A torsional compensation method for deformation sensing of ultra-weak grating optical cables

Abstract

A torsional compensation method for deformation sensing of ultra-weak grating optical cables is disclosed. First, the initial parameters of the ultra-weak grating composite optical cable are recorded. Then, the ultra-weak grating composite optical cable is straightened, and the wavelengths of all gratings in the cable are recorded as the initial wavelength matrix. When the cable undergoes deformation and bending, the wavelengths of all gratings are recorded as the deformation wavelength matrix. Next, the bending radius, the angle between the helical fiber ① and the bending direction, and the temperature change are calculated. Then, the torsion rate is calculated, and corrected according to the bending radius influence factor. The compensated bending direction angle is calculated. Finally, the bending radius and direction angle of all ultra-weak gratings are interpolated to reconstruct the deformation curve. This invention provides a torsional compensation method for deformation sensing of ultra-weak grating optical cables, offering a theoretical basis and specific implementation approach for correcting bending characteristic information during deformation measurement of composite optical cables.

Description

Technical Field

[0001] This invention relates to the field of fiber optic sensing technology, and in particular to a torsional compensation method for sensing the deformation of ultra-weak grating optical cables. Background Technology

[0002] Fiber optic deformation sensing technology boasts high sensitivity, strong anti-interference capabilities, and distributed measurement capabilities, making it widely applicable in fields such as intelligent robotics, minimally invasive medicine, aerospace, and infrastructure monitoring. When the object under test deforms, the strain difference experienced by multiple fiber cores / fibers in the sensing fiber / cable can be used to deduce the bending curvature and direction at that point. Initially, the multiple fiber cores / fibers are generally parallel, and the bending information positions of each monitoring point along the axial direction are consistent. However, in practical applications, it is difficult for multiple cores or fibers to remain parallel in a cable, and they may exhibit twisting. Therefore, during the manufacturing of optical fibers or cables, a twist is artificially added to form a spiral shape to overcome the unknown twisting.

[0003] In response to the challenges of applying spiral optical fibers / cables, researchers have proposed targeted technical solutions.

[0004] Reference (doi.org / 10.1109 / JLT.2022.3228235) establishes a theoretical model of total strain caused by bending and torsion, and proposes a distributed curvature and torsion measurement method for helical multi-core optical fibers. References (doi.org / 10.1109 / JSEN.2023.3337419) and (doi.org / 10.1364 / OE.386738) both establish torsional strain models for externally packaged triangular FBG sensor arrays. The former combines a material frame and a segmented constant curvature model to achieve shape reconstruction of a single-segment continuous robot, while the latter proposes a bending-torsion separation method to achieve 2D and 3D shape reconstruction.

[0005] The above method still models bending strain as a parallel structure and analyzes torsional strain as an independent quantity, thus separating it from wavelength drift caused by temperature. The sensing carrier is a helical multi-core optical fiber or an externally embedded FBG sensing array. Due to limitations in manufacturing methods, the sensing distance is short, limiting its application to biomedical or robotic sensing fields.

[0006] In monitoring large-scale deformation of long-distance engineering structures such as pipelines and cables, the aforementioned methods have significant limitations in terms of sensing distance and multiplexing capacity. In contrast, sensing optical cables based on ultra-weak fiber gratings (FBGs), in addition to possessing the inherent advantages of fiber optic sensing, offer ultra-high multiplexing (up to thousands of sensing points per fiber) and high signal-to-noise ratio characteristics. These characteristics provide a distributed sensing carrier with higher spatial resolution and longer sensing distances (kilometer-scale), offering a new technical path for extending shape sensing technology from short-distance precision systems to the field of long-distance large-structure deformation monitoring. Summary of the Invention

[0007] To address the measurement deviation of bending characteristic information caused by the non-parallelism of the actual sensing optical fibers in existing deformation sensing processes, this invention provides a torsional compensation method for deformation sensing of ultra-weak grating optical cables. The method improves the algorithm of the optical cable by incorporating the cable's own helical structure and external torsion during bending into the axial strain of the ultra-weak grating. It utilizes the sensing wavelength changes of four ultra-weak gratings to separate deformation strain from non-deformation strain, thereby compensating for and correcting the radius and direction of the deformation bend. This invention provides a theoretical basis and concrete implementation method for correcting bending characteristic information during deformation measurement of composite optical cables, significantly improving the measurement accuracy and reliability of composite optical cables in long-distance, large-scale engineering structure deformation monitoring applications.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A torsional compensation method for deformation sensing of ultra-weak grating optical cables includes the following steps: Step 1: Record the initial parameters of the ultra-weak grating composite optical cable. The angle between one of the spiral fibers at the sensing starting point of the ultra-weak grating composite optical cable and the horizontal direction is... Record the sequence number of this spiral optical fiber as ①; Step 2: Straighten the ultra-weak grating composite optical cable to make it a natural straight line, and record the wavelengths of all gratings in the ultra-weak grating composite optical cable as the initial wavelength matrix. When the ultra-weak grating composite optical cable undergoes deformation and bending, all grating wavelengths are recorded as the deformation wavelength matrix. ; Step 3: Based on the initial wavelength matrix in Step 2 Deformation wavelength matrix Calculate the bending radius. The angle between the spiral optical fiber ① and the bending direction and temperature changes ; Step 4: Based on the helix ratio of the ultra-weak grating composite optical cable Calculate the torsion ratio And the torsion rate is corrected according to the bending radius influence factor; Step 5: Calculate the compensated bending direction angle ; Step 6: Determine the bending radius for all ultra-weak gratings and direction angle Interpolation is performed to reconstruct the deformation curve.

[0009] Note: The bending radius in step 3 The direction angle in step 5 Bending radius in step 6 and direction angle These all refer to the radius and orientation angle calculated from all raster points, without the subscript. j .

[0010] In step 1, the initial parameters of the ultra-weak grating composite optical cable (1) are recorded, with the eccentricity being... spiral rate .

[0011] In step 1, the ultra-weak grating composite optical cable consists of four ultra-weak grating optical fibers, including one central fiber and three spiral fibers. The central fiber is located on the center line of the ultra-weak grating composite optical cable, and the three spiral fibers are located on the periphery of the central fiber and are wound in an equidistant spiral.

[0012] In step 2, the initial wavelength matrix In this matrix, rows 1-3 sequentially represent the wavelength data of the three spiral optical fibers (4), and row 4 represents the wavelength data of the central optical fiber; the deformed wavelength matrix The first three rows represent the wavelength data of the three spiral optical fibers in sequence, and the fourth row represents the wavelength data of the central optical fiber. The calculation process in step 3 is as follows: Consider a small element within an outer spiral fiber containing an ultra-weak grating (denoted as the j-th ultra-weak grating of the i-th fiber, where i = 1, 2, 3, j = 1, ..., m). The element extends along its axial length... It unfolds along its surface to form a right-angled triangle; When the optical cable is laid out in a straight line, its two right-angled sides are respectively ,hypotenuse This indicates the micro-segment of the spiral fiber optic cable where the ultra-weak grating is located. After the optical cable is bent and twisted and then unfurled, the axial length change caused by the bending is as follows: The change in shear strain length in the tangential direction caused by torsion is ,hypotenuse This indicates the spiral fiber micro-segment where the bent ultra-weak grating is located. Axial strain of ultra-weak gratings It can be represented as: (4); Since the strain measured by the grating is very small, the changes in the axial and tangential directions are much smaller than the original length. Therefore, the above formula can be approximated as: (5); In the formula: This indicates the fourth of three spiral optical fibers. The first fiber Bending strain on ultra-weak gratings at various locations Indicates torsional strain; Indicates the first j The radius of curvature of the optical cable segment containing the ultra-weak grating Indicates the first The angle between the j-th ultra-weak grating of the optical fiber and the bending direction; Indicates the first j The twist rate of the optical cable segment containing the ultra-weak grating is caused by the twisting.

[0013] The relationship between the sensing wavelength change and strain temperature in ultra-weak grating optical fibers: The relationship between the wavelength change of the ultra-weak grating sensing on the central fiber and the three spiral fibers and the strain temperature: (6); In the formula: Indicates the first i The first on the root fiber j Wavelength variation of an ultra-weak grating Indicates the first i The first on the root fiber j The center wavelength of an ultra-weak grating Indicates the strain coefficient. Indicates the temperature coefficient. This represents the temperature change of the optical cable segment where the j-th ultra-weak grating is located.

[0014] The central fiber is located at the center, with an eccentricity of [missing information]. Theoretically, it is only affected by temperature. The relationship between the sensing wavelength change of the central optical fiber and the strain temperature is as follows: (7); The bending radius can be obtained from formulas (4) to (7). The angle between the spiral optical fiber ① and the bending direction and temperature changes : (8); (9); (10); In the formula: . Indicates the spiral fiber. i The first (=1,2,3) fiber on the fiber j The relative wavelength variation of each ultra-weak grating The central fiber is represented by the first j The relative wavelength variation of each ultra-weak grating It has no specific meaning; it is only for the sake of making the expression of (9) more concise.

[0015] In step 4, when the optical cable has no spiral or a very small spiral ratio, the twist rate... : (11); Its torsional direction is determined by the direction of the maximum bending strain on the same cross section; When the optical cable spiral rate is The torsion rate is : (12).

[0016] In step 4, The torsion rate was adjusted to .

[0017] In step 5, a coordinate system OXY is established on the cross-section (2) of the composite optical cable. The central optical fiber (3) is located at the center of the circle, with the horizontal direction as the x-axis. The angle between the three outer spiral optical fibers (4) and the positive x-axis is denoted as . ;in Indicates the fiber optic serial number. Options 1, 2, and 3 are acceptable. Indicates the grating number on the optical fiber; (1); (2); In the formula: This indicates the helix rate of the optical fiber cabling. When the helix direction is counterclockwise, the sign in front is "+". This indicates the torsion rate caused by bending; a "+" sign is used when the torsion direction is the same as the direction of the optical cable helix. When the ultra-weak grating composite optical cable (1) undergoes deformation and bending, the bending radius is The direction makes an angle with the x-axis. The angle between the three outer spiral optical fibers and the bending direction ,but

[0018] (3).

[0019] In step 6, the bending radius of all ultra-weak gratings is... and direction angle Interpolation is performed, and the continuous deformation curve is reconstructed using the discrete differential geometric integral method.

[0020] This invention provides a torsional compensation method for deformation sensing of ultra-weak grating optical cables, which has the following technical advantages: 1) Based on the axial strain sensing mechanism of ultra-weak grating, this paper systematically elucidates for the first time that the helical structure and external torsion of optical cable not only affect the measurement of deformation bending direction angle, but also lead to measurement error of bending radius (curvature), providing a complete theoretical explanation for the source of error in deformation sensing.

[0021] 2) By establishing a separation model between non-deformation strain and real deformation strain caused by helicity and torsion, an effective compensation and correction algorithm was proposed, which realized accurate correction of bending radius and direction angle, thereby significantly improving the sensing accuracy and reliability of composite optical cable in deformation reconstruction of large-scale engineering structures.

[0022] 3) For composite optical cables without helix or with low helix ratio, a method for identifying the direction of torsion caused by deformation bending is proposed, and the torsion ratio is corrected by combining curvature, thus improving the torsion correction of the bending direction angle of composite optical cables with any helix ratio. Attached Figure Description

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a three-dimensional perspective view of the ultra-weak grating composite optical cable of the present invention.

[0024] Figure 2 This is a cross-sectional view of the ultra-weak grating composite optical cable in this invention.

[0025] Figure 3 This is a schematic diagram of the spiral surface unfolding along the axis of the ultra-weak grating micro-segment in this invention. Figure 4 This is a flowchart of the present invention.

[0026] Figure 5 This is the reconstructed shape of the optical cable tail end offset by 30cm in this invention.

[0027] In the figure: 1. Ultra-weak grating composite optical cable; 2. Cross-section of composite optical cable (the j-th ultra-weak grating of the four optical fibers is on this cross-section); 3. Central optical fiber; 4. Spiral optical fiber; 5. Expansion of ultra-weak grating micro-segment along the axis during deformation; 6. Initial expansion of ultra-weak grating micro-segment along the axis. Detailed Implementation

[0028] The ultra-weak grating is a sensor device. After the grating senses the strain data, it needs to be processed by some algorithms to obtain the deformation curve. This invention is an improvement on the algorithm part.

[0029] The connection between deformation sensing of ultra-weak grating optical cables and the torsional compensation method of this invention: 1) Compared to ordinary fiber optic sensing, grating sensing provides more accurate sensor location. Ordinary fiber optic sensing relies on signals and algorithms for positioning using an optical frequency domain meter (OFDR), while the grating's position within the fiber is fixed and unchanging. Therefore, the distance between two adjacent sensing points is the same as the distance between adjacent gratings, unaffected by sensing signals or algorithms. This results in more accurate compensation length (distance between adjacent points) during torsion compensation.

[0030] 2) Ultra-weak gratings have the advantages of ordinary gratings, but with lower reflectivity, allowing for a greater number of multiplexed gratings to be written on a single fiber. While strong gratings (ordinary Bragg gratings) have a smaller number of multiplexed gratings per fiber, and can be corrected by individually calibrating each grating point, ultra-weak gratings have a large number of multiplexed gratings, making individual calibration difficult. Therefore, a unified calibration method is more necessary.

[0031] This invention addresses the error between the deformation derived from strain data acquired by ultra-weak grating optical cable sensors during deformation sensing and the actual deformation, and proposes a correction method for torsional error.

[0032] like Figure 1-2 As shown, the ultra-weak grating composite optical cable 1 of this invention consists of four ultra-weak grating optical fibers, including one central fiber 3 and three spiral fibers 4. The central fiber 3 is located on the center line of the ultra-weak grating composite optical cable 1, and the three spiral fibers 4 are located around the central fiber 3 and are wound in an equidistant spiral. The three spiral fibers 4 form an equilateral triangle on the cross-section 2 of the composite optical cable, with each pair of fibers having an included angle of 120°. The ultra-weak gratings engraved on the three ultra-weak grating optical fibers 4 are aligned along the axis, i.e., located on the same cross-section, and the distance between adjacent cross-sections (grating spacing) is... The distance between the spiral fiber 4 and the central fiber 3 is denoted as the eccentricity. .

[0033] like Figure 2 As shown, a coordinate system OXY is established on the cross-section 2 of the composite optical cable. The central optical fiber 3 is located at the center of the circle, with the horizontal direction as the x-axis. The three outer spiral optical fibers 4 are labeled ①, ②, and ③ in a counterclockwise order, and they make an angle with the positive x-axis. (Specifically, this refers to the angle between the line connecting the spiral fiber 4 to the center of the circle and the positive x-axis), where Indicates the fiber optic serial number. Options 1, 2, and 3 are acceptable. Indicates the grating number on the optical fiber; (1); (2); In the formula: This represents the angle between the line connecting the first spiral fiber 4 to the center of the circle and the x-axis. This indicates the helix rate of the optical fiber cabling (defined as the number of arcs the fiber travels per unit length along the axial direction, always positive). When the helix direction is counterclockwise, the sign before it is "+". This indicates the torsion rate caused by bending; a "+" sign is used when the torsion direction is the same as the direction of the optical cable helix.

[0034] When the ultra-weak grating composite optical cable 1 undergoes deformation and bending, the bending radius of the optical cable at the j-th grating point on each fiber is: The direction makes an angle with the x-axis. The angle between the three outer optical fibers and the bending direction ; It means the first j The bending radius of the optical cable where the grating is located. It generally refers to the bending radius of optical cables.

[0035] (3); like Figure 1 , Figure 3 As shown, take any micro-element with an ultra-weak grating in a section of the outer spiral fiber 4, along its axial length It unfolds along its surface to form a right triangle. Right triangle 6 represents the unfolding of the optical cable when it is in a straight state, with the two right-angled sides being... ,hypotenuse This represents the spiral fiber segment containing the ultra-weak grating. Right triangle 5 represents the unfolding of the optical cable after bending and twisting; the axial length change caused by bending is... The change in shear strain length in the tangential direction caused by torsion is ,hypotenuse This indicates the spiral fiber micro-segment where the bent ultra-weak grating is located.

[0036] Axial strain of ultra-weak gratings It can be represented as: (4); Since the strain measured by the grating is very small, the changes in the axial and tangential directions are much smaller than the original length. Therefore, the above formula can be approximated as: (5); In the formula: Indicates the third of the three optical fibers The first fiber Bending strain on ultra-weak gratings at various locations It indicates torsional strain.

[0037] The relationship between the sensing wavelength change and strain temperature in ultra-weak grating optical fibers: (6); In the formula: Indicates the first i The first on the root fiber j Wavelength variation of an ultra-weak grating Indicates the first i The first on the root fiber j The center wavelength of an ultra-weak grating Indicates the strain coefficient. Indicates the temperature coefficient. This represents the temperature change of the optical cable segment where the j-th ultra-weak grating is located.

[0038] Central fiber 3 is located at the center, with an eccentricity of 3. Theoretically, only affected by temperature, the relationship between the sensing wavelength change of the central fiber 3 and the strain temperature is as follows: (7); The bending radius can be obtained from formulas (4)-(7). The angle between the optical fiber ① and the bending direction and temperature changes

[0039] (8); (9); (10); In the formula: . Indicates the spiral fiber. i The first (=1,2,3) fiber on the fiber j The relative wavelength variation of each ultra-weak grating The central fiber is represented by the first j The relative wavelength variation of an ultra-weak grating.

[0040] When the optical cable has no spiral or a very small spiral ratio, the torsion ratio : (11); Its torsional direction is determined by the direction of the maximum bending strain on the same cross section. When the optical cable helix rate is... The torsion rate is : (12); Because the optical cable is a composite optical cable (anisotropic) and a non-rigid structure, its torsion is related to the degree of bending; therefore, the torsion rate is adjusted to... . This indicates the influence factor of bending radius. .

[0041] Combining equations (1)-(3), the bending direction angle after helical and torsional compensation can be obtained. .

[0042] The bending radius and bending direction angle of all ultra-weak grating groups (ultra-weak gratings with the same serial number are called ultra-weak grating groups) are interpolated to reduce the data dispersion. Finally, the discrete differential geometric integral method is used to reconstruct the continuous deformation curve.

[0043] A torsional compensation method for deformation sensing of ultra-weak grating optical cables includes the following steps: Step 1: Record the initial parameters of the ultra-weak grating composite optical cable, including the eccentricity. spiral rate The angle between any spiral optical fiber 4 at the sensing starting point and the horizontal direction Record the fiber number as ①, and mark the other two spiral fibers 4 counterclockwise as ② and ③ respectively. Record the angles between the other two spiral fibers 4 and the horizontal direction as follows: , ; Step 2: Straighten the ultra-weak grating composite optical cable 1 to make it a natural straight line, and record the wavelengths of all gratings in the four ultra-weak grating fibers in the ultra-weak grating composite optical cable 1 as the initial wavelength matrix. Rows 1-3 sequentially represent the wavelength data of the spiral fiber 4, and row 4 represents the wavelength data of the central fiber 3. When the ultra-weak grating composite optical cable 1 undergoes deformation and bending, all grating wavelengths are recorded as a deformation wavelength matrix. .

[0044] This indicates the total number of ultra-weak gratings on a single optical fiber.

[0045] Step 3: Substitute the two matrices into formulas (8)-(10) to calculate the bending radius. The angle between the optical fiber ① and the bending direction and temperature changes . Indicates the last (the) m The bending radius of the optical cable where the ultra-weak grating is located.

[0046] Step 4: Based on the optical cable spiral ratio Calculate the torsion ratio using equations (11)-(12). ;when Even if the condition is not met, the spiral rate The calculation is still performed using equation (11), and based on the bending radius influence factor. Correct the torsion ratio.

[0047] Step 5: and Substitute equations (1)-(3) to calculate the compensated bending direction angle. ; Step 6: Set the bending radius for all ultra-weak grating groups. and direction angle Interpolation is performed, and the continuous deformation curve is reconstructed using the discrete differential geometric integral method.

[0048] Example 1 Step 1: Record the initial parameters of the ultra-weak grating composite optical cable 1: parallel optical cable, helix rate. eccentricity The ultra-weak gratings are spaced 0.2m apart along the axial direction. The angle between any spiral fiber 4 at the sensing starting point and the horizontal direction is... Record the fiber number as ①, and mark the other two spiral fibers 4 counterclockwise as ② and ③.

[0049] Step 2: Straighten the composite optical cable 1 to make it a natural straight line, and record the wavelengths of all gratings in the four ultra-weak grating fibers in the composite optical cable as the initial wavelength matrix. Rows 1-3 sequentially represent the wavelength data of the spiral fiber 4, and row 4 represents the wavelength data of the central fiber 3. When the ultra-weak grating composite optical cable 1 undergoes deformation and bending, all grating wavelengths are recorded as a deformation wavelength matrix. .

[0050] Step 3: Substitute the two matrices into equations (8)-(10) to calculate the bending radius. The angle between the optical fiber ① and the bending direction and temperature changes .

[0051] Step 4: Based on the optical cable spiral ratio Calculate the torsion ratio using formula (12) However, it does not meet the requirements. Under the condition, use equation (11) for calculation, and based on the bending radius influence factor Correct the torsion ratio.

[0052] Step 5: and Substitute equations (1)-(3) to calculate the compensated bending direction angle. ; Step 6: Set the bending radius for all ultra-weak grating groups. and direction angle Interpolation is performed, and the continuous deformation curve is reconstructed using the discrete differential geometric integral method.

[0053] The reconstructed curve after compensation according to the present invention is compared with the uncompensated reconstructed curve.

[0054] like Figure 5As shown, the blue curve represents the actual curve in three-dimensional space, the red curve represents the uncompensated reconstructed curve, and the green curve represents the reconstructed curve after compensation according to the present invention. The green curve is generally closer to the blue curve than the red curve. The tail-end error of the reconstructed curve is as follows: actual curve tail-end coordinates [0.3345 0 9.9244], red curve [0.2474 -0.1323 9.9179], green curve [0.2611 -0.0926 9.919], all three directions are closer to the actual curve. The uncompensated reconstructed curve deviates from the actual curve by 0.1585m, while the compensated deviation is 0.1182m. The latter deviation is reduced by 4.03 cm, a relative reduction of 25.4%, indicating that the reconstructed curve after compensation according to the present invention has better accuracy.

Claims

1. A torsional compensation method for deformation sensing of ultra-weak grating optical cables, characterized in that, Includes the following steps: Step 1: Record the initial parameters of the ultra-weak grating composite optical cable (1). The angle between one of the spiral optical fibers (4) at the sensing starting point of the ultra-weak grating composite optical cable (1) and the horizontal direction is recorded. Record the serial number of this spiral optical fiber (4) as ①; Step 2: Straighten the ultra-weak grating composite optical cable (1) to make it a natural straight line, and record the wavelengths of all gratings in the ultra-weak grating composite optical cable (1) as the initial wavelength matrix. When the ultra-weak grating composite optical cable (1) undergoes deformation and bending, all grating wavelengths are recorded as the deformation wavelength matrix. ; Step 3: Based on the initial wavelength matrix in Step 2 Deformation wavelength matrix Calculate the bending radius. The angle between the spiral optical fiber ① and the bending direction and temperature changes ; Step 4: Based on the helix ratio of the ultra-weak grating composite optical cable (1) Calculate the torsion ratio And the torsion rate is corrected according to the bending radius influence factor; Step 5: Calculate the compensated bending direction angle ; Step 6: Determine the bending radius for all ultra-weak gratings and direction angle Interpolation is performed to reconstruct the deformation curve.

2. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: In step 1, the initial parameters of the ultra-weak grating composite optical cable (1) are recorded, with the eccentricity being... spiral rate .

3. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: In step 1, the ultra-weak grating composite optical cable (1) is composed of four ultra-weak grating optical fibers, including one central optical fiber (3) and three spiral optical fibers (4). The central optical fiber (3) is located on the center line of the ultra-weak grating composite optical cable (1), and the three spiral optical fibers (4) are located on the periphery of the central optical fiber (3) and are wound in an equidistant spiral.

4. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: In step 2, the initial wavelength matrix In this matrix, rows 1-3 sequentially represent the wavelength data of the three spiral optical fibers (4), and row 4 represents the wavelength data of the central optical fiber (3); The deformable wavelength matrix... In this context, rows 1-3 sequentially represent the wavelength data of the three spiral optical fibers (4), and row 4 represents the wavelength data of the central optical fiber (3). This indicates the total number of ultra-weak gratings on a single optical fiber.

5. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: The calculation process for step 3 is as follows: Take any micro-element with an ultra-weak grating in a section of the outer spiral fiber (4), along its axial length It unfolds along its surface to form a right-angled triangle; When the optical cable is laid out in a straight line, its two right-angled sides are respectively ,hypotenuse This indicates the micro-segment of the spiral fiber optic cable where the ultra-weak grating is located. After the optical cable is bent and twisted and then unfurled, the axial length change caused by the bending is as follows: The change in shear strain length in the tangential direction caused by torsion is ,hypotenuse This indicates the spiral fiber micro-segment where the bent ultra-weak grating is located. Axial strain of ultra-weak gratings Represented as: ； Since the strain measured by the grating is very small, the changes in the axial and tangential directions are much smaller than the original length. Therefore, the above formula can be approximated as: ； In the formula: This indicates the fourth of three spiral optical fibers. The first fiber The bending strain experienced by the ultra-weak grating at each location Indicates torsional strain; Indicates the first j The radius of curvature of the optical cable segment containing the ultra-weak grating Indicates the first The angle between the j-th ultra-weak grating of the optical fiber and the bending direction; Indicates the first j The torsion rate of the optical cable segment containing the ultra-weak grating is generated by the torsion. The relationship between the sensing wavelength change and strain temperature in ultra-weak grating optical fibers: The relationship between the wavelength change of the ultra-weak grating sensing on the central fiber (3) and the three spiral fibers (4) and the strain temperature: ； In the formula: Indicates the first i The first on the root fiber j Wavelength variation of an ultra-weak grating Indicates the first i The first on the root fiber j The center wavelength of an ultra-weak grating Indicates the strain coefficient. Indicates the temperature coefficient. This represents the temperature change of the optical cable segment containing the j-th ultra-weak grating; The central fiber (3) is located at the center, with an eccentricity of [missing information]. Theoretically, it is only affected by temperature. The relationship between the sensing wavelength change of the central optical fiber (3) and the strain temperature is as follows: 。 6. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 5, characterized in that: The bending radius can be obtained from formulas (4) to (7). The angle between the spiral optical fiber ① and the bending direction and temperature changes : ； ； ； In the formula: ; Indicating the first in a spiral optical fiber i The first (=1,2,3) fiber optic cable j The relative wavelength variation of each ultra-weak grating The central fiber is represented by the first j The relative wavelength variation of an ultra-weak grating.

7. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: In step 4, when the optical cable has no spiral or a very small spiral ratio, the twist rate... : ； Its torsional direction is determined by the direction of the maximum bending strain on the same cross section; When the optical cable spiral rate is The torsion rate is : 。 8. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: In step 4, the bending radius influence factor The torsion rate was adjusted to .

9. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: In step 5, a coordinate system OXY is established on the cross-section (2) of the composite optical cable. The central optical fiber (3) is located at the center of the circle, with the horizontal direction as the x-axis. The angle between the three outer spiral optical fibers (4) and the positive x-axis is denoted as . ;in Indicates the fiber optic serial number. Options 1, 2, and 3 are acceptable. Indicates the grating number on the optical fiber; ； ； In the formula: This indicates the helix rate of the optical fiber cabling. When the helix direction is counterclockwise, the sign in front is "+". This indicates the torsion rate caused by bending; a "+" is used when the torsion direction is the same as the direction of the optical cable helix. When the ultra-weak grating composite optical cable (1) undergoes deformation and bending, the bending radius is The direction makes an angle with the x-axis. The angle between the three outer spiral optical fibers and the bending direction ,but 。 10. The torsional compensation method for deformation sensing of ultra-weak grating optical cables according to claim 1, characterized in that: In step 6, the bending radius of all ultra-weak gratings is... and direction angle Interpolation is performed, and the continuous deformation curve is reconstructed using the discrete differential geometric integral method.

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