Submarine cable shape monitoring method, device, equipment, storage medium and product

Abstract

The application discloses a submarine cable shape monitoring method, device, equipment, storage medium and product, and relates to the technical field of submarine cable shape monitoring. The method comprises the following steps: acquiring fiber core sensing data of a multi-core optical fiber built in a submarine cable, the multi-core optical fiber comprising a plurality of spiral fiber cores; determining an initial curvature and an initial torsion rate of the submarine cable according to the fiber core sensing data; constructing an optimization function based on to-be-optimized variables, the to-be-optimized variables comprising the curvature and the torsion rate, initial values of the to-be-optimized variables being determined according to the initial curvature and the initial torsion rate; the optimization function being used to constrain the difference between a predicted vertical coordinate and an absolute vertical coordinate; iteratively solving by taking minimizing the optimization function as a target, a predicted vertical coordinate being obtained by recursively using variable values of the to-be-optimized variables; obtaining a target curvature and a target torsion rate; and determining a three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate. By using the above technical scheme, the accuracy of submarine cable shape monitoring can be improved.

Description

Technical Field

[0001] This invention relates to the field of submarine cable shape monitoring technology, and in particular to a method, apparatus, equipment, storage medium and product for submarine cable shape monitoring. Background Technology

[0002] Submarine cables are critical infrastructure for offshore wind power, island power supply, and cross-border power grid interconnection, and their operational safety is of paramount importance. Dynamic submarine cables, such as floating wind power cables, are prone to bending and torsion deformation under the influence of waves and ocean currents. Excessive bending radii may cause fatigue of the armor layer and damage to the insulation layer. Therefore, real-time monitoring of the three-dimensional spatial shape of submarine cables is of great significance to ensuring the safe operation of the cables.

[0003] Distributed fiber optic sensing technologies, such as the Brillouin Optical Time Domain Reflectometer (BOTDR), Brillouin Optical Time Domain Analyzer (BOTDA), and Ultra-Weak Fiber Bragg Grating (UWFBG) arrays, have become ideal means of monitoring submarine cables due to their advantages of resistance to electromagnetic interference, corrosion resistance, and ability to perform long-distance continuous measurements. By arranging multiple spirally wound sensing fibers inside the cable, the bending curvature and torsion of the cable can be inverted based on fiber strain, and then the three-dimensional shape can be reconstructed using formulas.

[0004] However, the applicant's research found that existing technologies for reconstructing 3D shapes using formulas typically involve obtaining global coordinates from local curvature integrals. However, due to inherent errors in curvature measurement, these errors propagate and accumulate segment by segment during the integration process. As the monitoring distance increases, the accuracy of long-distance monitoring becomes difficult to guarantee, leading to excessively large deviations in the end-point position and failing to meet engineering monitoring requirements.

[0005] The information contained in this background section is intended to enhance understanding of the background of this disclosure, and may include non-prior art and content that has not yet been disclosed, is available, or is in use. Summary of the Invention

[0006] This invention provides a method, apparatus, equipment, storage medium, and product for monitoring the shape of submarine cables, which can solve the problems of poor accuracy and low precision in monitoring the shape of submarine cables.

[0007] According to one aspect of the present invention, a method for monitoring the shape of a submarine cable is provided, comprising: Acquire fiber core sensing data of a multi-core optical fiber, wherein the multi-core optical fiber is embedded in a submarine cable and the multi-core optical fiber includes multiple helical fiber cores. The initial curvature and initial torsion of the submarine cable are determined based on the fiber core sensing data. An optimization function is constructed based on the variables to be optimized, wherein the variables to be optimized include curvature and torsion rate, the initial value of the variables to be optimized is determined according to the initial curvature and the initial torsion rate, and the optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate, wherein the predicted vertical coordinate is obtained recursively through the variable values ​​of the variables to be optimized. The optimization function is iteratively solved to obtain the target curvature and target torsional rate. The three-dimensional shape of the submarine cable is determined based on the target curvature and the target torsion rate.

[0008] Furthermore, the construction of the optimization function based on the variable to be optimized includes: Based on the initial conditions and variables to be optimized, the strain fitting residuals of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residuals of each burial depth measuring point in the burial depth measuring point set are determined. The initial conditions include the initial coordinate values ​​of the starting reference point of the submarine cable. The burial depth measuring point set is a subset of the sampling point set. The vertical coordinate constraint residuals are determined based on the difference between the predicted vertical coordinates and the absolute vertical coordinates. The absolute vertical coordinates are determined based on the burial depth values ​​corresponding to the burial depth measuring points. An optimization function is constructed based on the strain fitting residual and the vertical coordinate constraint residual.

[0009] Furthermore, the absolute vertical coordinates are determined based on the difference between the vertical elevation value and the burial depth value in the seabed elevation profile corresponding to the burial depth measuring point.

[0010] Furthermore, determining the initial curvature and initial torsion of the submarine cable based on the fiber core sensing data includes: The initial curvature, initial torsion rate, and initial bending direction angle of the submarine cable are determined based on the fiber core sensing data. The step of determining the three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate includes: The three-dimensional shape of the submarine cable is determined based on the tangent direction of the starting reference point, the target curvature value, the target torsion value, and the initial bending direction angle.

[0011] Furthermore, methods for monitoring the shape of submarine cables also include: The parameterized variable to be optimized is obtained by using a spline function, wherein the parameterized variable to be optimized is represented by the product of the basis function and the coefficient to be optimized; The step of determining the strain fitting residual of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residual of each burial depth measuring point in the burial depth measuring point set based on initial conditions and variables to be optimized includes: Based on the initial conditions and parameterized variables to be optimized, the strain fitting residuals of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residuals of each burial depth measuring point in the burial depth measuring point set are determined. The step of iteratively solving the optimization function to obtain the target curvature and target torsional rate includes: The optimization function is iteratively solved to obtain the target curvature coefficient and the target torsional coefficient. The target curvature is calculated based on the target curvature coefficient and the corresponding basis function, and the target torsion rate is calculated based on the target torsion rate coefficient and the corresponding basis function.

[0012] Furthermore, the step of constructing an optimization function based on the strain fitting residual and the vertical coordinate constraint residual includes: The product of at least one of the strain fitting residual and the vertical coordinate constraint residual with the corresponding weight coefficient is determined to obtain the target strain fitting residual and the target vertical coordinate constraint residual. An optimization function is constructed based on the sum of the squares of the target strain fitting residual and the target vertical coordinate constraint residual.

[0013] According to another aspect of the present invention, a submarine cable shape monitoring device is provided, comprising: A sensor data acquisition module is used to acquire fiber core sensing data of a multi-core optical fiber, wherein the multi-core optical fiber is embedded in a submarine cable and the multi-core optical fiber includes multiple spiral fiber cores. The initial parameter value acquisition module is used to determine the initial curvature and initial torsion rate of the submarine cable based on the fiber core sensing data. An optimization function construction module is used to construct an optimization function based on the variables to be optimized, wherein the variables to be optimized include curvature and torsion rate, the initial value of the variables to be optimized is determined according to the initial curvature and the initial torsion rate, and the optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate, wherein the predicted vertical coordinate is obtained recursively from the variable values ​​of the variables to be optimized; The optimization function solving module is used to iteratively solve the optimization function with the objective of minimizing the optimization function, and obtain the target curvature and the target torsional rate. A shape determination module is used to determine the three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate.

[0014] According to another aspect of the present invention, an electronic device is provided, the electronic device comprising: At least one processor; and a memory communicatively connected to the at least one processor; The memory stores a computer program that can be executed by the at least one processor, which is then executed by the at least one processor to enable the at least one processor to perform the submarine cable shape monitoring method according to any embodiment of the present invention.

[0015] According to another aspect of the present invention, a computer-readable storage medium is provided, the computer-readable storage medium storing computer instructions for causing a processor to execute and implement the submarine cable shape monitoring method according to any embodiment of the present invention.

[0016] According to another aspect of the present invention, a computer program product is provided, the computer program product comprising a computer program that, when executed by a processor, implements the submarine cable shape monitoring method according to any embodiment of the present invention.

[0017] The technical solution of this invention involves acquiring fiber core sensing data from a multi-core optical fiber embedded in a submarine cable. The multi-core optical fiber includes multiple helical cores. Based on the fiber core sensing data, the initial curvature and initial torsion rate of the submarine cable are determined. An optimization function is constructed based on variables to be optimized, including curvature and torsion rate. The initial values ​​of the variables to be optimized are determined based on the initial curvature and initial torsion rate. The optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate. The predicted vertical coordinate is obtained recursively from the variable values ​​of the variables to be optimized. The optimization function is iteratively solved with the goal of minimizing it, resulting in target curvature and target torsion rate. The three-dimensional shape of the submarine cable is determined based on the target curvature and target torsion rate. By adopting the above technical solution, using the absolute vertical coordinate as the anchor point for shape reconstruction and constraining the predicted vertical coordinate obtained by recursively from the variable values ​​of the variables to be optimized, long-distance error accumulation can be effectively suppressed, resulting in more accurate shape monitoring results for the submarine cable.

[0018] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of the present invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1This is a schematic diagram of the structure of a submarine cable monitoring system according to an embodiment of the present invention; Figure 2 A flowchart of a method for monitoring the shape of a submarine cable according to an embodiment of the present invention; Figure 3 This is a flowchart of another method for monitoring the shape of a submarine cable according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the structure of a submarine cable shape monitoring device according to an embodiment of the present invention; Figure 5 This is a schematic diagram of the structure of an electronic device that implements the submarine cable shape monitoring method of this invention. Detailed Implementation

[0021] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0022] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0023] To facilitate understanding of the technical solutions of the embodiments of the present invention, the composition of the submarine cable monitoring system is first introduced. The monitoring system mainly includes a multi-core optical fiber, a demodulator, a processing unit (or processor), and several optional auxiliary devices. The submarine cable can be a linear device on the seabed (generally a tubular structure), such as a cable, optical cable, or optoelectronic composite cable, etc., and is not specifically limited. Figure 1 This is a schematic diagram of a submarine cable monitoring system according to an embodiment of the present invention. The monitoring system includes a multi-core optical fiber 101, an optical switch 102 (optional, indicated by dashed lines), a demodulator 103, and a processing unit 104.

[0024] For example, each core of a multi-core optical fiber is connected to an optical switch (if used) via an optical fiber patch cord. The optical switch is connected to the detection optical port of the demodulator. The demodulator and the processing unit are connected via a data cable. The processing unit is connected to the optical switch and the demodulator via a control line to achieve collaborative operation.

[0025] Multi-core optical fibers are the core sensing elements of the monitoring system, pre-embedded within the internal structure of the submarine cable and tightly integrated with the cable body. Multi-core optical fibers are special optical fibers containing multiple independent cores within the same fiber cladding. This structure allows a single fiber to simultaneously transmit multiple signals or measure multiple parameters, improving fiber utilization efficiency and monitoring capabilities. Multi-core optical fibers include helical cores and may also include a central core. The central core is located at the geometric center of the cable cross-section and is primarily used to measure temperature changes; because it is near the neutral axis, the strain caused by bending is negligible. Helical cores include multiple cores, such as at least three, arranged in a spiral around the central core. This spiral arrangement makes them more sensitive to bending and torsional changes, enabling more accurate detection of these physical quantity changes. The helical angle β can be selected within the range of 0° to 90° according to sensitivity requirements, preferably β greater than or equal to 60°. This range ensures good torsional sensitivity while suppressing axial strain (the ratio of the change in length along the axial direction to the original length, reflecting the degree of tension or compression of the cable). When β is less than 60°, the influence of axial strain on the measurement of the helical fiber core increases, leading to measurement deviation. The helical radius r is determined based on the cable size and bending sensitivity requirements, typically selected from 1 to 20 mm. This takes into account both the internal space constraints of the cable and the sensitivity requirements for sensing bending strain. The pitch L... h The helix angle is calculated to ensure consistency among all fiber cores, maintaining a constant optical path difference between the helical cores and thus achieving a stable phase difference to guarantee the accuracy of the measurement data. The phase difference refers to the difference in phase change between fiber cores at different spatial positions in a multi-core optical fiber under the same external physical quantity change (such as bending or torsion). Disturbances include temperature, strain, and dynamic vibration. This embodiment of the invention primarily focuses on strain changes caused by bending and torsion. Temperature disturbances are compensated for by the central fiber core, and dynamic vibrations are suppressed by averaging during sensor measurement. High thermal conductivity materials, such as thermally conductive putty or metal powder composite materials, can be filled between the fiber cores to ensure that the radial temperature gradient of the cable is negligible, meaning that the temperature change of the central fiber core and the helical cores at the same axial position is considered to be identical. The optical cable is led out from the cable terminal at both ends and connected to subsequent equipment via standard fiber optic connectors.

[0026] The demodulator is the core device for signal acquisition. It measures Brillouin frequency shift or wavelength drift data along the fiber by emitting probe light pulses to each core of a multi-core optical cable and receiving backscattered or reflected light. This invention does not rely on specific distributed fiber optic sensing technologies; any technology capable of distributed strain and temperature measurement of each core of a multi-core optical fiber is applicable. For example, the demodulator can be an instrument based on Brillouin scattering technology, such as a Brillouin optical time-domain reflectometer (BOTDR) or a Brillouin optical time-domain analyzer (BOTDA); it can also be an instrument based on fiber grating array technology, such as an ultra-weak fiber grating (UWFBG) demodulation system; or it can be an instrument based on Rayleigh scattering optical frequency domain reflectionometry (OFDR), etc. In practical applications, the appropriate instrument can be selected based on the specific application scenario (such as monitoring distance, accuracy requirements, and site conditions). The demodulator typically has multiple optical channels. When the number of channels is less than the number of fiber cores, different fiber cores can be accessed through a time-division multiplexing method using an external optical switch. The demodulator can be controlled by the processing unit, and its output raw measurement data can be transmitted to the processing unit in real time through a high-speed data interface.

[0027] The optical switch is either a 1xY (Y greater than or equal to 4) mechanical optical switch or a Micro-Electro-Mechanical Systems (MEMS) optical switch. One end connects to the probe optical port of the demodulator, and the other end connects to each fiber core of the multi-core optical cable. The switching of the optical switch can be controlled by the processing unit, sequentially connecting the demodulator to different fiber cores according to a preset timing sequence to achieve time-division multiplexing measurement of multiple fiber cores. For demodulators with a sufficient number of channels, this device can be omitted.

[0028] The processing unit can be considered an electronic device, such as a computer, specifically an industrial computer or embedded processor. It can have a built-in high-speed data acquisition card (if the demodulator already integrates digital output, no additional acquisition card is needed) and signal processing program. The processing unit can control the operating parameters of the demodulator and the switching sequence of the optical switches. Specifically, it can ensure the accuracy and stability of the system measurements by precisely controlling parameters such as the probe pulse width, repetition frequency, and average number of times of the demodulator, as well as the switching sequence and time interval of the optical switches. The processing unit can receive and store the raw sensing data of each fiber core. Using high-speed data storage technology, it ensures the rapid and accurate storage of large amounts of sensing data, providing a data foundation for subsequent processing. The processing unit can be used to execute the submarine cable shape monitoring method of this invention, obtaining the three-dimensional shape data of the submarine cable. The obtained data can be transmitted to a higher-level monitoring platform via a network. For example, the processed data can be encapsulated according to a standard format and transmitted to the higher-level monitoring platform in real time via wired or wireless communication networks, realizing remote monitoring and management of the data.

[0029] Figure 2 This is a flowchart of a submarine cable shape monitoring method according to an embodiment of the present invention. This embodiment is applicable to situations involving shape monitoring of submarine cables. The method can be executed by a submarine cable shape monitoring device, which can be implemented in hardware and / or software. The submarine cable shape monitoring device can be configured in an electronic device, which can be configured as a processing unit in a monitoring system. Figure 2 As shown, the method includes: Step 201: Obtain fiber core sensing data of a multi-core optical fiber, wherein the multi-core optical fiber is embedded in a submarine cable and the multi-core optical fiber includes multiple spiral fiber cores.

[0030] For example, the processing unit sends a configuration command to the demodulator, setting parameters such as the probe pulse width, repetition frequency, and average number of times, specifying the switching sequence of the fiber core under test (if an optical switch is used), and loading pre-calibrated relevant parameters. These relevant parameters may include fiber sensing parameters and helical geometry parameters, as well as thermal inversion model parameters and absolute coordinate reference parameters.

[0031] Among them, fiber optic sensing parameters may include temperature coefficient. and strain coefficient The temperature coefficient is the proportionality factor that converts Brillouin frequency shift or wavelength drift into temperature change. It can be calibrated through temperature control experiments. In these experiments, the optical fiber is placed under different temperature environments, and the relationship between the Brillouin frequency shift or wavelength drift and temperature change is measured to determine the temperature coefficient. The strain coefficient is the proportionality factor that converts Brillouin frequency shift or wavelength drift into strain. It can be calibrated through tensile experiments. In these experiments, different tensile forces are applied to the optical fiber, and the correspondence between the measured signal and strain is recorded to obtain the strain coefficient. The helical geometric parameters include the helical radius r, helical angle β, and pitch L. h Initial phase of each fiber core (Typically, 0°, 120°, and 240° are used). Thermal inversion model parameters may include the cable's own thermal resistance, cable outer diameter, and AC resistance, as well as the soil's thermal conductivity, which can be obtained through geological surveys or in-situ heat flow measurements. Historical temperature databases may also be included to eliminate the influence of temperature variations. Absolute coordinate reference parameters may include the seabed elevation profile, i.e., the height distribution of the seabed surface relative to an absolute reference (such as mean sea level), which can be obtained through multibeam bathymetry or route surveys. In practical engineering, a finite number of discrete points of seabed elevation can be obtained for absolute vertical coordinate calculations. The selection of discrete points can follow certain principles, such as appropriately increasing the point density in areas with significant topographic changes to ensure calculation accuracy.

[0032] For example, fiber core sensing data may include Brillouin frequency shift or wavelength drift data along each fiber core. The demodulator emits light pulses to each fiber core, receives the back signal, and acquires Brillouin frequency shift or wavelength drift data along each fiber core. If an optical switch is used, the processing unit switches the fiber cores according to a preset timing sequence to ensure that all fiber core data acquisition is completed. The data received by the processing unit is recorded as raw data and can be transmitted to the processing unit in the form of a time-distance matrix.

[0033] For example, the received raw data can be preprocessed by the processing unit to obtain the fiber core sensing data described in this step. Preprocessing may include multiple cumulative averaging, feature extraction, physical quantity conversion, and outlier removal.

[0034] The multiple cumulative averaging can be achieved as follows: Data can be repeatedly collected at each measurement location, typically 1000 to 10000 times, and the average value is taken to suppress white noise. When the number of collections is small, the noise suppression effect is not significant, and the measurement data fluctuates greatly. When the number of collections is too large, although the noise suppression effect is better, it increases the data acquisition time and processing cost.

[0035] Feature extraction can be achieved in the following ways: for the Brillouin scheme, the center frequency shift is extracted from the Brillouin gain spectrum by Lorentz fitting; for the grating scheme, the center wavelength is extracted from the reflection spectrum by peak detection.

[0036] The conversion of physical quantities can be achieved by using pre-calibrated strain and temperature coefficients to convert frequency shift or wavelength into strain and temperature. The central fiber core is located near the neutral axis, and the strain caused by bending is negligible. Under normal operating conditions, the axial tensile strain is typically low relative to the bending strain, and by preferably using a helix angle greater than or equal to 60°, the influence of axial strain on the helical fiber core can be further suppressed. Therefore, as an engineering approximation, the measured values ​​of the central fiber core can be primarily attributed to temperature changes, and these measured values ​​can be directly converted into temperature variations. The current temperature is obtained based on the initial calibration of the demodulator. The measured values ​​of the helical fiber core are converted into the original strain. .

[0037] Outlier removal can be achieved in the following ways: median filtering or standard deviation methods are used to identify and remove outlier data points, which are then replaced with neighborhood interpolation. Median filtering is suitable for removing impulse noise; its principle is to sort the data within the window by size and replace the center data with the median value. The standard deviation method, on the other hand, calculates the standard deviation of the data and sets a threshold to determine whether the data is outlier.

[0038] Step 202: Determine the initial curvature and initial torsion of the submarine cable based on the fiber core sensing data.

[0039] For example, curvature is a geometric quantity used to describe the degree of bending of a curve, referring to the rate of change of the tangent direction per unit length; bending direction angle is an angular parameter indicating the bending direction of the curve at a certain point, which can be used together with curvature to describe the bending shape of the cable; torsion is the torsion angle of the cross section per unit length, describing the degree of torsional deformation of the cable.

[0040] For example, the temperature contribution is subtracted from the original strain of each helical fiber core to obtain the strain containing only bending and torsion, which is denoted as the compensated strain. :

[0041] Based on the geometric properties of helical optical fibers, the compensated strain and curvature after temperature compensation... Bending direction angle Torsion rate The relationship is:

[0042] in, For the first The azimuth angle of the root helical fiber core. For spatial frequency, This is the torsional sensitivity coefficient.

[0043] For each position The three helical fiber cores correspond to three equations and three unknowns, which can be uniquely solved:

[0044]

[0045]

[0046] Among them, the solution , and These can be denoted as the initial parameter values ​​of curvature, bending direction angle, and torsion rate, respectively, or as the initial curvature, initial bending direction angle, and initial torsion rate of the submarine cable.

[0047] Step 203: Construct an optimization function based on the variables to be optimized, wherein the variables to be optimized include curvature and torsion rate, the initial value of the variables to be optimized is determined according to the initial curvature and the initial torsion rate, and the optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate, wherein the predicted vertical coordinate is obtained recursively from the variable values ​​of the variables to be optimized.

[0048] In related technologies, after calculating the curvature and torsion rate based on fiber optic sensing data, global coordinates are obtained through integration, and then the three-dimensional shape is reconstructed. However, during the integration recursion process, these errors are propagated and accumulated segment by segment. As the monitoring distance increases, the accuracy of long-distance monitoring becomes difficult to guarantee, resulting in excessive deviations in the end-point position.

[0049] In this embodiment of the invention, absolute vertical coordinates can be used as anchor points for shape reconstruction, and curvature and torsion can be used as variables to be optimized. The predicted vertical coordinates obtained by recursion through curvature and torsion are constrained, thereby obtaining more accurate curvature and torsion, suppressing the accumulation of long-distance errors, and obtaining more accurate shape monitoring results for submarine cables.

[0050] Optionally, multiple sampling points for the submarine cable can be set according to actual needs, forming a sampling point set, and multiple burial depth measuring points for the submarine cable can be set, forming a burial depth measuring point set. The burial depth measuring point set can be the same as the sampling point set, that is, each sampling point can also be a burial depth measuring point. To reduce the amount of computation, the burial depth measuring point set can be a subset of the sampling point set. For each burial depth measuring point, the corresponding burial depth value is determined, and the absolute vertical coordinate can be determined based on the burial depth value corresponding to the burial depth measuring point. Optionally, the absolute vertical coordinate is determined based on the difference between the vertical elevation value in the seabed elevation profile corresponding to the burial depth measuring point and the burial depth value. The burial depth value can be determined using a burial depth inversion method, and the specific determination method is not limited. Any technology for inverting burial depth based on distributed fiber optic temperature data is applicable. For example, the burial depth inversion mode can be a mud temperature mode or a load mode, etc., and can be dynamically selected or switched according to the actual operating conditions. Among them, the mud-temperature model extracts ambient temperature reference values ​​from historical temperature data and separates the ambient temperature component through load fluctuations. It is suitable for scenarios with complete historical data, such as submarine cable monitoring projects with long-term stable operation and complete historical data records. The mud-temperature model can make full use of the accumulated data advantage to accurately invert the burial depth. The load model uses the temperature difference under different loads to eliminate ambient temperature and directly invert the burial depth. It has strong resistance to ambient temperature changes and is suitable for scenarios where no ambient temperature reference is needed, load fluctuations are large, and multiple sets of temperature data can be obtained. For example, in submarine cable monitoring of offshore wind farms, the cable load fluctuates greatly due to the change in wind turbine power generation. The load model can better adapt to this condition and achieve accurate burial depth inversion. Of course, other burial depth inversion methods based on thermal circuit models, such as finite element simulation and data fusion and machine learning models, are also applicable.

[0051] Optionally, if a seabed elevation profile cannot be obtained in advance, an alternative approach can be adopted: loading a finite number of known absolute vertical coordinates, where the absolute vertical coordinates include preset vertical coordinates. For example, the preset vertical coordinates can be determined based on the absolute coordinates of the cable's top platform, the coordinates of the landing section, or the coordinates of a finite number of measuring points obtained through GPS and underwater acoustic positioning. These known points are used as anchor points for subsequent shape reconstruction constraints. For instance, in some special cases where a complete seabed elevation profile cannot be obtained through conventional means, using the absolute coordinates of the cable's top platform as a reference point, combined with other finite measuring points, can still provide effective constraints for shape reconstruction, ensuring the accuracy of monitoring.

[0052] For example, curvature and torsion are used as variables to be optimized. The global coordinates are obtained recursively based on curvature and torsion using the Frenet-Serret formula. An optimization function is constructed based on the difference between the vertical coordinates (denoted as the predicted vertical coordinates) and the absolute vertical coordinates in the global coordinates. The Frenet-Serret formula is a system of differential equations describing the changes of the tangent, normal, and binormal directions of a space curve with arc length, and can be used to reconstruct three-dimensional curves from curvature and torsion.

[0053] For example, an optimization function can be constructed based on the sum of the absolute values ​​(or squares) of the differences between the predicted vertical coordinates and the absolute vertical coordinates corresponding to each sampling point of the submarine cable.

[0054] Step 204: Iteratively solve the optimization function with the goal of minimizing it to obtain the target curvature and target torsion rate.

[0055] For example, with the optimization function as the objective, the optimal solution is gradually approximated through iteration to obtain the optimized curvature and torsional rate, denoted as the target curvature and target torsional rate, respectively. The specific solution method is not limited; for example, the Gauss-Newton method can be used.

[0056] Step 205: Determine the three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate.

[0057] For example, after determining the target curvature and target torsion rate, the Fleur-Serre formula can be used to recursively obtain the global coordinates based on the target curvature and target torsion rate, thereby obtaining the accurate three-dimensional shape of the submarine cable.

[0058] The submarine cable shape monitoring method of this invention acquires core sensing data of a multi-core optical fiber embedded in the submarine cable. The multi-core optical fiber includes multiple helical cores. Based on the core sensing data, the initial curvature and initial torsion of the submarine cable are determined. An optimization function is constructed based on variables to be optimized, including curvature and torsion. The initial values ​​of the variables to be optimized are determined based on the initial curvature and initial torsion. The optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate. The predicted vertical coordinate is obtained by recursively solving the optimization function with the goal of minimizing the value of the variables to be optimized, resulting in the target curvature and target torsion. The three-dimensional shape of the submarine cable is determined based on the target curvature and the target torsion. By adopting the above technical solution, using the absolute vertical coordinate as the anchor point for shape reconstruction and constraining the predicted vertical coordinate obtained by recursively solving the variable values ​​to be optimized, the accumulation of long-distance errors can be effectively suppressed, resulting in more accurate shape monitoring results for the submarine cable.

[0059] Figure 3 This is a flowchart of another method for monitoring the shape of a submarine cable according to an embodiment of the present invention. This embodiment is an optimization based on the above-mentioned optional embodiments, optimizing the construction process of the optimization function, adding constraints for strain fitting, and further improving the optimization effect of curvature and torsion. Figure 3 As shown, the method includes: Step 301: Obtain fiber core sensing data of the multi-core optical fiber, wherein the multi-core optical fiber is embedded in the submarine cable and includes multiple spiral fiber cores.

[0060] Step 302: Determine the initial curvature and initial torsion of the submarine cable based on the fiber core sensing data.

[0061] Optionally, this step may include: determining the initial curvature, initial torsion rate, and initial bending direction angle of the submarine cable based on the fiber core sensing data. For the specific solution process, please refer to the relevant content above.

[0062] Step 303: Based on the initial conditions and the variables to be optimized, determine the strain fitting residuals of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residuals of each burial depth measuring point in the burial depth measuring point set. The variables to be optimized include curvature and torsion. The initial conditions include the initial coordinate values ​​of the starting reference point of the submarine cable. The burial depth measuring point set is a subset of the sampling point set. The vertical coordinate constraint residuals are determined based on the difference between the predicted vertical coordinates and the absolute vertical coordinates. The absolute vertical coordinates are determined based on the burial depth values ​​corresponding to the burial depth measuring points. The predicted vertical coordinates are obtained recursively from the variable values ​​of the variables to be optimized.

[0063] The initial values ​​of the variables to be optimized are determined based on the initial curvature and initial torsional rate. The optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate, as well as the difference between the predicted strain and the measured strain. The predicted strain is calculated based on the current curvature and current torsional rate corresponding to the sampling point, while the measured strain is determined based on the fiber core sensing data.

[0064] The process of determining the burial depth value will be introduced below.

[0065] Taking the mud temperature model as an example, in the early stages of cable operation, temperature distribution data along the cable line can be continuously collected for a whole year, and a historical temperature database can be established according to time. Each time point corresponds to a set of temperature distributions along the line, covering various seasons and ambient temperature changes, ensuring the comprehensiveness and representativeness of the historical temperature database. The historical temperature database includes the superposition of ambient temperature and load heat generation, represented using a thermal circuit model. The thermal circuit model is a mathematical model describing cable heating and heat transfer to the surrounding soil. Analogous to Ohm's law in circuits, it analyzes cable heat dissipation and determines burial depth by establishing the relationship between parameters such as thermal resistance and heat capacity of the cable and soil media and temperature. The basic form of the thermal circuit model is as follows:

[0066] in, For ambient temperature, Due to the cable's own thermal resistance, For soil thermal resistance, Joule heat per unit length of cable ,in This is the load current (obtained in real time by current monitoring). It is an AC resistance.

[0067] For example, to extract ambient temperature, it's necessary to select a time when the load is extremely low. From historical data, filter for the period with the lowest load current (i.e.,...). (approximately equal to 0) For example, during late night or power outage maintenance periods, the temperature at that time can be approximated as the ambient temperature.

[0068] If it does not exist At times approximately equal to 0, multiple times with different loads can be selected to establish... and The linear relationship is obtained by least-squares fitting, and the intercept is the ambient temperature. If there is no low-load period and linear fitting cannot be performed (e.g., the load is stable at the current time), then the temperature of the period closest to the current time is used for interpolation.

[0069] As can be seen from the preceding text, the current measured temperature distribution is as follows: The temperature rise is:

[0070] Substitute into the thermal circuit model:

[0071] in, This indicates the current Joule temperature.

[0072] With burial depth There exists a transmission model:

[0073] in, The thermal conductivity of the soil, This refers to the outer diameter of the cable.

[0074] The burial depth can be obtained by solving the above equation:

[0075] Taking load mode as an example, select two different load times t1 and t2, and record the load current respectively. and Calculate Joule heat as well as The obtained measured temperature distribution and Calculate the temperature difference between the two moments, eliminating the ambient temperature during the subtraction:

[0076] The soil thermal resistance is obtained by solving:

[0077] Substitute into the soil thermal resistance conduction model:

[0078] If the ambient temperature varies greatly, multiple sets of temperature data under different loads can be collected, and the burial depth can be inverted through least squares fitting to improve robustness.

[0079] Subsequently, the absolute vertical coordinates are calculated, assuming the seabed elevation profile has been obtained. Then the absolute vertical coordinates of each point on the submarine cable for:

[0080] The coordinates are absolute reference values ​​obtained through temperature inversion, which do not depend on the starting point or path of shape recursion and can be used to correct recursion errors.

[0081] For example, curvature distribution and torsion distribution are used as variables to be optimized so that the adjusted curve still conforms to the strain measurement data. At the same time, the adjusted predicted vertical coordinate is close to the absolute vertical coordinate over the entire cable length. This transforms the optimization task into a multi-objective optimization problem that requires both fitting the strain data and satisfying the vertical coordinate constraint.

[0082] For example, curvature and torsion rate The bending direction angle is the variable to be optimized. Instead of being optimized independently, it is determined by natural recursion in each iteration based on the current curvature and torsion.

[0083] Optionally, spline functions are used to parameterize the variables to be optimized, resulting in parameterized variables to be optimized. The parameterized variables to be optimized are represented by the product of basis functions and coefficients to be optimized. This step can be specifically as follows: based on the initial conditions and the parameterized variables to be optimized, determine the strain fitting residuals of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residuals of each burial depth measuring point in the burial depth measuring point set.

[0084] For example, to reduce the number of variables and ensure curve smoothness, spline functions are used to parameterize the curvature and torsion:

[0085] in, and These are pre-defined smooth basis functions (or simply basis functions, such as cubic B-spline basis functions). and The coefficients to be optimized are: and The number of control points is typically much smaller than the number of sampling points. Spline function parameterization is used because spline functions can describe complex curves with fewer control points, reducing the number of optimization variables while ensuring curve smoothness and avoiding discontinuities or abrupt changes, resulting in an optimized shape that better reflects actual physical conditions. Optionally, the variables to be optimized are uniformly denoted as vectors. .

[0086] For example, in each iteration, the geometric parameters of the entire curve are calculated first from the fixed initial conditions, i.e., from the initial coordinate value of the starting reference point, based on the current curvature and torsion (generated by spline coefficients), without relying on the bending direction angle calculated above, according to the standard Frenet-Serret formula.

[0087] Within the Frenet-Serret formula framework, each point on a space curve requires three mutually perpendicular unit vectors to describe the local direction: the tangent direction... The direction of travel along the curve; normal direction The direction pointing to the curvature of the curve (i.e., the direction of the center of curvature); the direction of the binormal. Perpendicular to the tangent and normal, satisfying These three vectors form a right-handed orthogonal coordinate system. It changes continuously as the curve extends.

[0088] The initial tangent direction can be the tangent direction of the starting reference point of the submarine cable. The starting reference point can be considered the starting point for shape reconstruction and can be selected according to actual needs. The initial tangent direction is unknown in actual laying and can be obtained through an assumption, denoted as . To avoid overall shape rotation caused by assumptions and to improve the accuracy of monitoring results, the method for determining the initial tangent direction can be optimized.

[0089] Optionally, the tangent direction of the starting reference point of the submarine cable is determined in the following way: starting from the starting reference point of the submarine cable, the predicted tangent direction of the starting point is obtained by recursively extrapolating the assumed tangent direction of the starting reference point, the initial curvature, the initial torsion rate, and the initial bending direction angle to the starting point of a preset section of the submarine cable, wherein the preset section is a section of the submarine cable whose geometry is known; a rotation matrix is ​​determined based on the predicted tangent direction and the actual tangent direction of the starting point; and the actual tangent direction of the starting reference point is determined based on the assumed tangent direction and the rotation matrix.

[0090] During submarine cable laying, there may be sections with known geometry. This invention can fully utilize the relevant information of these sections to determine the actual tangential direction of the starting reference point. For example, identified sections with known geometry can be designated as preset sections, and the number of preset sections can be one or more. Optionally, the preset sections include at least one of vertical and horizontal sections; the vertical section includes a vertically suspended section on the platform side; the horizontal section includes a horizontally laid constraint section. The vertical section, for example, can be a section near the platform where the cable naturally sags under gravity, with a true curvature of approximately 0 and a true tangential direction (i.e., the actual tangential direction) that is vertically downward. The horizontal section, for example, can be a landing section, a flat seabed section, or a horizontal restraint end, with a true curvature of approximately 0 and a true tangential direction that is horizontal. The azimuth angle can be determined by the platform's Global Positioning System (GPS) or the laying path.

[0091] For example, shape reconstruction needs to be recursively deduced from the initial reference point. The initial tangent direction, i.e., the actual tangent direction of the initial reference point, is unknown. By comparing the tangent direction recursively to the starting point of a known shape segment with the known true direction, the initial tangent direction can be deduced. A coordinate system can be defined, with the x-axis horizontally pointing in a fixed direction, the y-axis horizontally perpendicular to the x-axis, and the z-axis vertically upward. The assumed tangent direction of the initial reference point is denoted as... Starting from the assumed tangential direction, the initial parameter values ​​of the deformation parameters are used to recursively deduce the starting point of the predetermined section of the submarine cable. This allows us to obtain the tangent direction at that point, denoted as the predicted tangent direction. For example, the product of the predicted tangent direction at the starting point and the rotation matrix is ​​the actual tangent direction at the starting point.

[0092] Assume the actual tangent direction at the starting point is There exists a rotation matrix. Make:

[0093] The rotation matrix can be calculated using Rodriguez's rotation formula, which is used to calculate the new vector in three-dimensional space after a vector is rotated by a specific angle around a specified rotation axis. Let the rotation axis be a unit vector. and rotation angle :

[0094] The rotation matrix is ​​then:

[0095] in, It is the identity matrix. for Cross product matrix:

[0096] For example, the actual tangent direction of the starting reference point is determined based on the product of the assumed tangent direction and the rotation matrix.

[0097] Regarding the initial reference point, i.e. the actual tangent direction, it can be:

[0098] The actual tangent direction mentioned above is determined as the initial tangent direction.

[0099] Optionally, there can be multiple preset segments. If multiple segments exist, they can be calibrated together to improve accuracy. Determining the rotation matrix based on the predicted tangent direction and the actual tangent direction of the starting point includes: for each preset segment, determining the tangent error corresponding to the current preset segment, wherein the tangent error is represented by the difference between the actual tangent direction of the starting point corresponding to the current preset segment and the transformed tangent direction, and the transformed tangent direction is represented by the product of the rotation matrix and the predicted tangent direction of the starting point corresponding to the current preset segment; constructing an objective function based on the tangent error corresponding to each preset segment; and solving the objective function to obtain the rotation matrix.

[0100] The objective function is determined by the following expression:

[0101] in, Represents the rotation matrix. Describe the objective function. Indicates the number of preset segments. Indicates the current preset segment. This indicates the actual tangent direction of the starting point corresponding to the current preset segment. This indicates the predicted tangent direction of the starting point corresponding to the current preset segment. The square of the norm is represented. Solving the objective function to obtain the rotation matrix includes: solving for the rotation matrix with the objective function as the goal.

[0102] Therefore, the initial tangent direction is denoted as For the initial normal direction Since the initial bending state is unknown, any point perpendicular to can be selected. unit vector as For example, take (like (Not parallel to the vertical direction), otherwise take This selection is based on the lack of prior information regarding cable bending in the initial stage, and is determined according to the principle of perpendicularity to the initial tangent. Although different selections will affect the overall rotation, they will not affect the relative shape. The overall deviation can be corrected later through burial depth constraints; the initial secondary normal direction... .

[0103] Discretize the cable into N micro-segments, each micro-segment arc length Given curvature and torsion rate Bending and rotating (around the binormal) Rotational bending angle ):

[0104] Twist and rotate (around the new tangent) Rotation twist angle ):

[0105]

[0106]

[0107] Location update:

[0108]

[0109] The above recursive process depends only on curvature Torsion rate The initial conditions do not require the bending direction angle as input. Through this recursion, each sampling point is obtained. Local coordinate system at the location and position coordinates .

[0110] In this embodiment, the variable optimization process needs to satisfy two types of constraints simultaneously. Therefore, two sets of residuals are defined: strain fitting residuals and vertical coordinate constraint residuals.

[0111] For the strain fitting residuals, for each sampling point (N points in total) and each spiral fiber core (Total 3), calculate the current curvature and reversal Corresponding theoretical strain and measured strain The difference.

[0112] Definition of the first The unit vector of the direction of the root helical fiber core on the cross section is:

[0113] in The azimuth angle of the fiber core is a known quantity.

[0114] In the strain model, the theoretical value of the bending term can be expressed as: This is because It is the unit vector of the actual bending direction, while Therefore, the theoretical response should be:

[0115] The strain fitting residual is:

[0116] The residual measures the degree of deviation between the current curvature and torsional rate and the strain measurement values. Its significance lies in reflecting the degree of conformity between the curve and the actual measurement data under the current optimized variables by comparing the theoretical strain and the measured strain. The smaller the difference, the closer the curve is to the actual situation.

[0117] For the vertical coordinate constrained residuals, for each burial depth measuring point (common (points), calculate the predicted vertical coordinates obtained by recursively calculating the current curvature and torsion. perpendicular coordinates The difference:

[0118] Step 304: Construct an optimization function based on the strain fitting residual and the vertical coordinate constraint residual.

[0119] The above residuals are combined into a total residual vector. The optimization function is half the sum of the squares of all residuals:

[0120] The goal is to find a set ,make Minimum.

[0121] Optionally, this step may include: determining the product of at least one of the strain fitting residual and the vertical coordinate constraint residual with its corresponding weighting coefficient to obtain the target strain fitting residual and the target vertical coordinate constraint residual; and constructing an optimization function based on the sum of squares of the target strain fitting residual and the target vertical coordinate constraint residual. Thus, the importance of the two types of residuals can be balanced by introducing weighting coefficients.

[0122] For example, the product of the vertical coordinate constraint residual and the corresponding weight coefficient can be expressed as:

[0123] in, This represents the weighting coefficient corresponding to the vertical coordinate constraint residuals. If the weighting coefficient is large, the optimization will focus more on the accuracy of the vertical coordinates; if the weighting coefficient is small, the optimization will focus more on fitting the strain data. Typically, the weighting coefficient is set to 1 to make the magnitudes of the two types of residuals comparable, or it can be determined through cross-validation. Cross-validation involves dividing the dataset into multiple subsets, performing optimization calculations on different subsets, and comparing the optimization effects under different weighting coefficient values ​​to select the weighting coefficient value that yields the best overall result. This allows for adaptive determination of weighting coefficients based on the actual data characteristics, improving the accuracy of the optimization.

[0124] Step 305: Iteratively solve the optimization function with the goal of minimizing it to obtain the target curvature and target torsion rate.

[0125] Optionally, this step may include: iteratively solving the optimization function with the goal of minimizing it to obtain the target curvature coefficient and the target torsion coefficient; calculating the target curvature based on the target curvature coefficient and the corresponding basis function; and calculating the target torsion coefficient based on the target torsion coefficient and the corresponding basis function.

[0126] For example, the solution process can be viewed as a nonlinear least squares problem, solved using the Gauss-Newton method. The optimal solution is approximated iteratively. The least squares method is an optimization algorithm that finds the best function match for the data by minimizing the sum of squared errors, used to solve overdetermined systems of equations or fitted curves. The Gauss-Newton iterative method is an iterative solution method for nonlinear least squares problems, linearizing the residuals through Taylor expansion to gradually approximate the optimal solution. The iterative process is as follows: initial value By solving the discrete curvature in the previous section and torsion rate The spline curve is fitted using the least squares method, which solves a linear least squares problem to make the spline curve as close as possible to the discrete values ​​at the sampling points. The principle of this step is to use the least squares method to find a set of coefficients that make the spline curve fit the discrete curvature and torsion data as closely as possible, providing a reasonable initial point for subsequent iterative optimization and avoiding getting trapped in local optima during the iteration process.

[0127] Calculate the Jacobian matrix, which is the partial derivative matrix of the residual vector with respect to the optimization variables. It describes the rate of change of the residuals with respect to the variables. It can be calculated using numerical differencing, by applying a small perturbation to each variable and calculating the change in the residuals.

[0128] The Jacobian matrix plays a crucial role in the optimization process. It reflects the sensitivity of the optimization function to each optimization variable. It can determine the adjustment direction and step size of the optimization variables in each iteration, so that the optimization function can iterate in the direction of reduction.

[0129] Solve the incremental equations to construct a system of linear equations:

[0130] Solving this system of linear equations yields the variable increments. This system of linear equations is constructed based on the principle of the Gauss-Newton method. By solving it, we can obtain the increment of the optimization variable in the current iteration step, so that the optimization function can be updated in the direction of decreasing in this step.

[0131] Update parameters:

[0132] Based on the calculated variable increments For optimization variables The update is performed, and the next iteration begins. After each update, the value of the optimization function gradually decreases, and the optimization variable gradually approaches the optimal solution.

[0133] For example, when the preset iteration cutoff condition is met, the target curvature coefficient and the target torsion coefficient can be obtained, and then the target curvature can be calculated based on the target curvature coefficient and the corresponding basis function, and the target torsion coefficient can be calculated based on the target torsion coefficient and the corresponding basis function.

[0134] The preset iteration cutoff condition can be set according to actual needs, and may include at least one of the following (1)-(3): (1) The parameter change is less than the first threshold, for example:

[0135] in, For extremely small quantities, usually take At this point, the parameter update is already very small, meaning that the optimization variable is close to the optimal solution, and continuing the iteration will not significantly improve the objective function.

[0136] (2) The change in the optimization function is less than the second threshold, for example:

[0137] in, For extremely small quantities, usually take Around 100°C, the optimization function no longer decreases significantly, indicating that the optimization process has converged to a better solution.

[0138] (3) The number of iterations has reached the preset maximum number of iterations.

[0139] Optionally, in addition to the Gauss-Newton method, a segmented recursive method can be used to achieve burial depth constraint correction. The entire cable segment is divided into several sub-segments at certain intervals and anchor points. Each segment undergoes independent recursion from curvature to strain to burial depth. Upon reaching the segment point, the predicted coordinates (calculated coordinates) are aligned with the measured absolute coordinates, trunculating accumulated errors. Applicable scenarios include long-distance error suppression scenarios where known burial depth points are available at the shore or platform ends. For example, in areas near the coast or offshore platforms, relatively accurate known burial depth information is usually available. In such cases, the segmented recursive method can fully utilize these known points and effectively suppress error accumulation in long-distance monitoring.

[0140] Step 306: Determine the three-dimensional shape of the submarine cable based on the target curvature and target torsion rate.

[0141] Optionally, the three-dimensional shape of the submarine cable is determined based on the tangent direction of the starting reference point, the target curvature value, the target torsion rate value, and the initial bending direction angle. The tangent direction of the starting reference point can be the aforementioned initial tangent direction.

[0142] For example, with the initial tangent direction Starting with the Frenet-Serret formula, the three-dimensional coordinates of the entire cable are recalculated to obtain the final high-precision three-dimensional shape. Through the above global optimization and correction process, the absolute vertical coordinates obtained by the burial depth inversion are used to constrain and correct the preliminary shape, which effectively suppresses the accumulation of long-distance recursive errors, thereby obtaining a high-precision three-dimensional shape that is more in line with the actual situation.

[0143] For example, for the first A micro segment, with known curvature (Target curvature), bending direction angle Torsion rate (Target torsion rate), and the tangent direction at the current point. Normal direction , direction of the secondary normal .

[0144] Bending and rotation cause the curve to deflect within the bending plane, and the bending angle corresponding to the arc length of the infinitesimal segment is:

[0145] The direction of bending is:

[0146] The axis of rotation is:

[0147] Using Rodriguez's rotation formula, a new local coordinate system is obtained after rotation:

[0148]

[0149]

[0150] Torsional rotation causes the cross-section to rotate about the tangent direction. The torsion angle corresponding to the arc length of the micro-segment is:

[0151] Around the new tangent Rotation The final local coordinate system is obtained:

[0152]

[0153]

[0154] Location update: A spatial segment can be approximated as a circular arc, and its chord vector is:

[0155] The next position coordinates are:

[0156] Repeat this process until the end of the entire cable or the end of the section where shape monitoring is required. Determine the coordinates in the global coordinate system based on the local coordinate system and the updated position to obtain the three-dimensional shape of the submarine cable.

[0157] The submarine cable shape monitoring method provided in this invention determines the initial curvature and initial torsion rate using fiber core sensing data, and then determines the strain fitting residual and vertical coordinate constraint residual based on the initial conditions and the variables to be optimized. The two residuals are used to construct an optimization function, which constrains the cable in two different aspects. This can more effectively suppress the accumulation of long-distance errors and obtain more accurate submarine cable shape monitoring results.

[0158] Optionally, the submarine cable shape monitoring method also includes: converting the three-dimensional shape and burial depth data of the submarine cable into a preset standard format for storage.

[0159] Optionally, the submarine cable shape monitoring method may further include: drawing a target image and displaying the target image. The target image may include at least one of a three-dimensional curve, a curvature distribution map, a torsion distribution map, and a burial depth profile.

[0160] For example, a three-dimensional graph shows the spatial morphology of the cable. It supports interactive rotation and zoom, allowing operators to observe the actual shape of the cable from different angles and promptly detect any abnormal bending or twisting. The curvature distribution map includes a curve showing the curvature change along the cable, marking areas exceeding the safety threshold. This allows staff to intuitively understand the curvature of various parts of the cable and take preventative measures for areas with abnormal curvature to prevent damage from excessive bending. The torsion distribution map includes a curve showing the torsion rate change along the cable, helping monitoring personnel to grasp the degree of torsional deformation and determine if there are any potential risks due to excessive torsion. The burial depth profile includes a curve showing the burial depth change along the cable, which can be overlaid with the seabed elevation to clearly show the cable's burial depth in the seabed and its relative position to the seabed surface, providing an important reference for cable maintenance and management.

[0161] Optionally, the submarine cable shape monitoring method also includes: in response to the curvature at the target location exceeding a first preset threshold (such as the curvature corresponding to the minimum bending radius), the torsion rate exceeding a preset safety threshold (such as the maximum allowable torsion angle), or the burial depth being less than the allowable value, the system automatically issues an alarm and records the abnormal location and time. Through real-time monitoring and timely alarms, abnormal situations during cable operation can be responded to quickly, ensuring the safe and stable operation of the submarine cable.

[0162] Optionally, the above embodiments are illustrated using the case where axial tension is ignored. If axial tension cannot be ignored (such as when the dynamic cable is under high tension or during a brief period of high tension during the laying process), two sets of helical fiber cores with different helix angles can be used, and the axial strain, temperature and torsion can be solved simultaneously by solving a system of equations.

[0163] Suppose there are a total of 6 helical fiber cores, divided into two groups, with helix angles of respectively. and ( For each fiber core group, the relationship between temperature-compensated strain and curvature, torsion, and axial strain is as follows: Group 1 (Helix Angle) ):

[0164] Second group (helix angle) ):

[0165] in , , For axial strain.

[0166] For each position z, there are 6 equations, and the unknowns are... , , , (4 unknowns). This is an overdetermined system of equations, solved using the least squares method: Construct the residual vector:

[0167] The objective function is:

[0168] The optimal solution is obtained using the Gauss-Newton method. The central fiber core remains as a temperature reference for temperature compensation. This extended scheme provides more complete decoupling of mechanical parameters when axial tension is not negligible, ensuring accurate monitoring of the cable morphology even under complex stress conditions.

[0169] Figure 4This is a schematic diagram of a submarine cable shape monitoring device provided according to an embodiment of the present invention. Figure 4 As shown, the device includes: The sensing data acquisition module 401 is used to acquire fiber core sensing data of a multi-core optical fiber, wherein the multi-core optical fiber is embedded in a submarine cable and the multi-core optical fiber includes multiple spiral fiber cores. The initial parameter value acquisition module 402 is used to determine the initial curvature and initial torsion of the submarine cable based on the fiber core sensing data. The optimization function construction module 403 is used to construct an optimization function based on the variable to be optimized, wherein the variable to be optimized includes curvature and torsion rate, the initial value of the variable to be optimized is determined according to the initial curvature and the initial torsion rate, and the optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate, wherein the predicted vertical coordinate is obtained recursively from the variable value of the variable to be optimized; The optimization function solving module 404 is used to iteratively solve the optimization function with the objective of minimizing the optimization function, so as to obtain the target curvature and the target torsion rate. The shape determination module 405 is used to determine the three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate.

[0170] The submarine cable shape monitoring device provided in this invention acquires core sensing data from a multi-core optical fiber embedded in the submarine cable. The multi-core optical fiber includes multiple helical cores. Based on the core sensing data, the initial curvature and initial torsion of the submarine cable are determined. An optimization function is constructed based on variables to be optimized, including curvature and torsion. The initial values ​​of the variables to be optimized are determined based on the initial curvature and initial torsion. The optimization function is used to constrain the difference between the predicted vertical coordinates and the absolute vertical coordinates. The predicted vertical coordinates are obtained iteratively by recursively calculating the values ​​of the variables to be optimized, with the goal of minimizing the optimization function, to obtain the target curvature and target torsion. The three-dimensional shape of the submarine cable is determined based on the target curvature and the target torsion. By adopting the above technical solution, using the absolute vertical coordinates as the anchor point for shape reconstruction and constraining the predicted vertical coordinates obtained by recursively calculating the values ​​of the variables to be optimized, the accumulation of long-distance errors can be effectively suppressed, resulting in more accurate shape monitoring results for the submarine cable.

[0171] Optionally, the optimization function construction module includes: The residual determination unit is used to determine the strain fitting residual of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residual of each burial measurement point in the burial depth measurement point set based on initial conditions and variables to be optimized. The initial conditions include the initial coordinate value of the starting reference point of the submarine cable, the burial depth measurement point set is a subset of the sampling point set, the vertical coordinate constraint residual is determined based on the difference between the predicted vertical coordinate and the absolute vertical coordinate, and the absolute vertical coordinate is determined based on the burial depth value corresponding to the burial depth measurement point. An optimization function construction unit is used to construct an optimization function based on the strain fitting residual and the vertical coordinate constraint residual.

[0172] Optionally, the absolute vertical coordinates are determined based on the difference between the vertical elevation value and the burial depth value in the seabed elevation profile corresponding to the burial depth measuring point.

[0173] Optionally, determining the initial curvature and initial torsion of the submarine cable based on the fiber core sensing data includes: determining the initial curvature, initial torsion, and initial bending direction angle of the submarine cable based on the fiber core sensing data; The step of determining the three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate includes: determining the three-dimensional shape of the submarine cable based on the tangent direction of the starting reference point of the submarine cable, the target curvature value, the target torsion rate value, and the initial bending direction angle.

[0174] Optionally, the device may also include: The parameterization module is used to perform parameterization processing on the variable to be optimized using spline functions to obtain the parameterized variable to be optimized, wherein the parameterized variable to be optimized is represented by the product of the basis function and the coefficient to be optimized; The step of determining the strain fitting residual of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residual of each burial measurement point in the burial depth measurement point set based on initial conditions and variables to be optimized includes: determining the strain fitting residual of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residual of each burial depth measurement point in the burial depth measurement point set based on initial conditions and parameterized variables to be optimized. The step of iteratively solving the optimization function with the objective of minimizing it to obtain the target curvature and the target torsion ratio includes: iteratively solving the optimization function with the objective of minimizing it to obtain the target curvature coefficient and the target torsion ratio coefficient; calculating the target curvature based on the target curvature coefficient and the corresponding basis function; and calculating the target torsion ratio based on the target torsion ratio coefficient and the corresponding basis function.

[0175] Optionally, the optimization function construction unit is used to: determine the product of at least one of the strain fitting residual and the vertical coordinate constraint residual with the corresponding weight coefficient to obtain the target strain fitting residual and the target vertical coordinate constraint residual; and construct an optimization function based on the sum of squares of the target strain fitting residual and the target vertical coordinate constraint residual.

[0176] The submarine cable shape monitoring device provided in this embodiment of the invention can execute the submarine cable shape monitoring method provided in any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the method.

[0177] Figure 5 A schematic diagram of an electronic device 10, which can be used to implement embodiments of the present invention, is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0178] like Figure 5 As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor. The processor 11 can perform various appropriate actions and processes based on the computer program stored in the ROM 12 or loaded from storage unit 18 into the RAM 13. The RAM 13 can also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0179] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0180] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. Processor 11 performs the various methods and processes described above, such as the submarine cable shape monitoring method.

[0181] In some embodiments, the cable shape monitoring method may be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 18. In some embodiments, part or all of the computer program may be loaded and / or installed on electronic device 10 via ROM 12 and / or communication unit 19. When the computer program is loaded into RAM 13 and executed by processor 11, one or more steps of the cable shape monitoring method described above may be performed. Alternatively, in other embodiments, processor 11 may be configured to perform the cable shape monitoring method by any other suitable means (e.g., by means of firmware).

[0182] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0183] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0184] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0185] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0186] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0187] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0188] This disclosure provides a computer program product, including a computer program that, when executed by a processor, implements the submarine cable shape monitoring method provided in the above embodiments.

[0189] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0190] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for monitoring the shape of a submarine cable, characterized in that, include: Acquire fiber core sensing data of a multi-core optical fiber, wherein the multi-core optical fiber is embedded in a submarine cable and the multi-core optical fiber includes multiple helical fiber cores. The initial curvature and initial torsion of the submarine cable are determined based on the fiber core sensing data. An optimization function is constructed based on the variables to be optimized, wherein the variables to be optimized include curvature and torsion rate, the initial value of the variables to be optimized is determined according to the initial curvature and the initial torsion rate, and the optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate, wherein the predicted vertical coordinate is obtained recursively through the variable values ​​of the variables to be optimized. The optimization function is iteratively solved to obtain the target curvature and target torsional rate. The three-dimensional shape of the submarine cable is determined based on the target curvature and the target torsion ratio; The construction of the optimization function based on the variable to be optimized includes: Based on the initial conditions and variables to be optimized, the strain fitting residuals of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residuals of each burial depth measuring point in the burial depth measuring point set are determined. The initial conditions include the initial coordinate values ​​of the starting reference point of the submarine cable. The burial depth measuring point set is a subset of the sampling point set. The vertical coordinate constraint residuals are determined based on the difference between the predicted vertical coordinates and the absolute vertical coordinates. The absolute vertical coordinates are determined based on the burial depth values ​​corresponding to the burial depth measuring points. An optimization function is constructed based on the strain fitting residual and the vertical coordinate constraint residual.

2. The method according to claim 1, characterized in that, The absolute vertical coordinates are determined based on the difference between the vertical elevation value and the burial depth value in the seabed elevation profile corresponding to the burial depth measuring point.

3. The method according to claim 1, characterized in that, in, The step of determining the initial curvature and initial torsion of the submarine cable based on the fiber core sensing data includes: The initial curvature, initial torsion rate, and initial bending direction angle of the submarine cable are determined based on the fiber core sensing data. The step of determining the three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate includes: The three-dimensional shape of the submarine cable is determined based on the tangent direction of the starting reference point, the target curvature value, the target torsion value, and the initial bending direction angle.

4. The method according to claim 1, characterized in that, Also includes: The parameterized variable to be optimized is obtained by using a spline function, wherein the parameterized variable to be optimized is represented by the product of the basis function and the coefficient to be optimized; The step of determining the strain fitting residual of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residual of each burial depth measuring point in the burial depth measuring point set based on initial conditions and variables to be optimized includes: Based on the initial conditions and parameterized variables to be optimized, the strain fitting residuals of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residuals of each burial depth measuring point in the burial depth measuring point set are determined. The step of iteratively solving the optimization function to obtain the target curvature and target torsional rate includes: The optimization function is iteratively solved to obtain the target curvature coefficient and the target torsional coefficient. The target curvature is calculated based on the target curvature coefficient and the corresponding basis function, and the target torsion rate is calculated based on the target torsion rate coefficient and the corresponding basis function.

5. The method according to claim 1, characterized in that, The construction of the optimization function based on the strain fitting residual and the vertical coordinate constraint residual includes: The product of at least one of the strain fitting residual and the vertical coordinate constraint residual with the corresponding weight coefficient is determined to obtain the target strain fitting residual and the target vertical coordinate constraint residual. An optimization function is constructed based on the sum of the squares of the target strain fitting residual and the target vertical coordinate constraint residual.

6. A submarine cable shape monitoring device, characterized in that, include: A sensor data acquisition module is used to acquire fiber core sensing data of a multi-core optical fiber, wherein the multi-core optical fiber is embedded in a submarine cable and the multi-core optical fiber includes multiple spiral fiber cores. The initial parameter value acquisition module is used to determine the initial curvature and initial torsion rate of the submarine cable based on the fiber core sensing data. An optimization function construction module is used to construct an optimization function based on the variables to be optimized, wherein the variables to be optimized include curvature and torsion rate, the initial value of the variables to be optimized is determined according to the initial curvature and the initial torsion rate, and the optimization function is used to constrain the difference between the predicted vertical coordinate and the absolute vertical coordinate, wherein the predicted vertical coordinate is obtained recursively from the variable values ​​of the variables to be optimized; The optimization function solving module is used to iteratively solve the optimization function with the objective of minimizing the optimization function, and obtain the target curvature and the target torsional rate. A shape determination module is used to determine the three-dimensional shape of the submarine cable based on the target curvature and the target torsion rate; The optimization function construction module includes: The residual determination unit is used to determine the strain fitting residual of each sampling point in the sampling point set of the submarine cable and the vertical coordinate constraint residual of each burial measurement point in the burial depth measurement point set based on initial conditions and variables to be optimized. The initial conditions include the initial coordinate value of the starting reference point of the submarine cable, the burial depth measurement point set is a subset of the sampling point set, the vertical coordinate constraint residual is determined based on the difference between the predicted vertical coordinate and the absolute vertical coordinate, and the absolute vertical coordinate is determined based on the burial depth value corresponding to the burial depth measurement point. An optimization function construction unit is used to construct an optimization function based on the strain fitting residual and the vertical coordinate constraint residual.

7. An electronic device, characterized in that, The electronic device includes: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the submarine cable shape monitoring method according to any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the submarine cable shape monitoring method according to any one of claims 1-5.

9. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the submarine cable shape monitoring method according to any one of claims 1-5.

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