A background flow field sound propagation calculation method based on improved Gaussian beam tracking

Abstract

The application discloses a kind of based on improved Gaussian beam tracking background flow field sound propagation calculation method, specifically related to background flow field sound propagation technical field, according to the number of input rays, sound source position and the emission angle of ray, the trajectory of ray from sound source place outward propagation is acquired by ray tracing equation in flowing medium, and the ray center coordinate system is set, the geometric extension of ray is acquired by dynamic ray tracing equation, according to the propagation time and geometric extension of ray from sound source place outward propagation, and according to flow correction parameter, the influence of Gaussian beam solution on flow effect is analyzed and operated, by linear superposition method, the energy of these beams is superimposed at predetermined observation point, so as to obtain the total sound pressure value of observation point, complete sound propagation calculation operation in flow field;So as to realize the calculation of background flow field sound propagation, reduce the calculation error caused by shadow area, focal point and the like, improve the calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of background flow field sound propagation technology, specifically to a method for calculating background flow field sound propagation based on improved Gaussian beam tracking. Background Technology

[0002] With my country's urgent need for more advanced marine engineering equipment in marine resource exploration, development, and maritime rights protection, sound waves play a crucial role in underwater communication, underwater detection, and other marine engineering fields. The underwater propagation of sound waves is directly related to these engineering applications. Currently, there are two main theoretical approaches to solving the sound wave propagation problem: wave-based theory and geometric acoustics theory. Wave-based theory derives and solves the sound wave equations from fluid dynamics equations, while geometric acoustics theory treats sound waves as rays emitted from a sound source, with sound energy propagating along these rays. The basic equations of geometric theory are a system of ordinary differential equations, making the solution process relatively simple. Wave-based theory, derived from fluid dynamics equations, includes the influence of background flow, facilitating the calculation of sound field propagation within background flow. However, when the sound frequency is high, the required mesh size must be denser, significantly increasing computational costs. Furthermore, for broadband problems, each frequency requires extensive computation, further increasing the cost. While geometric theory offers a more efficient high-frequency approximation of the wave equation, it relies on rays to calculate sound fields, which can lead to shadowed areas and caustics. Therefore, it presents significant computational challenges in addressing acoustic problems encountered in marine engineering, requiring urgent solutions. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a method for calculating the sound propagation in a background flow field based on an improved Gaussian beam tracking, which addresses the current state of existing technology. The method analyzes the influence of the Gaussian beam solution constructed based on the propagation time and geometric expansion of the ray from the sound source outward and the flow correction parameters on the flow effect. Then, the method performs energy superposition on the constructed beam at a preset observation point through a linear superposition operation to obtain the total sound pressure value at the observation point, thus completing the sound propagation calculation in the background flow field.

[0004] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking, characterized by comprising the following steps:

[0005] S1: Based on the number of input rays, the location of the sound source, and the emission angle of the rays, the trajectory of the rays propagating outward from the sound source is obtained through the ray tracing equation in the flowing medium.

[0006] S2: Set the coordinate system of the ray center according to the trajectory of the sound ray propagating outward from the sound source, and obtain the geometric extension of the ray through the dynamic ray tracing equation;

[0007] S3: An analysis is performed based on the propagation time and geometric spread of the ray from the sound source outwards, and the influence of the Gaussian beam solution constructed according to the flow correction parameters on the flow effect. The expression for the Gaussian beam solution is as follows:

[0008] In the formula, u beam (s,q) represents the Gaussian beam solution, and (s,q) represents the coordinates of the point in the coordinate system of the ray center. Here, c is the velocity of sound, Q is the geometric spread, τ is the ray velocity, ω is the angular frequency of the sound wave, and P is the derivative of the slowness vector with respect to the ray coordinate system.

[0009] The expression for the flow correction parameter is as follows:

[0010]

[0011] In the formula, Ω is the angular velocity of the ray. For the velocity of the ray, n is the unit tangent vector of the ray.

[0012] S4: The energy of the constructed beam is superimposed at the preset observation point through linear superposition operation to obtain the total sound pressure value at the observation point, thus completing the sound propagation calculation operation in the background flow field.

[0013] Furthermore, the ray path is obtained from the ray tracing equations using numerical methods. The ray tracing equations are expressed as follows:

[0014]

[0015]

[0016]

[0017]

[0018] In the formula, x1 is the abscissa of each ray, x2 is the ordinate of each ray, τ is the ray propagation time, u1 is the abscissa component of the velocity of the flowing medium, u2 is the ordinate component of the velocity of the flowing medium, p1 is the abscissa component of the slowness vector, and p2 is the ordinate component of the slowness vector.

[0019] Furthermore, the numerical method performs calculations using initial conditions in a two-dimensional case, the expression for which is as follows:

[0020] X1(τ=0)=Xs

[0021] x²(τ=0)=y s

[0022]

[0023]

[0024] In the formula, x1 is the x-coordinate of the sound source location, x2 is the y-coordinate of the sound source location, and x... s and y s Let p1 be the x-axis component of the slowness vector, p2 be the y-axis component of the slowness vector, and θ be the position of the sound source. j Let u1 be the emission angle of the j-th ray, u2 be the abscissa component of the velocity of the flowing medium, and u3 be the ordinate component of the velocity of the flowing medium.

[0025] Furthermore, in step S2, the geometric extension of the ray is obtained by solving a dynamic ray tracing equation system by constructing a ray center coordinate system. The expression of the dynamic ray tracing equation system is as follows:

[0026]

[0027]

[0028] In the formula, Q is the geometric extension, c0 is the speed of sound on the ray, and C is the second derivative of the speed of sound with respect to the coordinate system of the ray center.

[0029] Furthermore, the energy of the radiation is obtained through the transport equation of the radiation, the expression of which is as follows:

[0030]

[0031] In the formula, A is the amplitude of the ray energy.

[0032] Furthermore, the expression for the ray energy is as follows:

[0033]

[0034] In the formula, ψ0 is a constant that remains consistent on each ray, and (s, θ) are the coordinates of the point in the ray coordinate system.

[0035] Furthermore, the observation points are set according to the calculation requirements.

[0036] Furthermore, the total sound pressure level at the observation point is obtained by superimposing energy at the observation point, and the expression for the total sound pressure level is as follows:

[0037]

[0038] In the formula, R is the location of the observation point, and φ is the weighting function.

[0039] Furthermore, the weighting function can be expressed as follows based on the monopole source:

[0040]

[0041] In the formula, ∈ is a constant that controls the beamwidth and curvature, and c0 is the sound speed at the sound source.

[0042] Compared with the prior art, the present invention has at least the following beneficial effects:

[0043] (1) The present invention provides a method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking, which constructs Gaussian beam solution by flow correction parameters to analyze the influence of flow effects and reduce calculation errors;

[0044] (2) The Gaussian beam tracking method can effectively avoid the errors caused by shadow areas and foci during the calculation process;

[0045] (3) By using Gaussian beam tracking, a geometric acoustic method, the cost of high-frequency acoustic calculations is greatly reduced and the calculation efficiency is improved. Attached Figure Description

[0046] Figure 1 This is a flowchart of a background flow field acoustic propagation calculation method based on improved Gaussian beam tracking provided by the present invention;

[0047] Figure 2 This invention provides a two-dimensional coordinate system diagram of the ray center for calculating the background flow field acoustic propagation based on an improved Gaussian beam tracking method. Detailed Implementation

[0048] The following are specific embodiments of the present invention, which are described in conjunction with the accompanying drawings. However, the present invention is not limited to these embodiments.

[0049] Example 1

[0050] To improve the computational efficiency of sound propagation in the background flow field, such as Figure 1 The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking is characterized by the following steps:

[0051] S1: Based on the number of input rays, the location of the sound source, and the emission angle of the rays, the trajectory of the rays propagating outward from the sound source is obtained through the ray tracing equation in the flowing medium.

[0052] S2: Set the coordinate system of the ray center according to the trajectory of the sound ray propagating outward from the sound source, and obtain the geometric extension of the ray through the dynamic ray tracing equation;

[0053] S3: An analysis is performed based on the propagation time and geometric spread of the ray from the sound source outwards, and the influence of the Gaussian beam solution constructed according to the flow correction parameters on the flow effect. The expression for the Gaussian beam solution is as follows:

[0054] In the formula, u beam (s,q) represents the Gaussian beam solution, and (s,q) represents the coordinates of the point in the coordinate system of the ray center. Here, c is the velocity of sound, Q is the geometric spread, τ is the ray velocity, ω is the angular frequency of the sound wave, and P is the derivative of the slowness vector with respect to the ray coordinate system.

[0055] The expression for the flow correction parameter is as follows:

[0056]

[0057] In the formula, Ω is the angular velocity of the ray. For the velocity of the ray, n is the unit tangent vector of the ray.

[0058] S4: The energy of the constructed beam is superimposed at the preset observation point through linear superposition operation to obtain the total sound pressure value at the observation point, thus completing the sound propagation calculation operation in the background flow field.

[0059] Based on the problem to be solved, the type of background flow and flow field information are determined. The number of rays, the location of the sound source, and the emission angle of the rays are defined. The initial slowness vector is determined by using the sound source location as the initial point of the ray and the emission angle. The propagation trajectory of the rays is obtained by solving the ray tracing equations. Then, a ray center coordinate system is established with each ray as the center, and the dynamic ray tracing equations are solved to obtain the geometric extension of the ray. A Gaussian beam solution is constructed based on flow correction parameters to fully consider the influence of flow effects. Then, using the linear superposition method, the energy of these beams is superimposed at predetermined observation points to obtain the total sound pressure value at the observation points, completing the sound propagation calculation in the flow field. The ray tracing equations are expressed as follows:

[0060]

[0061]

[0062]

[0063]

[0064] In the formula, x1 is the abscissa of each ray, x2 is the ordinate of each ray, τ is the ray propagation time, u1 is the abscissa component of the velocity of the flowing medium, u2 is the ordinate component of the velocity of the flowing medium, p1 is the abscissa component of the slowness vector, and p2 is the ordinate component of the slowness vector.

[0065] The j-th ray must satisfy relevant initial conditions, the expressions for which are as follows:

[0066] x1(τ=0)=x s

[0067] x²(τ=0)=y s

[0068]

[0069]

[0070] In the formula, x1 is the x-coordinate of the sound source location, x2 is the y-coordinate of the sound source location, and x... s and y s Let p1 be the x-axis component of the slowness vector, p2 be the y-axis component of the slowness vector, and θ be the position of the sound source. j Let u1 be the emission angle of the j-th ray, u2 be the abscissa component of the velocity of the flowing medium, and u3 be the ordinate component of the velocity of the flowing medium. The dynamic ray tracing equations are solved using the relevant initial conditions.

[0071] Furthermore, the geometric extension of the ray is obtained through the dynamic ray tracing equations, which are expressed as follows:

[0072]

[0073]

[0074] In the formula, Q represents the geometric extension, c0 is the speed of sound along the ray, and C is the second derivative of the speed of sound with respect to the coordinate system of the ray's center. The geometric extension is the area of ​​the ray tube.

[0075] The analysis is performed based on the propagation time and geometric spread of the ray from the sound source outward, and the influence of the Gaussian beam solution constructed according to the flow correction parameters on the flow effect. The expression of the Gaussian beam solution is as follows:

[0076] In the formula, u beam (s,q) represents the Gaussian beam solution, and (s,q) represents the coordinates of the point in the coordinate system of the ray center. Here, c is the velocity of sound, Q is the geometric spread, τ is the ray velocity, ω is the angular frequency of the sound wave, and P is the derivative of the slowness vector with respect to the ray coordinate system.

[0077] The expression for the flow correction parameter is as follows:

[0078]

[0079] In the formula, Ω is the angular velocity of the ray. For the velocity of the ray, n is the unit tangent vector of the ray. Beam solutions are constructed near each ray using flow correction parameters, and the total sound pressure level is obtained through linear superposition. The improved Gaussian beam tracking method can better reduce computational errors caused by shadow regions, foci, etc., and improve the computational efficiency of sound propagation in the background flow field.

[0080] Measurements are typically taken at a specific location or region where sound pressure levels are desired. The location of the observation point becomes the target location for calculating the sound pressure. At the observation point, the energies of all Gaussian beam solutions constructed near the ray are superimposed. The ray energy is obtained through the ray's transport equation, which is expressed as follows:

[0081]

[0082] In the formula, A is the amplitude of the ray energy.

[0083] The expression for ray energy is as follows:

[0084]

[0085] In the formula, ψ0 is a constant that remains consistent on each ray, and (s, θ) are the coordinates of the point in the ray coordinate system.

[0086] The total sound pressure level is obtained by superimposing the beam solutions at each observation point. This value represents the combined effect of the sound pressure contributed by all rays at the observation point. The expression for the total sound pressure level is as follows:

[0087]

[0088] In the formula, R is the location of the observation point, and φ is the weighting function.

[0089] The weighting function, based on the monopole source, can be expressed as follows:

[0090]

[0091] In the formula, ∈ is a constant that controls the beamwidth and curvature, and c0 is the sound speed at the sound source.

[0092] By setting the location of the observation point, calculating the ray trajectory, propagation time, and geometric expansion, and performing the process of constructing Gaussian beamforms, correcting for flow effects, and linearly superimposing beamforms, the propagation of sound waves and the characteristics of the sound field can be obtained quickly and accurately.

[0093] In summary, the present invention provides a method for calculating background flow field sound propagation based on improved Gaussian beam tracing. Based on the input number of rays, the location of the sound source, and the emission angle of the rays, the method obtains the trajectory of the rays propagating outward from the sound source using ray tracing equations in the flowing medium. A coordinate system for the ray center is established, and the geometric extension of the rays is obtained through dynamic ray tracing equations. Based on the propagation time and geometric extension of the rays propagating outward from the sound source, and considering the influence of the Gaussian beam solution constructed according to flow correction parameters on the flow effect, the method performs an analysis. Then, using a linear superposition method, the energy of these beams is superimposed at predetermined observation points to obtain the total sound pressure value at the observation points, thus completing the sound propagation calculation in the flow field. By correcting the superimposed beam solution in the background flow environment using flow correction parameters, the energy on the rays is calculated, thereby realizing the calculation of background flow field sound propagation, reducing calculation errors caused by shadow areas, caustics, etc., and improving calculation efficiency.

[0094] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0095] Furthermore, in this invention, descriptions involving terms such as "first," "second," and "a" are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0096] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0097] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are feasible for those skilled in the art. If the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0098] The specific embodiments described herein are merely illustrative examples illustrating the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the scope defined by the spirit of the invention.

Claims

1. A method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking, characterized in that, Including the following steps: S1: Based on the number of input rays, the location of the sound source, and the emission angle of the rays, the trajectory of the rays propagating outward from the sound source is obtained through the ray tracing equation in the flowing medium. S2: Set the coordinate system of the ray center according to the trajectory of the sound ray propagating outward from the sound source, and obtain the geometric extension of the ray through the dynamic ray tracing equation; S3: An analysis is performed based on the propagation time and geometric spread of the ray from the sound source outwards, and the influence of the Gaussian beam solution constructed according to the flow correction parameters on the flow effect. The expression for the Gaussian beam solution is as follows: In the formula, u beam (s,q) represents the Gaussian beam solution, and (s,q) represents the coordinates of the point in the coordinate system of the ray center. Here, c is the velocity of sound, Q is the geometric spread, τ is the ray velocity, ω is the angular frequency of the sound wave, and P is the derivative of the slowness vector with respect to the ray coordinate system. The expression for the flow correction parameter is as follows: In the formula, Ω is the angular velocity of the ray. For the velocity of the ray, n is the unit tangent vector of the ray; S4: The energy of the constructed beam is superimposed at the preset observation point through linear superposition operation to obtain the total sound pressure value at the observation point, thus completing the sound propagation calculation operation in the background flow field.

2. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 1, characterized in that, The ray path is obtained from the ray tracing equations using numerical methods. The ray tracing equations are expressed as follows: In the formula, x1 is the abscissa of each ray, x2 is the ordinate of each ray, τ is the ray propagation time, u1 is the abscissa component of the velocity of the flowing medium, u2 is the ordinate component of the velocity of the flowing medium, p1 is the abscissa component of the slowness vector, and p2 is the ordinate component of the slowness vector.

3. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 2, characterized in that, The numerical method performs calculations using initial conditions in a two-dimensional case, and the expression for these initial conditions is as follows: x1(τ=0)=x s x2(τ=0)=y s In the formula, x1 is the x-coordinate of the sound source location, x2 is the y-coordinate of the sound source location, and x... s and y s Let p1 be the x-axis component of the slowness vector, p2 be the y-axis component of the slowness vector, and θ be the position of the sound source. j Let u1 be the emission angle of the j-th ray, u2 be the abscissa component of the velocity of the flowing medium, and u3 be the ordinate component of the velocity of the flowing medium.

4. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 1, characterized in that, In step S2, the dynamic ray tracing equations are solved by constructing a ray center coordinate system to obtain the geometric extension of the ray. The expression of the dynamic ray tracing equations is as follows: In the formula, Q is the geometric extension, c0 is the speed of sound on the ray, and C is the second derivative of the speed of sound with respect to the coordinate system of the ray center.

5. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 1, characterized in that, The energy of the radiation is obtained through the transport equation of the radiation, which is expressed as follows: In the formula, A is the amplitude of the ray energy.

6. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 5, characterized in that, The expression for the ray energy is as follows: In the formula, ψ0 is a constant that remains consistent on each ray, and (s, θ) are the coordinates of the point in the ray coordinate system.

7. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 1, characterized in that, The observation points are set according to the calculation requirements.

8. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 1, characterized in that, The total sound pressure level at the observation point is obtained by superimposing energy at that point, and the expression for the total sound pressure level is as follows: In the formula, R is the location of the observation point, and φ is the weighting function.

9. The method for calculating background flow field acoustic propagation based on improved Gaussian beam tracking according to claim 8, characterized in that, The weighting function, based on the monopole source, can be expressed as follows: In the formula, ∈ is a constant that controls the beamwidth and curvature, and c0 is the sound speed at the sound source.

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