Underwater suspended cable detection method, device, equipment and storage medium

By combining forward-view sonar detection and multi-sensor data fusion in the underwater drag body system, the problem of difficulty in accurately detecting suspended cables in underwater environments is solved, and efficient and accurate underwater suspended cable detection is achieved, suitable for Complex underwater environment.

CN119179121BActive Publication Date: 2025-02-07HARBIN ENGINEERING UNIVERSITY SANYA NANHAI INNOVATION & DEVELOPMENT BASE +1
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Patent Information

Application Number
CN202411696912.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-11-26
Publication Date
2025-02-07
Estimated Expiration
2044-11-26

AI Technical Summary

Technical Problem

In complex and changeable underwater environments, it is difficult for the prior art to accurately detect unknown suspended cables.

Method used

The drag body system is adopted to detect whether there is a suspended cable in the direction of travel of the carrier through forward-looking sonar assistance, and to obtain the tension data of the cable, the state perception data of the drag body and the vibration data in real time, and conduct comprehensive processing to determine whether it is in contact with the suspended cable.

Benefits of technology

It improves the efficient detection efficiency of underwater suspended cables, enhances identification accuracy, and improves the system's rapid response capabilities, and is suitable for a variety of complex underwater operation scenarios.

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Abstract

The present invention provides an underwater suspended cable detection method, device, equipment and storage medium, which relates to the technical field of underwater target detection and is applied to a towed body system, wherein the towed body system includes a carrier and a towed body, and the carrier and the towed body are connected by a cable; the underwater suspended cable detection method includes: releasing the towed body, and when the towed body system is in a stable working state, using a forward-looking sonar to assist in detecting whether there is a suspended cable to be searched in the direction of the carrier's travel; if not, obtaining the cable tension data, the state perception data of the towed body and the vibration data of the towed body in real time; performing comprehensive processing based on the tension data, the state perception data and the vibration data to obtain evaluation data, and comparing the evaluation data with a preset value to determine whether the suspended cable to be searched is in contact. Through high-precision real-time detection, the present invention enables the towed body to more quickly identify and monitor the suspended cable, avoid operation delays caused by obstacles, and thus improve the overall efficiency of the operation.
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Description

Technical Field

[0001] The present invention relates to the technical field of underwater target detection, and in particular to an underwater suspended cable detection method, device, equipment and storage medium. Background Art

[0002] In the current underwater security field, detecting underwater suspended cables that are unknown or potential threats is an important task.

[0003] Existing detection methods mainly include visual recognition, sonar detection and magnetometer detection. Among them, underwater target visual recognition technology mainly relies on the analysis of underwater images to identify specific target objects. This method is simple and has good real-time performance, but it is limited by the size change, rotation, occlusion, shooting angle change and species change of the target object, resulting in poor recognition accuracy. Sonar technology forms images by emitting sound wave pulses and receiving echoes, which has the advantage of fast imaging. However, the resolution of sonar images is usually lower than that of optical images, and decreases with increasing distance, which makes it difficult to effectively identify targets at a safe distance. In addition, the quality of sonar imaging may be affected by the complex underwater environment and the motion state of the platform, resulting in low signal-to-noise ratio, unstable imaging quality and high false alarm rate. Magnetometer technology can work effectively in low visibility or obstructed sound wave propagation. It locates metal objects by measuring tiny magnetic field changes around underwater targets. However, the accuracy of this method is usually affected by the interference of the magnetic field between the target and other metal objects in the environment. In addition, magnetometers have a limited detection range and usually require a closer distance to accurately detect the presence of cables, which increases the risk of close-range operations. Summary of the invention

[0004] The problem solved by the invention is how to accurately detect unknown suspended cables in a complex and changeable underwater environment.

[0005] In order to solve the above problems, the present invention provides an underwater suspended cable detection method, device, equipment and storage medium.

[0006] In a first aspect, the present invention provides an underwater suspended cable detection method, which is applied to a towed body system, wherein the towed body system includes a carrier and a towed body, wherein the carrier and the towed body are connected by a cable; the underwater suspended cable detection method includes:

[0007] The towing body is released, and when the towing body system is in a stable working state,

[0008] By using a forward-looking sonar installed on the towed body to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier;

[0009] If the to-be-searched suspension cable does not exist, obtaining in real time the tension data of the cable, the state sensing data of the towed body and the vibration data of the towed body;

[0010] Comprehensive processing is performed based on the tension data, the state sensing data and the vibration data to obtain evaluation data, and the evaluation data is compared with a preset value to determine whether the suspended cable to be searched is in contact.

[0011] Optionally, the comprehensive processing based on the tension data, the state sensing data and the vibration data to obtain the evaluation data includes:

[0012] The tension data, the state sensing data and the vibration data are estimated based on a Kalman filter to obtain the evaluation data.

[0013] Optionally, the Kalman filter includes a state transfer model, and the state estimation process based on the Kalman filter includes:

[0014] Determining basic parameters of the Kalman filter, the basic parameters comprising an initial state estimate and an initial error covariance;

[0015] Based on the state transition model, the predicted state data is obtained by using the initial state estimation, and the predicted error covariance is obtained by using the initial error covariance and the process noise covariance;

[0016] The evaluation data is obtained according to the measurement data, the predicted state data and the corresponding prediction error covariance.

[0017] Optionally, obtaining the evaluation data according to the measurement data, the predicted state data and the corresponding prediction error covariance includes:

[0018] Calculate the current Kalman gain according to the predicted state data and the corresponding prediction error covariance;

[0019] Obtaining an updated state estimate and an error covariance based on the current Kalman gain and measurement data, wherein the measurement data includes the tension data, the state sensing data, and the vibration data;

[0020] Obtain corresponding residual data according to the updated state estimate and the measurement data;

[0021] The evaluation data is obtained according to the residual data and the corresponding error covariance.

[0022] Optionally, the comprehensive processing based on the tension data, the state sensing data and the vibration data includes:

[0023] Acquiring a preset trigger condition, wherein the preset trigger condition includes at least one of a preset tension threshold, a preset vibration threshold, and a preset state perception abnormality;

[0024] Based on the tension data, the state sensing data or the vibration data, it is determined whether to perform a comprehensive processing process according to the preset trigger condition.

[0025] Optionally, the step of detecting whether there is a suspended cable to be searched in the direction of travel of the carrier by means of a forward-looking sonar installed on the towed body comprises:

[0026] Sending a sound wave signal based on the forward-looking sonar, wherein the sound wave signal is emitted in the direction of travel of the carrier and forms a signal echo;

[0027] If there is no signal echo within a preset time range, it is determined that the suspended cable to be searched does not exist in the direction of travel of the carrier;

[0028] If the signal echo exists, the direction of the suspended cable to be searched is extracted according to the signal echo, and according to the direction of the suspended cable to be searched and the traveling direction of the towing body, it is determined whether the suspended cable to be searched is located in a preset width range of the towing body track.

[0029] Optionally, comparing the evaluation data with a preset value to determine whether the to-be-searched suspension cable is in contact includes:

[0030] When the evaluation data is greater than the preset value, it is determined that the suspended cable to be searched is contacted, and the towed body system is controlled to stop, and the detection system on the towed body is used for observation and identification.

[0031] In a second aspect, the present invention provides an underwater suspended cable detection device, which is applied to a towed body system, wherein the towed body system includes a carrier and a towed body, wherein the carrier and the towed body are connected by a cable; the underwater suspended cable detection device includes:

[0032] An auxiliary detection unit is used to release the towed body, and when the towed body system is in a stable working state, to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier through a forward-looking sonar installed on the towed body;

[0033] A processing unit, configured to obtain in real time the tension data of the cable, the state sensing data of the towed body and the vibration data of the towed body if the to-be-searched suspension cable does not exist;

[0034] The processing unit is further used to perform comprehensive processing based on the tension data, the state sensing data and the vibration data to obtain evaluation data, and compare the evaluation data with a preset value to determine whether the suspended cable to be searched is in contact.

[0035] In a third aspect, the present invention provides an underwater suspended cable detection device, including a memory and a processor;

[0036] The memory is used to store computer programs;

[0037] The processor is used to implement the underwater floating cable detection method as described in the first aspect when executing the computer program.

[0038] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the underwater suspended cable detection method as described in the first aspect is implemented.

[0039] The underwater suspended cable detection method, device, equipment and storage medium of the present invention have the following beneficial effects:

[0040] In the above-mentioned underwater suspended cable detection method, efficient detection of underwater suspended cables is achieved through a series of technical steps. First, the towed body is released and the towed body system (including the carrier and the towed body) is ensured to be in a stable working state, in order to ensure the accuracy of the sensor data and the reliability of the system. The forward-looking sonar is used to scan the direction of travel of the carrier to detect whether there is a suspended cable to be searched. The forward-looking sonar can provide real-time information on the seabed terrain and obstacles, which helps to find the cable in time.

[0041] If the sonar does not detect the cable, the cable tension data, the state perception data (such as position, attitude) and vibration data of the towed body will be acquired in real time. These data are crucial for subsequent data analysis and processing. Next, the acquired tension data, state perception data and vibration data will be processed comprehensively. This may include steps such as data fusion, feature extraction and pattern recognition to obtain more comprehensive and accurate state information.

[0042] Finally, the processed evaluation data is compared with the preset value. The preset value is a threshold value set based on historical data and experience under normal working conditions of the system. Through comparison, it can be determined whether the current system is in contact with the suspended cable to be searched.

[0043] In summary, through real-time sonar scanning and multi-sensor data fusion, large sea areas can be quickly covered, improving the detection efficiency of underwater suspended cables. At the same time, by comprehensively processing multiple sensor data, the misjudgment that may be introduced by a single data source can be reduced, thereby enhancing the accuracy of identifying underwater suspended cables. In addition, real-time data analysis and judgment means that once an abnormality is found (such as sudden changes in cable tension, state perception data, and vibration data), operators can quickly obtain feedback and take immediate measures, such as adjusting the course or conducting more detailed detection, thereby improving the system's rapid response capability.

[0044] Therefore, in underwater environments with characteristics such as insufficient light, large fluctuations, and buoyancy changes, the present invention uses multiple data sources and sonar detection technology to continuously adapt to these complex conditions and ensure the effectiveness of the detection system. This means that the system performance will not be affected by environmental changes, enhancing the wide applicability of the method in a variety of underwater operation scenarios.

[0045] Through high-precision real-time detection, the towed body can identify and monitor the suspended cable more quickly. At the same time, the continuous data monitoring and analysis capabilities enable the system to quickly issue an alarm when an abnormal situation is found, providing safety protection for operators and taking timely countermeasures. In addition, the effective monitoring system reduces the need for repeated inspections, making the entire underwater operation process smoother and more efficient, so that tasks can be completed in a shorter time. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 A schematic diagram of a flow chart of an underwater suspended cable detection method according to an embodiment of the present invention;

[0047] Figure 2 is a schematic diagram of a towed body system according to an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of the winch constant tension logic of an embodiment of the present invention;

[0049] Figure 4 It is a schematic diagram of the stress of the armored cable (cable) according to an embodiment of the present invention;

[0050] Figure 5 It is a schematic diagram of the stress condition of the cable after being acted upon by the suspension cable according to an embodiment of the present invention;

[0051] Figure 6 A schematic diagram of a process for obtaining partial posture data of a towed object according to an embodiment of the present invention;

[0052] Figure 7 A schematic diagram of a process for obtaining speed data of a towed body according to an embodiment of the present invention;

[0053] Figure 8 A schematic diagram of the cable structure and force parameter aggregation of an embodiment of the present invention;

[0054] Fig. 9 A schematic diagram of a time series of a generated spectrum and a corresponding generation speed according to an embodiment of the present invention;

[0055] Fig.10 A schematic diagram of a heave motion spectrum characteristic curve generated in an embodiment of the present invention;

[0056] Fig.11 It is a schematic diagram of the armored cable (cable) before and after interference according to an embodiment of the present invention;

[0057] Fig.12 It is a structural schematic diagram of an underwater suspended cable detection device according to an embodiment of the present invention;

[0058] Fig.13 The figure is a schematic structural diagram of an underwater suspended cable detection device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. Although certain embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be interpreted as being limited to the embodiments described herein. On the contrary, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the drawings and embodiments of the present invention are only for exemplary purposes and are not intended to limit the scope of protection of the present invention.

[0060] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0061] The term "including" and its variations used in this document are open inclusions, that is, "including but not limited to"; the term "based on" means "based at least in part on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one other embodiment"; the term "some embodiments" means "at least some embodiments"; the term "optionally" means "optional embodiments". The relevant definitions of other terms will be given in the following description. It should be noted that the concepts of "first", "second", etc. mentioned in the present invention are only used to distinguish different devices, modules or units, and are not used to limit the order or interdependence of the functions performed by these devices, modules or units.

[0062] It should be noted that the modifications of "one" and "plurality" mentioned in the present invention are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise clearly indicated in the context, it should be understood as "one or more".

[0063] The names of the messages or information exchanged between multiple devices in the embodiments of the present invention are only used for illustrative purposes, and are not used to limit the scope of these messages or information.

[0064] like Figure 1 As shown, an underwater suspended cable detection method provided by an embodiment of the present invention is applied to a towed body system, wherein the towed body system includes a carrier and a towed body, wherein the carrier and the towed body are connected by a cable; the underwater suspended cable detection method includes:

[0065] S100, releasing the towed body, and when the towed body system is in a stable working state, using a forward-looking sonar installed on the towed body to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier;

[0066] Specifically, Figure 2 , Schematic diagram of the towed body system, with a constant tension sensor on the carrier, and an altimeter, depth gauge, acoustic Doppler velocimeter (DVL), inertial navigation unit, ultra-short baseline (USBL), magnetometer, optical system, sonar and manipulator on the towed body. Before releasing the towed body, ensure that all equipment and sensors are properly installed and calibrated, and the connection (cable) between the towed body and the carrier (such as a ship or submarine) has been checked and confirmed to be safe.

[0067] Release operation: The towed body is released from the carrier into the water through remote control commands or automatic release mechanisms. When releasing, it is necessary to ensure that the towed body can enter the water smoothly to avoid damage to the equipment due to rapid sinking or improper angles. For example, in 1,100 meters deep sea water, the carrier maintains a constant speed and places the towed body in the water. The towed body moves in the water at a fixed depth, height, attitude and speed. Despite the influence of unstable currents in the water, the towed body can still quickly return to a stable inspection state. This is achieved through the weight and shape design of the towed body itself, as well as the retraction and release operation of the rudder control system and the winch cable.

[0068] Before starting the forward-looking sonar, perform a self-check to ensure that the sonar equipment, including the sonar transmitter, receiver, and data processing unit, is working properly. According to the underwater environment and the detection target, set the sonar operating parameters, such as the transmission frequency, pulse width, gain, and scanning range, and evaluate whether there are objects suspected of cables by monitoring the sonar data in real time. During the entire detection process, continuously monitor the status of the towed body and environmental changes. If the water flow or other factors cause the towed body to deviate from the set state, the control system will automatically adjust to ensure the stability and effectiveness of the detection process.

[0069] When the forward-looking sonar detects the signal characteristics of the suspension cable, it will enter the early warning state. Based on the distance and direction data of the sonar signal, the automatic navigation system on the carrier will execute a deceleration procedure to reduce the risk of potential collision.

[0070] S200, if the to-be-searched suspension cable does not exist, acquiring in real time the tension data of the cable, the state sensing data of the towed body, and the vibration data of the towed body;

[0071] Specifically, after the forward-looking sonar detection results show that no suspension cables are found, first confirm to ensure that all acquired data and signals are stable and reliable. Ensure that the towed body is in the predetermined working state and is ready for data collection.

[0072] The cable tension between the towing body and the carrier is monitored in real time through built-in sensors (such as constant tension sensors). The tension sensor can continuously record the mechanical state of the cable and analyze the tension and resistance that the towing body is subjected to during its movement in the water. These data can reflect the impact of water flow on the towing body and the stability of the towing body's operation.

[0073] The towed body is equipped with a series of sensors, such as depth sensors (such as depth gauges), attitude sensors and speed sensors, which are used to monitor its working status in real time. The depth sensor determines the depth of the towed body, while the attitude sensor monitors the tilt angle of the towed body, and the speed sensor records the speed of the towed body in the water. For example: through the acoustic Doppler velocimeter, inertial navigation unit, ultra-short baseline, altimeter and depth gauge on the towed body, the dynamic changes of the surrounding environment can be continuously perceived in real time (that is, the status perception data can be obtained).

[0074] The built-in vibration sensor of the towed body is used to monitor the vibration generated by the movement in the water, such as the three-axis accelerometer in the inertial navigation unit carried by the towed body, to detect and analyze the vibration frequency (vibration data). The vibration data can reflect the interaction between the towed body and the water flow, the stability of the equipment and possible hidden dangers of failure. The system regularly records the vibration signal and filters the noise through the signal processing algorithm to extract effective information.

[0075] The cable tension, towed body state sensing data and vibration data obtained above. Through data fusion technology, it can provide an evaluation of the overall performance of the towed body and provide intuitive data display for operators, including real-time charts and trend forecasts. At the same time, by setting up abnormal detection and early warning mechanisms, the monitored data can be compared and analyzed in real time. Once the cable tension, towed body state or vibration data are found to exceed the preset safety range, an alarm will be issued to prompt the operator to take corresponding measures.

[0076] S300, performing comprehensive processing based on the tension data, the state sensing data and the vibration data to obtain evaluation data, and comparing the evaluation data with a preset value to determine whether the suspension cable to be searched is in contact.

[0077] Specifically, the acquired tension data, state sensing data and vibration data are cleaned and standardized. The cleaning process includes removing noise, eliminating outliers and processing missing data to ensure the accuracy and consistency of the input data.

[0078] The pre-processed tension data, state perception data and vibration data are fused to form evaluation data. Methods such as weighted averaging, principal component analysis (PCA) and Kalman filtering can be used to merge the data to extract characteristic information related to the underwater environment and towed body performance.

[0079] During the processing, special attention is paid to the changes in cable tension, because the fluctuation of instantaneous tension may directly reflect the contact between the towing body and the suspension cable.

[0080] The preset value is determined based on empirical data, historical records, and equipment parameters. By comparing the evaluation data with the set value, it is determined whether contact with the suspended cable to be searched has occurred. If contact is confirmed, the towed body movement will be stopped and specific inspections will be carried out; if contact is not confirmed, monitoring will continue to ensure continuous acquisition of valid data and rapid response when conditions change.

[0081] In this embodiment, in the above-mentioned underwater suspended cable detection method, efficient detection of underwater suspended cables is achieved through a series of technical steps. First, the towed body is released and the towed body system (including the carrier and the towed body) is ensured to be in a stable working state, which is to ensure the accuracy of the sensor data and the reliability of the system. The forward-looking sonar is used to scan the direction of travel of the carrier to detect whether there is a suspended cable to be searched. The forward-looking sonar can provide real-time seabed terrain and obstacle information, which helps to find the cable in time.

[0082] If the sonar does not detect the cable, the cable tension data, the state perception data (such as position, attitude) and vibration data of the towed body will be acquired in real time. These data are crucial for subsequent data analysis and processing. Next, the acquired tension data, state perception data and vibration data will be processed comprehensively. This may include steps such as data fusion, feature extraction and pattern recognition to obtain more comprehensive and accurate state information.

[0083] Finally, the processed evaluation data is compared with the preset value. The preset value is a threshold value set based on historical data and experience under normal working conditions of the system. Through comparison, it can be determined whether the current system is in contact with the suspended cable to be searched.

[0084] In summary, through real-time sonar scanning and multi-sensor data fusion, large sea areas can be quickly covered, improving the detection efficiency of underwater suspended cables. At the same time, by comprehensively processing multiple sensor data, the misjudgment that may be introduced by a single data source can be reduced, thereby enhancing the accuracy of identifying underwater suspended cables. In addition, real-time data analysis and judgment means that once an abnormality is found (such as sudden changes in cable tension, state perception data, and vibration data), operators can quickly obtain feedback and take immediate measures, such as adjusting the course or conducting more detailed detection, thereby improving the system's rapid response capability.

[0085] Therefore, in underwater environments with characteristics such as insufficient light, large fluctuations, and changes in buoyancy, this embodiment uses multiple data sources and sonar detection technology to continuously adapt to these complex conditions and ensure the effectiveness of the detection system. This means that system performance will not be affected by environmental changes, enhancing the wide applicability of this method in a variety of underwater operation scenarios.

[0086] Through high-precision real-time detection, the towed body can more quickly identify and monitor the suspended cables, avoiding delays caused by obstacles, thereby improving the overall efficiency of the operation. At the same time, continuous data monitoring and analysis capabilities enable the system to quickly issue an alarm when an abnormal situation is found, providing safety protection for operators and taking timely countermeasures. In addition, an effective monitoring system reduces the need for repeated inspections, making the entire underwater operation process smoother and more efficient, so that tasks can be completed in a shorter time.

[0087] Optionally, the comprehensive processing based on the tension data, the state sensing data and the vibration data to obtain the evaluation data includes:

[0088] The tension data, the state sensing data and the vibration data are estimated based on a Kalman filter to obtain the evaluation data.

[0089] Optionally, the Kalman filter includes a state transfer model, and the state estimation process based on the Kalman filter includes:

[0090] Determining basic parameters of the Kalman filter, the basic parameters comprising an initial state estimate and an initial error covariance;

[0091] Based on the state transition model, the predicted state data is obtained by using the initial state estimation, and the predicted error covariance is obtained by using the initial error covariance and the process noise covariance;

[0092] The evaluation data is obtained according to the measurement data, the predicted state data and the corresponding prediction error covariance.

[0093] Optionally, obtaining the evaluation data according to the measurement data, the predicted state data and the corresponding prediction error covariance includes:

[0094] Calculate the current Kalman gain according to the predicted state data and the corresponding prediction error covariance;

[0095] Obtaining an updated state estimate and an error covariance based on the current Kalman gain and measurement data, wherein the measurement data includes the tension data, the state sensing data, and the vibration data;

[0096] Obtain corresponding residual data according to the updated state estimate and the measurement data;

[0097] The evaluation data is obtained according to the residual data and the corresponding error covariance.

[0098] Specifically, a Kalman filter is used to fuse data from multiple sensors into a unified state estimate. The process includes:

[0099] Initialize the Kalman filter, that is, determine the initial state estimate and initial error covariance.

[0100] first,

[0101] Define the state vector: system state vector It includes the key parameters of the towed body, such as position, attitude, vibration state and cable tension.

[0102] ;

[0103] in , , It's the location. , , is the attitude angle (such as roll, pitch, yaw), is the vibration frequency and T is the cable tension.

[0104] Defining the measurement vector: sensor measurements Contains the tension data of the constant tension sensor, the attitude and position of the inertial navigation unit, the vibration frequency of the three-axis accelerometer and the tension of the cable.

[0105] Define the initial state estimate and the error covariance matrix These two parameters can be set based on the initial conditions and uncertainties of the system.

[0106] 2) The state transfer equation and measurement equation of the system are.

[0107] ;

[0108] ;

[0109] in, The system state vector at time k+1 is: is the state transition matrix, is the process noise, is the measurement matrix, is the measurement noise.

[0110] 3) Prediction stage.

[0111] Predict the next state:

[0112] ;

[0113] The covariance matrix of the errors:

[0114] ;

[0115] in, To predict the state estimate, it represents the state at time k, based on the information at time k-1. represents the state estimate at time k-1. is the prediction error covariance matrix, which represents the error covariance prediction at time k at time k−1. represents the estimated error covariance matrix of the state at time k-1. Q represents the process noise covariance matrix.

[0116] 4)Update phase.

[0117] Calculate Kalman gain

[0118] ;

[0119] Update the state estimate:

[0120] ;

[0121] Update the error covariance:

[0122] ;

[0123] in, is the updated Kalman gain, is the updated state estimate, The updated error covariance, R is the measurement noise covariance matrix.

[0124] in is the residual between the predicted observation and the actual observation. is the covariance matrix of the residuals.

[0125] 5) Use the residuals and their covariance to calculate the chi-square statistic.

[0126] ;

[0127] Comparative evaluation data and threshold (preset value). If If it is greater than the critical value, it means that the residual is too large and there may be an abnormality. Otherwise, the residual is within the expected range.

[0128] Optionally, the comprehensive processing based on the tension data, the state sensing data and the vibration data includes:

[0129] Acquiring a preset trigger condition, wherein the preset trigger condition includes at least one of a preset tension threshold, a preset vibration threshold, or a preset state perception abnormality;

[0130] Based on the tension data, the state sensing data or the vibration data, it is determined whether to perform a comprehensive processing process according to the preset trigger condition.

[0131] Specifically, in the process of acquiring cable tension data, towed body state perception data and vibration data in real time, it is also possible to determine whether comprehensive processing is required to determine whether the suspension cable is in contact by setting and identifying preset trigger conditions. Multiple trigger conditions are preset, mainly including: preset tension threshold: a tension threshold is set according to the material properties, historical data and operating experience of the cable. When the real-time tension data exceeds this threshold, it may indicate that the towed body has come into contact with an underwater object.

[0132] Preset vibration threshold: used to identify abnormal vibration of the towed body. This threshold can be based on vibration frequency, amplitude or other vibration characteristics.

[0133] Preset state perception anomalies: including abnormal conditions such as the attitude, depth or speed of the towed body. These abnormal conditions are analyzed and compared with normal operation data to determine whether they violate the preset operating specifications.

[0134] Through sensors, the cable tension data, state perception data and vibration data are continuously acquired. This process is real-time, ensuring that any changes can be quickly captured and recorded. It also ensures that all sensor data are synchronized in time for accurate analysis, while denoising and filtering the acquired data to improve data quality.

[0135] The data received in real time will be monitored, and the current monitoring results will be compared with the preset trigger conditions regularly.

[0136] Tension judgment: Compare the real-time tension data with the preset tension threshold to determine whether the trigger condition is met.

[0137] Vibration judgment: Analyze vibration data, compare it with preset vibration thresholds, and identify abnormal vibrations.

[0138] State perception anomaly judgment: Check whether the state perception data indicates an abnormal situation

[0139] If any preset trigger condition is met, it is initially marked as "potential contact", and the carrier can be stopped directly to conduct detailed detection, or it will enter the comprehensive processing stage of step S300 to integrate tension data, state perception data and vibration data for in-depth analysis to determine whether contact has occurred with the suspension cable to be searched.

[0140] If all preset trigger conditions are not met, it may be decided not to perform comprehensive processing, or to continue monitoring until the conditions are met.

[0141] Based on the results of comprehensive processing, from trigger conditions to decision feedback, the system will provide real-time data and analysis results to the operator and define recommendations for subsequent operations (such as stopping, adjusting the towed body or changing the motion path, etc.).

[0142] Through the above steps, real-time data can be effectively detected, and it can be determined whether further comprehensive processing is required based on preset trigger conditions to ensure real-time monitoring and response to the safety and performance of the towed body.

[0143] In some embodiments, the process of obtaining the cable tension data includes detecting through a constant tension sensor of a winch on a carrier, that is, through a tension sensor on a pulley, realizing tension feedback and thus realizing a constant tension function, such as Figure 3As shown in the figure, the schematic diagram of the winch constant tension logic is used to sense the load on the umbilical cable through the tension sensor installed in the center of the swing stop pulley. The tension sensor can convert the tension value of the umbilical cable into an electrical signal and transmit it to the winch system as an input of the external tension.

[0144] Armored cable (cable) stress analysis: Figure 4 As shown in the figure, the tension provided by the winch (F1): The tension applied by the winch to the armored cable is used to maintain the position and posture of the towing body underwater. The reverse force of the towing body (F2): When the towing body moves in the water, it will generate a force in the opposite direction to the tension of the armored cable. This force is the result of the difference between the weight and buoyancy of the towing body. The gravity and water resistance of the armored cable: Each section of the armored cable in the water will be affected by its own gravity and water resistance. The direction of these forces is usually perpendicular to the cable.

[0145] When the surface carrier is sailing steadily, the force between the armored cable and the winch is relatively stable. Although waves and currents can affect the surface carrier and the underwater cable, causing the tension F1 to fluctuate, these changes are usually within a certain range. When the armored cable physically interferes with the underwater unknown floating cable, such as Figure 5 As shown in the figure, the armored cable will suddenly be subjected to a horizontal tension F3. This tension F3 will increase rapidly in a short period of time, causing the winch's tension F1 on the armored cable to also suddenly increase. And the amplitude of the tension change caused by interference is much larger than the amplitude of the change caused by waves and currents during normal cruising. By monitoring the changes in F1, it can be determined whether the armored cable of the towing body has interfered with the unknown floating cable in the water, and corresponding measures can be taken. That is, if the increase in F1 exceeds the normal fluctuation range, this may indicate that the armored cable has interfered with the unknown underwater floating cable.

[0146] In some embodiments, the state perception data of the towed body mainly includes the attitude data (such as angular velocity, linear acceleration, etc.) and position data of the towed body. The attitude data mainly relies on the inertial navigation unit (IMU) to provide the angular velocity and linear acceleration of the towed body. First, the data collected by the accelerometer inside the IMU is low-pass filtered to remove high-frequency noise and vibration, so as to obtain smoother and more accurate acceleration data. The accelerometer data after low-pass filtering is fused with the gyroscope data. The gyroscope provides angular velocity information for measuring the rotation of the towed body. Through the sensor data calibration process, it is ensured that the data of the accelerometer and the gyroscope are in the same coordinate system and calibrated with each other to improve the consistency and accuracy of the data. The calibrated data is processed by the Kalman filter to solve the attitude transformation matrix. The Kalman filter is an effective recursive filter that can estimate the state of a dynamic system from a series of measurements containing noise. The Kalman filter continuously optimizes the estimated value of the attitude transformation matrix through two steps of prediction and update. This process involves the establishment of the state equation and the calculation of the error covariance.

[0147] The attitude transformation matrix obtained after processing by the Kalman filter is used to describe the attitude of the towed body relative to the reference coordinate system (such as the earth coordinate system). Using the attitude transformation matrix, the pitch angle, roll angle and yaw angle of the towed body can be calculated, which is crucial for determining the spatial direction of the towed body.

[0148] Describe the attitude transformation matrix of the navigation coordinate system relative to the towing body coordinate system in mathematical form for:

[0149] ;

[0150] in, Pitch angle, Roll angle, Heading angle.

[0151] Quaternion is used as the state quantity of the system. Figure 6 As shown, a schematic diagram of the process of obtaining partial posture data of the towed body.

[0152] The process of obtaining speed and position information, such as Figure 7 As shown, firstly, the acceleration information output by the accelerometer in the inertial navigation is converted into the navigation coordinate system, and then integrated and combined with the speed information output by the DVL to obtain the real-time speed of the carrier. Then, the real-time speed of the carrier is integrated and combined with the position information output by the depth meter, altimeter and USBL to obtain the real-time position of the carrier.

[0153] When the towing body physically interferes with the underwater suspended cable, the stress state change of the armored cable will be sensed in real time by the sensor on the towing body, thereby determining the interference event. This process ensures the stability and safety of the towing body during underwater operations, which is crucial to the success of underwater cable detection missions.

[0154] The armored cable is subjected to horizontal tension at the contact point with the suspended cable. The stress state of the armored cable changes, causing the speed, posture, height and depth of the towed body to change. The acoustic Doppler velocimeter, inertial navigation unit, ultra-short baseline, altimeter and depth gauge on the towed body can sense it in real time and determine whether the armored cable of the towed body interferes with the unknown suspended cable in the water.

[0155] In some embodiments, during the acquisition of vibration data of the towing body, the structure of the towing system is divided into several continuous segments according to the basic idea of ​​the agglomeration parameter method, and the distributed force on the cable segments can be "concentrated" on the nodes. If there are enough cable segments, the description of the movement and force of the cable is also accurate enough. When the cable is long enough, the cable can be regarded as a flexible cable with a homogeneous force response that does not change along the cable. The force caused by cable torsion and bending is not considered, and the motion and force analysis of the nodes is performed using Newton's second law.

[0156] like Figure 8 As shown, in the global coordinate system In the example, the cable is discretized into N-1 segments, so the cable has a total of N nodes. The forces at any node n include tension T, gravity G, buoyancy B, additional mass force E, and water flow resistance D. If there are other hanging objects, additional force S must be considered. For the convenience of computer program design, , , The directions are written in matrix form as ;

[0157] in, is the mass matrix, is the acceleration matrix, is the force matrix.

[0158] The mass matrix at any node n exist , , The directions are ;

[0159] in, and is the cable length of two adjacent cable segments at node n, is the additional mass coefficient of the cable, and is the linear density of the cable.

[0160] Using the cable's velocity to describe the matrix exist , , The directions meet the following requirements:

[0161] ;

[0162] in, Represents the velocity components in the x, y, and z directions at time t+1 of node n. Represents the velocity components in the x, y, and z directions at time t of node n. Represents the time step, that is, the time interval from time t to t+1.

[0163] Any node The force matrix at ;

[0164] The various forces acting on the cable are modeled separately below, and the relative position of the cable segment in space is described by the node coordinates. For cable segment exist Cable length at time:

[0165] ;

[0166] in, Represents the position vector of the nth node at time t. Represents the position vector of the n-1th node at time t.

[0167] The following equation approximates the tension state of the cable using a linear elastic relationship between cable segments:

[0168] ;

[0169] in, represents the Young's modulus of the cable segment at node n, at time t+1, represents the cross-sectional area of ​​the cable segment at node n, at time t+1, express The unit direction vector of For cable segment The cable length at time t+1 is, For cable segment The length of the cable at time t.

[0170] The following two equations are the gravity and buoyancy of the node:

[0171] ;

[0172] ;

[0173] in, It indicates the coefficient, which is related to the material, density or size of the cable. represents the acceleration due to gravity, represents the mass of the nth cable segment at time t+1, represents the density of the medium, represents the cross-sectional area of ​​the cable segment at node n at time t+1, is the gravity of the cable segment at node n at time t+1, is the buoyancy of the cable segment at node n at time t+1.

[0174] Assuming the cable is not affected by the upwelling, the force of the water flow is Satisfies the following transformation relationship:

[0175] ;

[0176] Among them, the component of the inflow direction With global coordinate system Coordinate plane The angle is , projection and The angle between the axes is , the inflow velocity amplitude is C, and the node motion velocity vector is

[0177] ;

[0178] Relative speed between node n and water flow ;

[0179] The water flow force on node n is

[0180] ;

[0181] in , , is the water flow resistance coefficient of the cable segment, Relative water velocity, Indicates the diameter of the cable segment.

[0182] If a towed body is suspended by a cable at node n, the towed body can be regarded as a particle, and the particle motion model can be used to describe the motion of the towed body. According to Newton's second law, the towed body can be simplified into a particle motion and written as

[0183] ;

[0184] The non-zero elements of the quality coefficient matrix are

[0185] ; ; ;

[0186] ; ;

[0187] ; ; ;

[0188] in, is the mass of the towed body, , , is the additional mass of the towed body; , , is the displacement of the towing body; , , The external forces acting on the towing body are still the aforementioned buoyancy, inertia, water flow, and cable tension. The density of the fluid needs to be used. Fluid velocity Towing body displacement volume and the characteristic length of the dragging body , , To calculate the force of water flow.

[0189] Usually the towing speed is given at the surface end , which belongs to the first type of boundary condition. In this embodiment, the time history of the heave motion generated by the wave spectrum is used as the motion boundary of the winch end.

[0190] ;

[0191] In the formula, is the specified drag speed, It is obtained by differentiating the wave height time series generated by the JONSWAP spectrum. The spectrum formula represented by wave height and wave period uses the motion spectrum of the JONSWAP spectrum disturbance source.

[0192] ;

[0193] There are five spectral parameters, meaning respectively: is 1 / 3 of the significant wave height, is the peak period, is the wave frequency, is the peak frequency, constant coefficient The generated spectrum and the corresponding velocity time series are as follows Fig. 9 shown.

[0194] It should be noted that, for the formula letters involved in the article, the same letter with an arrow represents a vector, and the one without an arrow represents an amplitude.

[0195] In underwater operations, the vibration transfer characteristics of the towed system are key detection parameters. When the towed body cruises along a predetermined path, its vibration mode remains consistent between the surface end and the towed body, such as Fig.10 However, once the armored cable of the towing body comes into physical contact with the underwater suspension cable, as shown in Fig.11As shown in the figure, this contact changes the propagation characteristics of the vibration, similar to how pressing on a musical instrument string changes the string's vibration frequency. Therefore, by comparing the vibration frequency detected by the triaxial accelerometer on the towed body with the vibration frequency of the surface carrier end, it is possible to effectively determine whether the armored cable of the towed body has interfered with the unknown suspended cable underwater. This detection method provides a new safety guarantee for underwater operations, which helps to promptly discover and deal with potential safety hazards.

[0196] Optionally, the step of detecting whether there is a suspended cable to be searched in the direction of travel of the carrier by means of a forward-looking sonar installed on the towed body comprises:

[0197] Sending a sound wave signal based on the forward-looking sonar, wherein the sound wave signal is emitted in the direction of travel of the carrier and forms a signal echo;

[0198] If there is no signal echo within a preset time range, it is determined that the suspended cable to be searched does not exist in the direction of travel of the carrier;

[0199] If the signal echo exists, the direction of the suspended cable to be searched is extracted according to the signal echo, and according to the direction of the suspended cable to be searched and the traveling direction of the towing body, it is determined whether the suspended cable to be searched is located in a preset width range of the towing body track.

[0200] Optionally, comparing the evaluation data with a preset value to determine whether the to-be-searched suspension cable is in contact includes:

[0201] When the evaluation data is greater than the preset value, it is determined that the suspended cable to be searched is contacted, and the towed body system is controlled to stop, and the detection system on the towed body is used for observation and identification.

[0202] Specifically, when it is determined that the suspended cable to be searched is in contact, the towed body system is controlled to stop and collect. When the towed body approaches the target cable, a series of detection and operation systems will be used to confirm the target. That is, the detection equipment on the towed body includes an underwater camera, a lighting lamp, a magnetometer, and an acoustic combined detection system integrating imaging and depth sounding. It mainly has the capabilities of underwater acoustic imaging, optical imaging, magnetic detection, noise reduction, image transmission and processing, and acquisition of optical images, acoustic images, and magnetic detection of underwater targets. Ultimately, high-definition observation and identification of underwater thin wire diameter and small targets are achieved. The manipulator is responsible for handling possible complex situations, such as being able to perform delicate operation tasks such as grabbing, carrying and releasing objects, and even performing complex assembly work in underwater environments. The flexibility and precision of the manipulator make it an indispensable tool in underwater operations.

[0203] Through these devices, the system can obtain optical images, acoustic images and magnetic detection data of underwater targets. After noise reduction, image transmission and processing, these data can finally achieve high-definition observation and recognition of underwater thin wire diameter and small targets.

[0204] In summary, this underwater suspended cable detection method can effectively observe, identify and process underwater targets by comprehensively utilizing a variety of sensors and manipulators, thereby improving the efficiency and safety of underwater operations.

[0205] like Fig.12 As shown, an underwater suspended cable detection device provided by an embodiment of the present invention is applied to a towed body system, wherein the towed body system includes a carrier and a towed body, wherein the carrier and the towed body are connected by a cable; the underwater suspended cable detection device includes:

[0206] An auxiliary detection unit is used to release the towed body, and when the towed body system is in a stable working state, to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier through a forward-looking sonar installed on the towed body;

[0207] A processing unit, configured to obtain in real time the tension data of the cable, the state sensing data of the towed body and the vibration data of the towed body if the to-be-searched suspension cable does not exist;

[0208] The processing unit is further used to perform comprehensive processing based on the tension data, the state sensing data and the vibration data to obtain evaluation data, and compare the evaluation data with a preset value to determine whether the suspended cable to be searched is in contact.

[0209] like Fig.13 As shown, an underwater suspended cable detection device provided by an embodiment of the present invention includes a memory and a processor; the memory is used to store a computer program; the processor is used to implement the underwater suspended cable detection method as described above when executing the computer program.

[0210] In other words, an underwater floating cable detection device includes a memory and a processor coupled to the memory; the memory is configured to store a computer program; and the processor is configured to perform the following operations when executing the computer program:

[0211] The towing body is released, and when the towing body system is in a stable working state,

[0212] By using a forward-looking sonar installed on the towed body to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier;

[0213] If the to-be-searched suspension cable does not exist, obtaining in real time the tension data of the cable, the state sensing data of the towed body and the vibration data of the towed body;

[0214] Comprehensive processing is performed based on the tension data, the state sensing data and the vibration data to obtain evaluation data, and the evaluation data is compared with a preset value to determine whether the suspended cable to be searched is in contact.

[0215] An embodiment of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the underwater floating cable detection method as described above is implemented.

[0216] In other words, a non-volatile computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the processor performs the following operations:

[0217] The towing body is released, and when the towing body system is in a stable working state,

[0218] By using a forward-looking sonar installed on the towed body to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier;

[0219] If the to-be-searched suspension cable does not exist, obtaining in real time the tension data of the cable, the state sensing data of the towed body and the vibration data of the towed body;

[0220] Comprehensive processing is performed based on the tension data, the state sensing data and the vibration data to obtain evaluation data, and the evaluation data is compared with a preset value to determine whether the suspended cable to be searched is in contact.

[0221] An underwater suspended cable detection device that can be used as a server or client of the present invention will now be described, which is an example of a hardware device that can be applied to various aspects of the present invention. The underwater suspended cable detection device is intended to represent various forms of digital electronic computer equipment, such as laptop computers, desktop computers, workbenches, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The underwater suspended cable detection device can also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present invention described and / or required herein.

[0222] The underwater floating cable detection device includes a computing unit, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) or a computer program loaded from a storage unit into a random access memory (RAM). In the RAM, various programs and data required for the operation of the device can also be stored. The computing unit, ROM, and RAM are connected to each other through a bus. An input / output (I / O) interface is also connected to the bus.

[0223] A person of ordinary skill in the art can understand that all or part of the processes in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, the storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc. In the present application, the unit described as a separate component may or may not be physically separated, and the component displayed as a unit may or may not be a physical unit, that is, it may be located in one place, or it may be distributed on multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the embodiment of the present invention. In addition, each functional unit in each embodiment of the present invention can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of a software functional unit.

[0224] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A method for detecting an underwater suspended cable, characterized in that: Applied to a towed body system, the towed body system comprises a carrier and a towed body, the carrier and the towed body are connected by a cable; the underwater suspended cable detection method comprises: The towing body is released, and when the towing body system is in a stable working state, By using a forward-looking sonar installed on the towed body to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier; If the to-be-searched suspension cable does not exist, obtaining in real time the tension data of the cable, the state sensing data of the towed body and the vibration data of the towed body; Comprehensive processing is performed based on the tension data, the state sensing data and the vibration data to obtain evaluation data, including: Performing state estimation on the tension data, the state sensing data and the vibration data based on a Kalman filter to obtain the evaluation data; The evaluation data is compared with a preset value to determine whether the suspended cable to be searched is in contact.

2. The underwater suspended cable detection method according to claim 1, characterized in that: The Kalman filter includes a state transfer model, and the state estimation process based on the Kalman filter includes: Determining basic parameters of the Kalman filter, the basic parameters comprising an initial state estimate and an initial error covariance; Based on the state transition model, the predicted state data is obtained by using the initial state estimation, and the predicted error covariance is obtained by using the initial error covariance and the process noise covariance; The evaluation data is obtained according to the measurement data, the predicted state data and the corresponding prediction error covariance.

3. The underwater suspended cable detection method according to claim 2, characterized in that: The obtaining of the evaluation data according to the measurement data, the predicted state data and the corresponding prediction error covariance comprises: Calculate the current Kalman gain according to the predicted state data and the corresponding prediction error covariance; Obtaining an updated state estimate and an error covariance based on the current Kalman gain and measurement data, wherein the measurement data includes the tension data, the state sensing data, and the vibration data; Obtain corresponding residual data according to the updated state estimate and the measurement data; The evaluation data is obtained according to the residual data and the corresponding error covariance.

4. The underwater suspended cable detection method according to claim 1, characterized in that: The comprehensive processing based on the tension data, the state sensing data and the vibration data includes: Acquiring a preset trigger condition, wherein the preset trigger condition includes at least one of a preset tension threshold, a preset vibration threshold, and a preset state perception abnormality; Based on the tension data, the state sensing data or the vibration data, it is determined whether to perform a comprehensive processing process according to the preset trigger condition.

5. The underwater floating cable detection method according to claim 1, characterized in that: The method of detecting whether there is a suspended cable to be searched in the direction of travel of the carrier by means of a forward-looking sonar installed on the towed body comprises: Sending a sound wave signal based on the forward-looking sonar, wherein the sound wave signal is emitted in the direction of travel of the carrier and forms a signal echo; If there is no signal echo within a preset time range, it is determined that the suspended cable to be searched does not exist in the direction of travel of the carrier; If the signal echo exists, the direction of the suspended cable to be searched is extracted according to the signal echo, and according to the direction of the suspended cable to be searched and the traveling direction of the towing body, it is determined whether the suspended cable to be searched is located in a preset width range of the towing body track.

6. The underwater floating cable detection method according to claim 1, characterized in that: The step of comparing the evaluation data with a preset value to determine whether the suspended cable to be searched is in contact includes: When the evaluation data is greater than the preset value, it is determined that the suspended cable to be searched is contacted, and the towed body system is controlled to stop, and the detection system on the towed body is used for observation and identification.

7. An underwater suspended cable detection device, characterized in that: Applied to a towed body system, the towed body system comprises a carrier and a towed body, the carrier and the towed body are connected by a cable; the underwater suspended cable detection device comprises: An auxiliary detection unit is used to release the towed body, and when the towed body system is in a stable working state, to assist in detecting whether there is a suspended cable to be searched in the direction of travel of the carrier through a forward-looking sonar installed on the towed body; A processing unit, configured to obtain in real time the tension data of the cable, the state sensing data of the towed body and the vibration data of the towed body if the to-be-searched suspension cable does not exist; The processing unit is also used to perform comprehensive processing based on the tension data, the state perception data and the vibration data to obtain evaluation data, including: performing state estimation on the tension data, the state perception data and the vibration data based on a Kalman filter to obtain the evaluation data, and comparing the evaluation data with a preset value to determine whether the suspended cable to be searched is in contact.

8. An underwater suspended cable detection device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the underwater floating cable detection method according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by the processor, the underwater floating cable detection method according to any one of claims 1 to 6 is implemented.

Citation Information

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