A method for predicting multiple acoustic scattering characteristics of underwater vehicles, electronic equipment and program product

By iterating the physical and acoustic multi-layer grouping model and octree structure, the efficiency and accuracy problems of multiple acoustic scattering forecasts of complex underwater submarines are solved, and the rapid prediction and accurate simulation of multiple scattering characteristics of underwater targets are achieved, and the detection capability of underwater monitoring sonar is improved.

CN119249614BActive Publication Date: 2025-09-02SHANGHAI JIAOTONG UNIV
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Patent Information

Application Number
CN202411508115.1
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-10-28
Publication Date
2025-09-02
Estimated Expiration
2044-10-28

AI Technical Summary

Technical Problem

The existing technology lacks an efficient multi-scattering prediction model for complex underwater submarine vehicles, which cannot meet the needs of modern underwater security, and the test and measurement cost is high and the cycle is long, making it difficult to achieve the acoustic scattering characteristics of non-cooperative underwater submarine vehicles.

Method used

It uses an iterative physical acoustic multi-layer grouping model, and uses an octree structure to establish a multi-layer grouping element model of the submarine. Combined with iterative algorithms to accelerate physical acoustic simulation, calculate the multiple scattered sound field of the submarine, and obtain the multiple scattered sound field of the target through coherent superposition.

Benefits of technology

It realizes rapid prediction of the multiple acoustic scattering characteristics of complex underwater submarine vehicles, improves detection accuracy and efficiency, provides accurate simulation of multiple scattering echoes of underwater targets and target intensity, and supports the identification ability of underwater monitoring sonar.

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Abstract

The present invention discloses a method for predicting the multiple acoustic scattering characteristics of underwater vehicles. The method includes a preprocessing step, which constructs a geometric model of the vehicle for subsequent acoustic simulation and calculation; meshing the vehicle model, based on the geometric model, to divide the vehicle model into smaller units for numerical calculation; and establishing a multi-layer grouped surface element model of the vehicle, dividing the surface of the vehicle into multiple surfaces to simulate the complex structure of the vehicle. The solution step includes using an iterative algorithm to accelerate the physical acoustic simulation process; calculating scattered sound fields of different orders, targeting the multiple scattering phenomenon of the vehicle, to obtain accurate simulation results. The post-processing step includes analyzing and obtaining the acoustic characteristics of the underwater vehicle in the underwater environment, including the time-domain echoes of the underwater vehicle's multiple acoustic scattering and the target intensity.
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Description

Technical Field

[0001] The present invention belongs to the technical field of underwater acoustic engineering, and in particular relates to a method for predicting multiple sound scattering characteristics of an underwater vehicle, electronic equipment and a program product. Background Art

[0002] Underwater vehicles, key equipment for marine resource development, are diverse in type and complex in shape. Their detection and identification is a key development direction for underwater security. Active sonar is a more effective means of detecting and identifying underwater unmanned vehicles (UUVs) than optical, electromagnetic, or passive acoustic detection methods. To improve the accuracy and efficiency of active sonar detection systems, a certain understanding of the echo characteristics of the vehicle is necessary. For example, an ROV (Remote Operated Vehicle), a type of underwater vehicle, features a complex structure including an extended operating chassis, a nozzle, propeller channels, propeller ducts, an electronics compartment, and a hydraulic unit. Incident sound waves are subject to multiple scattering from these surfaces. This is because the electronics compartment and hydraulic unit of an ROV can be a single unit, and the extended operating chassis supporting this unit is made of acoustically transparent materials, allowing sound waves to penetrate the chassis. Similarly, the thrusters of an ROV can be a single unit. When the thruster channels are designed with concave surfaces, this can also cause acoustic scattering of the incident wave.

[0003] Therefore, when underwater submersibles are assigned to perform complex missions, they carry a variety of sensors and equipment. However, there is currently little research on the fine echo characteristics caused by multiple acoustic scattering from the complex surface structures of such complex underwater submersibles. There is also a lack of efficient multiple acoustic scattering prediction models for complex submersibles, which cannot meet the needs of modern underwater security. Summary of the Invention

[0004] One embodiment of the present disclosure provides a method for rapidly predicting multiple acoustic scattering characteristics of a complex underwater vehicle, comprising:

[0005] Preprocessing steps include:

[0006] Construct a geometric model of the submersible for subsequent acoustic simulation and calculation;

[0007] Divide the submersible model into grids. Based on the geometric model, perform grid division to divide the submersible model into smaller units to facilitate numerical calculations.

[0008] A multi-layer grouped facet model of a submersible is established, dividing the surface of the submersible into multiple facets to simulate the complex structure of the submersible.

[0009] The solution steps include:

[0010] Use iterative algorithms to accelerate the physical acoustics simulation process;

[0011] Calculate different orders of scattered sound fields and target multiple scattering phenomena of submarines to obtain accurate simulation results;

[0012] Post-processing steps include:

[0013] The acoustic characteristics of the underwater vehicle in the underwater environment are analyzed and obtained, including the underwater vehicle's multiple acoustic scattering time domain echoes and target intensity. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily apparent by reading the following detailed description with reference to the accompanying drawings, in which several embodiments of the present invention are shown by way of example and not limitation, in which:

[0015] Figure 1 Flowchart of a method for predicting multiple acoustic scattering characteristics of an underwater vehicle according to one embodiment of the present invention.

[0016] Figure 2 A two-dimensional schematic diagram of the lth layer and the (l+1)th layer grouping according to one embodiment of the present invention.

[0017] Figure 3 Schematic diagram of a simplified ROV geometric model and multi-layer grouping of its facets according to one embodiment of the present invention.

[0018] in, Figure 3 -a is the geometric model, Figure 3 -b is the mesh model, Figure 3 -c is a multi-layer grouping model.

[0019] Figure 4 Schematic diagram of far-field pairing within a calculation area according to one embodiment of the present invention.

[0020] Figure 5 A schematic diagram of the time-angle spectrum of scattered echoes of an operational-level ROV model according to one embodiment of the present invention. Figure 5 -a is the simulation result, Figure 5 -b is the test result.

[0021] Figure 6 Schematic diagram of the acoustic target intensity pointing distribution (80kHz) of an operational-level ROV according to one embodiment of the present invention.

[0022] Figure 7 Schematic diagram of the effect of the number of facets on the computation time of the proposed method according to one embodiment of the present invention. DETAILED DESCRIPTION

[0023] Acoustic scattering refers to the phenomenon in which sound waves propagating through a medium, when they encounter obstacles or medium inhomogeneities, scatter in all directions in a patterned manner. This scattering phenomenon is closely related to factors such as the physical properties, shape, and size of the obstacle or medium, as well as the wavelength of the sound wave. Acoustic scattering is particularly important in the research of underwater unmanned submersibles, as these properties influence the submersible's detection, positioning, and communication capabilities in water.

[0024] Existing approaches to studying the acoustic scattering characteristics of underwater unmanned vehicles (UUVs) primarily focus on measuring their acoustic target intensity through testing. However, these tests, which require specific test sites, test models, and test personnel, are associated with high costs and long testing cycles, making them unacceptable for rapid R&D and design. Furthermore, experimental measurement of acoustic scattering from non-cooperative UUVs is difficult to implement. Therefore, modeling the acoustic scattering characteristics of complex underwater UUVs is of great significance.

[0025] The main approaches for modeling the acoustic scattering characteristics of complex underwater targets can be broadly categorized into two categories: low-frequency numerical methods and medium- and high-frequency approximation methods. Low-frequency numerical methods, such as finite element and boundary element methods, offer advantages in high accuracy and stability, but they also suffer from high computational load and storage requirements as the target size increases.

[0026] In recent years, most research has turned to high-frequency approximation methods to address acoustic scattering from large, complex targets. Ray-bouncing methods, when considering coupling, essentially only account for the effects caused by mirror reflections. This leads to ray divergence for targets with large concave curvatures, resulting in low computational accuracy. The plate element method based on the Kirchhoff approximation offers high computational efficiency but fails to account for multiple scattering, resulting in low computational accuracy for complex underwater targets.

[0027] The high-frequency approximation method, as used here, is a simplified computational approach for high-frequency sound waves. It's based on the assumption of geometric acoustics that, at high frequencies, the propagation and scattering of sound waves can be treated analogously to light, with sound waves primarily reflecting and diffracting when encountering a target. This approach is particularly useful when dealing with large, complex targets because it reduces computational complexity.

[0028] The ray-bouncing method is a high-frequency approximate numerical calculation method that divides the incident sound wave into several beams and calculates the reflection direction and energy loss of each beam on the target surface using geometric acoustic methods. This method takes into account multiple reflections of the sound beam on the target surface and calculates the scattered field of the entire target by superimposing the scattered fields generated by all beams.

[0029] The Kirchhoff approximation is a classic acoustic scattering theory that assumes that the incident and scattered waves can be approximated by plane waves at every point on the target surface. The plate element method based on the Kirchhoff approximation decomposes the target into many small planar elements, calculates the scattering of the sound wave by each element, and then superimposes these scattered fields to predict the acoustic scattering characteristics of the entire target.

[0030] Due to the limitations of the above-mentioned methods, the present disclosure proposes a method for quickly predicting the multiple sound scattering characteristics of complex underwater submersibles. This method uses an iterative physical acoustic multi-layer grouping model to approximate the multiple scattered sound field of the submersible as the coherent superposition result of scattered sound fields of different orders of discrete surface elements within a non-empty group. It has the advantages of clear physical meaning, high calculation accuracy and efficiency.

[0031] According to one or more embodiments, a method for quickly predicting the multiple sound scattering characteristics of a complex underwater vehicle is generally divided into two parts. One is preprocessing, that is, using an octree structure to establish a multi-layer grouped facet model of a complex underwater vehicle; the other is using an iterative physical acoustic acceleration algorithm to calculate the order-scattering sound field of discrete facets in a non-empty group, and then coherently superimposing the facet order-scattering sound field to obtain the target's overall order-scattering sound field, and finally coherently superimposing different order scattering sound fields to obtain the target's overall total multiple sound scattering sound field. Combining the above schemes, the multiple sound scattering characteristics of a complex underwater vehicle can be quickly predicted. Figure 1 shown.

[0032] Preprocessing includes:

[0033] Construct a geometric model of the submersible for subsequent acoustic simulation and calculation;

[0034] Divide the submersible model into grids. Based on the geometric model, perform grid division to divide the submersible model into smaller units to facilitate numerical calculations.

[0035] A multi-layer grouped surface element model of a submersible is established, and the surface of the submersible is divided into multiple surfaces to simulate the complex structure of the submersible.

[0036] The further solution process includes:

[0037] Use iterative algorithms to accelerate the physical acoustics simulation process;

[0038] Calculate scattered sound fields of different orders and target the multiple scattering phenomenon of submarines to obtain more accurate simulation results.

[0039] Further post-processing includes:

[0040] Analyze the acoustic characteristics of the submersible in the underwater environment, including the time domain echoes and target intensity of multiple acoustic scattering of complex underwater submersibles.

[0041] From the construction of the geometric model to the calculation of acoustic characteristics, each step is to more accurately simulate and predict the acoustic behavior of the submersible in the underwater environment.

[0042] The multi-layer grouped facet model is constructed using an octree structure. The octree is a tree-like data structure for three-dimensional spatial data. It divides the three-dimensional space into multiple cubic units, each of which can be further subdivided into eight smaller cubic units. This process can be performed recursively. The specific process is as follows:

[0043] For the three-dimensional case, the solution area is surrounded by a cube and then subdivided into 8 sub-cubes, which is recorded as the first layer.

[0044] Each sub-cube is further subdivided into 8 smaller sub-cubes to obtain the second layer.

[0045] The same logic is used to get finer layers. The number of sub-cubes in the first layer is 8. l , thus completing the multi-layer grouping of the octree for the target. Here, the grouping is based on:

[0046] First, we define parent groups and parent layers, child layers and child groups, and distant relative groups. Let the current layer be the lth layer, and the finer layer it is subdivided into be the (l+1)th layer. In this case, the lth layer is the parent layer of the (l+1)th layer, and the (l+1)th layer is the child layer of the lth layer. The non-empty group on the parent layer is the parent group, and the non-empty group on its child layer is the child group. If the two groups on the (l+1)th layer are near-field groups, and their parent group is also a far-field group, then they are distant relative groups, such as Figure 2 shown.

[0047] The significance of grouping here lies in describing physical properties at different levels through parent and child groups, including the scattering characteristics of sound waves over regions of varying sizes. Distant-family groups are used to describe groups interacting at greater distances, enabling the solution of long-distance sound wave propagation problems. This grouping approach allows for abstraction and simplification of the problem at different levels, thereby improving computational efficiency.

[0048] like Figure 2 As shown, a square is subdivided into smaller squares, each representing a group. These groups are labeled as parent, child, or distant relative to indicate their position and relationship within the octree structure. The source group serves as the starting point for the calculation; the facets it contains are used to calculate the scattered acoustic field generated by the direct action of the incident sound wave. The main differences between nearby groups, distant relative groups, and far-field groups lie in their distance from the source group and how they interact. Interactions between nearby groups require precise calculation, while interactions between distant relative groups and far-field groups can be handled using approximate methods.

[0049] Further, if Figure 4 As shown, the criteria for the far-field group include:

[0050] The number of groups using the interval between group i and group j To determine whether the two groups are far-field groups, when When , the two groups are far-field groups, when When , the two groups are near-field groups. Here, is a positive integer, which can be obtained by The value of is used to control the calculation accuracy of the algorithm. In general, the far-field criteria at different levels are:

[0051]

[0052] in, represents the ceiling function, Δ l Indicates the side length of the l-th layer group.

[0053] For example, because the geometric configuration of the ROV physical model is very complex, it is difficult to directly construct a multi-layer grouped surface element model for it. Therefore, on the basis of not affecting the sound scattering of the ROV model in general, the main framework and components are retained, and the simplified ROV model is as follows: Figure 3 (a) The main frames and components retained include: bow anti-collision rubber, protective plate, buoyancy block, power box, electronic compartment, multi-function compartment, 80L hydraulic source, 2 stern hydraulic thrusters, 8 power thrusters and telescopic tray. The simplified ROV model is discretized into 532378 triangular elements, as shown in Figure 3 (b) According to the method of the embodiment of the present disclosure, a seven-layer grouping method is adopted, and the third layer is selected as the coarsest layer. The multi-layer grouping of the facets is as follows: Figure 3 (c) shown.

[0054] The iterative physical acoustic acceleration algorithm includes:

[0055] Applying the Helmholtz integral formula, the scattered sound field at any point in space is:

[0056]

[0057] Φ (q) =G mul Φ (q-1) ,q≥2, (1b)

[0058] Among them, r A is the coordinate vector of the sound source A, r B is the coordinate vector of field point B, G mul is the coupled scattering kernel function matrix, G radi External field radiation function matrix, G radi Φ(1) represents the first-order scattered field of the target, represents the sum of the high-order scattered fields of the target, Φ (q) represents the qth-order surface acoustic field of the target, Φ (q-1) Represents the (q-1)th order surface acoustic field of the target.

[0059] like Figure 4 As shown, assuming that the i-th group and the j-th group are far-field pairs, and the m-th surface element and the n-th surface element belong to the i-th group and the j-th group respectively, then the distance R between the surface elements m and n is nm It can be expressed as

[0060] R nm =|r cn -r cm |=|R ji +R nj -R mi |, (2)

[0061] Among them, R ji =r ci -r ci , R mi =r cm -r ci , R nj =r cn -r cj , r cm and r cn are the geometric center position vectors of the mth and nth surface elements, r ci and r cj are the geometric center position vectors of group i and group j respectively. According to Taylor series expansion, the distance R between the surface elements m and n is nm α-th power term It can be approximated as

[0062]

[0063] Among them, the power index α=1,-1,-2, R is the distance between the center of the face n and the jth group n The α-th power term, is the distance between the face m and the center of the i-th group R m Therefore, the coupled scattering kernel function of the mth and nth bins can be approximated as

[0064]

[0065] in, and represents the type I and type II clustering factors for the transfer of the mth facet center to the i-th group geometric center, and Represents the type I and type II divergence factors for the transfer of the j-th group geometric center to the n-th panel center.

[0066] After grouping, the right side of formula (1b) can be approximately expressed in a multi-level form

[0067]

[0068] Among them, i l and j l represents the i-th group and the j-th group of the l-th layer, Indicates i l and j l The group is a near-field pair. Indicates i l and j l Groups are distant relatives, J is the number of non-empty groups, and V is the number of near-field groups. Formula (5) divides the coupling between the surface elements into two terms. The first term is It represents the coupling between the elements in the thinnest near-field group. The second term represents the coupling effect between the distant relatives of each layer. Substituting formula (5) into formula (1a) we can get

[0069]

[0070] Formula (6) is the theoretical formula of the multi-layer group iterative physical acoustic acceleration algorithm. The first-order scattered sound field of the target is obtained by coherently superposing the first-order scattered sound field of the discrete surface elements in the non-empty group. The right-hand side of formula (6a)

[0071]

[0072] The q(≥2)th order scattered sound field of the target is obtained by coherently superposing the q(≥2)th order scattered sound field of the discrete surface element in the non-empty group. The right-hand side of formula (6a)

[0073]

[0074] =(N log N) / (N log N) / (N log N) = (N log N) / ( ...

[0075] To further illustrate the effects of the embodiments of the present disclosure, the following calculation example is given.

[0076] For example Figure 3The work-class ROV shown in the figure performs a 0-360-degree horizontal omnidirectional time-domain echo simulation, using a 4ms short pulse and a 60kHz-120kHz linear frequency modulation signal as the transmission signal. The acoustic wave transmission point and receiving point are 16.8m and 6.8m away from the model's acoustic center, respectively.

[0077] Figure 5 (a) and (b) respectively give the simulation and experimental results of the time-angle distribution of the received echo pulse sequence in each azimuth direction, where the horizontal axis represents the incident azimuth angle, the vertical axis represents the echo pulse time, and the color represents the echo amplitude. i =0° corresponds to the stern incidence, θ i =90° and 270° correspond to normal transverse incidence, θ i =180° corresponds to the bow incidence. Figure 5 It can be seen that the echo structures of the test and simulation are quite consistent, both showing the external contour characteristics of the "WW". The target's multiple scattered echo bright spots can be clearly observed in the echo, which shows that the disclosed method can accurately predict the multiple scattered echo bright spots of complex underwater submersibles, providing identifiable fine features for underwater target recognition.

[0078] For example Figure 3 The work-level ROV shown in the figure performs 0-360 degree horizontal omnidirectional target strength simulation. Figure 6 The experimental and simulation comparison results of the acoustic target intensity of the ROV model at a frequency of 80kHz are given, where θ i =0° corresponds to the stern incidence, θ i =90° and 270° correspond to normal transverse incidence, θ i =180° corresponds to the bow incidence. Figure 6 As can be seen, the experimental and simulation results are in good agreement, validating the effectiveness of the proposed method for calculating the scattered acoustic field of a complex underwater vehicle. Both the experimental and simulation results exhibit a "WW"-shaped azimuth characteristic, with peaks in target intensity near the bow, stern, and two abseil locations.

[0079] Continue with Figure 3 Taking the operation-level ROV shown in the figure as an example, the relationship between the calculation time of the method proposed in this disclosure and the number of discrete bins N is analyzed. The logarithmic proportional relationship curve of the required CPU time and the number of discrete bins N is shown in FIG. Figure 7 As shown. Figure 7 It can be seen that as the number of surfels increases, the computational advantage of the proposed fast method is fully reflected. The relationship between its computational time and the number of surfels is on the order of O(N log N), which is consistent with the previous analysis.

[0080] Therefore, the beneficial effects of the present disclosure include: utilizing the proposed method for rapidly predicting the multiple acoustic scattering characteristics of complex underwater vehicles, the omnidirectional time-domain echo and target intensity of the multiple scattered echoes of complex underwater vehicles can be rapidly predicted. This provides theoretical support for predicting the fine characteristics of the multiple scattered echoes of complex underwater vehicles and improving the recognition capabilities of underwater monitoring sonars.

[0081] It should be understood that in the embodiments of the present invention, the term "and / or" merely describes the relationship between associated objects, indicating that three possible relationships exist. For example, "A and / or B" can represent three possible situations: A exists alone, A and B exist simultaneously, or B exists alone. Furthermore, the character " / " in this document generally indicates that the associated objects are in an "or" relationship.

[0082] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of the two. In order to clearly illustrate the interchangeability of hardware and software, the above description has generally described the composition and steps of each example according to function. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0083] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the existing technology, or all or part of the technical solution can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program code.

[0084] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and such modifications or substitutions are intended to be within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for predicting multiple acoustic scattering characteristics of an underwater vehicle, characterized in that: The method comprises the following steps: Step 1, pre-processing step, specifically includes: Construct a geometric model of the submersible for subsequent acoustic simulation and calculation; Divide the submersible model into grids. Based on the geometric model, perform grid division to divide the submersible model into smaller units to facilitate numerical calculations. A multi-layer grouped facet model of a submersible is established, dividing the surface of the submersible into multiple facets to simulate the complex structure of the submersible. Step 2, solution step, specifically includes: Use iterative algorithms to accelerate the physical acoustics simulation process; Calculate different orders of scattered sound fields and target multiple scattering phenomena of submarines to obtain accurate simulation results; Step 3, post-processing step, specifically includes: Analyze and obtain the acoustic characteristics of the underwater vehicle in the underwater environment, including the underwater vehicle's multiple acoustic scattering time domain echo and target intensity, Among them, in step 1, the multi-layer grouping facet model of the underwater vehicle is established using an octree structure. In step 2, the iterative physical acoustic acceleration algorithm is used to calculate the order scattered sound field of the discrete surface elements in the non-empty group, and then the surface element order scattered sound field is coherently superimposed to obtain the order scattered sound field of the underwater submersible. The scattered sound field at any point in the underwater space is, F (q) =G mul F (q-1) ,q≥2, (1b) Among them, r A is the coordinate vector of the sound source A, r B is the coordinate vector of field point B, G mul is the coupled scattering kernel function matrix, G radi External field radiation function matrix, G radi Φ (1) represents the first-order scattered field of the target, represents the sum of the high-order scattered fields of the target, Φ (q) represents the qth-order surface acoustic field of the target, Φ (q-1) Represents the (q-1)th order surface acoustic field of the target.

2. The method according to claim 1, characterized in that In step three, the different-order scattered sound fields are coherently superimposed to obtain the total multiple scattered sound field of the underwater vehicle.

3. The method according to claim 2, characterized in that The specific process of establishing the underwater vehicle multi-layer grouping facet model using the octree structure is as follows: Use a cube to surround the solution area, and then subdivide it into 8 sub-cubes. This layer is recorded as the first layer. Subdivide each sub-cube into 8 smaller sub-cubes to obtain the second layer; The same logic is used to get finer layers. The number of sub-cubes in the first layer is 8. l , thus completing the octree multi-layer grouping of the target.

4. The method according to claim 1, wherein The underwater submersible comprises: a bow anti-collision rubber, a protective plate, a buoyancy block, a power box, an electronic cabin, a multifunctional cabin, a hydraulic source, a stern hydraulic propeller, a power propeller and a telescopic tray.

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: The processor runs the computer program to implement the method according to any one of claims 1 to 4.

6. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 4 is implemented.

7. A computer program product comprising a computer program, characterized in that The computer program is executed by a processor to implement the method according to any one of claims 1 to 4.

Citation Information

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