Convergence zone extraction method, system, and storage medium based on ray tracing and kernel density estimation

Abstract

The application discloses a kind of based on sound ray tracing and kernel density estimation's convergence zone extraction method, system and storage medium, method includes the following steps: S1, the environmental parameter in the range of target area is acquired, and sound ray tracing is carried out according to this using underwater acoustic simulation tool, and sound ray trajectory data is output;S2, analysis sound ray trajectory data, and the sound ray that the collision times with sea surface and seabed are all zero is regarded as candidate convergence zone sound ray;S3, based on the depth-distance curve of candidate convergence zone sound ray confirms its valley point, and the sound ray with the depth of valley point not less than preset threshold is screened as convergence zone sound ray;S4, according to the horizontal distance of valley point, convergence zone sound ray is grouped, and the horizontal distance of valley point in each group convergence zone sound ray is kernel density estimation, and the center distance, width and typical depth of convergence zone are determined according to estimation result;The application can objectively and accurately and efficiently identify convergence zone without relying on artificial judgment.

Description

TECHNICAL FIELD

[0001] The present application relates to underwater acoustics, and in particular to a convergence zone extraction method, system and storage medium based on ray tracing and kernel density estimation. BACKGROUND

[0002] In the field of underwater acoustics, the sound propagation mode based on convergence zone can realize long-distance transmission and is widely used in long-range detection, communication and sonar performance evaluation. The formation of the convergence zone depends on the specific sound speed profile environment, and its typical feature is that the sound ray is refracted during propagation and focused at a certain horizontal distance, forming a strong sound energy concentration area. Accurate estimation of the position, depth and width of the convergence zone is the key to realizing stable long-distance transmission and improving detection performance.

[0003] Most of the existing methods rely on artificial experience or visual analysis of sound field calculation results, and there is no effective technical solution that can realize automatic identification. The main problems are as follows:

[0004] (1) Strong subjectivity, the existing methods mainly rely on researchers to manually interpret sound field images or ray trajectories, which is low in efficiency and greatly influenced by personal experience, and lacks an objective and unified process from ray data to convergence zone extraction.

[0005] (2) Lack of full use of acoustic physical mechanism, there are deficiencies in the identification of convergence zone related sound rays, and the differences between different types of sound rays such as sea surface contact, sea bottom contact and direct arrival are not fully considered, and there is a lack of unified and objective criteria. Based on the ray tracing model (such as BELLHOP), the sound ray trajectory or sound pressure distribution can be output, but the convergence zone sound ray cannot be directly identified, and researchers often still need to observe the energy concentration area to infer the position and range of the convergence zone.

[0006] (3) Ignoring the non-uniform distribution characteristics of sound rays in the convergence zone, the existing methods mostly approximate the convergence zone as a uniform energy concentration, and fail to quantify the non-uniformity and anisotropy of the internal sound rays in terms of spatial distribution, incident angle and energy contribution, resulting in systematic bias in the estimation of the position, width and intensity of the convergence zone.

[0007] (4) Artificial interpretation is difficult to distinguish which sound rays can form a stable convergence zone in complex environments, and the method lacks robustness and timeliness, making it difficult to meet the requirements of rapidity and accuracy in engineering applications. SUMMARY

[0008] The purpose of the present application is to provide a convergence zone extraction method, system and storage medium based on ray tracing and kernel density estimation, which can objectively and accurately identify the convergence zone without relying on artificial judgment and is highly efficient.

[0009] Technical solution: The convergence zone extraction method based on sound ray tracing and kernel density estimation provided by the application comprises the following steps:

[0010] S1, collect the sound source position related information, obtain the environmental parameters in the target area range in combination with the environmental database, perform sound ray tracing according to the environmental parameters by using an underwater acoustic simulation tool, and output sound ray trajectory data;

[0011] S2, analyze the sound ray trajectory data, and take the sound ray with zero collision times with the sea surface and the seabed as a candidate convergence zone sound ray;

[0012] S3, confirm the valley point of the depth-distance curve based on the candidate convergence zone sound ray, and screen the sound ray with a depth not less than a preset threshold value as a convergence zone sound ray;

[0013] S4, group the convergence zone sound rays according to the horizontal distance of the valley point from the sound source, perform kernel density estimation on the horizontal distance of the valley point in each group of convergence zone sound rays, take the horizontal distance of the main peak of the kernel density estimation curve from the sound source as the center distance of the convergence zone, and calculate the width and typical depth of the convergence zone according to the center distance.

[0014] The method first collects sound source related data, obtains environmental parameters in the target area range in combination with the environmental database, outputs sound ray trajectories by using an underwater acoustic simulation tool, then performs preliminary screening based on clear rules, that is, no sea surface and seabed collision, further screens the convergence zone sound ray by introducing the valley point and the depth threshold, the above preliminary screening and further screening ensure the physical rationality of the screened sound ray, and ensure the accuracy of the final recognition result; subsequently, the convergence zone sound rays are grouped according to the horizontal distance of the valley point, which can avoid the problem that the weak peak at a long distance is easily submerged by the dense distribution at a short distance during subsequent kernel density estimation, resulting in the failure of identifying the convergence zone at a long distance; finally, the kernel density estimation method is adopted to statistically analyze the convergence zone sound rays by fully considering the non-uniform distribution characteristics of the sound rays in the convergence zone, the region with the highest energy density of the convergence zone is confirmed, and the center position, width and typical depth of the convergence zone are extracted, which are more accurate than the convergence zone information extracted by approximating the convergence zone as a uniform energy aggregate;

[0015] The method constructs a clear, repeatable and standardized data processing flow, eliminates the problem of inconsistent judgments caused by experience differences of different operators by eliminating manual subjective judgment, makes the result of the convergence zone extraction highly repeatable and objective, and is more efficient than manual subjective judgment; and finally, accurate structured information: the center position, width and typical depth of the convergence zone are extracted, which are more convenient for direct application in sound field visualization, sonar performance evaluation and remote communication link design, and have strong engineering application value.

[0016] Preferably, the sound source position related information in step S1 comprises longitude, latitude and depth of the sound source.

[0017] The above information provides accurate geospatial reference, longitude and latitude ensure that the convergence zone identification result can correspond to the real ocean map, which is crucial for regional marine environment research, cross-platform collaborative detection and other applications. Depth information is one of the most critical initial conditions in sound ray tracing calculation, different sound source depths will significantly change the sound ray propagation path and convergence zone position. Clear acquisition of this information is the cornerstone to ensure the accuracy of the entire method calculation.

[0018] Preferably, the environmental database in step S1 comprises sound speed profile, seabed topography and seabed bottom acoustic characteristic data.

[0019] The environmental database contains the above information to ensure the fidelity and integrity of the sound field simulation environment. The sound speed profile determines the refraction law of the sound ray, which is the primary condition for the formation of the convergence zone; the seabed topography affects the reflection and scattering of the sound ray; and the seabed bottom acoustic characteristics determine the energy loss of the sound wave when reflected on the seabed. Integrating these environmental factors enables sound ray tracing based on this to highly simulate sound propagation in real marine environments, making the subsequently extracted convergence zone parameters more realistic and enhancing the applicability and generalization ability of the method, which is suitable for complex environments in different sea areas.

[0020] Preferably, in step S3, the point satisfying the following conditions is identified as a valley point

[0021] and ,

[0022] wherein, is the depth of the sound ray at the horizontal distance , and are the first derivative and the second derivative of , is the horizontal distance of the i-th point on the sound ray from the sound source.

[0023] The valley point is identified by the above conditions, providing an objective, accurate and programmable mathematical criterion to replace the subjective judgment of observing the curve fluctuations with the human eye. This criterion can be executed by a computer without error, ensuring that each valley point is identified by a unified standard, avoiding omissions or misjudgments that may occur in manual interpretation, and improving the accuracy of data preparation from the bottom up. Technical, providing high-quality and consistent input data for subsequent statistical analysis.

[0024] Preferably, in step S4, the sound rays of the convergence zone are divided into three groups, and the range of the horizontal distance of each group of valley points from the sound source is selected according to the historical data of the convergence zone in the target area range.

[0025] Generally, only the first three convergence zones are needed to be identified, and the farther convergence zones are not significant to be identified. The grouping operation effectively solves the problem of "peak submergence" in multi-convergence zone identification. In deep sea sound channel, there are usually multiple convergence zones distributed at different distances from the sound source. If all the valley points are globally kernel density estimated without distinction, the weak peaks of the far convergence zone (fewer sound rays, more scattered distribution) are easily submerged by the strong signal of the near convergence zone (denser sound rays, sharper peak), resulting in failure to identify. The grouping strategy is equivalent to setting an "analysis window" for each convergence zone, ensuring that each potential convergence zone can be independently and clearly analyzed and extracted, greatly improving the identification ability of multiple convergence zones.

[0026] As a preferred, the expression of kernel density estimation in step S4 is

[0027] ,

[0028] wherein, is the relative density of the valley point distribution of the nth group of convergence zone sound rays at the horizontal distance r from the sound source, is the total number of valley points in the nth group of convergence zones, is a Gaussian kernel function, and h is the bandwidth.

[0029] The Gaussian kernel function is used to perform kernel density estimation on the grouped valley point horizontal distance distribution, which is highly consistent with the non-uniform and asymmetric distribution characteristics of the convergence zone sound rays in the actual space. Moreover, kernel density estimation is a non-parametric estimation method, which is less sensitive to the "bin" position and size than a histogram, and generates a smooth and continuous probability density curve. This facilitates accurate positioning of the peak of the distribution density (i.e., the center of the convergence zone), and provides a smooth function basis for subsequent calculation of the width (such as the full width at half maximum), making the calculation results more stable and accurate.

[0030] As a preferred, h in step S4 is determined according to an empirical formula related to the sample variance and the interquartile range.

[0031] The bandwidth parameter h is not a fixed value, but is adaptively determined according to the statistical characteristics (such as variance and quartile range) of the sample data by an empirical formula (such as Silverman's rule), realizing intelligent processing according to data. The bandwidth h determines the smoothness of the kernel density estimation curve: if h is too large, the curve is too smooth, which may blur the details and may not be able to distinguish adjacent peaks; if h is too small, the curve is greatly affected by random fluctuations, and many false peaks will appear. By adaptively determining the bandwidth in the above method, the method can cope with the differences in sample quantity and distribution caused by different sea areas and different sound source configurations. Whether the valley point data is dense or sparse, concentrated or dispersed, a suitable bandwidth can be automatically selected to obtain a density curve that is most helpful for peak identification, significantly enhancing the robustness and adaptability of the method.

[0032] As preferred, the width of the convergence zone in step S4 is calculated by the formula

[0033] ,

[0034] wherein, is the width of the nth convergence zone, and are the values of the kernel estimation density curve on the right and left sides of the main peak, corresponding horizontal distance, is the horizontal distance from the main peak of the kernel density estimation curve corresponding to the nth group of convergence zone sound ray to the sound source;

[0035] The formula for calculating the typical depth is

[0036] ,

[0037] wherein, is the typical depth of the nth convergence zone, is the total number of valley points of the nth convergence zone within its width range.

[0038] According to the calculation formula of the width, it is equivalent to the "full width at half maximum" of the kernel density curve, which is a widely used index in the fields of optics and signal processing that can effectively reflect the width of the energy concentration region. It is more scientific and objective than artificially setting a fixed distance range or relying on visual estimation. The typical depth uses the arithmetic mean, which integrates the depth information of all effective sound ray valley points in the convergence zone, and is more representative than the depth of a single sound ray or a subjective selected depth value, and can better reflect the average position of the convergence zone in the vertical direction. The above two calculation formulas provide a repeatable calculation standard, and the explicit formula enables anyone to execute this method at any time, as long as the same input is input, the same parameter result can be obtained, and the uncertainty of the output result caused by human subjective factors is completely eliminated.

[0039] The convergence zone extraction system based on ray tracing and kernel density estimation comprises:

[0040] The ray tracing module is used to collect the sound source position related information, obtain the environmental parameters in the target area range in combination with the environmental database, perform ray tracing according to the environmental parameters by using an underwater acoustic simulation tool, and output ray trajectory data;

[0041] The convergence zone ray preliminary screening module is used to analyze the ray trajectory data, and the rays with zero collision times with the sea surface and the sea bottom are taken as candidate convergence zone rays;

[0042] The convergence zone ray determination module is used to confirm the valley points of the candidate convergence zone rays based on the depth-distance curves of the candidate convergence zone rays, and screen the rays with the depth of the valley points not less than a preset threshold as the convergence zone rays;

[0043] The convergence zone information output module is used to group the convergence zone rays according to the horizontal distance of the valley points from the sound source, perform kernel density estimation on the horizontal distance of the valley points in each group of convergence zone rays, take the horizontal distance of the main peak of the kernel density estimation curve from the sound source as the center distance of the convergence zone, and calculate the width and typical depth of the convergence zone according to the center distance.

[0044] The computer readable storage medium storing one or more programs comprises one or more programs comprising instructions that, when executed by a computing device, cause the computing device to perform any of the above methods.

[0045] Beneficial effects: the ray tracing is performed by using a professional underwater acoustic model, then the data preliminary screening is performed based on the collision conditions of the sea surface and the sea bottom, and then the accurate screening is performed by introducing the valley points and the depth threshold, so that the screened rays conform to the real physical characteristics, at the same time, the surface waveguide rays are effectively eliminated, and the misjudgment caused by the shallow layer interference is avoided; finally, the grouped kernel density estimation is used to quantitatively analyze the screened data, the grouping can avoid that the weak peak at a long distance is covered by the strong peak at a short distance, the stable recognition effect can be maintained in different sea area environments and sample scales, and the robustness and adaptability of the method are enhanced; the kernel density estimation method can accurately extract the center position and the width of the convergence zone in the non-uniform and multi-peak distribution, so that the accuracy of the recognition result is significantly improved; the whole method is realized by a standardized process, and does not depend on manual judgment, so that the accuracy and the efficiency are improved. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is the overall flowchart of the method;

[0047] Figure 2 is a configuration file schematic diagram generated based on user input;

[0048] Figure 3 This is a schematic diagram of sound velocity profiles and seabed topography data extracted based on configuration files and built-in databases. Figure (a) is a schematic diagram corresponding to 0° clockwise from due north, Figure (b) is a schematic diagram corresponding to 60° clockwise from due north, Figure (c) is a schematic diagram corresponding to 120° clockwise from due north, Figure (d) is a schematic diagram corresponding to 180° clockwise from due north, Figure (e) is a schematic diagram corresponding to 240° clockwise from due north, and Figure (f) is a schematic diagram corresponding to 300° clockwise from due north.

[0049] Figure 4 This is a diagram of the sound trajectory results generated after running Bellhop. The red sound lines are the identified convergence zone sound lines, and the green sound lines are the sea surface contact sound lines. Figures (a) to (f) correspond to... Figure 3 The result diagram of the sound ray trajectory in the corresponding figure;

[0050] Figure 5 This is a kernel density fitting result of the horizontal distance between the valley points of the convergence region;

[0051] Figure 6 This is a schematic diagram of the convergence region parameter table generated based on the recognition results. Detailed Implementation

[0052] As shown in the figure, the convergence region extraction method based on ray tracing and kernel density estimation described in this invention includes the following steps:

[0053] S1. Collect information related to the location of the sound source and combine it with the environmental database to obtain environmental parameters within the target area. Use underwater acoustic simulation tools to track sound ray based on the environmental parameters and output sound ray trajectory data.

[0054] The information related to the sound source location includes the longitude, latitude, and depth of the sound source; the environmental database includes sound velocity profiles, seabed topography, and acoustic characteristics of the seabed sediment. Here, we select environmental database information that is no more than 200km away from the sound source, because the first three convergence zones will not exceed this distance under normal circumstances. The specific upper limit of the horizontal distance can be adjusted according to the conditions of different sea areas.

[0055] Underwater acoustic simulation tools can be used with Bellhop. Based on its usage guidelines, data such as sound velocity profiles, seabed topography, and acoustic properties of the seabed within the target area are reformatted into *.env, *.ssp, and *.bty files that Bellhop can recognize. The calculation mode is then set to R in the *.env file to output the depth-distance trajectory of the sound rays. After executing Bellhop.exe, the calculation results are saved in a *.ray file.

[0056] S2, analyze the sound ray trajectory data, and take the sound ray with zero collision times with the sea surface and the sea bottom as the candidate convergence zone sound ray;

[0057] By analyzing the sound ray trajectory data, the collision of the sound ray with the sea surface and the sea bottom can be known, and the sound ray is classified according to this:

[0058] Direct sound ray: NumTopBnc=0, NumBotBnc=0;

[0059] Sea surface contact sound ray: NumTopBnc>=1, NumBotBnc=0;

[0060] Sea bottom contact sound ray: NumTopBnc=0, NumBotBnc>=1;

[0061] Sea surface-sea bottom multiple reflection sound ray: NumTopBnc>=1, NumBotBnc>=1.

[0062] Wherein, NumTopBnc is the sea surface collision times, and NumBotBnc is the sea bottom collision times.

[0063] The direct sound ray is marked as a candidate convergence zone sound ray.

[0064] S3, confirm the valley point of the depth-distance curve of the candidate convergence zone sound ray, and screen the sound ray with a depth not less than a preset threshold as a convergence zone sound ray;

[0065] Derivate the depth-distance curve of the candidate convergence zone sound ray, if a point meets the following conditions, it is determined as a valley point:

[0066] And ,

[0067] Wherein, is the depth of the sound ray at the horizontal distance , and are the first derivative and the second derivative of , respectively, is the horizontal distance of the i-th point on the sound ray from the sound source.

[0068] To distinguish the surface waveguide ray from the convergence zone ray in the direct ray, the invention further introduces a depth criterion. The valley point of the surface waveguide ray is generally located in the shallow thermocline, with a depth of only hundreds of meters; while the valley point of the typical convergence zone ray often appears near the deep sound channel axis, with a depth of thousands of meters or even deeper. Therefore, the invention preferably adopts 1000 m as the threshold, and when the depth of the valley point is <1000 m, the ray is determined as a surface waveguide ray and is rejected; when the depth of the valley point is ≥1000 m, it is determined as a convergence zone ray. The threshold can be adjusted according to the sound speed profile characteristics of the actual sea area.

[0069] S4, group the convergence zone rays according to the horizontal distance of the valley points from the sound source, and perform kernel density estimation on the horizontal distance of the valley points in each group of convergence zone rays, taking the horizontal distance of the main peak of the kernel density estimation curve from the sound source as the center distance of the convergence zone, and calculating the width and typical depth of the convergence zone accordingly.

[0070] According to the physical characteristics of the typical deep sound channel, the convergence zone is distributed in a ring belt, for example, the first convergence zone is generally 30-80 km, the second convergence zone is 80-130 km, and a third convergence zone may appear at a further distance. If direct statistical analysis is performed on all valley points, the weak peaks at a long distance are easily submerged by the dense distribution at a short distance, leading to recognition failure. To avoid this problem, the invention first divides the valley points into multiple groups according to the physical characteristics of the sound channel: if km, it is a near-field or non-convergence zone area and is rejected; if km, it is a first convergence zone candidate window, and the set of points in this window is denoted as ; if km, it is a second convergence zone candidate window, and the set of points in this window is denoted as ; if km, it is a long-distance convergence zone candidate window, and the set of points in this window is denoted as , where are the total number of valley points in the first, second and third convergence zone groups, respectively. The horizontal distance range of each group of valley points from the sound source can be adjusted according to the historical data of the convergence zone in the target area range.

[0071] In each candidate window, since the convergence zone ray distribution is often non-uniform and asymmetric, the position with the most dense ray distribution needs to be identified as the position of the convergence zone, so the kernel density estimation is performed on the horizontal distance set of the valley points from the sound source in each window.

[0072] The expression of the kernel density estimation is

[0073] ,

[0074] wherein, is the relative density of the sound ray in the nth group of convergence zones at the valley point of the horizontal distance r from the sound source, is the total number of valley points in the nth group of convergence zones, is a Gaussian kernel function; h is a bandwidth which can be calculated by an empirical formula related to sample variance and quartile distance such as Silverman rule, and automatically calculates a reasonable bandwidth according to sample quantity and distribution characteristics, so that appropriate smoothing degree can be obtained in different sea areas and different sample sizes.

[0075] The horizontal distance of the main peak of the kernel density estimation curve from the sound source is taken as the center distance of the group of convergence zones;

[0076] The width of the convergence zone is calculated by the formula

[0077] ,

[0078] wherein, is the width of the nth convergence zone, and are the values of the kernel estimation density curve on the right and left sides of the main peak, corresponding horizontal distances, is the horizontal distance of the main peak of the kernel density estimation curve of the sound ray corresponding to the nth group of convergence zones from the sound source; that is, half of the main peak value of the kernel density estimation curve of the group of convergence zones is taken to determine two horizontal distances as and .

[0079] The calculation formula of the typical depth is

[0080] ,

[0081] wherein, is the typical depth of the nth convergence zone, is the total number of valley points of the nth convergence zone within the width range thereof.

[0082] Finally, the triplet parameters of each group of convergence zones are obtained which can be saved in the form of *.nc file for sound field visualization and sonar performance evaluation.

[0083] The convergence zone extraction system based on sound ray tracing and kernel density estimation provided by the application comprises:

[0084] A sound ray tracing module: used for collecting sound source position related information, combining with environment database to obtain environment parameters in the target area range, and using underwater acoustic simulation tools to perform sound ray tracing according to the environment parameters and output sound ray track data;

[0085] The converging zone sound ray preliminary screening module is configured to analyze the sound ray track data and screen the sound ray with zero collision times with the sea surface and the sea bottom as a candidate converging zone sound ray.

[0086] The converging zone sound ray determining module is configured to confirm the valley point of the depth-distance curve of the candidate converging zone sound ray, and screen the sound ray with a depth not less than a preset threshold as a converging zone sound ray.

[0087] The converging zone information output module is configured to group the converging zone sound rays according to the horizontal distance of the valley point from the sound source, perform kernel density estimation on the horizontal distance of the valley point in each group of converging zone sound rays, take the horizontal distance of the main peak of the kernel density estimation curve from the sound source as the center distance of the converging zone, and calculate the width and typical depth of the converging zone according to the center distance.

[0088] The computer readable storage medium storing one or more programs of the present application comprises one or more programs including instructions, which, when executed by a computing device, cause the computing device to perform the above method.

[0089] In order to better illustrate the method, a specific example is further described as follows:

[0090] Step 1: The user first inputs the sound source position and analysis parameters, for example, in the present embodiment, the sound source is located at longitude 124.5°, latitude 23.0°, depth 300 m, the analysis horizontal distance is set to 200 km, the angle resolution is set to 60°, and the calculation time is June 23, 2025, 8:00. The Bellhop system automatically generates a configuration file for sound field analysis according to the user input, as shown in Figure 2 The parameter meanings are as follows: longitude explong, latitude explat, sound source depth sd_target, calculation distance range_lim, angle resolution deltaa, and calculation time time.

[0091] The system automatically calls the built-in marine environment database to extract the environmental parameters of the corresponding region, including the sound velocity profile, the sea bottom topography and the acoustic characteristics of the sea bottom, and automatically formats these parameters into environment description files that can be analyzed by the Bellhop software, including.env,.ssp and *.bty files, to ensure that the Bellhop sound ray tracing can run smoothly. The visualization results of these files are as shown in Figure 3 .

[0092] Step 2: The system automatically executes the Bellhop.exe program to obtain the sound ray tracing results stored in the *.ray file, parses the sound ray trajectory, and divides the sound rays into direct type, sea surface contact type, sea bottom contact type, and sea surface-sea bottom multiple reflection type according to the number of sea surface and sea bottom collisions (NumTopBnc, NumBotBnc). Among them, the direct type sound ray with NumTopBnc = 0 and NumBotBnc = 0 is separately marked as a candidate convergence zone sound ray.

[0093] Step 3: The valley point detection is performed on the depth-distance curve z(r) of the direct type sound ray. If the valley point depth is less than 1000 m (this threshold value can be adjusted according to the thermocline position of the target sea area sound speed profile or the deep sea channel axis depth.), it is determined as a surface waveguide sound ray and is removed; if the valley point depth is greater than 1000 m, it is determined as a convergence zone sound ray, as shown by the red trajectory marked in Figure 4 .

[0094] Step 4: According to Figure 4 , there are convergence zone sound rays only in the 120° and 180° directions clockwise from the north, so only the convergence zone parameters in these two directions are calculated. First, according to the physical characteristics of the typical deep sea channel, the valley points are divided into different candidate windows according to the horizontal distance, such as the 1st convergence zone (30-80 km), the 2nd convergence zone (80-130 km), and the 3rd convergence zone (130-200 km). Then, the system uses the kernel density estimation method to model the horizontal distance distribution of the valley points in each candidate window to extract the main peak value as the center distance of the convergence zone. The bandwidth parameter h of the kernel density function is determined adaptively by the data (such as the Silverman rule), which ensures reasonable smoothing effect under different sample sizes. The fitting results are shown in Figure 5 .

[0095] Through the fitting results, the main peak position is extracted as the center distance of the convergence zone, the half peak width is used to determine the left and right boundaries and the width of the convergence zone, and the average depth of the valley points in this interval is combined to obtain the three-tuple parameters (center distance, width, depth) of each convergence zone. The final output of the convergence zone parameters is saved in the form of a table and output as a *.nc file, which is called by the sound field visualization and sonar performance evaluation, as shown in Figure 6 .

[0096] Under the embodiment, the system automatically identifies the first three convergence zones in the ray calculation results of 120° and 180° azimuths, and outputs the center distance, width and typical depth of each convergence zone. The identification result shows that the method can realize the automatic extraction of the convergence zone parameters under the actual sea area conditions, avoids the manual image interpretation method depending on experience, significantly reduces the workload of manual analysis, and effectively overcomes the problems of uneven distribution of sound rays in the convergence zone and unstable local aggregation due to the introduction of the statistical modeling method based on the kernel density estimation, thereby improving the robustness of identification and the reliability of the result.

Claims

1. A method for extracting convergent regions based on ray tracing and kernel density estimation, characterized in that, Includes the following steps: S1. Collect information related to the location of the sound source and combine it with the environmental database to obtain environmental parameters within the target area. Use underwater acoustic simulation tools to track sound ray based on the environmental parameters and output sound ray trajectory data. S2. Analyze the sound trajectory data and select the sound ray that has zero collisions with the sea surface and seabed as candidate convergence zone sound rays; S3. Based on the depth-distance curve of the candidate convergence zone sound line, identify its valley point, and filter the sound lines whose valley point depth is not less than the preset threshold as convergence zone sound lines. S4. Group the sound lines of the convergent region according to the horizontal distance between the valley point and the sound source. Perform kernel density estimation on the horizontal distance between the valley points in each group of convergent region sound lines. Take the horizontal distance between the main peak of the kernel density estimation curve and the sound source as the center distance of the convergent region of that group, and calculate the width and typical depth of the convergent region accordingly.

2. The method according to claim 1, characterized in that: The information related to the location of the sound source in step S1 includes the longitude, latitude, and depth of the sound source.

3. The method according to claim 1, characterized in that: The environmental database in step S1 includes sound velocity profiles, seabed topography, and acoustic properties data of the seabed sediment.

4. The method according to claim 1, characterized in that: In step S3, points that meet the following conditions are identified as valley points. and , in, For the sound ray at horizontal distance The depth at that location and They are respectively The first and second derivatives, Let be the horizontal distance from the i-th point on the sound line to the sound source.

5. The method according to claim 1, characterized in that: In step S4, the convergent sound lines are divided into three groups, and the horizontal distance range of the valley point of each group from the sound source is selected based on the historical data of the convergent area of ​​the target region.

6. The method according to claim 1, characterized in that: The expression for kernel density estimation in step S4 is: ， in, Let be the relative density of the sound rays in the nth convergence region at the valley point at a horizontal distance r from the sound source. The total number of valley points in the nth convergence region. Here, h is the Gaussian kernel function, and h is the bandwidth.

7. The method according to claim 6, characterized in that: In step S4, h is determined based on an empirical formula related to the sample variance and interquartile range.

8. The method according to claim 1, characterized in that: The formula for calculating the width of the convergence zone in step S4 is as follows: ， in, Let the width of the nth convergence region be . and The values ​​for the kernel estimation density curves on the right and left sides of the main peak are respectively... The corresponding horizontal distance, The horizontal distance between the main peak of the kernel density estimation curve corresponding to the sound ray in the nth convergence region and the sound source. The formula for calculating typical depth is: ， in, The typical depth of the nth convergence region. This represents the total number of valley points within the width of the nth convergence region.

9. A convergence region extraction system based on ray tracing and kernel density estimation, characterized in that, include: Sound ray tracing module: used to collect information related to the location of the sound source and combine it with an environmental database to obtain environmental parameters within the target area. It then uses underwater acoustic simulation tools to perform sound ray tracing based on the environmental parameters and outputs sound ray trajectory data. Convergence zone acoustic ray initial screening module: used to analyze acoustic ray trajectory data and select acoustic rays with zero collisions with the sea surface and seabed as candidate convergence zone acoustic rays; Convergence zone sound ray determination module: used to identify the valley point of the candidate convergence zone sound ray based on the depth-distance curve of the candidate convergence zone sound ray, and filter the sound rays whose valley point depth is not less than a preset threshold as convergence zone sound rays; Convergence Zone Information Output Module: This module is used to group convergence zone sound lines according to the horizontal distance between the valley point and the sound source, perform kernel density estimation on the horizontal distance between the valley points in each group of convergence zone sound lines, take the horizontal distance between the main peak of the kernel density estimation curve and the sound source as the center distance of the group of convergence zones, and calculate the width and typical depth of the convergence zone accordingly.

10. A computer-readable storage medium for storing one or more programs, characterized in that: The program includes one or more instructions that, when executed by a computing device, cause the computing device to perform any of the methods according to claims 1 to 8.

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