signal in one cycle is as follows Figure 3 As shown in the figure, the horizontal axis represents time and the vertical axis represents the received voltage response. Figure 3 As shown, it is the original signal obtained by the device through step (a).

[0081] The frequency response curve of the received sound pressure level of the hydrophone is as follows: Figure 4 As shown in the figure, two acquisitions were carried out in total. The first acquisition was performed by 1# hydrophone as 1_1, the first acquisition was performed by 2# hydrophone as 1_2, the second acquisition was performed by 1# hydrophone as 2_1, and the second acquisition was performed by 2# hydrophone as 2_2. Figure 4 Shown is the result obtained by the device through steps (b)-(e).

[0082] The bubble inversion results are as follows Figure 5 The result shown is the result obtained by the device through steps (f)-(g), which is also the output result of the device.

[0083] The comparison chart of the scattering coefficient of the measured bubble group and the scattering coefficient corresponding to the measured results is as follows: Figure 6 As shown, Figure 6 The measured scattering coefficient in the experiment and the scattering coefficient corresponding to the measurement results have a good fit, which reflects that the measurement error of the device is small.

[0084] From the above examples, it can be seen that the device of the present invention can be used to invert the bubble scale distribution parameters, reflect the influence of bubble group vibration and scattering on sound wave propagation, and realize the calculation of backscattered sound pressure of non-uniformly distributed bubbles, adapt to the non-uniform distribution of bubbles, fit the reality, and the calculation is simple and fast.

[0085] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. The acoustic inversion method for underwater bubble group size distribution based on forward and backscattering is characterized by: The following steps are involved: (a) The device is deployed and the transmitting transducer sends a signal; Taking the transmitting transducer as the origin , along the axial direction Place the 1# hydrophone at the location, along the axial direction 2# hydrophone is deployed at The frequency of the emission into the water medium containing bubbles to be tested is The single-frequency pulse sound signal is collected by the 1# hydrophone and the 2# hydrophone simultaneously; (b) Measure the incident sound pressure amplitude ; (c) Measure the forward scattered sound pressure amplitude ; (d) Measure the backscattered sound pressure amplitude ; (e) Change the transmission frequency to sweep the frequency, the sweep range is , repeat steps (b)-(d) and obtain the inversion equation in matrix form according to the discretized inversion equation of the forward and backscattering joint theory; In step (e), the radius range of the bubble-containing water medium to be tested is , according to the joint theory of forward and backscattering: ； in, , Frequency The radius under excitation is The bubble backscattering cross section, The radius is The number of bubbles, is the viscous damping coefficient, The radius is The bubble resonance frequency; Discretize formula (1) to obtain the inverse equation in matrix form: ； (f) The mathematical expression of the inversion equation under positive and finite constraints is: ； (g) Tikhonov regularization is introduced into the inversion equation, and the bubble group size distribution parameters of the bubble-containing water medium to be measured are obtained by calculation. The specific calculation formula is: ； in, is the exact solution of the inverse equation, is the initial estimate, is the regularization parameter, is a tridiagonal matrix; the canonical solution of the bubble group size distribution parameters of the bubble-containing water medium to be measured is obtained by calculation .

2. The acoustic inversion method for underwater bubble group size distribution based on forward and backscattering according to claim 1 is characterized in that: In step (b), the direct wave signal waveform received by hydrophone #1 is Fourier transformed to read the corresponding frequency The incident sound pressure amplitude of the water medium containing bubbles to be tested is .

3. The acoustic inversion method for underwater bubble group size distribution based on forward and backscattering according to claim 1 is characterized in that: In step (c), the direct wave signal waveform received by hydrophone #2 is Fourier transformed to read the corresponding frequency The forward scattered sound pressure amplitude of the bubble water medium to be tested .

4. The acoustic inversion method for underwater bubble group size distribution based on forward and backscattering according to claim 1 is characterized in that: In step (d), calculate the time delay of the single-frequency pulse echo signal emitted in the bubble-containing water medium to be tested , the delay received by hydrophone #1 Perform Fourier transform on the backscattered signal waveform and read the corresponding frequency Backscattered sound pressure amplitude of the water medium containing bubbles to be tested .

Images