A method for estimating the radiated sound pressure of shallow water complex targets based on near-field vertical array

Abstract

The present invention relates to a method for estimating the radiated sound pressure of a shallow water complex target based on a near-field vertical array, comprising the following steps: S1, using a vertical array equal to the water depth to measure the near-field sound pressure of a sound wave emission point, and measuring a virtual cylindrical measurement surface that can completely enclose the sound wave emission point at different orientations of the sound wave emission point; S2, substituting the measurement data of each array element point of the vertical array into the general solution form of the radiated sound pressure in the virtual cylindrical coordinate system and constructing a matrix equation; S3, then solving the coefficient matrix of the radiated sound pressure, substituting the obtained coefficient matrix into the modal expansion form solution of the radiated sound pressure in the virtual cylindrical coordinate system, and calculating the radiated sound pressure of any point outside the virtual cylindrical measurement surface in the shallow water ocean waveguide. The beneficial effect is that in the ocean waveguide, the far-field sound pressure is estimated using the near-field vertical measurement data array.

Description

Technical field

[0001] The present invention relates to the technical field of marine fluid mechanics, and in particular to a method for estimating the radiated sound pressure of a shallow water complex target based on a near-field vertical array. [Background Technology]

[0002] Multipath effect: When sound waves propagate in water, there are multiple propagation paths from the transmitting point to the receiving point due to the refraction of the water medium and the reflection of the sound waves on the water surface and bottom.

[0003] In shallow-water environments, the propagation of acoustic signals in the channel becomes extremely complex due to the existence of multipath effects. However, taking advantage of the multipath characteristics of shallow-water channels, a virtual source method has been proposed to calculate the radiated acoustic field of some point source targets or targets that can be regarded as point sources in shallow-water channels. This method has a simple principle, clear physical meaning, and can adapt to the characteristics of medium and boundary level changes. However, for some complex targets that cannot be approximated by point sources, the calculation of their radiated acoustic field is more difficult. This is because, in addition to the influence of multipath effects, multiple scattering problems will also occur between the target itself and the upper and lower interfaces of the water in which it is located, resulting in changes in the vibration characteristics of the target itself and the characteristics of the acoustic radiation source. This makes the solution of the acoustic radiation problem of complex targets in ocean waveguides more complicated.

[0004] Acoustic radiation pressure (radiated sound pressure) is a physical concept involved in studying sound waves in fluids. It is proportional to the sound energy density. It is the average forward pressure exerted by a sound wave propagating through a fluid medium upon impact with an obstacle. Its direction is the same as the direction of sound propagation.

[0005] For complex targets in shallow water environments, determining the radiated sound pressure at any point in the sound field requires first determining the sound pressure and vibration velocity on the target's surface. However, measuring these surface pressures and vibration velocities is not easy. Furthermore, in shallow water environments, multipath effects and multiple scattering between the target and its interface further complicate the propagation of sound waves radiated by the target.

[0006] Ocean acoustic waveguide: The ocean acts as a sound waveguide. Sound propagation is limited by the sea surface above and the seabed below. Similar to the refractive index of light, acoustic waveguides play a similar role in the propagation of sound. A waveguide is a conductive structure (acoustic, optical, and light) that guides acoustic, optical, and light waves along a path.

[0007] The Helmholtz equation is an elliptic partial differential equation that describes electromagnetic waves. It is named after the German physicist Helmholtz. Its basic form is as follows: in is the Hamiltonian operator, k is the wave number, and A is the amplitude.

[0008] Aiming at the technical problem that it is difficult to measure the surface sound pressure and vibration velocity of complex targets in shallow water environments, the present invention makes technical improvements to the method for estimating the radiated sound pressure of complex targets in shallow water environments. [Summary of the invention]

[0009] The purpose of the present invention is to provide a method for estimating the radiated sound pressure of a shallow water complex target in an ocean waveguide by using a near-field vertical measurement data array to estimate the far-field sound pressure.

[0010] To achieve the above object, the technical solution adopted by the present invention is a method for estimating the radiated sound pressure of a shallow water complex target based on a near-field vertical array, comprising the following steps:

[0011] S1. Use a vertical array equal to the water depth to measure the near-field sound pressure at the acoustic wave emission point, and measure a virtual cylindrical measurement surface that can completely enclose the acoustic wave emission point at different directions of the acoustic wave emission point;

[0012] S2. Substitute the measured data of each element point of the vertical array into the general solution form of the radiated sound pressure in the virtual cylindrical coordinate system and construct a matrix equation;

[0013] S3. Then, the coefficient matrix of the radiated sound pressure is solved and substituted into the modal expansion form of the radiated sound pressure in the virtual cylindrical coordinate system to calculate the radiated sound pressure at any point outside the virtual cylindrical measurement surface in the shallow water ocean waveguide.

[0014] Preferably, step S1 specifically includes the following sub-steps:

[0015] S11, first measuring the sound velocity, density, and water depth of the water area where the acoustic wave emission point is located, and then determining the number of array elements J in the vertical array based on the depth of the water area to be measured and the frequency of the excitation signal at the acoustic wave emission point, wherein the array element spacing is less than or equal to half the acoustic wavelength;

[0016] S12. Then determine the radius of the virtual cylindrical measurement surface and the initial azimuth angle, and measure the sound pressure p of the vertical array every fixed angle θ in the clockwise or counterclockwise direction of the circumference of the virtual cylindrical measurement surface. i , until a complete circumference is measured and record the measurement results.

[0017] Preferably, step S2 specifically includes the following sub-steps:

[0018] S21. Consider the measured virtual cylindrical measurement surface as a virtual cylinder with a certain directionality to establish a virtual cylindrical coordinate system, with the center of the upper surface of the virtual cylinder as the coordinate origin, one of the radial directions as the positive direction of the r-axis, the downward direction of the central axis of the virtual cylinder as the positive direction of the z-axis, φ as the angle between any two-dimensional vertical plane and the rOz plane, that is, the azimuth angle, and the position of any field point in the virtual cylindrical space is determined by (r, φ, z);

[0019] S22. The sound field of a virtual cylinder in water satisfies the nonhomogeneous Helmholtz equation is the Hamiltonian operator, k is the wave number, and the separation of variables method can be used to solve the simple normal series solution of the potential function Φ(r,φ,z,t) in the virtual cylindrical coordinate system;

[0020] S23. Because there is a relatively fixed functional relationship between sound pressure and potential function, the radiation sound pressure at any point in the ocean waveguide can be further simplified to in, is the first kind of Hankel function, Ψ(·) is the eigenfunction, ω is the angular frequency, n is the simple normal wave order, m is the circumferential expansion coefficient, k rn is the horizontal wave number;

[0021] S24. At each azimuth, the sound pressure results measured at each element point of the vertical array meet the analytical expression of the radiated sound pressure. Substitute the sound pressure measurement data P of each element of the vertical array into the analytical expression of the radiated sound pressure to obtain an equation that is consistent with the expansion coefficient A. mn The relevant system of equations, abbreviated as [G] J×(n×m) [A] (n×m)×K =[p] J×K , where n is the horizontal wave order, m is the circumferential modal expansion number, J is the number of array elements, and K is the number of circumferential measurements.

[0022] Preferably, step S3 specifically includes the following sub-steps:

[0023] S31, in solving the expansion coefficient A mn When solving the overdetermined equations, we need to solve the overdetermined equations to get the convergent solution A. mn , so the expansion orders m and n are set to satisfy J≥(m×n), and the unknown number A mn The number of is less than the number of equations formed by the measurement points, and the equation is solvable;

[0024] S32. The horizontal wave order needs to be determined based on the input waveguide depth, sound source location, and frequency parameters. First, the horizontal wave order n is calculated using the maximum order calculation method for simple normal waves. Then, the circumferential modal expansion number m is determined based on the product of m and n being less than or equal to J.

[0025] S33. Using the equivalent source method, the relationship matrix between the normal vibration velocity on the cylinder surface and the point source intensity is: Q = [D] -1 U or Q = [D] +1 U, in the above formula [D] +1 is the generalized inverse matrix when the matrix D is not a square matrix, Q is the column matrix of the point sound source intensity, and U is the column matrix of the normal vibration velocity of the shell surface; and the expansion coefficient A is solved mn Similarly, the matrix is ​​solved using the same method as the equivalent source method, that is: [A] (n×m)×K =[[G] J×(n×m) ] -1 [p] J×K , and then solve it by the least square method to get the expansion coefficient A mn .

[0026] S34, expand the coefficient A mn Substitute into the radiation analysis expression In the ocean waveguide, the radiated sound pressure at any point outside the virtual cylindrical measurement surface is obtained.

[0027] The present invention provides a method for estimating the radiated sound pressure of a shallow water complex target based on a near-field vertical array, which has the following beneficial effects: calculation of the long-distance propagation characteristics of the radiated noise of a complex structure in an ocean waveguide, formal solution of the sound field modal expansion in a cylindrical coordinate system, and solution of the coefficient matrix; using a vertical array, by measuring the sound pressure results on a virtual cylindrical surface that can completely enclose the target at different orientations at a certain distance from the target, and substituting the sound pressure data on the cylindrical surface into the general solution of the sound field modal expansion in a cylindrical coordinate system, and obtaining the coefficient matrix, the radiated sound pressure of any point outside the virtual cylindrical surface in the sound field can be calculated, which is simple, easy, efficient and accurate.

Brief Description of the Drawings

[0028] Figure 1 This is a schematic diagram of the principle of a method for estimating the radiated sound pressure of a shallow water complex target based on a near-field vertical array.

[0029] Figure 2 This is a schematic diagram of the experimental layout for measuring the sound pressure of a virtual cylindrical surface according to the present invention.

[0030] Figure 3 It is a side view of the cylindrical shell of the experiment for measuring the sound pressure of a virtual cylindrical surface according to the present invention.

[0031] Figure 4 It is a top view of the cylindrical shell of the experiment for measuring the sound pressure of a virtual cylindrical surface according to the present invention.

[0032] Figure 5 It is a pseudo-color image of the radiation expression expansion coefficient Amn in the present invention.

[0033] Figure 6This is a diagram showing the measurement results of the vertical array of the target virtual cylindrical surface in the present invention.

[0034] Figure 7 This is a sound field result diagram obtained by simulating the measured sound pressure based on a virtual cylindrical surface in the present invention.

[0035] Figure 8 This is a diagram of the sound field sound pressure results measured in actual experiments of the present invention.

[0036] Figure 9 This is a diagram showing the simulation results of the sound pressure horizontal propagation curve at the depth of the exciter of the present invention.

[0037] Figure 10 This is a graph showing the measurement results of the sound pressure horizontal propagation curve at the depth of the exciter according to the present invention. [Specific implementation method]

[0038] The features and exemplary embodiments of various aspects of the present invention will be described in detail below. In the detailed description below, many specific details are proposed to provide a comprehensive understanding of the present invention. However, it is obvious to those skilled in the art that the present invention can be implemented without the need for some of these specific details. The following description of the embodiments is merely to provide a better understanding of the present invention by illustrating examples of the present invention. The present invention is in no way limited to any specific configuration and algorithm proposed below, but covers any modification, replacement and improvement of elements, components and algorithms without departing from the concept of the present invention. In the accompanying drawings and the following description, well-known structures and technologies are not shown to avoid unnecessary ambiguity in the present invention.

[0039] Example 1

[0040] This embodiment implements a method for estimating the radiated sound pressure of a shallow water complex target based on a near-field vertical array.

[0041] Figure 1 This is a schematic diagram of the principle of the method for estimating the radiation sound pressure of shallow water complex targets based on a near-field vertical array. Figure 1 As shown, the method of this embodiment is a method for inferring far-field sound pressure in an ocean waveguide using near-field vertical array measurement data; first, a vertical array equal to the water depth is used to measure the near-field sound pressure of the model, and a virtual cylindrical measurement surface that can completely enclose the target is measured at different orientations of the target; then, the measurement data of each array element point is substituted into the general solution form of the radiation sound pressure in the cylindrical coordinate system, a matrix equation is constructed, and then the coefficient matrix of the radiation sound pressure is solved; then, the obtained coefficient matrix is ​​substituted into the modal expansion form solution of the radiation sound pressure in the cylindrical coordinate system, and finally, the radiation sound pressure of any point outside the virtual cylindrical surface in the ocean waveguide is calculated.

[0042] In order to achieve the above research objectives, this embodiment method now proposes the following technical solution, including the following steps:

[0043] First, measure the sound speed, density and water depth of the target water area, and then determine the number of array elements J in the vertical array based on the depth of the water area to be measured and the frequency of the target excitation signal. Generally, the array spacing should be less than or equal to half a wavelength.

[0044] Then determine the radius of the virtual cylinder and the initial azimuth angle, and measure the sound pressure p of the vertical array every fixed angle θ in the clockwise or counterclockwise direction of the circumference of the virtual cylinder. i , until a complete circumference is measured and record the measurement results.

[0045] The measured virtual cylindrical surface is considered a cylindrical shell with a certain directionality. The center of the upper surface of the virtual cylinder is used as the coordinate origin. A radial direction is defined as the positive direction of the r-axis. The downward direction of the cylinder's central axis is defined as the positive direction of the z-axis. φ is the angle between a two-dimensional vertical plane and the rOz plane, i.e., the azimuth angle. Therefore, the position of any field point in space can be determined from (r, φ, z).

[0046] The acoustic field of the virtual cylinder in the water should satisfy the nonhomogeneous Helmholtz equation, which is expressed as follows:

[0047] The separation of variables method can be used to solve the simple normal series solution of the potential function Φ(r,φ,z,t) in the cylindrical coordinate system. Since there is a relatively fixed functional relationship between the sound pressure and the potential function, the expression of the radiated sound pressure at any point in the ocean waveguide can be further simplified to: in, is the first kind of Hankel function, Ψ(·) is the eigenfunction, ω is the angular frequency, n is the simple normal wave order, m is the circumferential expansion coefficient, k rn is the horizontal wave number.

[0048] Without loss of generality, the sound pressure results measured at each array element point on the vertical array at each orientation should satisfy the analytical expression of the radiated sound pressure. Therefore, by substituting the measured data P of each vertical array into the analytical expression, we can obtain a formula that is consistent with the expansion coefficient A. mn The relevant system of equations can be abbreviated as: [G] J×(n×m) [A] (n×m)×K =[p] J×K , where n is the horizontal wave number order, m is the circumferential modal expansion number, J is the number of array elements, and K is the number of circumferential measurements.

[0049] However, when solving the system of equations, it is necessary to solve the overdetermined equations to obtain the convergent solution A mn, so the expansion order m and n should satisfy: J ≥ (m × n), so the unknown number A mn The number of is less than the number of equations formed by the measurement points, and the equation can be solved.

[0050] Because the wave order in the horizontal direction needs to be determined based on input parameters such as waveguide depth, sound source position, and frequency, n can be calculated first according to the maximum order of the simple normal wave, and then the size of the circumferential modal expansion number m can be determined based on the fact that the product of m and n must be less than or equal to J.

[0051] Next, when solving the matrix, we can refer to the solution method in the equivalent source method. In the equivalent source method, the relationship matrix between the normal vibration velocity of the cylinder surface and the point source intensity is: Q = [D] -1 U or Q = [D] +1 U; in the above formula [D] +1 is the generalized inverse matrix when the matrix D is not a square matrix, Q is the column matrix of the point sound source intensity, and U is the column matrix of the normal vibration velocity of the shell surface. This is the same as solving the expansion coefficient A mn Similar, so the same method can be used to solve it, that is: [A] (n×m)×K =[[G] J×(n×m) ] -1 [p] J×K .

[0052] Then, by using the least squares method, we can solve the above equations to obtain the expansion coefficient A. mn .

[0053] The expansion coefficient A mn Substituting this into the analytical expression for radiation, we can obtain the radiated sound pressure at any point outside the measuring cylindrical surface in the shallow water waveguide.

[0054] Example 2

[0055] This embodiment implements a method for estimating the radiated sound pressure of a shallow water complex target based on a near-field vertical array. This embodiment is a specific application of Example 1.

[0056] Step 1: Before deploying the experimental equipment, first measure the background noise of the experimental field environment; then measure and record the water depth, underwater sound speed, and density in the experimental environment; at the same time, determine the array spacing and the number of array elements J of the vertical array based on the frequency of the target excitation signal and the measured water parameters. The array spacing is generally not greater than half the wavelength of the signal; (a 20-element array with an array spacing of 0.4m is used in this experiment). Then determine the horizontal distance between the target center and the vertical array, that is, the radius of the virtual cylinder (in this experiment, the radius of the virtual cylinder is approximately 3m).

[0057] Step 2: Figure 2This is a schematic diagram of the experimental layout for measuring the sound pressure of a virtual cylindrical surface according to the present invention. Figure 3 It is a side view of the cylindrical shell of the experiment for measuring the sound pressure of a virtual cylindrical surface according to the present invention. Figure 4 This is a top view of the cylindrical shell of the present invention for measuring the sound pressure of a virtual cylindrical surface. Figure 2 、 Figure 3 、 Figure 4 As shown, according to Figure 2 The experimental instrument layout diagram in Figure 3 、 4 The experimental cylindrical shell shown is placed in water at a certain depth and mounted on a turntable via a lifting flange. The turntable is fixed to a lifting platform. At the same time, the angle of the model is calibrated and the 0° orientation is defined as the initial angle position.

[0058] Step 3: Extending outward along the 0° direction of the model, place a 4032 hydrophone at the outermost end of the work platform, about 20 meters horizontally from the model, and name it 4032-1.

[0059] Step 4: Extending outward along the 0° direction of the model, place another 4032 hydrophone 3 meters away from the model for vertical array position calibration. Name it 4032-2, and then deploy the vertical array here. At the same time, move 4032-2 to a position about 3.25 meters away from the model to indicate the position of the subsequent vertical array saw.

[0060] Step 5: Adjust the above experimental equipment so that they are all on the same vertical plane, and the center of the cylindrical shell model and the receiving centers of 4032-1 and 4032-2 are on the same horizontal axis.

[0061] Step 6: The transmitted excitation signal is a single-frequency signal. When the exciter is excited, the acoustic signal received by each array element in the vertical array is measured and recorded.

[0062] Step 7: After completing the above measurements, rotate the cylindrical shell model clockwise or counterclockwise by a certain angle θ (15° clockwise in the experiment). After the model stabilizes, repeat step 6 above until a full rotation is completed (a total of 24 rotations were required in this experiment) to obtain the time domain signal of the target cylindrical shell on the virtual cylinder surface.

[0063] Step 8: Adjust the model's orientation to its initial position and transmit a single-frequency excitation signal. When the shaker is energized, move the vertical array to position 4032-2 along the model's 0° direction and secure it. Then, move 4032-2 to a distance of approximately 3.5 meters from the model as the next vertical array distance calibration. Then, use the vertical array to collect and record the radiation signal at this location.

[0064] Step 9: Move 4032-2 in 0.25m increments, calibrate the vertical array's position for each pull-distance measurement, and then collect and record the radiation signal at each measurement position. This process continues until 4032-2 and 4032-1 coincide, completing the entire pull-distance measurement step. (The experimental distance range from the model was [2m, 18.75m]).

[0065] Step 10: Perform Fourier transform on the time domain signal obtained from the vertical array measurement to obtain the frequency domain result. Take the logarithm of the frequency domain result and add it to the sensitivity of the hydrophone to obtain the sound pressure level at the measurement point. Then, convert these processed results into sound pressure results according to the calculation formula of sound pressure and sound pressure level. In this way, the sound pressure matrix [p] of the virtual cylinder can be obtained. J×K , and the sound field distribution in the 0° direction.

[0066] Step 11: Consider the virtual cylindrical surface as a cylindrical shell with a certain directionality, and use the center of the upper surface of the virtual cylinder as the coordinate origin, and one of the radial directions as the positive direction of the r axis; the downward direction of the central axis of the cylinder is the positive direction of the z axis; φ is the angle between a two-dimensional vertical plane and the rOz plane, that is, the azimuth angle, such as Figure 1 As shown. Therefore, the position of any field point in space can be determined by (r, φ, z). At the same time, the sound field of the virtual cylinder in the water should satisfy the non-homogeneous Helmholtz equation, that is,

[0067]

[0068] Then, using the method of separation of variables, we can solve the simple normal series solution in the cylindrical coordinate system:

[0069]

[0070] Step 12: Because there is the following relationship between sound pressure and potential function

[0071]

[0072] Therefore, the expression of the radiated sound pressure at any point in the channel space can be further solved as:

[0073]

[0074] in is the first kind of Hankel function, Ψ(·) is the eigenfunction, ω is the angular frequency, n is the simple normal wave order, m is the circumferential expansion coefficient, k rn is the horizontal wave number.

[0075] Step 13: To avoid loss of generality, the sound pressure results measured at each element point on the vertical array should satisfy the analytical expression of the radiated sound pressure at each azimuth. Assuming that the total number of measurement points on the virtual cylinder is J×K=L, the data of each measurement point p i Substituting into the analytical expression, we can get a formula that is consistent with the expansion coefficient A. mn The relevant system of equations can be simplified as:

[0076]

[0077] Since the sound pressure at each element point on the virtual cylinder is known, the above formula can be organized into the following form:

[0078]

[0079] The above matrix equation can be simplified as:

[0080] [G] N×(n×m) [A] (n×m)×1 =[p] N×1

[0081] Step 14: Multiply both sides of the equation by the inverse matrix [G], and we have:

[0082]

[0083] Solving the above equations, we can get the expansion coefficient A mn . However, before solving the problem, it is necessary to determine the horizontal wave order n and the circumferential modal expansion coefficient m. Theoretically, the value range of the simple normal wave order n is 1 to +∞, and the value range of the circumferential expansion coefficient m is -∞ to +∞. However, in the actual ocean sound propagation process, due to the attenuation of the channel and the absorption of the seabed, these two parameters can be intercepted to the maximum values ​​N0 and M0 that can ensure the convergence of the structure. Among them, the value of N0 can be determined by the horizontal wave number k rn To determine, as the modal expansion order increases, k rn will gradually become an imaginary number, so when k rn When it is 0, it is the maximum value of N0. The value of m can be obtained by plotting the coefficient A mn The pseudo-color image is used to determine the Figure 5 It is a pseudo-color image of the radiation expression expansion coefficient Amn in the present invention. Figure 5 As shown, this is the expansion coefficient A calculated by solving the equations based on the measurement results of the virtual cylinder in the experiment. mn Pseudo-color image.

[0084] Step 15: Figure 6 This is a diagram showing the measurement results of the vertical array of the target virtual cylindrical surface in the present invention. Figure 7This is the sound field result diagram obtained by simulating the measured sound pressure based on the virtual cylindrical surface in the present invention. Figure 6 、 Figure 7 As shown, the calculated expansion coefficient A mn Substitute it into the analytical expression of the radiated sound field and calculate the sound pressure of the sound field outside the virtual cylinder.

[0085] Step 16: Figure 8 This is the sound field pressure result diagram measured in the actual experiment of the present invention. Figure 8 As shown in the figure, the sound pressure at vertical array draw distance is plotted. Comparing the measured results with the calculated results, it is found that the sound field calculated using the virtual cylinder closely matches the actual sound field in terms of distribution. The sound pressure is primarily concentrated near the depth of the sound source and decreases rapidly with distance, reaching a drop of nearly 20dB at approximately 18m. A key difference between the finite element method simulation results and the actual measured sound field is the appearance of alternating light and dark fringes in the measured field. This phenomenon is caused by near-field Fresnel interference, which is not observed in the simulated results. Figure 9 This is a diagram showing the simulation results of the sound pressure horizontal propagation curve at the depth of the exciter of the present invention. Figure 10 This is the measurement result of the sound pressure level propagation curve at the depth of the exciter of the present invention. Figure 9 、 Figure 10 As shown in the figure, the two are relatively consistent in terms of numerical value and overall trend of sound field propagation. Figure 9 、 Figure 10 Therefore, in actual engineering applications, a near-field vertical array can be used to measure a virtual cylinder, and then quickly predict and calculate the far-field acoustic radiation of complex targets in shallow water environments.

[0086] In general, the sound field calculated using the measurement results of the virtual cylinder in this embodiment is basically consistent with the actual experimental results, but further improvements are still needed when calculating the Fresnel half-wave zone problem of the sound field. In addition, since the research of this embodiment was only carried out in shallow water areas and the pull-off distance was not particularly far, it is uncertain whether the measurement results for extremely long distances are still applicable. This is because when using the method of this embodiment for far-field extrapolation, the water bottom is calculated as if it is horizontal and without undulations. In actual water environments, when the water bottom is close to horizontal, the calculated results are more consistent with the actual results; however, it is not very applicable to environments with complex undulating bottom terrain. At the same time, since vertical array measurements need to be performed throughout the entire water depth area, the method of this embodiment is not applicable to deep water environments. Firstly, deep water environments require more array elements for measurement, which will result in a large amount of subsequent calculations; secondly, the technical implementation is difficult and the cost is high.

[0087] Those skilled in the art will appreciate that all or part of the steps for implementing the above embodiments may be accomplished by hardware, or may be accomplished by a program instructing the relevant hardware, and the program may be stored in a computer-readable storage medium, wherein the storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM), etc.

[0088] The above is only a preferred embodiment of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and supplements without departing from the principles of the present invention. These improvements and supplements should also be regarded as the scope of protection of the present invention.

Claims

1. A method for estimating the radiated sound pressure of shallow water complex targets based on a near-field vertical array, characterized in that The following steps are involved: S1. Use a vertical array equal to the water depth to measure the near-field sound pressure of the sound wave emission point, and measure a virtual cylindrical measurement surface that can completely surround the sound wave emission point at different directions of the sound wave emission point; specifically, S11, first measuring the sound velocity, density, and water depth of the water area where the acoustic wave emission point is located, and then determining the number of array elements J in the vertical array based on the depth of the water area to be measured and the frequency of the excitation signal at the acoustic wave emission point, wherein the array element spacing is less than or equal to half the acoustic wavelength; S12. Then determine the radius of the virtual cylindrical measurement surface and the initial azimuth angle, and measure the sound pressure p of the vertical array every fixed angle θ in the clockwise or counterclockwise direction of the circumference of the virtual cylindrical measurement surface. i , until a complete circumference is measured and the measurement results are recorded; S2. Substitute the measured data of each element point of the vertical array into the general solution form of the radiated sound pressure in the virtual cylindrical coordinate system and construct the matrix equation; specifically, S21. Consider the measured virtual cylindrical measurement surface as a virtual cylinder with a certain directionality to establish a virtual cylindrical coordinate system, with the center of the upper surface of the virtual cylinder as the coordinate origin, one of the radial directions as the positive direction of the r-axis, the downward direction of the central axis of the virtual cylinder as the positive direction of the z-axis, φ as the angle between any two-dimensional vertical plane and the rOz plane, that is, the azimuth angle, and the position of any field point in the virtual cylindrical space is determined by (r, φ, z); S22. The sound field of a virtual cylinder in water satisfies the nonhomogeneous Helmholtz equation , ∇ is the Hamiltonian operator, k is the wave number, and the separation of variables method can be used to solve the simple normal series solution of the potential function Φ(r,φ,z,t) in the virtual cylindrical coordinate system; S23. Because there is a relatively fixed functional relationship between sound pressure and potential function, the radiation sound pressure at any point in the ocean waveguide can be further simplified to ,in, is the Hankel function of the first kind, is the eigenfunction, ω is the angular frequency, n is the simple normal wave order, m is the circumferential expansion coefficient, k rn is the horizontal wave number; S24. At each azimuth, the sound pressure results measured at each element point of the vertical array meet the analytical expression of the radiated sound pressure. Substitute the sound pressure measurement data P of each element of the vertical array into the analytical expression of the radiated sound pressure to obtain an equation that is consistent with the expansion coefficient A. mn The relevant system of equations is abbreviated as , where n is the horizontal wave number order, m is the circumferential mode expansion number, J is the number of array elements, and K is the number of circumferential measurements; S3. Then, the coefficient matrix of the radiated sound pressure is solved and substituted into the modal expansion form of the radiated sound pressure in the virtual cylindrical coordinate system to calculate the radiated sound pressure at any point outside the virtual cylindrical measurement surface in the shallow water ocean waveguide. Specifically, S31, in solving the expansion coefficient A mn When solving the overdetermined equations, we need to solve the overdetermined equations to get the convergent solution A. mn , so the expansion orders m and n are set to satisfy , unknown number A mn The number of is less than the number of equations formed by the measurement points, and the equation is solvable; S32. The horizontal wave order needs to be determined based on the input waveguide depth, sound source location, and frequency parameters. First, the horizontal wave order n is calculated using the maximum order calculation method for simple normal waves. Then, the circumferential modal expansion number m is determined based on the product of m and n being less than or equal to J. S33. Using the equivalent source method as a reference, the relationship matrix between the normal vibration velocity on the cylinder surface and the point source intensity is: or , in the above formula [D] +1 is the generalized inverse matrix when the matrix D is not a square matrix, Q is the column matrix of the point sound source intensity, and U is the column matrix of the normal vibration velocity of the shell surface; and the expansion coefficient A is solved mn Similarly, the matrix is ​​solved using the same method as the equivalent source method, that is: , and then solve it by the least square method to get the expansion coefficient A mn ; S34, expand the coefficient A mn Substitute into the radiation analysis expression In the method, the radiated sound pressure at any point outside the virtual cylindrical measurement surface in the ocean waveguide is obtained.

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