Acoustic scattering and modulation calculation method and device for ultralow frequency waves of underwater target

Abstract

The invention relates to an underwater target ultralow frequency wave sound scattering and modulation calculation method and device, and the method comprises the steps: calculating a ULF wave based on a fluid-solid coupling numerical model taking a heaving sphere as a target; the numerical model comprises an incompressible NS equation, a turbulence model and a dynamic grid; mapping a flow field variable of the ULF wave in a stable period from a flow field grid to an acoustic grid based on a mapping model, and calculating an acoustic scattering field of the ULF wave based on a frequency domain acoustic disturbance equation; and in a stable period of the ULF wave, according to the scattering sound pressure amplitudes of the ULF wave at the moment when the vertical displacement of the center point of the free liquid level is 0 and the moment when the vertical displacement of the center point of the free liquid level is the maximum value, the amplitude modulation depth of the ULF wave on the incident sound wave signal is calculated. An effective calculation method is provided for calculation of sound scattering and modulation of the surface wave generated by underwater target movement through numerical simulation of the whole process of target movement, ULF surface wave and sound scattering and amplitude modulation calculation.

Description

Technical Field

[0001] This application relates to the field of underwater target acoustic scattering technology, specifically to a method and apparatus for calculating the acoustic scattering and modulation of ultra-low frequency waves from underwater targets. Background Technology

[0002] With the development of vibration reduction and noise reduction technologies, conventional passive methods for detecting underwater vehicles are becoming increasingly difficult, and the focus is shifting towards ultra-low frequency and active methods. Ultra-low frequency (ULF) surface gravity waves (ULF waves) generated by underwater vehicles during their movement can be detected and identified using forward scattering modulation technology, thus achieving the goal of detecting underwater vehicles. This method is known as the ULF method.

[0003] Existing acoustic scattering calculation methods are mainly used to calculate the acoustic scattering of underwater targets themselves, but there is a lack of effective numerical calculation methods for the acoustic scattering and modulation of surface waves generated by the target's motion. Summary of the Invention

[0004] This application provides a method and apparatus for calculating the acoustic scattering and modulation of ultra-low frequency waves from underwater targets, which can solve the technical problem of the lack of effective calculation methods for the acoustic scattering and modulation of surface waves generated by the motion of underwater targets in the prior art.

[0005] To achieve the above objectives, in a first aspect, this application provides a method for calculating the acoustic scattering and modulation of ultra-low frequency waves from underwater targets, the method comprising: ULF waves are calculated based on a fluid-structure interaction numerical model targeting a heaving sphere; the numerical model includes incompressible Navier-Stokes equations, a turbulence model, and a dynamic mesh.

[0006] The flow field variables of the ULF wave within a stable period are mapped from the flow field grid to the acoustic grid based on the mapping model, and the acoustic scattering field of the ULF wave is calculated based on the frequency domain acoustic perturbation equation.

[0007] Within a stable period of the ULF wave, the amplitude modulation depth of the ULF wave on the incident acoustic signal is calculated based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value.

[0008] Furthermore, in one embodiment, calculating the ULF wave based on a fluid-structure interaction numerical model targeting a heaving sphere includes: The heave motion of a sphere is simulated using an arbitrary Lagrange-Euler moving mesh method, forming fluctuations on the free liquid surface. Surface tension and gravity are directly applied to the free liquid surface as boundary conditions.

[0009] Transient calculations based on the incompressible Navier-Stokes equations yield periodically stable ULF waves.

[0010] Furthermore, in one embodiment, the incompressible NS equations consist of continuity equations and RANS equations, and employ... The turbulence model is closed.

[0011] Furthermore, in one embodiment, the flow field variables include background flow field velocity, pressure, and vertical displacement of the free liquid surface.

[0012] Furthermore, in one embodiment, the mapping model is constructed based on the background fluid-flow coupled multiphysics method and a dedicated mapping technique.

[0013] Furthermore, in one embodiment, the calculation of the ULF wave acoustic scattering field based on the frequency domain acoustic perturbation equation includes: Based on the frequency domain acoustic perturbation equation, the acoustic scattering field of the sphere without ULF wave and the acoustic scattering field under the combined action of the sphere and ULF wave are calculated respectively. The difference between the two is the ULF wave acoustic scattering field.

[0014] Furthermore, in one embodiment, the method further includes verifying the mapping model and the frequency domain acoustic perturbation equation, wherein the verification method includes: The accuracy of the mapping was verified by comparing the velocity distribution at the same location on the free surface before and after the mapping.

[0015] Under conditions without ULF waves, the spherical acoustic scattering results calculated by the frequency domain acoustic perturbation equation and the wave equation are compared to verify the effectiveness of the frequency domain acoustic control equation.

[0016] Furthermore, in one embodiment, the computational domains of both the ULF wave and the ULF wave acoustic scattering field are set as cuboids, and the computational domain of the acoustic scattering field is less than or equal to the computational domain of the ULF wave.

[0017] Furthermore, in one embodiment, calculating the amplitude modulation depth of the ULF wave on the incident sound wave signal based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value, respectively, includes: The difference between the ULF wave scattered sound pressure amplitude at the moment when the vertical displacement of the center point of the free liquid surface is at its maximum value and the ULF wave scattered sound pressure amplitude at the moment when the vertical displacement of the center point of the free liquid surface is 0 is calculated to obtain the modulation signal amplitude.

[0018] The amplitude modulation depth is obtained by calculating the ratio of the amplitude of the modulating signal to the amplitude of the carrier signal.

[0019] Secondly, this application provides a calculation device for acoustic scattering and modulation of ultra-low frequency waves from underwater targets, the device comprising: The flow field calculation module is used to calculate ULF waves based on a fluid-structure interaction numerical model targeting a heaving sphere; the numerical model includes incompressible Navier-Stokes equations, a turbulence model, and a dynamic mesh.

[0020] The acoustic scattering field calculation module is used to map the flow field variables of the ULF wave from the flow field grid to the acoustic grid within a stable period based on the mapping model, and to calculate the acoustic scattering field of the ULF wave based on the frequency domain acoustic perturbation equation.

[0021] The amplitude modulation depth calculation module is used to calculate the amplitude modulation depth of the ULF wave on the incident sound wave signal within a stable period of the ULF wave, based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value.

[0022] The beneficial effects of the technical solutions provided in this application include: This application calculates ULF waves based on a fluid-structure interaction numerical model targeting a heaving sphere. Using a mapping model, the flow field variables of the ULF waves within a stable period are mapped from the flow field mesh to the acoustic mesh, and the acoustic scattering field of the ULF waves is calculated based on the frequency domain acoustic perturbation equation. Within a stable period of the ULF waves, the amplitude modulation depth of the incident acoustic wave signal by the ULF waves is calculated based on the amplitude of the scattered acoustic pressure at the moments when the vertical displacement of the center point of the free surface is 0 and at its maximum value. Through numerical simulation of the entire process of target motion, ULF surface waves, acoustic scattering, and amplitude modulation calculation, an effective calculation method is provided for the calculation of acoustic scattering and modulation of surface waves generated by underwater target motion. Attached Figure Description

[0023] Figure 1 This is a schematic diagram illustrating the process of envelope detection and envelope spectrum acquisition for amplitude modulation signals implemented in this application.

[0024] Figure 2 This is a flowchart illustrating the acoustic scattering and modulation calculation of ultra-low frequency waves from an underwater target according to an embodiment of this application.

[0025] Figure 3 This is a schematic diagram of the overall computational framework for acoustic scattering and modulation in an embodiment of this application.

[0026] Figure 4 This is a schematic diagram of the flow field computation domain and boundary conditions in an embodiment of this application.

[0027] Figure 5 This is a schematic diagram of the flow field mesh in an embodiment of this application.

[0028] Figure 6 This is a schematic diagram of the sound field calculation domain and boundary conditions in an embodiment of this application.

[0029] Figure 7This is a schematic diagram of the sound field grid in an embodiment of this application.

[0030] Figure 8 This is a schematic diagram of the distribution of the vertical velocity Vz of the ULF wave before and after mapping, and a magnified free liquid surface, as shown in the embodiments of this application.

[0031] Figure 9 This is a schematic diagram comparing the radial velocity of the free liquid surface before and after mapping in an embodiment of this application.

[0032] Figure 10 This is a schematic diagram comparing the vertical velocity of the free liquid surface before and after mapping in an embodiment of this application.

[0033] Figure 11 This is a schematic diagram comparing the acoustic perturbation equation and the wave equation for the spherical acoustic scattering results under ULF wave-free conditions in this application embodiment.

[0034] Figure 12 This is a schematic diagram showing the changes in the vertical displacement z and vertical velocity Vz of the center point of the free liquid surface over time in an embodiment of this application.

[0035] Figure 13 This is a schematic diagram of the vertical velocity distribution of the ULF wave at time points 6.84s and 7.22s in the embodiments of this application.

[0036] Figure 14 This is a schematic diagram of the ULF wave scattering results at time points 6.84s and 7.22s in the embodiments of this application.

[0037] Figure 15 This is a schematic diagram of the spatial distribution of the scattered acoustic pressure difference and modulation depth in an embodiment of this application.

[0038] Figure 16 This is a block diagram for calculating the acoustic scattering and modulation of ultra-low frequency waves from an underwater target according to an embodiment of this application. Detailed Implementation

[0039] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0040] First, the method of this application is based on the theory of ULF wave scattering and modulation. ULF wave is used as the modulation signal, single-frequency sound signal (i.e., the incident sound wave used to detect ULF wave) is used as the carrier signal, and amplitude modulation (AM) is used as the research object. The principle of signal amplitude modulation and demodulation is given below.

[0041] Compared to the DNS (Direct Numerical Simulation) equations, this application uses acoustic perturbation equations for sound field calculations. These equations are simplified versions of the NS (Navier-Stokes) equations, making them suitable for solving and reducing computational complexity. Acoustic and fluid variables are calculated separately, assuming that the acoustic variables are perturbations much smaller in magnitude than the fluid variables. Indicates the presence of background flow field Convection acoustics If we consider the sound field variable, then the following relationship holds: (1), in, Indicates total pressure. Indicates total density, Indicates the total speed. Indicates the pressure of the background flow field. This represents the density of the background flow field. Represents the velocity of the background flow field. The sound pressure level represents the sound field. Represents the density of the sound field. This indicates the velocity of the vibration point.

[0042] For motion in water, after linearizing the Navier-Stokes equations, based on isentropic adiabatic conditions (energy equations disappear) and the inviscidity assumption, the fluid dynamics equations under source-free conditions consist of a continuity equation, a motion equation, and a state equation: (2), in, This represents the entropy of the background flow field.

[0043] Substituting equation (1) into equation (2), we can obtain the simplified acoustic field control equation for acoustic scattering in the flow field: (3), in, c It indicates the speed of sound.

[0044] Reaction term And the process of substituting formula (1) into formula (2) to simplify and obtain formula (3) It is the background average flow. and gradient , Harmony field vibration velocity The interaction term; the reaction term represents sound reflection, refraction, and diffraction during sound transmission; the convection term... For average fluid flow Multiplying by the sound field velocity gradient, the effect of flow on sound is not merely a small increase in sound velocity. Equation (3) can theoretically analyze and numerically solve the flow-sound coupling effect between ULF waves and the sound field.

[0045] To theoretically reveal the acoustic scattering modulation mechanism of ULF waves, a velocity potential function is introduced to transform equation (3) into a single-variable acoustic perturbation equation. Velocity potential function The relationship between sound pressure and vibration velocity is as follows: (4), in, The mass derivative is the sum of the local derivative and the convective derivative. The local derivative represents the rate of change caused by changes in local time, while the convective derivative represents the rate of change caused by spatial motion.

[0046] velocity potential function Substituting into formula (3) and rearranging, we obtain the acoustic perturbation equation that ignores higher-order terms: (5), in, The wave equation is not coupled with the flow; these are uncoupled terms. express. For the flow-sound coupling term, use express.

[0047] The oscillation frequency is gravitational wave velocity It can be represented as: (6), Substituting equation (6) into the coupling term for: (7), Based on the properties of the Fourier transform and Euler's formula: (8), Coupling terms Transforming from the time domain to the frequency domain yields: (9), in, (10) (11), (12).

[0048] This indicates that ULF waves can change the spatial distribution of the sound field, but will not change the sound wave frequency, producing a scattered sound field with the frequency of the incident sound wave (i.e., the frequency of the aforementioned carrier signal). The strength of the scattered sound field depends on... size. , This indicates that the ULF wave field not only alters the spatial distribution of the sound field, but also scatters sound waves and generates a double-sideband modulated sound field containing the oscillation frequency of the ULF wave field, with the sidebands being... and The strength of the modulated sound field depends on the scattering modulation term. , The size of the sound wave. In summary, the scattering of sound waves by the ULF wave field will simultaneously produce sound scattering and sound modulation effects.

[0049] For the modulated signal received by the sensor, the amplitude-modulated signal (AM signal) can be simplified mathematically as follows: (13) in, Indicates the modulated signal. Indicates the amplitude of the modulated signal. Indicates the modulation frequency. Indicates carrier signal, Indicates the amplitude of the carrier signal. Indicates the carrier frequency.

[0050] For a received modulated signal, the envelope and envelope spectrum can be detected using an envelope detector. See also Figure 1 As shown, Figure 1 This diagram illustrates the process of envelope detection and envelope spectrum acquisition for amplitude-modulated signals. It shows that normalizing the envelope spectrum using the carrier signal amplitude yields the modulation depth. m .

[0051] The modulation coefficient (modulation depth) of an AM signal is defined as the modulation amplitude divided by the carrier amplitude, i.e.: (14).

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0053] In a first aspect, embodiments of this application provide a method for calculating the acoustic scattering and modulation of ultra-low frequency waves from underwater targets.

[0054] In one embodiment, see Figure 2As shown, the above-mentioned method for calculating the acoustic scattering and modulation of ultra-low frequency waves from underwater targets includes: S1. Calculate ULF waves based on a fluid-structure interaction numerical model targeting a heaving sphere; the numerical model includes the incompressible Navier-Stokes equations, a turbulence model, and a dynamic mesh.

[0055] S2. Based on the mapping model, the flow field variables of the ULF wave within a stable period are mapped from the flow field grid to the acoustic grid, and the acoustic scattering field of the ULF wave is calculated based on the frequency domain acoustic perturbation equation. In this embodiment, the flow field variables include the background flow field velocity, pressure, and vertical displacement of the center point of the free liquid surface.

[0056] S3. Within one stable period of the ULF wave, calculate the amplitude modulation depth of the incident acoustic signal by the ULF wave based on the amplitude of the scattered acoustic pressure of the ULF wave at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value.

[0057] In this embodiment, a fluid-structure interaction numerical model targeting a heaving sphere is used to calculate the ULF wave. Then, a mapping model is used to losslessly map the flow field variables within a stable period to an acoustic mesh, and the acoustic scattering field of the ULF wave is calculated based on the frequency domain acoustic perturbation equation. This accurately extracts the scattered sound pressure distribution contributed solely by the ULF wave, solving the problem that traditional methods cannot decouple surface gravity waves from the target body's scattering. Finally, within a stable period of the ULF wave, the scattered sound pressure amplitude is captured at two characteristic moments: the vertical displacement of the center point of the free liquid surface is zero and its maximum value. The amplitude modulation depth is quantified, achieving full-chain numerical quantization of moving target-surface wave-acoustic modulation. These three steps collaboratively provide a repeatable and verifiable calculation process for the amplitude modulation of the incident acoustic signal by the ULF surface gravity wave, providing an effective calculation method for ULF wave forward scattering detection, thereby improving the probability of identifying long-range, concealed underwater vehicles.

[0058] See Figure 3 As shown, Figure 3 This diagram illustrates the overall computational framework for acoustic scattering and modulation, primarily comprising fluid-structure interaction (FSI) and fluid-acoustic interaction (FAI) to address the acoustic scattering and modulation of ULF waves generated by underwater structures. The main computational idea is as follows: In terms of fluid dynamics, the incompressible Navier-Stokes equations are time-averaged to obtain the Reynolds-averaged Navier-Stokes (NS) equations, which are then combined with… Turbulence models are used to perform time-domain calculations to simulate fluid-structure interaction, obtaining the ULF (ultra-fluid-free) flow field (i.e., background flow field) behind the flow-acoustic coupling. In terms of acoustics, the Navier-Stokes equations are linearized with small perturbation assumptions and are assumed to be inviscid (dynamic viscosity). μ and volume viscosity kThe acoustic disturbance equations are obtained by setting all values ​​to 0. Frequency domain calculations are then performed to simulate flow-acoustic coupling, yielding the sound field affected by the instantaneous ULF wave. To improve computational efficiency and accuracy, two sets of meshes with different numbers of meshes are used, depending on the computational load. The flow field mesh is used to simulate fluid-structure interaction, obtaining the ULF flow field variables. These variables are then mapped to the sound field mesh through mesh mapping to calculate the simulated flow-acoustic coupling, resulting in the acoustic scattering and modulation results of the ULF wave.

[0059] Furthermore, in one embodiment, in step S1 above, the ULF wave is calculated based on a fluid-structure interaction numerical model targeting a heaving sphere. The specific steps are as follows: The heave motion of a sphere is simulated using an arbitrary Lagrange-Euler moving mesh method, forming fluctuations on the free liquid surface. Surface tension and gravity are directly applied to the free liquid surface as boundary conditions.

[0060] Transient calculations based on the incompressible Navier-Stokes equations yield periodically stable ULF waves.

[0061] In this embodiment, in order to require less computational resources, the motion of underwater objects is simulated based on the arbitrary Lagrange-Eulerian dynamic mesh method. The model is a free liquid surface that does not involve any topological changes, and its surface tension and gravity are directly applied to the free liquid surface as boundary conditions.

[0062] Since the structural boundary is considered a rigid boundary, the incompressible Navier-Stokes equations can be solved using DNS, RANS (Reynolds-Averaged Navier-Stokes), LES (Large Eddy Simulation), and DES (etached Eddy Simulation), depending on the numerical simulation method used for turbulence. DES or LES methods can capture details of the flow field, such as cavitation, Wakefield evolution, and turbulent kinetic energy diffusion caused by vortices. However, these two methods require high-performance computers under high Reynolds number conditions, making them difficult to apply to engineering calculations. When qualitatively analyzing ULF waves generated by structural oscillations, the focus is on the relationship between the average pressure and velocity. Therefore, the RANS method is suitable and offers the best cost-effectiveness, capable of solving fluid variables on fixed Eulerian or bulk dynamic grids. In this embodiment, the aforementioned incompressible Navier-Stokes equations consist of the continuity equation and the RANS equation, and are closed using a turbulence model. Turbulence model. The formulas for the continuity equation and the RANS equation are as follows: (15) (16) in, , Represents the tensor exponent. This represents the average density by volume fraction. This represents the average speed. This represents the average pressure. This represents the corresponding speed fluctuation value, and the related terms for the fluctuating speed. This refers to Reynolds stress. Indicates spatial location, t Indicates time, μ Indicates the dynamic viscosity of a fluid. This represents the volumetric force component per unit mass.

[0063] In numerical simulation, the dimensions of the computational model should ideally be close to the actual solid size. Due to computational limitations, a scaled-down model can be selected. In this embodiment, a sphere with a radius of 0.1m is chosen as the oscillation simulation object. The computational domain of the ULF wave is a cuboid with a length of 10m, a width of 5m, and a depth of 5m. See [link to documentation]. Figure 4 and Figure 5 As shown, Figure 4 This diagram illustrates the computational domain and boundary conditions for the flow field, including a perfectly matched layer, walls, impedance boundaries, and symmetric boundaries. The impedance boundary represents the air impedance, indicating the water and air boundaries. The perfectly matched layer is used to simulate a non-reflective environment. Figure 5 The diagram shows the flow field mesh, which has 1.22 million degrees of freedom (the total degrees of freedom increase to 2.33 million if internal variables are introduced).

[0064] Furthermore, in one embodiment, the mapping model in step S2 above is constructed based on the background fluid-flow coupled multiphysics method and a dedicated mapping technique.

[0065] To perform mesh mapping, the computational domain of the acoustic scattering field is smaller than or equal to that of the ULF wave. In this embodiment, the numerical simulation is performed on a workstation with 512GB of memory. The computational domain of the ULF wave acoustic scattering field is a cuboid with a length of 8m, a width of 0.22m, and a depth of 1.3m. Figure 6 This diagram illustrates the computational domain and boundary conditions of the sound field, including free surfaces, no-slip walls, slipping walls, and symmetric boundaries. The sound field mesh is based on the sound scattering numerical simulation with a maximum frequency of 10 kHz, and 5 meshes per wavelength. See [link to relevant documentation]. Figure 7 As shown, Figure 7 This is a schematic diagram of the sound field mesh, which has 5 million degrees of freedom for solving.

[0066] In this embodiment, since the flow field and the sound field are solved on two different computational grids, it is necessary to map the computational variables of the flow field to the sound field. According to the acoustic perturbation equation, the flow field variables required are pressure and velocity. In Comsol software, the background flow field variables and water interface displacement can be mapped from the CFD (Computational Fluid Dynamics) grid to the sound field grid using the "background fluid-flow coupling" multiphysics method and the dedicated "mapping" study. This also allows the CFD interface results to be used for the Perfectly Matched Layer (PML).

[0067] Furthermore, in one embodiment, the method further includes verifying the mapping model and the frequency domain acoustic perturbation equation, wherein the verification method includes: The accuracy of the mapping was verified by comparing the velocity distribution at the same location on the free surface before and after the mapping.

[0068] Under conditions without ULF waves, the spherical acoustic scattering results calculated by the frequency domain acoustic perturbation equation and the wave equation are compared to verify the effectiveness of the frequency domain acoustic control equation.

[0069] In this embodiment, before numerical calculation, the correctness and effectiveness of the established mapping model and acoustic scattering and modulation model (i.e., frequency domain acoustic perturbation equations) need to be verified. Specifically: (1) Validate the mapping model: The simulation conditions are as follows: r =0.1m, d =0.5m, A 0 = 0.05 f s =0.67Hz, and Figures 4 to 7 The model has a perfectly matching layer region width of 0.1m, where... r Represents the radius of the sphere. d This represents the distance from the top of the ball to the surface of the still water. A 0 represents the oscillation amplitude. f s Indicates the hysteresis frequency.

[0070] The ULF flow field calculated on the flow field grid at 7.22s was studied by coupling and mapping with the background fluid flow to obtain the velocity field mapped on the acoustic grid, and then compared with the original velocity on the flow field grid. Figure 8 The diagram shows the distribution of the vertical velocity Vz of the ULF wave before and after mapping, and the magnified free liquid surface. It can be seen that the velocity distribution is consistent, and the boundary of the free liquid surface can be synchronously mapped to the boundary of the sound field. Figure 9 This is a schematic diagram comparing the radial velocities of the free liquid surface before and after mapping. Figure 10 This is a schematic diagram comparing the vertical velocities of the free surface before and after mapping. Figure 9 and Figure 10 It can be seen that the velocities of the free surface are completely identical before and after the mapping, proving the correctness and effectiveness of the mapping model.

[0071] (2) Verification of the acoustic scattering and modulation model: The aim is to analyze the correctness and effectiveness of the acoustic perturbation equations, and to apply them to the non-ULF wave ( The acoustic scattering results of a sphere simulated by the acoustic perturbation equation under the given conditions are compared with those simulated by the wave equation. The simulation conditions are consistent with the above-mentioned mapping model verification.

[0072] Figure 11 This is a schematic diagram comparing the acoustic perturbation equation and the wave equation for spherical acoustic scattering under ULF wave-free conditions. It shows the scattered sound pressure distribution at X=0m, Z=-1m, and Y=-4~4m when the carrier signal frequency is 2kHz, where X represents the downstream direction, Z represents the vertical direction, and Y represents the horizontal direction.

[0073] It can be seen that, The solution obtained from the acoustic perturbation equation under the given conditions is basically similar to the solution from the wave equation, but with a small error, on the order of 10. -3 The modulation depth of the stream is also on the order of magnitude and will be affected, so it is necessary to use [a specific method] when calculating the modulation depth. The acoustic perturbation equation under the given conditions is used as the solution equation in the absence of ULF waves, and the wave equation cannot be used.

[0074] Furthermore, in one embodiment, in step S2 above, the calculation of the ULF wave acoustic scattering field based on the frequency domain acoustic perturbation equation specifically involves the following steps: Based on the frequency domain acoustic perturbation equation, the acoustic scattering field of the sphere without ULF wave and the acoustic scattering field under the combined action of the sphere and ULF wave are calculated respectively. The difference between the two is the ULF wave acoustic scattering field.

[0075] Transforming the above formula (3) into a frequency domain equation, we obtain the frequency domain acoustic perturbation equation: (17).

[0076] The above calculation of the amplitude modulation depth of the ULF wave on the incident sound wave signal is based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value, respectively. The specific steps are as follows: The amplitude of the modulated signal is obtained by calculating the difference between the ULF wave scattered sound pressure amplitude at the moment when the vertical displacement of the center point of the free liquid surface is at its maximum value and the ULF wave scattered sound pressure amplitude at the moment when the vertical displacement of the center point of the free liquid surface is 0.

[0077] The amplitude modulation depth is obtained by calculating the ratio of the amplitude of the modulating signal to the amplitude of the carrier signal.

[0078] In this embodiment, see Figure 12 As shown, Figure 12 This diagram illustrates the variation of the vertical displacement z and vertical velocity Vz at the center point of the free liquid surface over time. The numbers 1, 2, 3, 4, 5, and 6 in the diagram represent the period numbers. Figure 12 There are 6 cycles. One cycle can be randomly selected; in this embodiment, the 5th cycle is chosen, with a time range of 5.72s to 7.22s. Two time points, A: 6.84s and B: 7.22s, are taken when the displacement of the free liquid surface center point is 0m and the maximum displacement, respectively, for ULF wave scattering and modulation analysis. The above formula (14) is used to calculate the modulation depth. m In numerical simulation, the background sound pressure is equivalent to the amplitude of the carrier signal. The sound pressure change from 6.84s to 7.22s, with a value of 1 Pa, represents the amplitude of the modulation signal. Therefore, modulation depth m The value represents the change in sound pressure amplitude from 6.84s to 7.22s.

[0079] The mapped vertical velocity distribution of the ULF wave and the ULF wave scattering results for the two time points mentioned above are respectively referred to in [reference 1]. Figure 13 and Figure 14 As shown, Figure 14 The ULF wave scattering result (i.e., the ULF wave acoustic scattering field) is obtained by subtracting the spherical scattering without ULF waves from the spherical and flow scattering under the condition of ULF wave presence. Figure 13 In the results, 6.84s and 7.22s correspond to the moments when the vertical displacement at the center point of the free liquid surface is 0 and at its maximum, respectively, and also to the moments when the vertical velocity is at its maximum and 0. These also correspond to the minimum and maximum values ​​of the ULF wave scattering field, respectively. The ULF wave scattering results show that the magnitude of the scattered field is mainly determined by the flow around the sphere and the amplitude of the vertical displacement at the center point of the free liquid surface. The scattering sources are mainly concentrated around the sphere and at the center point of the free liquid surface. The scattered field is mainly distributed near the sphere, forward, and backward, with forward scattering being greater than backward scattering.

[0080] The amplitude modulation of the acoustic signal by the ULF wave is reflected in the relative change of the scattered sound pressure amplitude over time. See also Figure 15 As shown, Figure 15 This is a schematic diagram of the spatial distribution of the scattered acoustic pressure difference and modulation depth, from Figure 15It can be seen that the modulation (i.e., modulation depth) of the single-frequency acoustic signal can be obtained by subtracting the scattered sound pressure of the ULF wave at 7.22s and 6.84s. When the acoustic signal frequency is 5kHz, the amplitude of the scattered sound pressure difference, i.e., the modulation depth, is on the order of 10⁻⁴ to 10⁻³; the forward scattered sound pressure difference is greater than the backward one. Therefore, the amplitude modulation of the acoustic signal by the time-varying ULF wave can be obtained by using the amplitude of the scattered sound pressure when the sum of the vertical displacement amplitudes of the center point of the free liquid surface is zero. When the acoustic signal frequency is 5kHz, the amplitude of the scattered sound pressure difference, i.e., the modulation depth, is on the order of 10⁻⁴ to 10⁻³. -4 ~10 -3 The magnitude of the forward-scattering sound pressure difference is greater than that of the backward-scattering sound pressure difference.

[0081] Secondly, embodiments of this application provide a calculation device for acoustic scattering and modulation of ultra-low frequency waves from underwater targets, see [link to relevant documentation]. Figure 16 As shown, the underwater target ultra-low frequency wave acoustic scattering and modulation calculation device includes a flow field calculation module, an acoustic scattering field calculation module, and an amplitude modulation depth calculation module, specifically: The flow field calculation module is used to calculate ULF waves based on a fluid-structure interaction numerical model targeting a heaving sphere; the numerical model includes the incompressible Navier-Stokes equations, a turbulence model, and a dynamic mesh.

[0082] The acoustic scattering field calculation module is used to map the flow field variables of the ULF wave from the flow field grid to the acoustic grid within a stable period based on the mapping model, and to calculate the acoustic scattering field of the ULF wave based on the frequency domain acoustic perturbation equation.

[0083] The amplitude modulation depth calculation module is used to calculate the amplitude modulation depth of the ULF wave on the incident sound wave signal within a stable period of the ULF wave, based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value.

[0084] This application constructs a complete numerical channel of "heavy rigid sphere - ULF wave - acoustic scattering modulation," forming a replicable and scalable method for calculating acoustic scattering and modulation. First, a rigid sphere is used to replace the actual underwater vehicle, and the incompressible Navier-Stokes equations are solved on the flow field grid to capture the ULF wave within the stable period. Then, a mapping model is used to map the flow field variables to the acoustic grid, and the forward and backward scattered sound pressures are obtained in one step using the linearized and inviscid frequency-domain acoustic perturbation equations with small perturbations. Finally, the amplitude modulation depth is defined by the difference in scattered sound pressure corresponding to the two phases of the extreme vertical displacement at the center point of the free liquid surface, achieving quantitative extraction of the modulation effect. Through numerical simulation of the entire process of target motion, ULF surface waves, and acoustic scattering and amplitude modulation calculations, an effective calculation method is provided for calculating the acoustic scattering and modulation of surface waves generated by underwater target motion.

[0085] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0086] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.

[0087] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.

[0088] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.

[0089] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.

[0090] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods described in the various embodiments of this application.

[0091] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.

Claims

1. A method for calculating the acoustic scattering and modulation of ultra-low frequency waves from underwater targets, characterized in that, The method includes: ULF waves are calculated based on a fluid-structure interaction numerical model targeting a heaving sphere; the numerical model includes incompressible Navier-Stokes equations, a turbulence model, and a dynamic mesh. The flow field variables of the ULF wave within a stable period are mapped from the flow field grid to the acoustic grid based on the mapping model, and the acoustic scattering field of the ULF wave is calculated based on the frequency domain acoustic perturbation equation. Within a stable period of the ULF wave, the amplitude modulation depth of the ULF wave on the incident acoustic signal is calculated based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value.

2. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 1, characterized in that, The calculation of ULF waves based on the fluid-structure interaction numerical model targeting a heaving sphere includes: The heave motion of a sphere is simulated using the arbitrary Lagrange-Euler moving mesh method, forming a wave on the free liquid surface. Surface tension and gravity are directly applied to the free liquid surface as boundary conditions. Transient calculations based on the incompressible Navier-Stokes equations yield periodically stable ULF waves.

3. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 2, characterized in that, The incompressible NS equations consist of continuity equations and RANS equations, and employ... The turbulence model is closed.

4. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 1, characterized in that, The flow field variables include background flow field velocity, pressure, and vertical displacement of the free liquid surface.

5. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 1, characterized in that, The mapping model is constructed based on the background fluid-flow coupled multiphysics method and a dedicated mapping technique.

6. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 1, characterized in that, The calculation of the ULF wave acoustic scattering field based on the frequency domain acoustic perturbation equation includes: Based on the frequency domain acoustic perturbation equation, the acoustic scattering field of the sphere without ULF wave and the acoustic scattering field under the combined action of the sphere and ULF wave are calculated respectively. The difference between the two is the ULF wave acoustic scattering field.

7. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 1, characterized in that, It also includes verifying the mapping model and the frequency domain acoustic perturbation equation, and the verification methods include: Compare the velocity distribution at the same location on the free surface before and after mapping to verify the accuracy of the mapping; Under conditions without ULF waves, the spherical acoustic scattering results calculated by the frequency domain acoustic perturbation equation and the wave equation are compared to verify the effectiveness of the frequency domain acoustic control equation.

8. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 1, characterized in that, The computational domains of both the ULF wave and the ULF wave acoustic scattering field are set to cuboids, and the computational domain of the acoustic scattering field is less than or equal to the computational domain of the ULF wave.

9. The method for calculating acoustic scattering and modulation of ultra-low frequency waves from underwater targets as described in claim 1, characterized in that, The calculation of the amplitude modulation depth of the ULF wave on the incident sound wave signal based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value includes: The difference between the ULF wave scattered sound pressure amplitude at the moment when the vertical displacement of the center point of the free liquid surface is at its maximum value and the ULF wave scattered sound pressure amplitude at the moment when the vertical displacement of the center point of the free liquid surface is 0 is calculated to obtain the modulation signal amplitude. The amplitude modulation depth is obtained by calculating the ratio of the amplitude of the modulating signal to the amplitude of the carrier signal.

10. A computing device for acoustic scattering and modulation of ultra-low frequency waves from underwater targets, characterized in that, The device includes: The flow field calculation module is used to calculate ULF waves based on a fluid-structure interaction numerical model targeting a heaving sphere; the numerical model includes incompressible Navier-Stokes equations, a turbulence model, and a dynamic mesh. The acoustic scattering field calculation module is used to map the flow field variables of the ULF wave from the flow field grid to the acoustic grid within a stable period based on the mapping model, and to calculate the acoustic scattering field of the ULF wave based on the frequency domain acoustic perturbation equation. The amplitude modulation depth calculation module is used to calculate the amplitude modulation depth of the ULF wave on the incident sound wave signal within a stable period of the ULF wave, based on the ULF wave scattered sound pressure amplitude at the moments when the vertical displacement of the center point of the free liquid surface is 0 and at its maximum value.

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