Convergence region extraction method and system based on sound ray tracking and kernel density estimation, and storage medium

Abstract

The invention discloses a convergence region extraction method and system based on sound ray tracking and kernel density estimation, and a storage medium, and the method comprises the following steps: S1, obtaining environment parameters in a target region range, carrying out the sound ray tracking through employing an underwater acoustic simulation tool, and outputting sound ray trajectory data; s2, analyzing the sound ray trajectory data, and taking the sound rays with zero collision times with the sea surface and the seabed as candidate convergence area sound rays; s3, determining valley value points based on the depth-distance curve of the candidate convergence area sound rays, and screening the sound rays of which the depths of the valley value points are not less than a preset threshold value as convergence area sound rays; s4, grouping the convergence area sound rays according to the horizontal distance of the valley point, performing kernel density estimation on the horizontal distance of the valley point in each group of convergence area sound rays, and determining the center distance, width and typical depth of the convergence area according to an estimation result; the convergence area can be objectively, accurately and efficiently recognized without depending on manual judgment.

Description

Technical Field

[0001] This invention relates to underwater acoustics, and more particularly to a method, system, and storage medium for extracting convergence regions based on ray tracing and kernel density estimation. Background Technology

[0002] In underwater acoustics, convergence-based sound propagation modes enable long-distance propagation and are widely used in long-range detection, communication, and sonar performance evaluation. The formation of a convergence zone depends on a specific sound velocity profile environment; its typical characteristic is that sound rays refract during propagation and focus at a certain horizontal distance, forming a strong concentrated area of ​​sound energy. Accurate estimation of the location, depth, and width of the convergence zone is crucial for achieving stable long-distance propagation and improving detection performance.

[0003] Existing methods mostly rely on human experience or visual analysis of sound field calculation results, and have not yet formed an effective technical solution to achieve automated recognition. The main shortcomings are as follows:

[0004] (1) It is highly subjective. Existing methods mainly rely on researchers to manually interpret sound field images or sound trajectories, which is inefficient and greatly affected by personal experience. There is a lack of an objective and unified process from ray data to convergence zone extraction.

[0005] (2) There is a lack of full utilization of acoustic physical mechanisms, resulting in deficiencies in the identification of sound rays related to the convergence zone. The differences in the effects of different types of sound rays, such as those from sea surface contact, seabed contact, and direct contact, are not fully considered, and there is a lack of unified and objective criteria. Sound ray tracking models (such as BELLHOP) can output sound ray trajectories or sound pressure distributions, but they cannot directly identify sound rays in the convergence zone. Researchers often still need to infer the location and extent of the convergence zone by observing the energy accumulation area.

[0006] (3) Ignoring the non-uniform distribution characteristics of sound rays in the convergence zone, most existing methods approximate the convergence zone as a uniform energy aggregate, failing 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 location, width and intensity of the convergence zone.

[0007] (4) Manual interpretation is difficult to distinguish which sound lines can form a stable convergence zone in complex environments. The method is not robust and timely enough to meet the requirements of speed and accuracy in engineering applications. Summary of the Invention

[0008] Purpose of the invention: The purpose of this invention is to provide a method, system, and storage medium for extracting convergence regions based on ray tracing and kernel density estimation that can objectively, accurately, and efficiently identify convergence regions without relying on human judgment.

[0009] Technical solution: The convergence region extraction method based on ray tracing and kernel density estimation described in this invention includes the following steps:

[0010] 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.

[0011] 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;

[0012] 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.

[0013] 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.

[0014] This method first collects sound source-related data and combines it with an environmental database to obtain environmental parameters within the target area. It then uses underwater acoustic simulation tools to output sound ray trajectories. Subsequently, based on clear rules (i.e., no surface-to-seabed collision), it performs initial screening. Next, it introduces valley points and depth thresholds for further screening to obtain convergent sound rays. These initial and further screenings ensure the physical rationality of the selected sound rays, guaranteeing the accuracy of the final identification results. Then, it groups the convergent sound rays according to the horizontal distance of the valley points, preventing weak peaks at distant distances from being easily submerged by dense distributions at closer distances during subsequent kernel density estimation, thus avoiding the failure to identify distant convergent areas. Finally, taking into full account the non-uniform distribution characteristics of sound rays within the convergent area, it uses kernel density estimation to statistically analyze the convergent sound rays, identifying the region with the highest energy density. Based on this, it extracts the center position, width, and typical depth of the convergent area, which is more accurate than extracting convergent area information by treating the convergent area as an approximate uniform energy aggregate.

[0015] This method constructs a clear, repeatable, and standardized data processing workflow, eliminating the need for subjective human judgment and completely removing inconsistencies caused by differences in experience among different operators. This results in highly repeatable and objective convergence region extraction, and is also more efficient than subjective human judgment. Furthermore, it extracts accurate structured information: the center position, width, and typical depth of the convergence region, which, compared to simply providing the approximate location of the convergence region, is readily applicable to sound field visualization, sonar performance evaluation, and remote communication link design, demonstrating strong engineering application value.

[0016] Preferably, the sound source location information in step S1 includes the 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 results correspond to real ocean maps, which is crucial for regional marine environmental studies and cross-platform collaborative exploration applications. Depth information is one of the most critical initial conditions in ray tracing calculations. Different sound source depths significantly alter the propagation path of sound rays and the location of convergence zones. Explicitly obtaining this information is the cornerstone of ensuring the accuracy of the entire method.

[0018] Preferably, the environmental database in step S1 includes sound velocity profiles, seabed topography, and acoustic properties data of the seabed sediment.

[0019] The environmental database contains the above information to ensure the realism and completeness of the sound field simulation environment. The sound velocity profile determines the refraction law of sound rays and is the primary condition for the formation of the convergence zone; the seabed topography affects the reflection and scattering of sound rays; and the acoustic properties of the seabed sediment determine the energy loss of sound waves when reflected from the seabed. By considering these environmental factors, the sound ray tracing based on this data can highly simulate sound propagation in a real marine environment, thus making the subsequently extracted convergence zone parameters more realistic, enhancing the applicability and generalization ability of the method, and making it suitable for complex environments in different sea areas.

[0020] Preferably, in step S3, points that meet the following conditions are identified as valley points.

[0021] and ,

[0022] 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.

[0023] The above criteria for identifying valley points provide an objective, accurate, and programmable mathematical standard, replacing the subjective judgment of human observation of curve fluctuations. This standard can be executed by the computer without errors, ensuring that each valley point is identified through a unified standard, avoiding omissions or misjudgments that may occur with manual interpretation. This fundamentally improves the accuracy of data preparation and provides high-quality, consistent input data for subsequent statistical analysis.

[0024] Preferably, 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 according to the historical data of the convergent area of ​​the target region.

[0025] Typically, only the first three convergence zones need to be identified, as identifying more distant convergence zones is less meaningful. This grouping approach effectively solves the "peak submersion" problem in multi-convergence zone identification. In deep-sea acoustic channels, multiple convergence zones typically exist, distributed at varying distances from the sound source. If all valley points are indiscriminately estimated globally, the weak peaks of distant convergence zones (fewer, more scattered sound rays) are easily submerged by the strong signals of nearby convergence zones (dense sound rays, sharper peaks), making identification impossible. The grouping strategy essentially sets up an "analysis window" for each convergence zone, ensuring that each potential convergence zone can be independently and clearly analyzed and extracted, significantly improving the ability to identify multiple convergence zones.

[0026] Preferably, the expression for kernel density estimation in step S4 is:

[0027] ,

[0028] 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.

[0029] The Gaussian kernel function is used to estimate the kernel density of the horizontal distance distribution of the valley points after grouping. This is highly consistent with the non-uniform and asymmetric distribution characteristics of the sound lines in the convergence region in actual space. Moreover, kernel density estimation is a non-parametric estimation method, unlike histograms which are sensitive to the position and size of the "bins". It generates a smooth and continuous probability density curve. This makes it easy to accurately locate the peak of the distribution density (i.e., the center of the convergence region) and provides a smooth functional basis for subsequent calculation of the width (such as the full width at half maximum). The calculation results are more stable and accurate.

[0030] Preferably, in step S4, h is determined based on an empirical formula related to the sample variance and interquartile range.

[0031] The bandwidth parameter h is not a fixed value, but is adaptively determined based on the statistical characteristics of the sample data (such as variance and interquartile range) using empirical formulas (such as Silverman's rule), achieving intelligent processing "tailored to the data". The bandwidth h determines the smoothness of the kernel density estimation curve: if h is too large, the curve is too smooth, blurring details and making it impossible to distinguish adjacent peaks; if h is too small, the curve is greatly affected by random fluctuations, resulting in many spurious peaks. By adaptively determining the bandwidth using the above method, this method can cope with differences in sample size and distribution caused by different sea areas and different sound source configurations. Regardless of whether the valley point data is dense or sparse, concentrated or dispersed, it can automatically select a suitable bandwidth to obtain the density curve most conducive to peak identification, significantly enhancing the robustness and adaptability of this method.

[0032] Preferably, the formula for calculating the width of the convergence zone in step S4 is as follows:

[0033] ,

[0034] 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 from the sound source to the main peak of the kernel density estimation curve corresponding to the sound ray in the nth convergence region;

[0035] The formula for calculating typical depth is:

[0036] ,

[0037] 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.

[0038] The formula for calculating the width indicates that it is equivalent to the "full width at half maximum" (FWHM) of the kernel density curve. FWHM is a widely used indicator in optics and signal processing that effectively reflects the width of the energy concentration region. It is more scientific and objective than arbitrarily defining a fixed distance range or estimating by the naked eye. Typical depth uses an arithmetic mean, integrating the depth information of all effective sound ray valleys within the convergence region. This is more representative than the depth of a single sound ray or a subjectively chosen depth value, and better reflects the average position of the convergence region in the vertical direction. The two calculation formulas above provide repeatable calculation standards. The explicit formulas ensure that anyone performing this method at any time, with the same input, will obtain completely consistent parameter results, completely eliminating the uncertainty of the output results caused by subjective human factors.

[0039] The convergence region extraction system based on ray tracing and kernel density estimation described in this invention includes:

[0040] 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.

[0041] 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;

[0042] 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;

[0043] 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.

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

[0045] Beneficial effects: Sound ray tracking is performed using a professional underwater acoustic model. Data is then initially screened based on surface-seabed collision conditions, followed by precise screening using valley points and depth thresholds. This ensures that the selected sound rays conform to their actual physical characteristics while effectively eliminating surface waveguide sound rays, avoiding misjudgments caused by shallow interference. Finally, grouped kernel density estimation is used to quantify the selected data. Grouping prevents weak peaks at long distances from being masked by strong peaks at close distances, ensuring stable recognition performance under different sea environments and sample sizes, enhancing the method's robustness and adaptability. The kernel density estimation method can accurately extract the center position and width of convergence zones even in non-uniform, multi-peak distributions, significantly improving the accuracy of the recognition results. The entire method is implemented through a standardized process, completely independent of manual judgment, improving both accuracy and efficiency. Attached Figure Description

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

[0047] Figure 2 This is a schematic diagram of a configuration file 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 trajectory data and select the sound ray that has zero collisions with the sea surface and seabed as candidate convergence zone sound rays;

[0057] By analyzing sound trajectory data, we can understand the collisions between sound rays and the sea surface and seabed, and classify the sound rays accordingly.

[0058] Direct vocal range: NumTopBnc=0, NumBotBnc=0;

[0059] Sea surface contact sound rays: NumTopBnc≥1, NumBotBnc=0;

[0060] Undersea contact ray: NumTopBnc=0, NumBotBnc≥1;

[0061] Sea surface-seabed multiple reflections of sound: NumTopBnc≥1, NumBotBnc≥1.

[0062] NumTopBnc represents the number of collisions on the sea surface, and NumBotBnc represents the number of collisions on the seabed.

[0063] This invention separately marks direct sound ray as candidate convergence region sound ray.

[0064] 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.

[0065] Differentiate the depth-distance curve of the acoustic ray in the candidate convergence region. If a point satisfies the following condition, it is determined to be a valley point:

[0066] and ,

[0067] 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.

[0068] To distinguish between surface waveguide acoustic rays and converging region acoustic rays in direct-path acoustic rays, this invention further introduces a depth criterion. The trough points of surface waveguide acoustic rays are generally located in shallow mesospheric layers, with depths only on the order of hundreds of meters; while the trough points of typical converging region acoustic rays often appear near the deep-sea acoustic channel axis, with depths on the order of kilometers or even deeper. Therefore, this invention preferably uses 1000 m as a threshold. When the trough point depth is <1000 m, the acoustic ray is identified as a surface waveguide acoustic ray and discarded; when the trough point depth is ≥1000 m, it is identified as a converging region acoustic ray. This threshold can be adjusted according to the sound velocity profile characteristics of the actual sea area.

[0069] 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.

[0070] Based on the physical characteristics of typical deep-sea acoustic channels, convergence zones exhibit a ring-like distribution. For example, the first convergence zone is generally located at 30-80 km, the second at 80-130 km, and a third may appear at even greater distances. If a direct statistical analysis is performed on all valley points, the weak peaks at distant locations are easily overwhelmed by the dense distribution at closer locations, leading to recognition failure. To avoid this problem, this invention first divides the valley points into multiple groups based on the physical characteristics of the acoustic channel: if... km represents a near-field or non-converging region, and is therefore excluded; if km represents the first candidate window for the convergence region, and the set of points within this window is denoted as km. ;like km, the second convergence region candidate window, the set of points within this window is denoted as km. ;like A candidate window for a long-distance convergence region, the set of points within this window is denoted as . ,in These represent the total number of valley points in the first, second, and third convergence zone groups, respectively. The horizontal distance range of each valley point from the sound source can be adjusted based on historical data of the convergence zones within the target area.

[0071] Within each candidate window, since the sound ray distribution in the convergence zone is often non-uniform and asymmetrical, it is necessary to identify the location where the sound ray distribution is most dense as the location of the convergence zone. Therefore, kernel density estimation is performed on the set of horizontal distances from the valley points to the sound source within each window.

[0072] The expression for kernel density estimation is:

[0073] ,

[0074] 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. is the Gaussian kernel function; h is the bandwidth, which can be calculated using empirical formulas related to sample variance and interquartile range, such as the Silverman rule. It automatically calculates a reasonable bandwidth based on the number of samples and distribution characteristics, so as to obtain a suitable degree of smoothness in different sea areas and different sample sizes.

[0075] The horizontal distance from the main peak of the kernel density estimation curve to the sound source is taken as the center distance of the convergence region.

[0076] The formula for calculating the width of the convergence zone is:

[0077] ,

[0078] 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, Let the horizontal distance be the main peak of the kernel density estimation curve corresponding to the sound ray of the nth convergence region from the sound source; that is, take half of the main peak value of the kernel density estimation curve of this convergence region to determine two horizontal distances as... and .

[0079] The formula for calculating typical depth is:

[0080] ,

[0081] 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.

[0082] Finally, the triplet parameters for each convergence region are obtained. It can be saved as a *.nc file for sound field visualization and sonar performance evaluation.

[0083] The convergence region extraction system based on ray tracing and kernel density estimation described in this invention includes:

[0084] 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.

[0085] 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;

[0086] 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;

[0087] 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.

[0088] The computer-readable storage medium for storing one or more programs according to the present invention includes one or more programs comprising instructions that, when executed by a computing device, cause the computing device to perform the method described above.

[0089] To better illustrate this method, a specific example will be used below for further explanation:

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

[0091] The system automatically accesses the built-in marine environment database to extract environmental parameters for the corresponding area, including sound velocity profiles, seabed topography, and acoustic properties of the seabed sediment. These parameters are then automatically formatted into environmental description files that Bellhop software can parse, including .env, .ssp, and *.bty files, to ensure smooth operation of Bellhop ray tracing. The visualization results of these files are shown below. Figure 3 As shown.

[0092] Step 2: The system automatically executes the Bellhop.exe program, obtaining the ray tracing results and storing them in a *.ray file. It analyzes the ray trajectories and, based on the number of collisions between the sea surface and seabed (NumTopBnc, NumBotBnc), classifies the ray into direct-reaching, surface-contact, seabed-contact, and surface-seabed-multiple-reflection types. Direct-reaching ray trajectories with NumTopBnc=0 and NumBotBnc=0 are separately marked as candidate convergence zone ray trajectories.

[0093] Step 3: Detect valley points on the depth-distance curve z(r) of the direct-path acoustic ray. If the valley point depth is less than 1000 m (this threshold can be adjusted according to the strata location of the target sea area's sound velocity profile or the axial depth of the deep-sea acoustic channel), it is identified as a surface waveguide acoustic ray and discarded; if the valley point depth is greater than 1000 m, it is identified as a converging region acoustic ray. Figure 4 The trajectory marked in red is shown in the image.

[0094] Step 4: According to Figure 4 Converging acoustic rays exist only in the 120° and 180° clockwise directions from true north; therefore, the convergence parameters are calculated only for these two directions. First, based on the physical characteristics of typical deep-sea acoustic channels, valley points are divided into different candidate windows according to horizontal distance, such as the first convergence zone (30–80 km), the second convergence zone (80–130 km), and the third convergence zone (130–200 km). Then, the system uses a kernel density estimation method to smooth the horizontal distance distribution of valley points in each candidate window, extracting the main peak value as the center distance of the convergence zone. The bandwidth parameter h of the kernel density function is adaptively determined by the data (e.g., using the Silverman rule) to ensure a reasonable smoothing effect under different sample sizes. The fitting results are as follows: Figure 5 As shown.

[0095] Based on the fitting results, the main peak position is extracted as the center distance of the convergence zone. The left and right boundaries and width of the convergence zone are determined by the half-peak width. Combined with the average depth of the valley points within this interval, the triplet parameters (center distance, width, and depth) for each convergence zone are obtained. The final output convergence zone parameters are saved in tabular form and output as a *.nc file for use in sound field visualization and sonar performance evaluation, such as... Figure 6 As shown.

[0096] In this embodiment, the system automatically identified the first three convergence zones from the ray calculation results at 120° and 180° azimuths, and output parameters such as the center distance, width, and typical depth of each convergence zone. This identification result demonstrates that the method of this invention can automatically extract convergence zone parameters under actual sea area conditions, avoiding the reliance on manual experience for image interpretation. This not only significantly reduces the workload of manual analysis but also effectively overcomes problems such as uneven distribution of sound rays and unstable local aggregation within the convergence zone by introducing a statistical modeling method based on kernel density estimation, thereby improving the robustness and reliability of the identification results.

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 as follows: ， 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 1, 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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