A method for predicting transient radiated sound field of shallow water channel based on equivalent source method

Abstract

This invention discloses a transient radiated sound field prediction method for shallow sea channels based on the equivalent source method, solving the high-frequency calculation problem of complex models. By converting the time-domain excitation to the frequency-domain spectrum, the low-frequency response of the model is calculated, and the multipole equivalent source is inverted to form an equivalent source array. Through full-space external field calculation, radiation directivity data for any frequency band in the free field is obtained. This data is then used as the sound source input to the finite element shallow sea channel model to calculate the frequency-domain radiation characteristics at any location in the entire space. The result is then inversely transformed back to the time domain, achieving efficient transient sound field prediction. This method utilizes equivalent sources to achieve high- and low-frequency information conversion, avoiding direct high-frequency simulation, and is suitable for rapid sound field prediction of large targets in shallow sea channels.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic engineering technology, specifically to a method for predicting transient radiated sound fields in shallow sea channels based on the equivalent source method. Background Technology

[0002] In the field of underwater acoustic engineering, shallow sea channels, as a typical complex underwater acoustic propagation environment, exhibit complex characteristics of strong time-varying and multimodal superposition in their multipath effects, sound velocity profile layering, and boundary reflection. Accurate prediction of transient radiated sound fields is a core technological prerequisite for applications such as underwater target detection, underwater acoustic communication, and performance evaluation of underwater acoustic equipment, directly affecting the operational efficiency and reliability of underwater systems.

[0003] Existing methods for predicting the radiated acoustic field in shallow sea channels are mainly divided into direct numerical methods and semi-analytical methods. While direct numerical methods can handle acoustic field calculations for complex geometric models, they face challenges such as difficult mesh generation, high transient simulation time consumption, and the accuracy of far-field calculations being easily affected by boundary condition truncation, making it difficult to meet the needs of rapid prediction in engineering scenarios. Semi-analytical methods, while computationally efficient, are less adaptable to complex seabed topography, non-uniform sound velocity profiles, and complex models, and are prone to accuracy loss in the prediction of transient acoustic fields with multiple scattering paths superimposed.

[0004] The equivalent source method, as an efficient acoustic modeling approach, approximates the radiation field of a complex real-world model by arranging multipole equivalent sound sources and using the superposition of their radiation fields, without requiring fine meshing of the complex structure. When dealing with complex models, this method effectively avoids the high-frequency computational difficulties of direct numerical simulation—by rationally configuring the equivalent source parameters, the high-frequency radiation characteristics of the complex model are transformed into calculations of the radiation characteristics of the equivalent source, significantly reducing computational load and quickly obtaining accurate radiation directivity data. Existing equivalent source method-based solutions mostly focus on steady-state sound fields or uniform channel scenarios. Research on their adaptability to transient excitations in complex shallow sea channels still has room for improvement. Especially when using frequency-domain indirect methods to process transient signals, the coupling effect between complex channel characteristics and the equivalent source radiation field has not been fully studied, and the practicality and accuracy of related technical solutions still need further optimization.

[0005] Therefore, developing a transient radiated sound field prediction method that is adapted to complex shallow sea channels and models and balances computational efficiency and prediction accuracy is of great significance for promoting practical applications in the field of underwater acoustics engineering. Summary of the Invention

[0006] Purpose of the invention: The purpose of this invention is to provide a method for predicting transient radiated acoustic fields in shallow sea channels based on the equivalent source method, which can solve the problem of high-frequency calculation difficulties based on complex models of shallow sea channels.

[0007] Technical solution: The present invention provides a method for predicting transient radiated acoustic fields in shallow sea channels based on the equivalent source method, comprising:

[0008] The time-domain transient excitation signal is converted into a frequency-domain excitation spectrum using a frequency-domain indirect method; the frequency-domain excitation spectrum is used to transiently excite a complex model; after transient excitation, the low-frequency radiation directivity data of the response point is obtained by three-dimensional full-space external field calculation;

[0009] Based on the low-frequency radiation directivity data, an equivalent multipole sound source adapted to the complex model is inverted; the equivalent multipole sound source is arranged inside or on the surface of the complex model to form an equivalent source array;

[0010] Three-dimensional full-space external field calculations are performed on the equivalent source array to obtain full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band.

[0011] A shallow sea channel model is constructed, and the radiation directivity data of any profile in the entire space of the arbitrary frequency band is used as the sound source of the shallow sea channel model. Combined with the layered sound velocity profile, irregular boundary and multiple scattering path characteristics of the shallow sea channel, the frequency domain radiation characteristics of the complex model at any position in the entire space of the shallow sea channel model are calculated.

[0012] The frequency domain radiation characteristics are inversely transformed into time domain radiation characteristics to predict the transient radiated sound field of a complex shallow sea channel model.

[0013] Furthermore, the step of using the frequency domain excitation spectrum to transiently excite the complex model, and then obtaining the low-frequency radiation directivity data of the response point after excitation through three-dimensional full-space external field calculation, includes:

[0014] Import the frequency domain excitation spectrum into the simulation software and load the actual excitation position of the complex model; arrange three-dimensional monitoring points in the external field of the complex model, with the geometric center of the complex model as the origin and the distance between the points as the radius based on the size of the complex model and satisfying the external field conditions; run transient excitation simulation, and after the calculation is completed, extract the sound pressure amplitude and phase data of each monitoring point and convert them into sound pressure level to form low-frequency radiation directivity data.

[0015] Furthermore, the step of inverting and deriving the equivalent multipole sound source adapted to the complex model based on the low-frequency radiation directivity data includes:

[0016] Based on the geometric complexity of the complex model and the error requirements of its radiation characteristics, a multipole combination is set up. A suitable combination method is determined through error assessment to obtain the corresponding spherical harmonic functions, wavelengths, and recursive coefficients. Further calculations are then performed to obtain the amplitude and spacing of each pole, where the spherical harmonic function coefficients are:

[0017] ;

[0018] in, These are the coefficients of the spherical harmonic function; It is a conjugate complex number; It is the order; It is an ordinal number; It is a directional function; and These are the pitch angle and the azimuth angle, respectively.

[0019] Furthermore, the step of performing three-dimensional full-space external field calculations on the equivalent source array to obtain full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band includes:

[0020] A perfectly matched layer is set outside the water area to absorb boundary reflected sound waves; an equivalent source array is loaded onto the water area, and the finite element method is used to calculate and generate the free field radiation directivity data of the multipole equivalent source in any frequency band across the entire space.

[0021] Furthermore, the construction of the shallow sea channel model based on ray theory uses the arbitrary frequency band full-space arbitrary profile radiation directivity data as the sound source of the shallow sea channel model. Combining the layered sound velocity profile, irregular boundaries, and multi-scattering path characteristics of the shallow sea channel, the frequency domain radiation characteristics of the complex model at any location in the full space of the shallow sea channel model are calculated, including:

[0022] A shallow sea channel model is constructed based on seabed parameters, and the radiation directivity data is exported as a .sbp format to adapt to the shallow sea channel model and serve as the sound source for the shallow sea channel model.

[0023] By combining the layered sound velocity profile, irregular boundary and multiple scattering path characteristics of the shallow sea channel, the frequency domain radiation characteristics of the complex model at any position in the whole space of the shallow sea channel model are calculated.

[0024] The sound source location, receiver depth, number of receivers, and start and end points are set in the shallow sea channel model based on ray theory. The shallow sea channel model is run and the key indicators at any location in the entire space are output. The key indicators include propagation loss, sound pressure amplitude, and phase.

[0025] Furthermore, the inverse transformation of the frequency domain radiation characteristic results into the time domain radiation characteristic results to complete the prediction of the transient radiated sound field of the complex model of the shallow sea channel includes:

[0026] Using inverse Fourier transform, the frequency domain radiation characteristics of each receiving point are transformed into time domain radiation characteristics. The time domain radiation characteristics are then post-processed to extract the transient sound pressure waveform and peak sound pressure of each receiving point. Combined with shallow sea channel environmental parameters, a complete transient radiation sound field prediction report is formed.

[0027] Furthermore, the low-frequency radiation directivity data is obtained by performing low-frequency band calculations on a complex model using the finite element method.

[0028] Furthermore, the step of performing three-dimensional full-space external field calculations on the equivalent source array to obtain full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band includes:

[0029] Before constructing the multipole source finite element shallow sea channel model for full-space sound field calculation, target frequency bands and target spatial profiles are selected from the full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band, and one or more sets of specific radiation directivity files that match the sound source input format of the shallow sea channel model based on ray theory are generated.

[0030] Furthermore, the step of constructing a shallow-sea channel model based on ray theory according to seabed parameters, and exporting the radiation directivity data in .sbp format to adapt to the shallow-sea channel model, as the sound source for the ray theory-based shallow-sea channel model, includes:

[0031] The free-field full-space radiation directivity data of the multipole equivalent source is sampled and format-converted according to a preset frequency, azimuth, and elevation grid to generate a sound source directivity file that meets the input requirements of the shallow sea channel model based on ray theory.

[0032] Furthermore, the setting of the multipole combination to determine a suitable combination method through error includes:

[0033] By comparing the errors between the reconstructed sound field and the original low-frequency radiation directivity data at different orders, when the error is lower than a preset threshold, the order of the multipole combination and the corresponding spherical harmonic function coefficients are determined.

[0034] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows:

[0035] (1) The prediction method of the present invention adopts the frequency domain indirect method combined with the technical means of three-dimensional full-space field calculation, which solves the technical problem of large amount of calculation and low efficiency of direct transient time domain simulation of complex models. By converting the time domain transient excitation to frequency domain processing and completing the full-space field calculation of complex models in the frequency domain, the technical effect of efficiently and accurately extracting the low-frequency radiation directivity data of complex models is achieved;

[0036] (2) This invention solves the technical problem of complex models and computational infeasibility when a complex model is directly substituted into an ocean channel model by inverting a multipole equivalent sound source based on low-frequency radiation directivity data. By using a multipole sound source array to equivalently replace the original complex sound source, the technical effect of greatly simplifying the sound source model while maintaining its core radiation characteristics is achieved, making it possible to place the complex sound source in the ocean channel for direct calculation.

[0037] (3) The present invention inputs the equivalent source free field radiation data into a shallow sea channel model based on ray theory, and combines it with a shallow sea channel model that considers layered sound speed, irregular boundaries and multiple scattering paths for calculation, thereby achieving the effect of greatly improving the calculation efficiency while ensuring the simulation of marine environment propagation. Attached Figure Description

[0038] Figure 1 This is a flowchart illustrating the present invention;

[0039] Figure 2 This is a schematic diagram of a typical cross-section of the shallow sea channel in this invention.

[0040] Figure 3 This is a comparison diagram of the results of shallow sea channel model excitation and multipole equivalent sound source in this invention;

[0041] Figure 4 This is a comparison chart of the results of the multipole source finite element shallow sea channel model and the shallow sea channel model based on ray theory in this invention;

[0042] Figure 5 This is a noise signal diagram of different distances in the 0°-180° directional angle profile of this invention;

[0043] Figure 6 This is a propagation loss diagram of the 0°-180° directional angle profile in this invention;

[0044] Figure 7 It is a complex model diagram. Detailed Implementation

[0045] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0046] like Figure 1 As shown, the present invention provides a method for predicting transient radiated acoustic fields in shallow sea channels based on the equivalent source method, comprising the following steps:

[0047] S1. The time-domain transient excitation signal is converted into a frequency-domain excitation spectrum using a frequency-domain indirect method. The frequency-domain excitation spectrum is then used to transiently excite a complex model. After transient excitation, the low-frequency radiation directivity data of the response points is obtained through three-dimensional full-space external field calculations. Details are as follows:

[0048] Transient excitation and response data are obtained through a frequency domain indirect method. The time-domain transient excitation signal undergoes a Fast Fourier Transform (FFT) to convert it into a frequency-domain excitation spectrum, and the frequency domain analysis range is set. The frequency-domain excitation spectrum is imported into the simulation software, and the excitation location of the actual complex model is loaded. Three-dimensional monitoring points are arranged in the external field of the complex model, with the geometric center of the complex model as the origin and the distance between the points as the radius based on the size of the complex model and satisfying the external field conditions, in order to obtain radiation directivity data. The transient excitation simulation is run, and after the calculation is completed, the sound pressure amplitude and phase data of each monitoring point are extracted, converted into sound pressure level, and a raw radiation directivity dataset is formed and saved in .csv format. Figure 7 As shown, the entire complex model is made of 6061 stainless steel, with a total length of 3.078m and a shell radius of 0.334m. A launch tube is installed inside the bow shell. The bow has a round end cap for easy operation, facilitating the installation of sensors and connection to an external excitation rod. An internal counterweight is located in the middle to ensure negative buoyancy. The complex model includes a launch tube 1, bow section 2, bow connecting section 3, mid-section connecting section 4, counterweight frame 5, counterweight rod 6, mid-section section 7, lugs 8, stern connecting section 9, stern section 10, stern water tank section 11, stern wing 12, and stern propeller rudder 13.

[0049] S2. Based on the low-frequency radiation directivity data, the equivalent multipole sound source adapted to the complex model is inverted; the equivalent multipole sound source is arranged inside or on the surface of the complex model to form an equivalent source array.

[0050] The specific implementation process of step S2 is as follows:

[0051] S2.1. Based on the inversion of low-frequency radiation directivity data, a multipole equivalent sound source suitable for complex models is derived, as follows:

[0052] A multipole equivalent sound source is constructed, and the radiation directivity data obtained from the actual model simulation is used as the target benchmark for equivalent source inversion. Based on the complexity of the complex model's geometry and the error requirements of its radiation characteristics, a suitable combination of multipoles is determined through error assessment. The corresponding spherical harmonic functions, wavelengths, and recursive coefficients are obtained, and the amplitude and spacing of each pole are further calculated. The spherical harmonic function coefficients are:

[0053]

[0054] in, These are the coefficients of the spherical harmonic function; It is a conjugate complex number; It is the order; It is an ordinal number used to describe the symmetry of the function in the azimuth angle; It is a directional function; and These are the pitch angle and the azimuth angle, respectively.

[0055] The method for setting up a multipole combination is to determine the appropriate combination method based on the error. This includes comparing the error between the reconstructed sound field and the original low-frequency radiation directivity data at different orders. When the error is lower than a preset threshold, the order of the multipole combination and the corresponding spherical harmonic function coefficients are determined.

[0056] S2.2. Arrange multipole equivalent sound sources inside or on the surface of the complex model to form an equivalent source array, as follows:

[0057] The following is the specific calculation process, including the amplitude of each pole, the arrangement distance between poles, and the arrangement method in which different poles are arranged in advance in the code. The final arrangement is selected based on the calculation result that meets the error range. The arrangement is based on the center position inside the model.

[0058] The basic principle of the equivalent source method is to use a directivity function to describe the characteristics of a sound field. The radiation pattern of far-field radiation in free space can be represented by a directivity function, the expression of which is:

[0059]

[0060] in, It is a directional function. It is the size of A three-dimensional space vector, These are the pitch angle and azimuth angle, respectively. Far-field requirements: ,in It is the wavelength of the sound wave. It is the maximum distance from the point source to the origin of the coordinate system.

[0061] For a given For an omnidirectional point source distribution, the directionality function can be calculated using the following formula:

[0062]

[0063]

[0064] in, It is the amplitude of the point source. These are the coordinates of the point source. It is a unit vector in the Cartesian coordinate system. Formulas (2) and (3) are applicable to both compact and non-compact sound source distributions.

[0065] Through Taylor expansion, the directional function can be decomposed into multipole moments, such as monopole moments, dipole moments, and quadrupole moments, each corresponding to different fundamental source configurations. For example, fundamental source configurations such as monopoles, vertical dipoles, and axial dipoles can have their directional functions described by specific mathematical expressions.

[0066] In compact conditions The directional function can be further expressed as a multipole moment through Taylor expansion:

[0067]

[0068] Each term in formula (5) represents a given The multipole moments of a point source set (the first term is a singlet moment, the second term is a dipole moment, the third term is a quadrupole moment, etc.).

[0069] Monopole: , , The expression is:

[0070]

[0071] Axial dipole: , , , , The expression is:

[0072]

[0073] Axial dipole: , , , , The expression is:

[0074]

[0075] Axial dipole: , , , , The expression is:

[0076]

[0077] Furthermore, these basic source configurations can be transformed using displacement operators to generate higher-order source configurations. However, different displacement distances and different point source amplitudes will lead to physically different source configurations, although they all possess the same far-field directionality function. Examples of higher-order source configurations under the following conditions include:

[0078] Three-point source of axis ( Axial dipole through Operator transformation): , , , , , , The expression is:

[0079]

[0080] Axial plane quadrupole ( Axial dipole through Operator transformation): , , , , , , , , The expression is:

[0081]

[0082] To further analyze the sound field characteristics, the directional function can be decomposed into the form of a spherical harmonic function:

[0083]

[0084] in:

[0085]

[0086] It is a related Legendre polynomial.

[0087]

[0088] It is a conjugate complex number, and under compact conditions, formula (12) is completely equivalent to formula (14).

[0089] S3. Perform three-dimensional full-space external field calculations on the equivalent source array to obtain the full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band. Details are as follows:

[0090] Before constructing a multipole source finite element shallow sea channel model for full-space sound field calculation, a target frequency band and target spatial profile are selected from the full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band, and one or more sets of specific radiation directivity files that match the sound source input format of the shallow sea channel model based on ray theory are generated.

[0091] The shallow sea channel has a depth of 100m and a length of 3000m. The radiation directivity data of the multipole source was obtained through finite element field calculations and used as the sound source.

[0092] In this embodiment, the low-frequency radiation directivity data is obtained by performing low-frequency band calculations on a complex model using the finite element method.

[0093] The three-dimensional full-space external field calculation of the equivalent source was completed in simulation software, ensuring that the mesh met the requirement of one-sixth of the wavelength while setting up the aquatic environment. A perfectly matched layer was set outside the aquatic area to absorb boundary reflected sound waves and avoid non-physical interference. The equivalent source array configured in step S2 was loaded onto the aquatic area, and the finite element method was used to calculate and generate the full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band. For the aquatic profile to be studied, the entire aquatic space was sectioned, with typical sectioning methods as follows: Figure 3 As shown. A comparison between the actual model excitation radiation results and the equivalent sound source radiation results is shown below. Figure 4 As shown in the figure, the curves indicate that the results of the two types of radiation have a high degree of overlap, verifying the accuracy and feasibility of using an equivalent sound source to replace the actual model excitation.

[0094] S4. Construct a shallow sea channel model based on ray theory. Use arbitrary frequency band full space arbitrary profile radiation directivity data as the sound source of the shallow sea channel model based on ray theory. Combine the layered sound velocity profile, irregular boundary and multi-scattering path characteristics of the shallow sea channel to calculate the frequency domain radiation characteristics of the complex model at any position in the full space of the shallow sea channel model based on ray theory.

[0095] Specifically as follows:

[0096] The following is the calculation process of ray theory, including the impact of the marine environment, multipath effects, path, and human body.

[0097] This invention uses ray theory to construct a shallow sea channel model. In ray theory, waves are considered to consist of a set of rays propagating in a certain direction. Each ray represents the direction and path of wave propagation at that point. Ray theory is mainly applicable to high-frequency waves because, in this case, the details of the wave can be approximated by the trajectory of the rays, while ignoring the wave properties.

[0098] When the waveguide satisfies the high-frequency approximation condition: When the equation is simplified, the two fundamental equations of ray acoustics, the functional equation and the intensity equation, can be obtained:

[0099]

[0100] in, The speed of sound at the reference point For refractive index, For phase function, The sound pressure amplitude is a function of spatial location.

[0101] make Represents the radiated sound power per unit solid angle, solid angle element The cross-sectional area of ​​the element is Then the sound intensity can be expressed as:

[0102]

[0103] The grazing angle is and The two sound ray tubes rotate around the z-axis for one revolution, and the resulting sound ray tube bundle spans a three-dimensional infinitesimal element within the angle. Due to symmetry:

[0104]

[0105] In the formula, unit distance solid angle The area of ​​the subtended infinitesimal element. According to geometric relations, The cross-sectional area perpendicular to the sound ray:

[0106]

[0107] Substituting equations (14) and (15) into equation (13), and using r to represent the horizontal distance, the sound pressure amplitude is calculated as follows: (The constant factor is not considered.)

[0108]

[0109] Within the short-range, due to reflection loss and the increased distance between the virtual source and the receiver, higher-order virtual sources quickly become ineffective; in this case, ray theory is more convenient. For homogeneous waveguides, a distance criterion is derived:

[0110]

[0111] Where H represents ocean depth. It is the wavelength.

[0112] The equations in X-ray acoustics require that the sound wave amplitude satisfy the following approximation:

[0113]

[0114] High frequencies in X-ray acoustics can be understood as:

[0115]

[0116] Ray theory models often use uniform point sources for calculations. To solve complex sound source cases, directional sound sources are introduced to provide the sound energy radiation intensity at various angles of the sound source, which is then converted into sound intensity.

[0117]

[0118] in, As the reference sound intensity for water, These are the azimuth angle and the glancing angle, respectively. It is at the sound source level.

[0119] The sound intensity is then converted into the initial sound pressure amplitude of the ray:

[0120]

[0121] Considering energy attenuation during propagation, the real-time sound pressure amplitude during ray propagation is:

[0122]

[0123] in, For diffusion factor, The length of the ray propagation path. The sound absorption coefficient of seawater.

[0124] A shallow sea channel model based on ray theory is constructed based on seabed parameters. The radiation directivity data obtained in step S3 is exported as a .sbp format to adapt to the shallow sea channel model based on ray theory, serving as the sound source for the shallow sea channel model based on ray theory. Exporting the radiation directivity data as a .sbp format specifically includes: sampling and format conversion of the free field full-space radiation directivity data of the multipole equivalent source according to a preset frequency point, azimuth angle, and elevation angle grid to generate a sound source directivity file that meets the input requirements of the shallow sea channel model based on ray theory.

[0125] By combining the layered sound velocity profile, irregular boundaries, and multiple scattering path characteristics of the shallow sea channel, the frequency domain radiation characteristics of the complex model at any location in the entire space of the shallow sea channel model based on ray theory are calculated, as follows:

[0126] The sound source location, receiver depth, number of receivers, and start and end points are set in a shallow sea channel model based on ray theory. The shallow sea channel model based on ray theory is run, and key indicators such as propagation loss, sound pressure amplitude, and phase at any location in the entire space are output.

[0127] S5. Inversely transform the frequency domain radiation characteristic results into time domain radiation characteristic results to complete the prediction of the transient radiated sound field of the complex model of shallow sea channel. Details are as follows:

[0128] Using inverse Fourier transform, the frequency domain radiation characteristics of each receiving point obtained in step S4 are inversely transformed into time domain radiation characteristics. Post-processing is then performed on the time domain radiation characteristics to extract parameters such as transient sound pressure waveforms and peak sound pressure levels for each receiving point. Combined with shallow sea channel environmental parameters, a complete transient radiated sound field prediction report is generated, including frequency domain transfer function curves and time domain waveform diagrams. For example, the radiation results of the actual model-excited finite element shallow sea channel model and the equivalent sound source radiation results of the shallow sea channel model based on ray theory are compared. Figure 5 As shown, the result curves of the two calculation models have a high degree of overlap, indicating that it is feasible to use the shallow sea channel model based on ray theory to replace the finite element shallow sea channel model. Figure 5 Figure (a) shows the noise signal at a 200m cross-section of the 0°-180° azimuth angle. Figure 5 Figure (b) shows the noise signal at a 400m cross-section with a 0°-180° azimuth angle. Figure 5 Figure (c) shows the noise signal at a 600m cross-section of the 0°-180° azimuth angle. Figure 5 Figure (d) in the figure shows the noise signal at a cross-sectional angle of 0°-180° over a distance of 800m. Figure 5 Figure (e) shows the noise signal profile over 1000m along a 0°-180° azimuth angle. It can be seen that the peak time is delayed as the distance increases. This aligns with actual conditions and further demonstrates the reliability of the shallow sea channel model simulation based on ray theory.

[0129] Taking the scaled-down benchmark model as an example, some of the calculated results are as follows: Figure 6 As shown, Figure 6 Figure (a) in the figure is a propagation loss curve of the 0°-180° directional angle profile; Figure 6 Figure (b) shows the propagation loss contour plot across the 0°-180° azimuth angle profile. It can be seen that the propagation loss curves represent the propagation loss results at ten frequencies within the 0-300Hz frequency range, with a step size of 30Hz. As the frequency and distance increase, the propagation loss also increases accordingly. This conforms to the rule that low-frequency propagation loss is slower than high-frequency propagation loss, which is consistent with actual conditions and further confirms the correctness of the shallow sea channel model based on ray theory. The propagation loss contour plot, using refined frequencies and distances, further proves the correctness of the shallow sea channel model based on ray theory, demonstrating that the pattern is not specific to particular frequencies and distances.

[0130] In this invention, both the multipole source and the actual model are calculated using the finite element method, referred to as the multipole source finite element shallow sea channel model and the actual model finite element shallow sea channel model. After performing three-dimensional full-space external field calculations, the multipole source obtains radiation directivity data, which is used as the sound source for the shallow sea channel model based on ray theory.

[0131] This invention uses low-frequency complex model radiation directivity data to invert a multipole equivalent source to replace the model excitation, and uses the frequency domain indirect method to indirectly represent the time domain results. Based on the inverted multipole equivalent source, it calculates the full-space directivity data of any frequency band as the channel sound source, and uses ray theory to establish the shallow sea channel environment to calculate the sound radiation characteristics.

Claims

1. A method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method, characterized in that... include: The time-domain transient excitation signal is converted into a frequency-domain excitation spectrum using a frequency-domain indirect method. The complex model is transiently excited using the frequency domain excitation spectrum. After the transient excitation, the low-frequency radiation directivity data of the response point is obtained by three-dimensional full-space external field calculation. Based on the low-frequency radiation directivity data, a multipole equivalent sound source adapted to complex models is inverted and equivalently derived. The multipole equivalent sound sources are arranged inside or on the surface of a complex model to form an equivalent source array; Three-dimensional full-space external field calculations are performed on the equivalent source array to obtain full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band. A shallow sea channel model based on ray theory is constructed. The radiation directivity data of any frequency band and any profile in the whole space is used as the sound source of the shallow sea channel model based on ray theory. Combined with the layered sound velocity profile, irregular boundary and multi-scattering path characteristics of the shallow sea channel, the frequency domain radiation characteristics of the complex model at any position in the whole space in the shallow sea channel model based on ray theory are calculated. The frequency domain radiation characteristics are inversely transformed into time domain radiation characteristics to predict the transient radiated sound field of a complex shallow sea channel model.

2. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 1, characterized in that, The process involves using the frequency domain excitation spectrum to transiently excite a complex model, and then obtaining the low-frequency radiation directivity data of the response points after excitation through three-dimensional full-space external field calculations, including: Import the frequency domain excitation spectrum into the simulation software and load the actual excitation position of the complex model; arrange three-dimensional monitoring points in the external field of the complex model, with the geometric center of the complex model as the origin and the distance between the points as the radius based on the size of the complex model and satisfying the external field conditions; run transient excitation simulation, and after the calculation is completed, extract the sound pressure amplitude and phase data of each monitoring point and convert them into sound pressure level to form low-frequency radiation directivity data.

3. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 1, characterized in that, The process of inverting and deriving a multipole equivalent sound source adapted to a complex model based on the low-frequency radiation directivity data includes: Based on the geometric complexity of the complex model and the error requirements of its radiation characteristics, a multipole combination is set up. A suitable combination method is determined through error assessment to obtain the corresponding spherical harmonic functions, wavelengths, and recursive coefficients. Further calculations are then performed to obtain the amplitude and spacing of each pole, where the spherical harmonic function coefficients are: ； in, These are the coefficients of the spherical harmonic function; It is a conjugate complex number; It is the order; It is an ordinal number; It is a directional function; and These are the pitch angle and the azimuth angle, respectively.

4. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 1, characterized in that, The step of performing three-dimensional full-space external field calculations on the equivalent source array to obtain full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band includes: A perfectly matched layer is set outside the water area to absorb boundary reflected sound waves; an equivalent source array is loaded onto the water area, and the finite element method is used to calculate and generate the free field radiation directivity data of the multipole equivalent source in any frequency band across the entire space.

5. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 1, characterized in that, The construction of the shallow sea channel model based on ray theory uses the arbitrary frequency band full-space arbitrary profile radiation directivity data as the sound source of the ray theory-based shallow sea channel model. Combining the layered sound velocity profile, irregular boundaries, and multi-scattering path characteristics of the shallow sea channel, the frequency domain radiation characteristics of the complex model at any location in the full space within the ray theory-based shallow sea channel model are calculated, including: A shallow sea channel model based on ray theory is constructed based on seabed parameters. Radiation directivity data is exported as .sbp format to adapt to the shallow sea channel model and serve as the sound source for the ray theory-based shallow sea channel model. By combining the layered sound velocity profile, irregular boundary and multiple scattering path characteristics of the shallow sea channel, the frequency domain radiation characteristics of the complex model at any position in the whole space of the shallow sea channel model are calculated. The sound source location, receiver depth, number of receivers, and start and end points are set in the shallow sea channel model based on ray theory. The shallow sea channel model based on ray theory is run and the key indicators at any location in the entire space are output. The key indicators include propagation loss, sound pressure amplitude, and phase.

6. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 1, characterized in that, The process of inversely transforming the frequency domain radiation characteristic results into the time domain radiation characteristic results to predict the transient radiated sound field of the complex model of the shallow sea channel includes: Using inverse Fourier transform, the frequency domain radiation characteristics of each receiving point are transformed into time domain radiation characteristics. The time domain radiation characteristics are then post-processed to extract the transient sound pressure waveform and peak sound pressure of each receiving point. Combined with shallow sea channel environmental parameters, a complete transient radiation sound field prediction report is formed.

7. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 1, characterized in that, The low-frequency radiation directivity data is obtained by performing low-frequency calculations on a complex model using the finite element method.

8. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 1, characterized in that, The step of performing three-dimensional full-space external field calculations on the equivalent source array to obtain full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band includes: Before constructing a multipole source finite element shallow sea channel model for full-space sound field calculation, a target frequency band and target spatial profile are selected from the full-space radiation directivity data of the free field of the multipole equivalent source at any frequency band, and one or more sets of specific radiation directivity files that match the sound source input format of the shallow sea channel model based on ray theory are generated.

9. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 5, characterized in that, The process of constructing a shallow-sea channel model based on ray theory according to seabed parameters, and exporting radiation directivity data in .sbp format to adapt to the shallow-sea channel model, serves as the sound source for the ray theory-based shallow-sea channel model, including: The free-field full-space radiation directivity data of the multipole equivalent source is sampled and format-converted according to a preset frequency, azimuth, and elevation grid to generate a sound source directivity file that meets the input requirements of the shallow sea channel model based on ray theory.

10. The method for predicting transient radiated acoustic field in shallow sea channels based on the equivalent source method according to claim 3, characterized in that, The setting of a multipole combination to determine a suitable combination method based on error includes: By comparing the errors between the reconstructed sound field and the original low-frequency radiation directivity data at different orders, when the error is lower than a preset threshold, the order of the multipole combination and the corresponding spherical harmonic function coefficients are determined.

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