Submarine cable shape monitoring method based on ultra-weak fiber grating

Abstract

The invention discloses a submarine cable shape monitoring method based on an ultra-weak fiber bragg grating, which comprises the following steps of: obtaining curvatures # imgabs0 #, # imgabs1 # and # imgabs2 # in X-axis and Y-axis directions from curvatures in two orthogonal directions of curvatures calculated by three uniformly distributed optical fibers, representing angle offset from an ith sensing unit to an X-axis positive direction, and obtaining a bending curvature, an arc angle and a direction angle; and coordinate information in the space is further obtained by combining rotation and translation matrix iterative calculation of a shape reconstruction algorithm, namely, three-dimensional space coordinates of the measured curve can be determined point by point, and finally, complete shape reconstruction and other steps are realized. According to the invention, high-precision large-scale three-dimensional deformation monitoring can be realized. By optimizing the eccentric distance and the strain transmission efficiency of the optical fiber, the tiny deformation of the submarine cable is accurately captured, and by combining an innovative three-dimensional curve reconstruction algorithm, the bending, inclination and other deformation states of the cable can be accurately reflected in different environments. Therefore, the method has obvious advantages in a monitoring task with a high-precision requirement, especially in a complex marine environment.

Description

Technical Field

[0001] The present invention belongs to the field of optical fiber shape sensing, and in particular relates to a submarine cable shape monitoring method based on ultra-weak optical fiber grating, which performs shape sensing on a three-core optical fiber composited into a submarine cable. Background Art

[0002] With the rapid development of marine resources, submarine cables play a vital role in power transmission, communications, and ocean observation. Exposure to complex and ever-changing marine environments for extended periods, submarine cables are susceptible to external forces such as ocean currents, geological activity, and ship drag, which can cause them to bend, twist, or even break, seriously threatening their safety and reliability. Therefore, real-time monitoring of submarine cable shape changes is crucial to ensuring their normal operation and extending their service life.

[0003] Fiber-optic sensing technology, due to its excellent resistance to electromagnetic interference, corrosion resistance, and miniaturization, has gradually become a hot topic in submarine cable monitoring research. Fiber Bragg Grating (FBG) sensors, in particular, are widely used for strain and temperature monitoring due to their high sensitivity and excellent multiplexing capabilities. Traditional FBG sensors have limitations in multiplexing capacity, making them difficult to meet the needs of long-distance and high-density monitoring. Furthermore, traditional FBG sensors are typically surface-mounted or externally encapsulated, which are susceptible to the effects of the marine environment and have poor long-term stability.

[0004] As a new type of fiber sensor, ultraweak fiber Bragg grating (uwFBG) not only inherits the advantages of traditional FBG, but also features low reflectivity, high multiplexing capacity (a single fiber can accommodate tens of thousands of sensing units), and excellent mechanical properties. This makes it ideal for long-distance, high-density submarine cable shape monitoring. Therefore, ultraweak fiber Bragg grating shape sensing technology, with its high flexibility and submillimeter spatial resolution, demonstrates great potential for dynamic submarine cable shape monitoring. This technology measures the differentiated strain response of an ultraweak fiber Bragg grating array and uses corresponding algorithms to calculate curvature and azimuth angles to obtain spatial coordinate information, ultimately achieving high-precision three-dimensional shape reconstruction.

[0005] Defects and shortcomings of existing technology: 1. Traditional monitoring methods lack accuracy and real-time performance While current non-contact methods for submarine cable monitoring, such as visual and acoustic monitoring, have some applications, they suffer from significant limitations in accuracy and real-time performance. While acoustic methods can penetrate the seabed, they are susceptible to interference from ambient noise and reflections, resulting in low accuracy and the inability to provide real-time monitoring. These traditional methods are unable to effectively address the high-precision monitoring requirements for submarine cables in complex marine environments, limiting their application for long-distance, dynamic monitoring.

[0006] 2. Limitations of FBG sensors: poor multiplexing capability and long-term stability While fiber Bragg grating (FBG) sensors offer high sensitivity in strain and temperature monitoring, their multiplexing capabilities are limited, making them inadequate for long-distance, high-density submarine cable monitoring. Furthermore, FBG sensors typically require surface mounting or external packaging, making them susceptible to the effects of the marine environment and resulting in poor long-term stability. Multi-sensor layouts increase cabling complexity and maintenance costs. Summary of the Invention

[0007] To meet the high-precision and long-distance requirements for submarine cable shape monitoring, this paper provides a submarine cable shape monitoring method based on ultra-weak fiber Bragg gratings (uwFBGs). The core of this method is to utilize an uwFBG array to perform distributed strain measurement on submarine cables and, based on this, reconstruct the cable's three-dimensional shape. This method enables real-time and continuous monitoring of the dynamic deformation of submarine cables in complex marine environments.

[0008] The technical objectives of the present invention are achieved through the following technical solutions: A method for monitoring the shape of a submarine cable based on ultra-weak fiber Bragg gratings comprises the following steps: Step 1: Assume that the total number of initial wavelength signals detected by the uwFBG shape sensing optical cable is , where 3 represents the number of fiber cores, is the number of gratings; Step 2: When bending occurs, the wavelength drift trend of the two cores should be the same (same rise or fall). This is because the multi-core fiber to be tested is bent. The three cores are evenly distributed, and the central angle of each two cores is 120°, which will cause strain on the grating attached to it. , and the central wavelength of the grating's reflection spectrum will also drift , the drift at this time is proportional to the strain, and the total number of wavelength signals after the change is ; Step 3: Assume that the interval between adjacent gratings is , the fiber diameter is , and the eccentricity is the distance from the optical fiber to the center of the structure, and the radius of curvature is , we can derive the curvature calculation formula at each grating position: ; Step 4: The curvatures of the three optical fibers calculated are obtained from the curvatures in the two orthogonal directions to obtain the curvatures in the X-axis and Y-axis directions. and , The angular offset of the i-th sensor unit to the positive direction of the X-axis is expressed as follows: ; ; Step 5: Get the curvature and After that, the curvature K of the bending direction at the current section position can be calculated. The formula is as follows: ; Step 6: After obtaining the spatial discrete curvature information, assume that one of the optical fibers is located on the positive half axis of the Y axis. , , The curvature in the bending direction can be obtained Angle with the positive direction of the X axis , which includes calculations for four quadrants; Step 7: The length of the arc segment between the two sensing points is , set up the The direction of the point The angle between the positive semi-axis and the axis is , the radius of curvature is , then the arc angle is calculated as: ; Step 8: Get the curvature and arc angle and direction angle , and further combined with the rotation and translation matrices of the shape reconstruction algorithm to iteratively calculate the coordinate information in space, the three-dimensional spatial coordinates of the measured curve can be determined point by point, and finally the complete shape reconstruction can be achieved.

[0009] Preferably, in step 2, the specific steps of monitoring the wavelength change of the shape sensing optical cable before and after bending are: 2.1 After inserting the three-core ultra-weak fiber grating array cable into the submarine cable, first measure the initial wavelength of each grating point , when the submarine cable is bent, the changed wavelength is measured , according to the fiber optic sensing theory: ; 2.2 Among them is the original wavelength, is the wavelength drift, is the elastic-optical coefficient, is the strain change, is the thermal expansion coefficient of the optical fiber, is the thermo-optical effect coefficient of the optical fiber, is the temperature change; 2.3 Based on the above sensing principle, an ultra-weak fiber Bragg grating (FBG) interrogator is used to measure the wavelength of each optical fiber in the three-core shape sensing cable before and after bending to calculate the strain during bending. When the external temperature is constant, or the effect of temperature on the grating is not considered, assuming that the strain on the upper and lower sides can be calculated from the grating wavelength drift, the strain calculation formula can be obtained as follows: .

[0010] Preferably, in step 3, after the curvature formula is known, a detailed analysis is conducted on how to achieve high-precision curve reconstruction. The specific steps are: 3.1 According to bending theory, the strain on the cross section of a cylindrical structure under bending load will change along the bending distance. Assuming that the cross section of the cylinder after bending is circular, the distance from the center of the circular cross section to the center of the circle is Bending strain for: ; 3.2 Among them is the bending moment, is the radius of the circular cross section, is the elastic modulus of the cylindrical material, When the bending degree of the structural material of the cylinder does not change, the radius of the same cross section of the cylinder , elastic modulus and bending moment is a constant, then the formula can be simplified to: ; 3.3 Among them is a constant; from the above formula, we can know that the strain transfer efficiency for: ; 3.4 From the above formula, we can see that the strain transfer efficiency and eccentricity The strain response capability of the optical fiber sensor can be enhanced by increasing the eccentricity. Therefore, adjusting the eccentricity of the optical fiber can effectively improve its sensitivity and increase the strain transmission efficiency, thereby capturing small changes in shape and reflecting them in the curvature.

[0011] Preferably, in step 6, the angle is calculated using the inverse tangent function , the specific steps are: 6.1 According to the curvature of the two coordinate axes and To determine the direction and set the angle calculation method: ; in is a four-quadrant inverse tangent function, and the apparent curvature Can be used and Solution, and The angle between It can be obtained that the specific solution formula is: .

[0012] Preferably, in step 8, the coordinate information of each point in the space is calculated, and the specific steps are: 8.1 Using the above formula, we know a set of discrete curvature information and azimuth angles in space. By performing interpolation processing on the current data, we can obtain the curvature information of a set of discrete points on the spatial curve. On this basis, combined with the ideas of differential geometry, we introduce a spatial coordinate system to describe the geometric form of the curve. 8.2 First, select the z-axis, which represents the length of the structure, as the tangent direction of the curve's starting point. Next, select the position of a fiber core on the curve's cross section as the y-axis. Next, determine the direction of the x-axis according to the right-hand screw theorem, ensuring that the three coordinate axes satisfy the right-hand rule and thus the positivity of the coordinate system. Before the structure bends, all grating points use this initial coordinate system as a reference to establish a moving coordinate system M. Initially, this moving coordinate system coincides with the fixed coordinate system. 8.3 Notes Point in motion coordinate system The coordinates below are , the radius of curvature is , direction and The angle between the positive semi-axis and the axis is ,in: ; ; ; 8.4 Calculation of the Rotational Coordinate System in the above Formula Transition matrix required , the calculation steps are as follows: (5) The motion coordinate system Around Axis rotation , and generate a new motion coordinate system 、 、 ,axis Direction and point The curvature direction is the same, and the transformation matrix is ; (6) In the new coordinate system after transformation, Rotation , generate a new motion coordinate system 、 、 ,axis Direction and The tangent direction of the point is parallel, and the corresponding transformation matrix is ; (7) In the new coordinate system after transformation, Rotation , making the current point and next point The apparent curvature vectors of the points remain parallel, and the corresponding transformation matrix is ; (8) Finally, the coordinate axis rotation is completed, and the new coordinate system is obtained by translating a vector, and the corresponding transformation matrix is ​​obtained as follows: : ; ; ; ; ; 8.5 Then solve the problem from the motion coordinates To fixed coordinates The vector relationship is: ; ; ; 8.6 Since the first point coincides with the origin of the original coordinate system, is the unit matrix. By repeating the above calculation process, the absolute coordinates of each micro-segment endpoint can be obtained and converted to the base coordinate system in turn. By connecting all these points, the entire space curve can be reconstructed.

[0013] Compared with the prior art, the present invention has the following beneficial effects: (1) High-precision deformation monitoring and 3D reconstruction capabilities This method, based on ultra-weak fiber Bragg grating (uwFBG) technology, enables high-precision, large-scale, three-dimensional deformation monitoring. By optimizing the fiber's eccentricity and strain transmission efficiency, it accurately captures subtle deformations of submarine cables. Combined with an innovative three-dimensional curve reconstruction algorithm, it accurately reflects cable bending, tilt, and other deformation states in various environments. This makes this method a significant advantage in high-precision monitoring tasks, particularly in complex marine environments.

[0014] (2) Spatial curve reconstruction algorithm based on ultra-weak fiber Bragg grating This invention employs an innovative algorithm that analyzes wavelength drift in multi-core optical fibers to accurately calculate the coordinates of submarine cables in three-dimensional space. Leveraging the wavelength drift characteristics of ultra-wideband fiber-optic (UWFBG) technology, this algorithm extracts deformation data from multiple sensing points and, through a three-dimensional curve reconstruction algorithm, achieves high-precision reconstruction of the cable shape. Compared to traditional methods, this algorithm not only improves measurement accuracy but also enables large-scale deformation monitoring with limited sensing points, enhancing monitoring efficiency and accuracy.

[0015] (3) Long-term stability and anti-interference ability Compared to traditional electronic sensors, fiber-optic sensors offer greater anti-interference capabilities and long-term stability for submarine cable monitoring. Fiber-optic sensors are immune to electromagnetic interference, require no external power supply, and are highly durable, capable of continuous operation in harsh marine environments. This significantly reduces maintenance costs and failure rates, ensuring high reliability of the monitoring system.

[0016] (4) Real-time online monitoring and remote data transmission This method leverages the remote data transmission advantages of fiber optic sensing technology to achieve real-time online monitoring. When submarine cables deform, the system can quickly respond and provide real-time feedback, promptly identifying potential risks. This gives this method a strong emergency response capability, ensuring the safe operation of submarine cables and making it particularly suitable for applications such as submarine power transmission and resource development. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Flowchart of the present invention.

[0018] Figure 2 This is a schematic diagram of the algorithm reconstruction principle of the present invention.

[0019] Figure 3 This is the curve image reconstructed in Example 1.

[0020] Figure 4 This is the curve image reconstructed in Example 2.

[0021] Figure 5 This is the curve image reconstructed in Example 3. DETAILED DESCRIPTION

[0022] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0023] As a preferred embodiment of the present invention, this embodiment provides a submarine cable shape monitoring method based on ultra-weak fiber Bragg grating, comprising: Step 1: Assume that the total number of initial wavelength signals detected by the uwFBG shape sensing optical cable is , where 3 represents the number of fiber cores, is the number of gratings. Step 2: When bending occurs, the wavelength drift trend of the two cores should be the same (same rise or fall). This is because the multi-core fiber to be tested is bent. The three cores are evenly distributed, and the central angle of each two cores is 120°, which will cause strain on the grating attached to it. , and the central wavelength of the grating's reflection spectrum will also drift , the drift at this time is proportional to the strain, and the total number of wavelength signals after the change is .

[0024] 2.1 After inserting the optical cable into the submarine cable, first measure the initial wavelength of each grid point , when the submarine cable is bent, the changed wavelength is measured , according to the fiber optic sensing theory: ; 2.2 Among them is the original wavelength, is the wavelength drift, is the elastic-optical coefficient, is the strain change, is the thermal expansion coefficient of the optical fiber, is the thermo-optical effect coefficient of the optical fiber, is the temperature change.

[0025] 2.3 Based on the above sensing principle, we used the ultra-weak fiber Bragg grating interrogator (RS-HFBGA-01, data refresh time ≤ 6 Hz) from Yichang Ruichuan Optoelectronics Technology Co., Ltd. to calculate the strain applied during bending by measuring the wavelength values ​​of each fiber in the three-core shape sensing cable before and after bending. However, when the external temperature is constant, or the effect of temperature on the grating is not considered, assuming that the strain on the upper and lower sides can be calculated from the grating wavelength drift, the strain calculation formula can be obtained as follows: ; Step 3: Assume that the interval between adjacent gratings is , the fiber diameter is , and the eccentricity is the distance from the optical fiber to the center of the structure, and the radius of curvature is , we can derive the curvature calculation formula at each grating position: ; In step 3, after knowing the curvature formula, we analyze in detail how to achieve high-precision curve reconstruction. The specific steps are: 3.1 According to bending theory, the strain on the cross section of a cylindrical structure under bending load will change along the bending distance. Assuming that the cross section of the cylinder after bending is circular, the distance from the center of the circular cross section to the center of the circle is Bending strain for: ; 3.2 Among them is the bending moment, is the radius of the circular cross section, is the elastic modulus of the cylindrical material, When the bending degree of the structural material of the cylinder does not change, the radius of the same cross section of the cylinder , elastic modulus and bending moment is a constant, then the formula can be simplified to: ; 3.3 Where C is a constant. From the above formula, we can know that the strain transfer efficiency for: ; 3.4 From the above formula, we can see that the strain transfer efficiency and eccentricity The strain response of the optical fiber sensor can be enhanced by increasing the eccentricity. Therefore, adjusting the eccentricity of the optical fiber can effectively improve its sensitivity and increase the efficiency of strain transmission, thereby capturing tiny changes in shape and reflecting them in curvature.

[0026] Step 4: The curvatures of the three optical fibers calculated are obtained from the curvatures in the two orthogonal directions to obtain the curvatures in the X-axis and Y-axis directions. and , The angular offset of the i-th sensor unit to the positive direction of the X-axis is expressed as follows: ; ; Step 5: Get the curvature and After that, the curvature K of the bending direction at the current section position can be calculated. The formula is as follows: ; Step 6: After obtaining the spatial discrete curvature information, assume that one of the optical fibers is located on the positive half axis of the Y axis. , , , the curvature in the bending direction can be obtained Angle with the positive direction of the X axis , which includes calculations for four quadrants.

[0027] In step 6, the inverse tangent function is used to calculate the angle , the specific steps are: 6.1 According to the curvature of the two coordinate axes and To determine the direction and set the angle calculation method.

[0028] ; in is a four-quadrant inverse tangent function, and the apparent curvature Can be used and Solution, and The angle between Can be obtained.

[0029] Step 7: The length of the arc segment between the two sensing points is , set up the The direction of the point The angle between the positive semi-axis and the axis is , the radius of curvature is , then the arc angle is calculated as: .

[0030] Step 8: Get the curvature and arc angle and direction angle , and further combined with the rotation and translation matrices of the shape reconstruction algorithm to iteratively calculate the coordinate information in space, the three-dimensional spatial coordinates of the measured curve can be determined point by point, and finally the complete shape reconstruction can be achieved.

[0031] In step 8, the coordinate information of each point in the space is calculated. The specific steps are: 8.1 Using the above formula, we know a set of discrete curvature information and azimuth angles in space. By performing interpolation processing on the current data, we can obtain the curvature information of a set of discrete points on the spatial curve. On this basis, combined with the ideas of differential geometry, we introduce a spatial coordinate system to describe the geometric form of the curve.

[0032] 8.2 First, select the tangent direction of the curve starting point as the z-axis, which represents the length of the structure. Then select the position of a fiber core on the curve section as the y-axis, such as Figure 2 As shown. Next, the direction of the x-axis is determined according to the right-hand screw theorem, ensuring that the three coordinate axes satisfy the right-hand rule, thereby ensuring the positivity of the coordinate system. Before the structure bends, all grating points use this initial coordinate system as a reference to establish a moving coordinate system M. Initially, this moving coordinate system coincides with the fixed coordinate system.

[0033] 8.3 Notes Point in motion coordinate system The coordinates below are , the radius of curvature is , direction and The angle between the positive semi-axis and the axis is .in: ; ; .

[0034] 8.4 Calculation of the Rotational Coordinate System in the above Formula Transition matrix required , the calculation steps are as follows: (9) The motion coordinate system Around Axis rotation , and generate a new motion coordinate system 、 、 ,axis Direction and point The curvature direction is the same, and the transformation matrix is ; (10) In the new coordinate system after transformation, Rotation , generate a new motion coordinate system 、 、 ,axis Direction and The tangent direction of the point is parallel, and the corresponding transformation matrix is ; (11) In the new coordinate system after transformation, Rotation , making the current point and next point The apparent curvature vectors of the points remain parallel, and the corresponding transformation matrix is ; (12) Finally, the coordinate axis rotation is completed, and the new coordinate system is obtained by translating a vector, and the corresponding transformation matrix is ​​obtained as follows: .

[0035] ; ; ; ; .

[0036] 8.5 Then solve the problem from the motion coordinates To fixed coordinates The vector relationship is: ; ; .

[0037] 8.6 Since the first point coincides with the origin of the original coordinate system, is the unit matrix. By repeating the above calculation process, the absolute coordinates of each micro-segment endpoint can be obtained and converted to the base coordinate system in turn. By connecting all these points, the entire space curve can be reconstructed.

[0038] Example 1: The above algorithm can theoretically reconstruct large-scale 3D shapes. To verify the proposed algorithm's accuracy in deformation reconstruction, this paper used ANSYS Workbench to build a monitoring model based on a single inclinometer casing. First, mechanical loads were applied to deform the inclinometer casing and optical fiber, and strain data along the fiber path was extracted. Finally, this data was fed into the designed algorithm to reconstruct the inclinometer casing curve.

[0039] The inclinometer tube is 1.8 meters long and divided into 48 segments, each 0.0375 meters apart. The strain values ​​of three optical fibers and the coordinates of the central fiber were extracted. Using the algorithm described above, the fiber strain values ​​were converted into spatial coordinates, completing the morphological reconstruction. Figure 4 The actual and reconstructed shapes of the inclinometer casing under two loading conditions were compared. The results show that the algorithm can accurately reconstruct the inclinometer casing shape, and the reconstructed shape is basically consistent with the simulation result. Figure 4 (a) is load case 1, where the inclinometer casing is deformed by a force; Figure 4 (b) shows load case 2, where the inclinometer casing is deformed by two forces. Because load case 2 involves additional force directions and is slightly more complex, its reconstruction error is slightly greater than that of load case 1.

[0040] Finally, we evaluate the closeness of the reconstructed curve to the actual curve in the above two cases, so the focus of the evaluation is the error in the final position and the error per unit length. The calculation formula for the absolute position error is as follows: ; At the same time, the normalized error is introduced, where Indicates the optical fiber length between the measurement point and the starting point. The calculation formula is as follows: ; In addition, the root mean square error is also used to analyze the accuracy of calculation and measurement results. The calculation formula is as follows: ; in, 、 、 Indicates the actual coordinates of the inclinometer tube. 、 、 represents the coordinates calculated by the algorithm after the inclinometer tube shape is reconstructed; N represents the number of coordinate points. Under large-scale deformation conditions, the tail end normalized error can be used as an effective evaluation metric for deformation accuracy. Its value is calculated by substituting the terminal coordinate point (i=N) into the normalized error formula. The coordinates obtained from the finite element simulation loading experiment of the inclinometer tube are used as the actual coordinates. Finally, the actual coordinates of the inclinometer tube and the coordinates reconstructed by the algorithm are compared. 49 coordinates are uniformly extracted along the length of the actual curve and the reconstructed curve and substituted into the above error formula to calculate the error under the two loading methods. The error results are shown in Table 2: Table 2. Shape reconstruction error of inclinometer tube simulation experiment

[0041] Overall, although the error gradually accumulates with increasing inclinometer casing length, the rate of error increase is relatively slow compared to the increase in inclinometer casing length. Therefore, within a certain range of inclinometer casing length, the error level remains within the engineering requirement of 3%, fully meeting the accuracy requirements for large-scale 3D deformation reconstruction. This demonstrates the feasibility of this method in practical engineering applications and its ability to effectively support 3D reconstruction and deformation monitoring of large-scale structures.

[0042] Example 2: To further verify the accuracy of the algorithm under real landslide conditions and its practicality in actual engineering projects, we spliced ​​three 4-meter sections of PPR pipe into a 12-meter-long PPR pipe. Based on the principle of strain efficiency transfer described above, we selected the pipe wall with the largest eccentricity and the highest strain transfer efficiency, cut 1mm grooves at a 120° angle, and bonded a 0.9mm GFRP (glass fiber reinforced plastic) optical fiber. Finally, we bonded the pipe with epoxy resin glue to ensure that the optical fiber deformed as the PPR pipe deformed.

[0043] The experimental steps are as follows: First, fix the head end of the PPR tube, and apply a fixed displacement to the tail end through a slide rail to simulate the landslide phenomenon, causing the PPR tube to bend. The coordinate system takes the center of the circle as the origin, the direction of the optical fiber a is the positive direction of the Y axis, the length of the PPR tube is the positive direction of the Z axis, and the X axis is defined according to the right-hand spiral rule. In each set of experiments, after the wavelength in the optical fiber is stabilized, the wavelength change data of the grating point is recorded. The tail end displacement increases from 0 cm to 50 cm in steps of 10 cm. Due to the length and bending characteristics of the PPR tube, torsion and position offset occurred in the middle part, but the head end remained basically motionless throughout the process. Finally, we substituted 5 sets of wavelength change data under different displacements into the algorithm for reconstruction, verified the feasibility of the algorithm from the horizontal direction, and obtained the following Figure 5 results.

[0044] The reconstruction results show that certain errors were present during the experiment. Furthermore, because the PPR pipe joints were not effectively fixed in the experiment, excessive horizontal loading caused significant torsion in the pipes, leading to errors in the Y direction. These factors combined to affect the accuracy and stability of the experimental results. Table 3 summarizes the experimental errors, showing a gradual increase in absolute error, but the maximum error did not exceed 2.2%.

[0045] Table 3 Inclinometer test error analysis table

[0046] Analysis shows that the cumulative error of the interpolation algorithm leads to increasing measurement errors over long distances. In this experiment, we grooved the surface of the PPR tube and placed the optical fiber close to the outside of the tube wall, ensuring an eccentricity similar to that of an externally mounted device. We then used epoxy resin to cure the fiber, integrating it with the structure and effectively reducing the error. The overall error trend is consistent with the theoretical analysis results, further validating the effectiveness of the experimental method and demonstrating the improved accuracy of the improved sensor.

[0047] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A submarine cable shape monitoring method based on ultra-weak fiber Bragg grating, characterized in that: The following steps are involved: Step 1: Assume that the total number of initial wavelength signals detected by the uwFBG shape sensing optical cable is , where 3 represents the number of fiber cores, is the number of gratings; Step 2: When bending occurs, the wavelength drift trend of the two cores should be the same (same rise or fall). This is because the multi-core fiber to be tested is bent. The three cores are evenly distributed, and the central angle of each two cores is 120°, which will cause strain on the grating attached to it. , and the central wavelength of the grating's reflection spectrum will also drift , the drift at this time is proportional to the strain, and the total number of wavelength signals after the change is ; Step 3: Assume that the interval between adjacent gratings is , the fiber diameter is , and the eccentricity is the distance from the optical fiber to the center of the structure, and the radius of curvature is , we can derive the curvature calculation formula at each grating position: ； Step 4: The curvatures of the three optical fibers calculated are obtained from the curvatures in the two orthogonal directions to obtain the curvatures in the X-axis and Y-axis directions. and , The angular offset of the i-th sensor unit to the positive direction of the X-axis is expressed as follows: ； ； Step 5: Get the curvature and After that, the curvature K of the bending direction of the current section position can be calculated. The formula is as follows: ； Step 6: After obtaining the spatial discrete curvature information, assume that one of the optical fibers is located on the positive half axis of the Y axis. , , the curvature in the bending direction can be obtained Angle with the positive direction of the X axis , which includes calculations for four quadrants; Step 7: The length of the arc segment between the two sensing points is , set up the The direction of the point The angle between the positive semi-axis and the axis is , the radius of curvature is , then the arc angle is calculated as: ； Step 8: Get the curvature and arc angle and direction angle , and further combined with the rotation and translation matrices of the shape reconstruction algorithm to iteratively calculate the coordinate information in space, the three-dimensional spatial coordinates of the measured curve can be determined point by point, and finally the complete shape reconstruction can be achieved.

2. The method for monitoring the shape of a submarine cable based on ultra-weak fiber Bragg grating according to claim 1, characterized in that: In step 2, the specific steps for monitoring the wavelength change of the shape sensing optical cable before and after bending are as follows: 2.1 After inserting the optical cable into the submarine cable, first measure the initial wavelength of each grid point , when the submarine cable is bent, the changed wavelength is measured , according to the fiber optic sensing theory: ； 2.2 Among them is the original wavelength, is the wavelength drift, is the elastic-optical coefficient, is the strain change, is the thermal expansion coefficient of the optical fiber, is the thermo-optical effect coefficient of the optical fiber, is the temperature change; 2.3 Based on the above sensing principle, an ultra-weak fiber Bragg grating (FBG) interrogator is used to measure the wavelength of each optical fiber in the three-core shape sensing cable before and after bending to calculate the strain during bending. When the external temperature is constant, or the effect of temperature on the grating is not considered, assuming that the strain on the upper and lower sides can be calculated from the grating wavelength drift, the strain calculation formula can be obtained as follows: 。 3. The method for monitoring submarine cable shape based on ultra-weak fiber Bragg grating according to claim 1, characterized in that: In step 3, after knowing the curvature formula, we analyze in detail how to achieve high-precision curve reconstruction. The specific steps are: 3.1 According to bending theory, the strain on the cross section of a cylindrical structure under bending load will change along the bending distance. Assuming that the cross section of the cylinder after bending is circular, the distance from the center of the circular cross section to the center of the circle is Bending strain for: ； 3.2 Among them is the bending moment, is the radius of the circular cross section, is the elastic modulus of the cylindrical material, When the bending degree of the structural material of the cylinder does not change, the radius of the same cross section of the cylinder , elastic modulus and bending moment is a constant, then the formula can be simplified to: ； 3.3 Among them is a constant; from the above formula, we can know that the strain transfer efficiency for: ； 3.4 From the above formula, we can see that the strain transfer efficiency and eccentricity It is directly proportional to the strain, so by increasing the eccentricity, the strain response capability of the optical fiber sensor can be enhanced; Therefore, adjusting the eccentricity of the optical fiber can effectively improve its sensitivity and increase the efficiency of strain transmission, thereby capturing tiny changes in shape and reflecting them in curvature.

4. The method for monitoring submarine cable shape based on ultra-weak fiber Bragg grating according to claim 1, characterized in that: In step 6, the inverse tangent function is used to calculate the angle , the specific steps are: 6.1 According to the curvature of the two coordinate axes and To determine the direction and set the angle calculation method: ； in is a four-quadrant inverse tangent function, and the apparent curvature Can be used and Solution, and The angle between It can be obtained that the specific solution formula is: 。 5. The method for monitoring submarine cable shape based on ultra-weak fiber Bragg grating according to claim 1, characterized in that: In step 8, the coordinate information of each point in the space is calculated. The specific steps are: 8.1 Using the above formula, we know a set of discrete curvature information and azimuth angles in space. By performing interpolation processing on the current data, we can obtain the curvature information of a set of discrete points on the spatial curve. On this basis, combined with the ideas of differential geometry, we introduce a spatial coordinate system to describe the geometric form of the curve. 8.2 First, select the z-axis, which represents the length of the structure, as the tangent direction of the curve's starting point. Next, select the position of a fiber core on the curve's cross section as the y-axis. Next, determine the direction of the x-axis according to the right-hand screw theorem, ensuring that the three coordinate axes satisfy the right-hand rule and thus the positivity of the coordinate system. Before the structure bends, all grating points use this initial coordinate system as a reference to establish a moving coordinate system M. Initially, this moving coordinate system coincides with the fixed coordinate system. 8.3 Notes Point in motion coordinate system The coordinates below are , the radius of curvature is , direction and The angle between the positive semi-axis and the axis is ,in: ； ； ； 8.4 Calculation of the Rotational Coordinate System in the above Formula Transition matrix required , the calculation steps are as follows: (1) The motion coordinate system Around Axis rotation , and generate a new motion coordinate system 、 、 ,axis Direction and point The curvature direction is the same, and the transformation matrix is ; (2) In the new coordinate system after transformation, Rotation , generate a new motion coordinate system 、 、 ,axis Direction and The tangent direction of the point is parallel, and the corresponding transformation matrix is ; (3) In the new coordinate system after transformation, Rotation , making the current point and next point The apparent curvature vectors of the points remain parallel, and the corresponding transformation matrix is ; (4) Finally, the coordinate axis rotation is completed, and the new coordinate system is obtained by translating a vector, and the corresponding transformation matrix is ​​obtained as follows: : ； ； ； ； ； 8.5 Solving the motion coordinates To fixed coordinates The vector relationship is: ； ； ； 8.6 Since the first point coincides with the origin of the original coordinate system, is the unit matrix. By repeating the above calculation process, the absolute coordinates of each micro-segment endpoint can be obtained and converted to the base coordinate system in turn. By connecting all these points, the entire space curve can be reconstructed.

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