Cable shape sensing system and power cable

Abstract

This cable shape sensing system comprises: an optical fiber cable provided with an optical fiber tape core including a plurality of optical fibers, and a slot material in which a slot is formed so as to be twisted in the longitudinal direction, the plurality of optical fiber tape cores being accommodated in the slot; a strain measurement device for measuring the amount of strain at each position in the longitudinal direction of, among the plurality of optical fibers included in the optical fiber tape core, one optical fiber located at the center in the width direction or two optical fibers located at symmetrical positions with respect to the center in the width direction; and a calculation device for calculating the radius of curvature at each position in the longitudinal direction of the optical fiber cable on the basis of the measured amount of strain.

Description

Cable Shape Sensing System and Power Cable

[0001] The present invention relates to a cable shape sensing system and a power cable.

[0002] Wind power generation is a method of generating electricity from a natural energy source and contributes to CO ２ emissions reduction. Among wind power generation, there are mainly two advantages in offshore wind power generation implemented at sea. One is that at sea, a larger wind force can be continuously obtained compared to on land, enabling a stable and large power supply. The other is that since the power generation equipment is installed offshore, the risk of noise and potential human damage in case of an accident is low, and it is easy to secure an installation location.

[0003] Floating offshore wind power generation is a form in which a wind turbine is mounted on a floating body moored to the seabed for power generation. Floating offshore wind power generation has the advantages that in deep waters, it is less costly than the fixed-bottom type, it does not require a large-scale support structure, so it can be installed in a wider range of locations, and it has less impact on the seabed environment.

[0004] In floating offshore wind power generation, a high-voltage dynamic cable is used to connect the floating body on which the wind turbine for power generation is provided, the floating offshore substation / converter station, and between the floating offshore substation / converter station and the onshore relay station. This cable is constantly swaying in the sea under the influence of the floating body and the tidal current. For example, from a safety perspective, it is necessary to monitor the cable so that the position of the cable from the sea surface or the seabed and the forces acting on the cable (such as bending and tension) are always within the allowable values over an operation period of 20 years or more.

[0005] As a method for measuring bending and tension generated in a structure, a method has been proposed in which an optical fiber is attached to the structure to be measured and the strain of the fiber is measured (Patent Document 1). In recent years, a technique for sensing the shape in the longitudinal direction of a multi-core fiber having a plurality of cores in the cladding by sensing local bending in the longitudinal direction of the multi-core fiber has been disclosed (see Non-Patent Documents 1 to 3).

[0006] Japanese Patent Application Laid-Open No. 2024-37448

[0007] J. P. Moore, “Shape sensing using multi-core fiber,” in Proc. Opt. Fiber Commun. Conf., 2015, p. Th1C.2.J. P. Moore and M. D. Rogge, “Shape sensing using multi-core fiber optic cable and parametric curve solutions,” Opt. Express, vol. 20, no. 3, pp. 2967-2973, 2012.Paul S. Westbrook, Tristan Kremp, Kenneth S. Feder, Wing Ko, Eric. M. Monberg, Hongchao Wu, Debra A. Simoff, Thierry F. Taunay, and Roy M. Ortiz, “Continuous Multicore Optical Fiber Grating Arrays for Distributed Sensing Applications” J. Lightw. Technol., vol. 35, no. 6, pp. 1248-1252, March 2017.Y. Meng et all., “Shape Sensing Using Two Outer Cores of Multicore Fiber and Optical Frequency Domain Reflectometer” JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 39, NO. 20, pp 6624-6630, 2021M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter” Appl. Opt. 37, 1735-1740 1998.H. Ohno, H. Naruse, M. Kihara, and A.Shimada, “Industrial Applications of the BOTDR Optical Fiber Strain Sensor”Optical Fiber Technology 7, 45-64 2001.Y. Mizuno, W. Zou, Z. He,and K. Hotate, “Proposal of Brillouin optical correlation-domain reflectometry (BOCDR)” OPTICS EXPRESS Vol. 16, No. 16 12148-12153 2008.X. Bao, D. J. Webb and D. A. Jackson, “32km Distributed Temperature Sensor Based on Brillouin Loss in an Optical Fiber," Optics Letters, vol. 18, no. 18, p.1561, September 1993.(BOTDA)K. Hotate, T. Hasegawa, ”Measurement of Brillouin Gain Spectrum Distribution along an Optical Fiber Using a Correlation-Based Technique-Proposal, Experiment and Simulation“, IEICE TRANS. ELECTRON., Vol.,E83-C, No.3 405-412 2000.Y. Koyamada, M. Imahama, K. Kubota, K. Hogari “ Fiber-optic distributed strain and temperature sensing with very high measurand resolution over long-range using coherent OTDR. J. Lightwave Technol. 2009;27:1142-1146.K.Nishiguchi “Phase unwrapping for fiber-optic distributed acoustic sensing” Proceedings of the 47th ISCIE International Symposium on Stochastic Systems Theory and Its Applications Honolulu, Dec. 5-8, 2015T. Horiguchi, T. Kurashima, M. Tateda, K. Ishihara, and Y. Wakui “Brillouin Characterization of Fiber Strain in Bent Slot-Type Optical-Fiber Cables” J. Lightwave Technol. Vol.10, No.9 1196-1201 1992.

[0008] In shape sensing using multicore fibers, the longitudinal strain distribution in multiple cores within the cladding is measured, and the longitudinal curvature and torsion of the fiber are determined from this data to calculate three-dimensional coordinates.

[0009] For example, when a multicore fiber is bent, the cores on the inside of the bend contract relative to the central axis of the multicore fiber, while the cores on the outside stretch. Therefore, the amount of strain generated in each core differs depending on the direction of bending, and the curvature and bending angle of the bent state can be determined from the information on the amount of strain in these multiple cores. Note that measuring instruments for measuring the amount of strain have a measurement limit (minimum detectable strain), so a larger difference in the amount of strain generated in each core allows for a more accurate calculation of curvature and torsion ratio.

[0010] Generally, when a multicore fiber is bent with a radius of curvature R, the amount of strain ε generated in the core is expressed by the following formula: ε = d / R, where d is the distance from the central axis of the multicore fiber to the central axis of the core.

[0011] As can be seen from the above equation, when the radius of curvature of a bend in a multicore fiber is large, the amount of strain ε generated is small, making it more difficult to detect. Therefore, to more accurately measure bends with a large radius of curvature, d should be increased.

[0012] However, in multicore fibers, d is typically around 35 to 125 μm. To further increase d, the overall cladding diameter needs to be increased, but in optical fibers made from silica glass, increasing the cladding diameter reduces the elasticity of the optical fiber, making it more difficult to bend and potentially causing it to break.

[0013] The bending expected in dynamic cables is a gentle state with a radius of curvature of several tens of meters. Therefore, the inventors considered that a sensing structure more suitable than multicore fiber would be desirable for detecting the bending state of dynamic cables.

[0014] The present invention has been made in view of the above, and aims to provide a shape sensing system and a power fiber cable that can more suitably realize the sensing of shape in the longitudinal direction.

[0015] To solve the above-mentioned problems and achieve the objective, one aspect of the present invention is a cable shape sensing system comprising: an optical fiber ribbon core containing a plurality of optical fibers; a slot material formed such that the slots are twisted in the longitudinal direction, wherein the optical fiber ribbon core is housed in the slots; a strain measuring device for measuring the amount of strain at each position in the longitudinal direction of one optical fiber located at the center in the width direction or two optical fibers located symmetrically with respect to the center in the width direction among the plurality of optical fibers contained in the optical fiber ribbon core; and a calculation device for calculating the radius of curvature at each position in the longitudinal direction of the optical fiber cable based on the measured amount of strain.

[0016] The strain measuring device measures the amount of strain at each position in the longitudinal direction of the single optical fiber, and the calculation device may calculate the radius of curvature at each position in the longitudinal direction of the optical fiber cable using the following formula (1-1). However, ηa: strain reduction coefficient (0 ≤ η ａ ≤1) m: Strain confinement coefficient p: Slot twist pitch d: Distance from the center of the optical fiber cable to the center of the optical fiber ribbon core z: Position in the longitudinal direction of the optical fiber cable n: Integer ε(z): Measured strain of the optical fiber at position z R(z): Radius of curvature of the optical fiber cable at position z

[0017] The strain measuring device measures the amount of strain at each position in the longitudinal direction of the single optical fiber, and the calculation device calculates the curvature vector and twist ratio at each position in the longitudinal direction of the optical fiber cable using formula (1-1) based on the measured amount of strain, and may also calculate the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction based on the curvature vector and the twist ratio.

[0018] The optical fiber cable comprises a plurality of optical fiber ribbon cores and a slot material having a plurality of slots formed at different positions in the circumferential direction of the slot material. The strain measuring device measures the amount of strain at each position in the longitudinal direction of one optical fiber contained in each of two or more optical fiber ribbon cores housed in different slots. The calculation device calculates the curvature vector and twist ratio at each position in the longitudinal direction of the optical fiber cable based on the measured amount of strain, and may calculate the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction based on the curvature vector and twist ratio.

[0019] The strain measuring device measures the amount of strain at each position in the longitudinal direction of the two optical fibers, and the calculation device may calculate the radius of curvature at each position in the longitudinal direction of the optical fiber cable using the following formula (1-2). However, k: the number of optical fibers in the optical fiber ribbon, i: the position of one of the optical fibers to be measured within the optical fiber ribbon (i = 1 for the outermost optical fiber: 1 ≤ i ≤ k) η b　　　　 : Strain reduction coefficient (0 ≤ η) b ≤1) m: strain confinement coefficient p: twist pitch of slots z: position in the longitudinal direction of the optical fiber cable d ｆ　　　　 : Distance between adjacent optical fibers within the optical fiber ribbon core n: Integer ε(z): Difference in the amount of strain of the optical fiber measured at position z R(z): Radius of curvature of the optical fiber cable at position z

[0020] The strain measuring device may measure the amount of strain at each position in the longitudinal direction of the two optical fibers, and the calculation device may calculate the radius of curvature at each position in the longitudinal direction of the optical fiber cable using the following formula (1-3). However, k: the number of optical fibers in the optical fiber ribbon, i: the position of one of the optical fibers to be measured within the optical fiber ribbon (i = 1 for the outermost optical fiber: 1 ≤ i ≤ k) η ａ　　　　 : Strain reduction coefficient (0 ≤ η) ａ ≤1) m: strain confinement coefficient p: twist pitch of slots z: position in the longitudinal direction of the optical fiber cable d: distance from the center of the optical fiber cable to the center of the optical fiber ribbon core d ｆ　　　　 : Distance between adjacent optical fibers in the optical fiber ribbon core n: Integer ε(z): Sum of the measured strain amounts of the optical fibers at position z R(z): Radius of curvature of the optical fiber cable at position z

[0021] The strain measuring device measures the amount of strain at each position in the longitudinal direction of the two optical fibers, and the calculation device calculates the curvature vector and twist ratio at each position in the longitudinal direction of the optical fiber cable using formula (1-2) or (1-3) based on the measured amount of strain, and may also calculate the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction based on the curvature vector and the twist ratio.

[0022] The optical fiber cable includes a plurality of the optical fiber ribbon core wires and the slot material in which a plurality of the slots having different positions in the circumferential direction of the slot material are formed. The strain measuring device measures the amount of strain at each longitudinal position of the two optical fibers included in each of two or more of the optical fiber ribbon core wires accommodated in the slots different from each other. The arithmetic unit may calculate the curvature vector and the twist rate at each longitudinal position of the optical fiber cable based on the ε(z), and calculate the three-dimensional coordinates of the central axis of the optical fiber cable at each longitudinal position based on the curvature vector and the twist rate.

[0023] The arithmetic unit may calculate the curvature vector at each longitudinal position of the optical fiber cable and the torsion angle of the cable itself based on the measured amount of strain, and calculate the three-dimensional coordinates of the central axis of the optical fiber cable at each longitudinal position based on the twist rate corrected by the torsion angle.

[0024] The arithmetic unit is based on the measured amount of strain, f １ ≦ 1 / 10P (where P is the twist pitch of the slot) to determine the period f １ The following fluctuation components may be extracted, and the fluctuation components of the amount of strain may be converted into the torsion angle of the cable itself.

[0025] The arithmetic unit is based on the measured amount of strain, f １ ≦ 1 / 10P (where P is the twist pitch of the slot) to determine the period f １ and f ２ < f １ to determine the period f ２ and the f determined by ２ from f １ to f

[0026] The strain measuring device may measure the amount of strain at each longitudinal position of an optical fiber in another tape core within the slot containing the optical fiber to be measured, and the calculation device may calculate the twist angle of the cable itself based on the difference in the amount of strain measured in optical fibers in different tape cores within the same slot.

[0027] The optical fiber cable may include a plurality of fixing members that intermittently fix the optical fiber ribbon cores to the slots in the longitudinal direction.

[0028] The optical fiber cable may include jelly that fills the slot.

[0029] The shape sensing system includes a temperature distribution measuring device that measures the temperature distribution in the longitudinal direction of the optical fiber contained in the optical fiber ribbon core, and the calculation device may correct the measured amount of strain based on the measured temperature distribution.

[0030] The strain measuring device or the temperature distribution measuring device performs measurements using light scattering in the optical fiber being measured, and the optical fiber being measured may have a function to increase scattered light.

[0031] The strain measuring device detects Brillouin scattered light generated in the optical fiber, and the optical fiber to be measured may have a core made of pure silica.

[0032] The optical fiber cable is housed within a power cable, and the computing device may calculate the radius of curvature at each position in the longitudinal direction of the power cable based on the calculated radius of curvature of the optical fiber cable.

[0033] The optical fiber cable is housed within a power cable, and the computing device may calculate the three-dimensional coordinates of the central axis of the power cable at each position in the longitudinal direction based on the three-dimensional coordinates of the optical fiber cable calculated above.

[0034] The optical fiber cable is housed within a power cable, and the computing device may calculate the three-dimensional coordinates of the central axis of the power cable at each position in the longitudinal direction based on the three-dimensional coordinates of the optical fiber cable calculated above.

[0035] One aspect of the present invention is a power cable in which an optical fiber cable and a power line are integrated, comprising an optical fiber ribbon core containing a plurality of optical fibers and a slot material formed such that the slots are twisted in the longitudinal direction, wherein the optical fiber ribbon core is housed in the slots.

[0036] According to the present invention, sensing of the shape in the longitudinal direction can be more effectively realized.

[0037] Figure 1 is a schematic configuration diagram of the shape sensing system according to Embodiment 1. Figure 2A is a schematic cross-sectional view of the cable body. Figure 2B is a schematic cross-sectional view of the optical fiber ribbon core. Figure 3 is a schematic side view of the cable body. Figure 4 is a schematic configuration diagram of the input end. Figure 5 is a schematic configuration diagram of the far end. Figure 6 is a diagram showing an example of the amount of strain at various positions in the longitudinal direction of the optical fiber cable. Figure 7 is a diagram showing an example of the radius of curvature at various positions in the longitudinal direction of the optical fiber cable. Figure 8 is a schematic configuration diagram of the shape sensing system according to a modified example of Embodiment 1. Figure 9 is a schematic configuration diagram of the input end. Figure 10 is a schematic configuration diagram of the far end. Figure 11 is a schematic configuration diagram of the shape sensing system according to Embodiment 2. Figure 12 is a schematic configuration diagram of the shape sensing system according to Embodiment 2. Figure 13 is a diagram showing an example of a flowchart illustrating the data processing process performed by the strain measuring device and calculation device of the shape sensing system according to Embodiment 2. Figure 14 is a diagram showing an example of the amount of strain at each position in the longitudinal direction of three optical fibers. Figure 15 is a diagram showing an example of the three-dimensional coordinates at each position in the longitudinal direction of the central axis of the optical fiber cable. Figure 16 is a schematic configuration diagram of the shape sensing system according to Modification 1 of Embodiment 2. Figure 17 is a schematic configuration diagram of the shape sensing system according to Modification 1 of Embodiment 2. Figure 18 is a schematic configuration diagram of the shape sensing system according to Modification 2 of Embodiment 2. Figure 19 is a schematic configuration diagram of the shape sensing system according to Modification 2 of Embodiment 2. Figure 20 is a schematic configuration diagram of the shape sensing system according to Modification 3 of Embodiment 2. Figure 21 is a schematic configuration diagram of the shape sensing system according to Embodiment 3. Figure 22A is a schematic cross-sectional view of the cable body. Figure 22B is a schematic cross-sectional view of an optical fiber ribbon core. Figure 22C is a schematic cross-sectional view of another optical fiber ribbon core. Figure 23 is a schematic configuration diagram of the input end. Figure 24 is a schematic configuration diagram of the far end. Figure 25 shows an example of the difference in strain at various points along the longitudinal direction of an optical fiber cable. Figure 26 shows an example of the radius of curvature at various points along the longitudinal direction of an optical fiber cable.Figure 27 is a diagram showing an example of the sum of strain amounts at various positions along the longitudinal direction of an optical fiber cable. Figure 28 is a diagram showing an example of the radius of curvature at various positions along the longitudinal direction of an optical fiber cable. Figure 29 is a schematic configuration diagram of a shape sensing system according to a modified example of Embodiment 3. Figure 30 is a schematic configuration diagram of the input end. Figure 31 is a schematic configuration diagram of a shape sensing system according to Embodiment 4. Figure 32 is a schematic configuration diagram of a shape sensing system according to Embodiment 4. Figure 33 is a diagram showing an example of a flowchart illustrating the data processing process performed by the strain measuring device and calculation device of the shape sensing system according to Embodiment 4. Figure 34 is a diagram showing an example of the difference in strain amounts at various positions along the longitudinal direction of three sets of optical fibers. Figure 35 is a diagram showing an example of the three-dimensional coordinates of the central axis of an optical fiber cable at various positions along the longitudinal direction. Figure 36 is a diagram showing another example of a flowchart illustrating the data processing process performed by the strain measuring device and calculation device of the shape sensing system according to Embodiment 4. Figure 37 is a schematic configuration diagram of a shape sensing system according to Modification 1 of Embodiment 4. Figure 38 is a schematic configuration diagram of a shape sensing system according to modification 1 of Embodiment 4. Figure 39 is a schematic configuration diagram of a shape sensing system according to modification 2 of Embodiment 4. Figure 40 is a schematic configuration diagram of a shape sensing system according to modification 3 of Embodiment 4. Figure 41 is a diagram showing an example of a flowchart illustrating the data processing process performed by the strain measuring device and calculation device of the shape sensing system according to Embodiment A5. Figure 42A is a schematic configuration diagram of a shape sensing system equipped with a temperature distribution measuring device. Figure 42B is a schematic configuration diagram of a shape sensing system equipped with a temperature distribution measuring device. Figure 43A is a schematic configuration diagram of modification 1 of the cable body. Figure 43B is a schematic configuration diagram of modification 2 of the cable body. Figure 44 is a schematic configuration diagram of an offshore wind power generation system to which the shape sensing system according to the embodiment is applied. Figure 45 is a cross-sectional view perpendicular to the longitudinal direction of a dynamic cable. Figure 46 is a cross-sectional view perpendicular to the longitudinal direction of another example of a dynamic cable. Figure 47 is a diagram showing an example of the arrangement position of optical fiber cables.Figure 48 is a schematic diagram of a seabed exploration system to which the shape sensing system according to the embodiment is applied. Figure 49 is a cross-sectional view perpendicular to the longitudinal direction of the power cable in the seabed exploration system.

[0038] Embodiments will be described below with reference to the drawings. However, this embodiment does not limit the present invention. Furthermore, in the drawings, the same or corresponding elements are denoted by the same reference numerals as appropriate, and redundant explanations are omitted as appropriate. It should also be noted that the drawings are schematic, and the dimensional relationships and ratios of each element may differ from reality. Even between drawings, there may be parts where the dimensional relationships and ratios differ.

[0039] (Embodiment 1) [Configuration of the Shape Sensing System] Figure 1 is a schematic configuration diagram of the shape sensing system according to Embodiment 1. The shape sensing system 100 comprises an optical fiber cable 10, a strain measuring device 20, a calculation device 30, and a connecting optical fiber 40. The optical fiber cable 10 comprises a cable body 11, an input end 12, and a far end 13.

[0040] Figures 2A and 2B are schematic cross-sectional views of the cable body 11 and the optical fiber ribbon core in a plane perpendicular to the longitudinal direction, with Figure 2A being a cross-sectional view of the cable body and Figure 2B being a cross-sectional view of the optical fiber ribbon core. Figure 3 is a schematic side view of the cable body 11.

[0041] The cable body 11 comprises a tension member 11a, a slot material 11b, a plurality of optical fiber ribbon cores 11c, and an outer covering layer 11d. The tension member 11a is located approximately in the center of the cable body 11. The slot material 11b surrounds the tension member 11a and has five groove-shaped slots 11b1, 11b2, 11b3, 11b4, and 11b5 formed from the outer surface toward the center. The slots 11b1 to 11b5 are formed at equal intervals in the circumferential direction on the slot material 11b. The slots 11b1 to 11b5 are an example of a plurality of slots that are located at different positions in the circumferential direction on the slot material.

[0042] As shown in Figure 3, slot 11b1 is formed so that the fibers are twisted in one direction with a twist pitch p in the longitudinal direction. Although not shown in Figure 3, slots 11b2 to 11b5 are also formed so that the fibers are twisted with a twist pitch p. Since the optical fiber ribbon core 11c is not fixed within the slot, the distortion of the optical fiber ribbon core 11c caused by bending of the cable body 11 is mitigated to some extent. In a cable with such a structure in which optical fiber ribbon cores are mounted within slots, the distortion that occurs in the optical fiber when the cable is bent is described in detail in Non-Patent Document 12.

[0043] Returning to Figure 2A, five optical fiber ribbon cores 11c are housed in each slot. The outer covering layer 11d surrounds the slot material 11b. The cable body 11 may have the same material and structure as known optical fiber cables used in optical communications.

[0044] In this embodiment, as shown in Figure 2A, the optical fiber ribbon core 11c housed in the slot 11b1 that is closest to the center is designated as the optical fiber ribbon core 11ca.

[0045] In this embodiment, as shown in Figure 2B, the optical fiber ribbon cable 11c includes five optical fibers 11c1 arranged in the width direction and a tape covering 11c2 surrounding these optical fibers 11c1. The five optical fibers 11c1 are an example of multiple optical fibers. The distance between adjacent optical fibers 11c1 within the optical fiber ribbon cable 11c is d ｆIn addition, the optical fibers 11c1 may be numbered i sequentially from one end. If the number of optical fibers 11c1 included in the optical fiber ribbon 11c is k (5 in this embodiment), then i is between 1 and 5. In addition, in the optical fiber ribbon 11c of this embodiment, the optical fiber i=3 is the single optical fiber located at the center in the width direction of the optical fiber ribbon 11c. In this embodiment, the optical fiber i=3 in the optical fiber ribbon 11ca is referred to as optical fiber 11c1a. As shown in Figure 2A, the distance from the center of the cable body 11 to the optical fiber 11c1a is referred to as d. In addition, in this specification, an optical fiber whose strain amount is measured, such as optical fiber 11c1a, may be referred to as the optical fiber to be measured.

[0046] The strain measurement device 20 is, for example, OFDR (Optical Frequency Domain Reflectometry), BOTDR (Brillioun Optical Time Domain Relectometry), BOCDR (Brillioun Optical Coherent Domain Relectometry), TW-COTDR (Tunable Wavelength Coherent Optical Time Domain Reflectometry), or DAS (Distributed Acoustic Sensor). Of these measurement devices, the OFDR is described in Non-Patent Document 5, the BOTDR in Non-Patent Document 6, the BOCDR in Non-Patent Document 7, the TW-COTDR in Non-Patent Document 10, and the DAS in Non-Patent Document 11.

[0047] In this embodiment, as shown in Figure 3, the strain measuring device 20 is connected at its input end 12 to the optical fiber 11c1a included in the optical fiber ribbon core 11ca via a connecting optical fiber 40. The connecting optical fiber 40 is, for example, a known optical fiber used in optical communications.

[0048] Furthermore, as shown in Figure 4, the optical fiber 11c1a is terminated at its far end 13 by a non-reflective end 13a. The non-reflective end 13a has the function of preventing excessive Fresnel reflection at the end of the optical fiber 11c1a and improving the accuracy of measuring the amount of strain near the end.

[0049] Probe light is emitted from the strain measuring device 20 and transmitted through the optical fiber 11c1a. Backscattered light is generated in the optical fiber 11c1a and received by the strain measuring device 20. The backscattered light contains several components with different wavelengths, but the type of backscattered light detected differs depending on the type of strain measuring device 20. When using BOTDR or BOCDR, Brillouin scattered light is detected. When using OFDR, TW-COTDR, or DAS, Rayleigh scattered light is detected.

[0050] The calculation device 30 receives data on the amount of strain measured by the strain measuring device 20 and calculates the radius of curvature at each position along the longitudinal direction of the optical fiber cable body 11 based on the measured amount of strain. The calculation device 30 can be configured using, for example, a personal computer.

[0051] [Calculation of Radius of Curvature] Next, the calculation of the radius of curvature by the calculation device 30 in this embodiment will be described. The calculation device 30 calculates the radius of curvature at each position in the longitudinal direction of the cable body 11 using the following formula (1-1). However, η ａ : Strain reduction coefficient (0 ≤ η) ａ ≤1) m: Strain confinement coefficient p: Slot twist pitch d: Distance from the center of the optical fiber cable (cable body) to the center of the optical fiber ribbon core z: Position of the optical fiber cable (cable body) in the longitudinal direction n: Integer ε(z): Amount of optical fiber strain measured at position z R(z): Radius of curvature of the optical fiber cable (cable body) at position z

[0052] Here, p and d are known quantities set during the structural design of the optical fiber cable 10. For example, d is approximately 2 to 5 mm. Also, η ａm depends on the structure of the optical fiber cable 10, but can be determined experimentally beforehand. ａ This indicates the degree of relaxation of the strain in the optical fiber ribbon core 11c caused by the bending of the cable body 11, with a smaller value indicating a greater degree of relaxation. m indicates the degree of correction of the strain distribution caused by the longitudinal movement of the optical fiber ribbon core when it relaxes its strain within the slot. For example, if m = 1, it indicates that there is no movement of the optical fiber ribbon core within the slot.

[0053] For example, an optical fiber cable with the same structure as optical fiber cable 10 is prepared, and the optical fiber cable is made to have a known radius of curvature by, for example, winding it around a cylinder with a known radius of curvature. Then, the distribution of strain ε in the longitudinal direction of the optical fiber at the position corresponding to optical fiber 11c1a is measured. Next, the measured strain ε is fitted using equation (1-1). In equation (1-1), p, d, and R are known values, so by fitting, η ａ We can find m and η. Fitting can be done, for example, using the least squares method. Then the obtained η ａ Using m, and known p and d, the radius of curvature R can be determined from the measured strain ε using equation (1-1).

[0054] The inventor constructed a shape sensing system according to the configuration shown in Figure 1, bent a certain optical fiber cable, measured the distribution of the strain amount ε in the longitudinal direction, and conducted an experiment to calculate the distribution of the radius of curvature R based on this. The optical fiber cable used was η ａ A cable with a value of 0.05, m of 2, p of 0.5m, and d of 3mm was used. As a result, the amount of strain at each position along the longitudinal direction of the optical fiber cable was measured, as shown in Figure 6. In Figure 6, the horizontal axis represents the position from the input end, and the vertical axis represents the amount of strain ε. Based on the measured amount of strain ε, the radius of curvature at each position along the longitudinal direction of the optical fiber cable could be calculated, as shown in Figure 7. In Figure 7, the horizontal axis represents the position from the input end, and the vertical axis represents the radius of curvature R.

[0055] With the shape sensing system 100 configured as described above, the sensing of the shape in the longitudinal direction can be more effectively realized.

[0056] (Modified Version of Embodiment 1) Figure 8 is a schematic diagram of the shape sensing system according to a modified version of Embodiment 1. The shape sensing system 100A has a configuration in which the optical fiber cable 10 of the shape sensing system 100 shown in Figure 1 is replaced with 10A, the strain measuring device 20 is replaced with 20A, and a connecting optical fiber 41 is added.

[0057] The optical fiber cable 10A has a configuration in which the input end 12 and far end 13 of the optical fiber cable 10 are replaced with input end 12A and far end 13A, respectively. As shown in Figure 9, at input end 12A, the connecting optical fiber 40 is connected to the optical fiber 11c1a included in the optical fiber ribbon conductor 11ca. Also at input end 12A, the connecting optical fiber 41 is connected to an optical fiber 11c1a' which is an optical fiber other than the optical fiber 11c1a included in the optical fiber ribbon conductor 11ca. The optical fiber 11c1a' is, for example, the optical fiber i=5 in Figure 2(b). The connecting optical fiber 41 is, like the connecting optical fiber 40, a known optical fiber used, for example, in optical communication.

[0058] Furthermore, as shown in Figure 10, at the far end 13A, the optical fibers 11c1a and 11c1a' are connected by a connecting optical fiber 13b. The connecting optical fiber 13b, like the connecting optical fibers 40 and 41, is a known optical fiber used, for example, in optical communications.

[0059] The strain measuring device 20A is connected to the optical fiber 11c1a by a connecting optical fiber 40 at its input end 12A, and to the optical fiber 11c1a' by a connecting optical fiber 41. The strain measuring device 20A is a measuring device that can be connected to both ends of the optical fiber to be measured and measure the distribution of strain in the longitudinal direction of the optical fiber.

[0060] The strain measurement device 20A is, for example, BOTDA (Brillouin Optical Time Domain Analysis) or BOCDA (Brillouin Optical Correlation Domain Analysis). Of these measurement devices, details of BOTDA are described in Non-Patent Document 8, and details of BOCDA are described in Non-Patent Document 9.

[0061] Probe light is sent from the strain measuring device 20A through the optical fiber 11c1a, and pump light is sent through the optical fiber 11c1a'. As a result, the pump light and probe light are transmitted in opposite directions through the optical fibers 11c1a and 11c1a'. Consequently, backscattered light is generated in the optical fibers 11c1a and 11c1a' and is received by the strain measuring device 20A. When using BOTDA or BOCDA as the backscattered light, Brillouin scattered light is detected.

[0062] The calculation unit 30, similar to the shape sensing system 100, receives data on the amount of strain measured by the strain measuring device 20A, and calculates the radius of curvature at each position in the longitudinal direction of the cable body 11 of the optical fiber cable 10A based on the measured amount of strain.

[0063] With the shape sensing system 100A configured as described above, the sensing of the shape in the longitudinal direction can be more effectively realized, similar to the case of the shape sensing system 100.

[0064] (Embodiment 2) Figures 11 and 12 are schematic diagrams of the shape sensing system according to Embodiment 2. The shape sensing system 100B has a configuration in which the optical fiber cable 10 of the shape sensing system 100 shown in Figure 1 is replaced with an optical fiber cable 10B, and the computing device 30 is replaced with a 30B.

[0065] The optical fiber cable 10B has a configuration in which the input end 12 and far end 13 of the optical fiber cable 10 are replaced with input end 12B and far end 13B, respectively. As shown in Figure 11, at input end 12B, the connecting optical fiber 40 is connected to the optical fiber 11c1a included in the optical fiber ribbon conductor 11ca. Also at input end 12B, the connecting optical fiber 12a connects the optical fiber 11c1b and the optical fiber 11c1c. The connecting optical fiber 12a is, for example, a known optical fiber used in optical communications.

[0066] Here, optical fiber 11c1b is an optical fiber included in the optical fiber ribbon core 11c closest to the center among the optical fiber ribbon cores 11c housed in slot 11b3 (see Figure 2A), which is an example of a slot other than slot 11b1 in the optical fiber cable 10. Specifically, optical fiber 11c1b is a single optical fiber located at the center in the width direction of the optical fiber ribbon core 11cb. Also, optical fiber 11c1c is an optical fiber included in the optical fiber ribbon core 11cc closest to the center among the optical fiber ribbon cores 11c housed in slot 11b5, which is an example of a slot other than slots 11b1 and 11b3. Specifically, optical fiber 11c1c is a single optical fiber located at the center in the width direction of the optical fiber ribbon core 11cc.

[0067] Optical fibers 11c1a, 11c1b, and 11c1c are examples of optical fibers included in each of two or more optical fiber ribbon cores housed in different slots.

[0068] Furthermore, as shown in Figure 12, at the far end 13B, the connecting optical fiber 13c connects the optical fiber 11c1a and the optical fiber 11c1b. In addition, at the far end 13B, the optical fiber 11c1c is terminated by the non-reflective end 13a. The connecting optical fiber 13c, like the connecting optical fiber 13b, is a known optical fiber used, for example, in optical communications.

[0069] With the above configuration, optical fibers 11c1a, 11c1b, and 11c1c are connected in series in this order. As a result, in the shape sensing system 100B, the probe light from the strain measuring device 20 is input sequentially to optical fibers 11c1a, 11c1b, and 11c1c, so that the strain measuring device 20 can measure the amount of strain at each position in the longitudinal direction of these three optical fibers.

[0070] Next, the computing device 30B calculates the curvature vector and twist ratio at each position in the longitudinal direction of the optical fiber cable 10B based on the measured strain amount, and can also calculate the three-dimensional coordinates of the central axis of the optical fiber cable 10B at each position in the longitudinal direction based on the curvature vector and twist ratio.

[0071] The calculation of three-dimensional coordinates can be performed, for example, by using a three-dimensional shape calculation method for multicore fibers (for example, Non-Patent Documents 1, 2, and 4). This will be discussed later.

[0072] Figure 13 is a diagram showing an example of a flowchart illustrating the data processing process performed by the strain measuring device 20 and the calculation device 30B of the shape sensing system 100B according to Embodiment 2.

[0073] First, in step S101, the strain measuring device 20 measures the distribution of strain in the longitudinal direction of the optical fibers 11c1a, 11c1b, and 11c1c. The data of the strain distribution is transmitted to the arithmetic unit 30B.

[0074] Next, in step S102, the arithmetic unit 30B converts the measured strain amounts at each position in the longitudinal direction of each optical fiber into values ​​obtained by raising the absolute value of the value to the power of 1 / m, while retaining the sign of the value.

[0075] Next, in step S103, the arithmetic unit 30B applies the transformed values ​​at each position in the longitudinal direction to the cosine function as a function of position in the longitudinal direction, and calculates the phase angle at each position (i.e., the variable in the cosine function). Specifically, for example, it can be fitted with a function Acos(Bz+C)+D to determine the parameters A, B, C, and D. This allows the phase angle (Bz+D) in the z direction to be calculated.

[0076] Next, in step S104, the arithmetic unit 30B raises the cosine function applied in step S103 to the power of (m-1).

[0077] Next, in step S105, the arithmetic unit 30B divides the values ​​of the strain amount measured in step S101 at each position in the longitudinal direction by the values ​​of the function obtained in step S104 at each position in the longitudinal direction to obtain the divided value.

[0078] Next, in step S106, the curvature vector and torsion ratio in the longitudinal direction are calculated using the division value obtained for each optical fiber, using a method called the JP. Moore method or a method called the vector projection method.

[0079] Next, in step S107, the three-dimensional coordinates are calculated according to the Freinet-Serret formula, using the longitudinal curvature vector and torsion ratio calculated in step S106.

[0080] The flowchart in Figure 13 will be explained using mathematical formulas. In the following explanation, we will use the case where the strain confinement coefficient m is 2. First, by rearranging the above equation (1-1), the following equation (2-1) holds for the amount of strain ε.

[0081] If the conversion value obtained in step S102 is ε', then the following equation (3-1) holds for ε.

[0082] In step S103, the value of the phase angle 2πz / p+φ at position z in the longitudinal direction of the optical fiber is obtained from the data shown in equation (3-1). In step S104, cos(2πz / p+φ) is obtained using the value of the phase angle 2πz / p+φ at position z in the longitudinal direction of the optical fiber. In step S105, the relation in equation (2-1) is divided by cos(2πz / p+φ) to obtain the following equation (4-1).

[0083] From the relationship in equation (4-1), it can be seen that the relationship between 1 / R (curvature) and ε (strain) with respect to position z can be determined.

[0084] As an example of a method for calculating the three-dimensional coordinates of the central axis of an optical fiber cable at various points along its longitudinal direction, the calculation methods shown in Non-Patent Documents 1 and 2 are presented here. This calculation method is also known as the JP. Moore method. The general formula for the strain generated in a specific core due to bending of a multicore fiber can be expressed as shown in equation (5) below. Here, the local coordinates are defined as xy orthogonal coordinates in the cross-section of the multicore fiber, ε i : Axial strain r at the i-th core at any position in the longitudinal direction of the fiber ｉ θ: Distance from the i-th core to the center of the fiber b : Angle from the local x-axis to the fiber bending direction (bending angle) θ i :Angle from local x-axis to core i κ:Reciprocal of radius of curvature (=1 / R)

[0085] The curvature vector pointing from the center of a multicore fiber towards the i-th core is given by equation (6) below. Here, unit vector j: unit vector in the x-axis direction, unit vector k: unit vector in the y-axis direction.

[0086] When the number of cores in a multicore fiber is N, the vector sum of the curvature vectors is given by the following equation (7).

[0087] Substituting equation (5) into equation (7), the curvature vector κ is given by equation (8) or equation (9) depending on whether the positions of each core are symmetrical or asymmetrical with respect to the distance r from the center of the multicore fiber. In the case of an asymmetric core configuration

[0088] Also θ b This is shown by equation (10). Here, κ k κ is the y-component of the curvature vector κ, κ ｊ This is the x-component of the curvature vector κ.

[0089] The curvature vector and the angle in the fiber bending direction (bending angle) can also be calculated using the method described in Non-Patent Document 4. This calculation method is also called the vector projection method. Here, the fiber shape is calculated from strain data obtained from two cores located other than the fiber center of a multicore fiber. Let the two cores be i and j, and assume that the line connecting the other core to the other core does not pass through the fiber center. The strain of a specific core due to bending is shown by the following equation (11).

[0090] Here, the local coordinates are defined as xy orthogonal coordinates in the cross-section of the multicore fiber, ε i : Axial strain r in the i-th core i θ: Distance from the i-th core to the center of the fiber b : Angle from the local x-axis to the fiber bending direction (bending angle) θ i : Angle offset θ from the local x-axis to core i j :Angle offset from local x-axis to core j κ:Curvature vector d i : Distance from core i to the axis perpendicular to the curvature vector

[0091] Projection of the curvature vector κ from the fiber center to the core i i This is shown by the following equation (12).

[0092] The curvature vector κ is κ i (=κ x ) and the component perpendicular to it κ yThis can be expressed as shown in equation (13) below.

[0093] Bending angle θ b and κ y This is expressed by the following formula (14).

[0094] Using the method described above, a dataset of curvature vectors in the longitudinal direction and angles in the bending direction (bending angle) can be obtained from multiple cores. The torsion ratio can be determined by differentiating the bending angle in the longitudinal direction of the optical fiber. It is known that the three-dimensional coordinates representing the shape of the optical fiber can be calculated from this data (Non-Patent Documents 1 and 2). The trajectory r(s) (three-dimensional coordinates) of the central axis of the optical fiber cable is shown in equation (15) below. Here, r0: initial position, T(S): tangent vector.

[0095] T(S) satisfies the Freinet-Serret relation shown in equation (16) below. Here, T: tangent vector, N: normal vector, B: binormal vector, κ: curvature vector, τ: torsion.

[0096] The torsion ratio τ is the derivative of the angle in the fiber bending direction (bending angle) with respect to the fiber longitudinal direction, and the following equation (17) holds.

[0097] Given initial conditions T, N, and B at the initial position, i.e., one end of the optical fiber cable, and using longitudinal data for κ and τ, the shape of the spatial curve of the optical fiber cable can be constructed using numerical analysis methods such as the Runge-Kutta method for equation (16).

[0098] When applied to optical fiber cables, from the relationship in equation (4-1), the phase angle of the cosine function 2πz / p + φ is expressed as the sum of the angle change 2πz / p due to the twisting of the cable slot and the angle change φ due to other changes in the cable shape. Therefore, in order to calculate the cable shape from step S106 onward, subtract the angle change 2πz / p due to the twisting of the cable slot from the phase angle 2πz / p + φ. This can be applied to equation (11) in the form shown.

[0099] As described above, the shape sensing system 100B according to Embodiment 2 can calculate the three-dimensional coordinates of each position in the longitudinal direction of the central axis of the optical fiber cable 10B.

[0100] The inventor constructed a shape sensing system according to the configuration of the shape sensing system 100B according to Embodiment 2, bent a certain optical fiber cable, measured the distribution of the strain amount ε in the longitudinal direction, and conducted an experiment to calculate the three-dimensional coordinates of the central axis of the optical fiber cable 10B at each position in the longitudinal direction based on this. The optical fiber cable is η ａ A sample with a value of 0.05, m of 2, p of 0.5m, and d of 3mm was used. As a result, the amount of strain at each position in the longitudinal direction of the three optical fibers was measured, as shown in Figure 14. In Figure 14, the horizontal axis represents the position from the input end, and the vertical axis represents the amount of strain ε. Based on the measured amount of strain ε, it was possible to calculate the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction, as shown in Figure 15.

[0101] (Embodiment A) As a system for calculating the three-dimensional coordinates at each position in the longitudinal direction of an optical fiber cable, the curvature vector and torsion ratio in the longitudinal direction can be calculated using a method different from JP. Moore's method or the vector projection method, with the same configuration as in Embodiment 1 (Figures 1-5 or 8-10).

[0102] Similar to Embodiment 1, the amount of strain in the optical fiber 11c1a of the optical fiber ribbon core 11c shown in Figure 2B is measured. The radius of curvature is calculated using the measured amount of strain in the same manner as in Embodiment 1. The curvature vector κ(z) can be simply determined using the relationship with the radius of curvature shown in the following equation (A1).

[0103] Furthermore, the phase angle θ(z) (i.e., the variable in the cosine function) at each position in the longitudinal direction of the optical fiber is calculated in the same manner as shown in Embodiment 2. The calculated phase angle includes the rotation angle due to the twisting of the cable slot. Therefore, the bending angle θb(z) of the optical fiber cable at each position in the longitudinal direction of the optical fiber is given by the following equation (A2).

[0104] Similar to Embodiment 2, the torsion ratio τ is the derivative of the angle in the fiber bending direction (bending angle) with respect to the fiber longitudinal direction, and equation (17) holds.

[0105] The obtained curvature vector and torsion ratio can be introduced into the Freinet-Serret relation shown in equation (16), and the three-dimensional coordinates at each position in the longitudinal direction can be calculated in the same manner as in Embodiment 2.

[0106] (Modification 1 of Embodiment 2) Figures 16 and 17 are schematic configuration diagrams of a shape sensing system according to Modification 1 of Embodiment 2. The shape sensing system 100C has a configuration in which the optical fiber cable 10B of the shape sensing system 100B is replaced with an optical fiber cable 10C. The optical fiber cable 10C has a configuration in which the input end 12B and the far end 13B of the optical fiber cable 10 are replaced with an input end 12C and a far end 13C, respectively.

[0107] The input terminal 12C is equipped with a 1x3 optical switch 12b. One port of the optical switch 12b is connected to the connecting optical fiber 40. Each of the three ports of the optical switch 12b is connected to the optical fibers 11c1a, 11c1b, and 11c1c, respectively.

[0108] Furthermore, as shown in Figure 17, the far end 13C is equipped with three non-reflective ends 13a. Each of the three non-reflective ends 13a is connected to one of the optical fibers 11c1a, 11c1b, and 11c1c, respectively.

[0109] In the shape sensing system 100C, the optical switch 12b selectively outputs probe light from the strain measuring device 20 to one of the optical fibers 11c1a, 11c1b, or 11c1c. In this case, the backscattered light from that one optical fiber is input to the strain measuring device 20 via the optical switch 12b and the connecting optical fiber 40. Furthermore, the optical switch 12b can switch the optical fiber that receives the probe light and generates the backscattered light. As a result, the strain measuring device 20 can measure the amount of strain at each position in the longitudinal direction of the optical fibers 11c1a, 11c1b, and 11c1c. Furthermore, the calculation unit 30B can calculate the three-dimensional coordinates of the central axis of the optical fiber cable 10C at each position in the longitudinal direction.

[0110] (Modification 2 of Embodiment 2) Figures 18 and 19 are schematic configuration diagrams of a shape sensing system according to Modification 2 of Embodiment 2. The shape sensing system 100D has a configuration in which the optical fiber cable 10C of the shape sensing system 100C is replaced with the optical fiber cable 10D, the strain measuring device 20 is replaced with 20A, and a connecting optical fiber 41 is added.

[0111] The optical fiber cable 10D has a configuration in which the input end 12B and far end 13B of the optical fiber cable 10B shown in Figure 11 are replaced with input end 12D and far end 13D, respectively. As shown in Figure 18, at input end 12D, the connecting optical fiber 40 is connected to optical fiber 11c1a. Also at input end 12D, the connecting optical fiber 12a connects optical fiber 11c1b and optical fiber 11c1c. Furthermore, at input end 12D, the connecting optical fiber 41 is connected to optical fiber 11c1c', which is an optical fiber other than optical fiber 11c1c included in the optical fiber ribbon core 11cc. Optical fiber 11c1c' is, for example, the optical fiber i=5 in Figure 2B.

[0112] Furthermore, as shown in Figure 19, at the far end 13D, the connecting optical fiber 13b connects optical fibers 11c1c and 11c1c'. Also at the far end 13D, the connecting optical fiber 13c connects optical fiber 11c1a and optical fiber 11c1b.

[0113] With the above configuration, optical fibers 11c1a, 11c1b, 11c1c, and 11c1c' are connected in series in this order.

[0114] Similar to the modified example of Embodiment 1 shown in Figure 9, the strain measuring device 20A is connected to the optical fiber 11c1a by a connecting optical fiber 40 at the input end 12D, and to the optical fiber 11c1c' by a connecting optical fiber 41. The strain measuring device 20A is a measuring device that is connected to both ends of the optical fiber to be measured and can measure the distribution of strain in the longitudinal direction of the optical fiber.

[0115] The strain measuring device 20A sends probe light to the optical fiber 11c1a and pump light to the optical fiber 11c1c'. As a result, the pump light and probe light are transmitted in opposite directions in the optical fibers 11c1a, 11c1b, 11c1c, and 11c1c'. This generates backscattered light in the optical fibers 11c1a, 11c1b, 11c1c, and 11c1c', which is received by the strain measuring device 20A.

[0116] With the above configuration, the shape sensing system 100D allows the strain measuring device 20 to measure the amount of strain at each position in the longitudinal direction of the three optical fibers 11c1a, 11c1b, and 11c1c. Furthermore, the calculation device 30B can calculate the three-dimensional coordinates of each position in the longitudinal direction of the central axis of the optical fiber cable 10D.

[0117] (Modification 3 of Embodiment 2) Figure 20 is a schematic diagram of the shape sensing system according to Modification 3 of Embodiment 2. The shape sensing system 100E has a configuration in which the optical fiber cable 10D of the shape sensing system 100D is replaced with an optical fiber cable 10E. The optical fiber cable 10E has a configuration in which the input end 12D of the optical fiber cable 10D is replaced with an input end 12E. That is, the optical fiber cable 10E has a far end 13D.

[0118] The input terminal 12E is equipped with 1x2 optical switches 12c and 12d. One port of optical switch 12c is connected to the connecting optical fiber 40. Each of the two ports of optical switch 12c is connected to optical fibers 11c1a and 11c1c, respectively. One port of optical switch 12d is connected to the connecting optical fiber 41. Each of the two ports of optical switch 12d is connected to optical fibers 11c1b and 11c1c', respectively.

[0119] In the shape sensing system 100E, with the above configuration, the optical switch 12c selectively outputs probe light from the strain measuring device 20A to the optical fiber 11c1a and the optical fiber 11c1b connected in series with it, or to the optical fiber 11c1c and the optical fiber 11c1c' connected in series with it. In this case, scattered light from the series-connected optical fibers is input to the strain measuring device 20A via the optical switch 12c and the connecting optical fiber 40. On the other hand, the optical switch 12d selectively outputs pump light from the strain measuring device 20A to the optical fiber 11c1b and the optical fiber 11c1a connected in series with it, or to the optical fiber 11c1c' and the optical fiber 11c1c connected in series with it. As a result, in the optical fibers 11c1a, 11c1b, 11c1c, and 11c1c', the pump light and probe light are transmitted in opposite directions to each other. As a result, backscattered light is generated in the optical fibers 11c1a, 11c1b, 11c1c, and 11c1c', and is received by the strain measuring device 20A. When BOTDA or BOCDA is used as the backscattered light, Brillouin scattered light is detected. The strain measuring device 20A can measure the amount of strain at each position in the longitudinal direction of the optical fibers 11c1a, 11c1b, and 11c1c. Furthermore, the calculation device 30B can calculate the three-dimensional coordinates of the central axis of the optical fiber cable 10E at each position in the longitudinal direction.

[0120] (Embodiment 3) Figure 21 is a schematic diagram of the shape sensing system according to Embodiment 3. The shape sensing system 100F has a configuration in which the optical fiber cable 10 of the shape sensing system 100 shown in Figure 1 is replaced with an optical fiber cable 10F, and the computing device 30 is replaced with 30F. The optical fiber cable 10F comprises a cable body 11F, an input end 12F, and a far end 13F.

[0121] Figures 22A, 22B, and 22C are schematic cross-sectional views of the cable body 11F and the optical fiber ribbon core in a plane perpendicular to the longitudinal direction, where Figure 22A is a cross-sectional view of the body and Figure 22B is a cross-sectional view of the optical fiber ribbon core. Figure 22C is a cross-sectional view of an optical fiber ribbon core different from that of Figure 22B.

[0122] The cable body 11F has a configuration in which the multiple optical fiber ribbon cores 11c in the cable body 11 shown in Figure 2 are replaced with optical fiber ribbon cores 11Fc. Five optical fiber ribbon cores 11Fc are housed in each slot. Since the optical fiber ribbon cores 11Fc are not fixed within the slots, the distortion of the optical fiber ribbon cores 11Fc caused by bending of the cable body 11F is mitigated to some extent.

[0123] In this embodiment, as shown in Figure 22A, the optical fiber ribbon core 11Fc housed in slot 11b1 that is closest to the center is designated as optical fiber ribbon core 11Fca. The optical fiber ribbon core 11Fc housed in slot 11b1 that is furthest from the center is designated as optical fiber ribbon core 11Fca5.

[0124] In this embodiment, as shown in Figure 22B, the optical fiber ribbon cable 11Fc includes four optical fibers 11Fc1 and a tape covering 11c2 surrounding these optical fibers 11Fc1. The four optical fibers 11Fc1 are an example of multiple optical fibers. The distance between adjacent optical fibers 11Fc1 within the optical fiber ribbon cable 11Fc is d ｆIn addition, the optical fibers 11Fc1 may be numbered i sequentially from one end. If the number of optical fibers 11Fc1 included in the optical fiber ribbon cable 11Fc is k (4 in this embodiment), then i is between 1 and 4. In addition, in the optical fiber ribbon cable 11Fc of this embodiment, the optical fibers i=1 and i=4 are two optical fibers located symmetrically with respect to the center in the width direction of the optical fiber ribbon cable 11Fc. In this embodiment, the optical fibers i=1 and i=4 in the optical fiber ribbon cable 11Fca are referred to as optical fibers 11Fc1aa and 11Fc1ab. As shown in Figure 22A, the distance from the center of the cable body 11F to the center of the optical fiber ribbon cable 11Fc in the width direction is denoted as d. In addition, 11Fc1aa and 11Fc1ab may be described as the optical fibers to be measured.

[0125] Furthermore, the optical fibers i=1 and i=4 in the optical fiber ribbon core 11Fca5 are designated as optical fibers 11Fc5aa and 11Fc5ab.

[0126] Returning to Figure 21, similar to Embodiment 1, the strain measuring device 20 is a measuring device that is connected to one end of the optical fiber to be measured and can measure the distribution of strain in the longitudinal direction of the optical fiber (the amount of strain at each point in the longitudinal direction of the optical fiber).

[0127] In this embodiment, as shown in Figure 23, the strain measuring device 20 is connected at its input end 12F to the optical fiber 11Fc1aa included in the optical fiber ribbon core 11Fca by a connecting optical fiber 40. Also, at the input end 12F, the optical fiber 11Fc1ab is terminated by a non-reflective end 12e.

[0128] Furthermore, as shown in Figure 24, at the far end 13F, optical fibers 11Fc1aa and 11Fc1ab are connected by a connecting optical fiber 13b.

[0129] Probe light is emitted from the strain measuring device 20 and transmitted through the optical fibers 11Fc1aa and 11Fc1ab. Backscattered light is generated in the optical fibers 11Fc1aa and 11Fc1ab and is received by the strain measuring device 20.

[0130] The computing device 30F receives data on the amount of strain measured by the strain measuring device 20 and calculates the radius of curvature at each position in the longitudinal direction of the optical fiber cable body 11 based on the measured amount of strain. The computing device 30F can be configured using, for example, a personal computer.

[0131] [First example of calculating the radius of curvature: Calculation based on the difference in strain amount] Next, a first example of calculating the radius of curvature by the calculation device 30F in this embodiment will be described. The calculation device 30F calculates the radius of curvature at each position in the longitudinal direction of the cable body 11F using the following formula (1-2). It should be noted that in formula (1-2), ε(z) is the difference in the amount of strain of the optical fiber measured at position z. However, k: the number of optical fibers in the optical fiber ribbon, i: the position of one of the optical fibers to be measured within the optical fiber ribbon (i = 1 for the outermost optical fiber: 1 ≤ i ≤ k) η b　　　　 : Strain reduction coefficient (0 ≤ η) b ≤1) m: strain confinement coefficient p: twist pitch of slots z: position in the longitudinal direction of the optical fiber cable d ｆ　　　　 : Distance between adjacent optical fibers within the optical fiber ribbon core n: Integer ε(z): Difference in the amount of strain of the optical fiber measured at position z R(z): Radius of curvature of the optical fiber cable at position z

[0132] Similar to Embodiment 1, p and d are known quantities set during the structural design of the optical fiber cable 10F. Also, η b m depends on the structure of the optical fiber cable 10F, but as mentioned above, it can be determined experimentally beforehand. b Using m, and known p and d, the radius of curvature R can be determined from the measured strain ε using equation (1-2).

[0133] The inventor constructed a shape sensing system according to the configuration shown in Figure 21, bent a certain optical fiber cable, determined the distribution of the difference in strain ε in the longitudinal direction, and conducted an experiment to calculate the distribution of the radius of curvature R based on the method of the first example. The optical fiber cable was η b A cable with a length of 1, a length of 2, a length of 0.5m, and a length of 3mm was used. As a result, the difference in strain at each position along the longitudinal direction of the optical fiber cable was determined, as shown in Figure 25. In Figure 25, the horizontal axis represents the position from the input end, and the vertical axis represents the difference in strain. Based on the determined difference in strain, the radius of curvature at each position along the longitudinal direction of the optical fiber cable could be calculated, as shown in Figure 26. In Figure 26, the horizontal axis represents the position from the input end, and the vertical axis represents the radius of curvature R.

[0134] [Second example of calculating the radius of curvature: Calculation based on the sum of strain amounts] Next, a second example of calculating the radius of curvature by the calculation device 30F in this embodiment will be described. The calculation device 30F calculates the radius of curvature at each position in the longitudinal direction of the cable body 11F using the following formula (1-3). It should be noted that in formula (1-3), ε(z) is the sum of the strain amounts of the optical fibers measured at position z. However, k: the number of optical fibers in the optical fiber ribbon, i: the position of one of the optical fibers to be measured within the optical fiber ribbon (i = 1 for the outermost optical fiber: 1 ≤ i ≤ k) η a　　　　 : Strain reduction coefficient (0 ≤ η) a ≤1) m: strain confinement coefficient p: twist pitch of slots z: position in the longitudinal direction of the optical fiber cable d: distance from the center of the optical fiber cable to the center of the optical fiber ribbon core d ｆ　　　　 : Distance between adjacent optical fibers in the optical fiber ribbon core n: Integer ε(z): Sum of the measured strain amounts of the optical fibers at position z R(z): Radius of curvature of the optical fiber cable at position z

[0135] The inventors conducted an experiment to calculate the distribution of the radius of curvature R for an optical fiber cable in the aforementioned bending state, based on the method of the second example. As a result, the sum of the strain amounts at each position in the longitudinal direction of the optical fiber cable was obtained, as shown in Figure 27. In Figure 27, the horizontal axis represents the position from the input end, and the vertical axis represents the sum of the strain amounts. Based on the obtained sum of strain amounts, the radius of curvature at each position in the longitudinal direction of the optical fiber cable could be calculated, as shown in Figure 28. In Figure 28, the horizontal axis represents the position from the input end, and the vertical axis represents the radius of curvature R. The calculated radius of curvature was in good agreement with the result obtained by following the method of the first example shown in Figure 26.

[0136] With the shape sensing system 100F configured as described above, the sensing of the shape in the longitudinal direction can be more effectively realized according to the methods of the first and second examples described above.

[0137] (Modified Version of Embodiment 3) Figure 29 is a schematic diagram of the shape sensing system according to a modified version of Embodiment 3. The shape sensing system 100G has a configuration in which the optical fiber cable 10F of the shape sensing system 100F shown in Figure 21 is replaced with 10G, the strain measuring device 20 is replaced with 20A, and a connecting optical fiber 41 is added.

[0138] The optical fiber cable 10G has a configuration in which the input end 12F of the optical fiber cable 10F is replaced with the input end 12G. As shown in Figure 30, at the input end 12G, the connecting optical fiber 40 is connected to the optical fiber 11c1aa included in the optical fiber ribbon core 11Fca. Also at the input end 12G, the connecting optical fiber 41 is connected to the optical fiber 11c1ab included in the optical fiber ribbon core 11Fca.

[0139] At the far end 13F, the optical fibers 11c1aa and 11c1ab are connected via the connecting optical fiber 13b.

[0140] The strain measuring device 20A is connected to optical fiber 11c1aa via connecting optical fiber 40 and to optical fiber 11c1ab via connecting optical fiber 41 at its input end 12G. The strain measuring device 20A is a measuring device that can measure the distribution of strain in the longitudinal direction of the optical fiber by connecting it to both ends of the optical fiber to be measured.

[0141] The calculation unit 30F, similar to the shape sensing system 100F, receives data on the amount of strain measured by the strain measuring device 20A, and calculates the radius of curvature at each position in the longitudinal direction of the cable body 11F of the optical fiber cable 10G based on the difference or sum of the amounts of strain.

[0142] With the shape sensing system 100G configured as described above, the sensing of the shape in the longitudinal direction can be more effectively realized, similar to the case of the shape sensing system 100F.

[0143] (Embodiment 4) Figures 31 and 32 are schematic diagrams of the shape sensing system according to Embodiment 4. The shape sensing system 100H has a configuration in which the optical fiber cable 10F of the shape sensing system 100F shown in Figure 21 is replaced with an optical fiber cable 10H, and the computing device 30F is replaced with 30H.

[0144] The optical fiber cable 10H has a configuration in which the input end 12F and far end 13F of the optical fiber cable 10F are replaced by the input end 12H and far end 13H, respectively. As shown in Figure 31, at the input end 12H, the connecting optical fiber 40 is connected to the optical fiber 11c1aa. Also at the input end 12H, the connecting optical fiber 12f connects the optical fiber 11Fc1ab and the optical fiber 11Fc1ba. Furthermore, the connecting optical fiber 12g connects the optical fiber 11Fc1bb and the optical fiber 11Fc1ca. The connecting optical fibers 12f and 12g are, for example, known optical fibers used in optical communication. The optical fiber 11Fc1cb is terminated by a non-reflective end 12e.

[0145] Here, optical fibers 11Fc1ba and 11Fc1bb are optical fibers included in the optical fiber ribbon core 11Fb closest to the center, among the optical fiber ribbon cores 11Fc housed in slot 11b3, which is an example of a slot other than slot 11b1 (see Figure 22) in the optical fiber cable 10H. Specifically, optical fibers 11Fc1ba and 11Fc1bb are two optical fibers located symmetrically with respect to the center in the width direction of the optical fiber ribbon core 11Fcb. Also, optical fibers 11Fc1ca and 11Fc1cb are optical fibers included in the optical fiber ribbon core 11Fcc closest to the center, among the optical fiber ribbon cores 11Fc housed in slot 11b5, which is an example of a slot other than slots 11b1 and 11b3. Specifically, optical fibers 11Fc1ca and 11Fc1cb are two optical fibers located symmetrically with respect to the center in the width direction of the optical fiber ribbon core 11Fcc.

[0146] Optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb are examples of two optical fibers included in each of two or more optical fiber ribbon cores housed in different slots.

[0147] Furthermore, as shown in Figure 32, at the far end 13H, the connecting optical fiber 13b connects optical fiber 11Fc1aa and optical fiber 11Fc1ab. In addition, the connecting optical fiber 13d connects optical fiber 11Fc1ba and optical fiber 11Fc1bb. Furthermore, the connecting optical fiber 13e connects optical fiber 11Fc1ca and optical fiber 11Fc1cb. The connecting optical fibers 13d and 13e, like the connecting optical fiber 13b, are known optical fibers used, for example, in optical communications.

[0148] With the above configuration, the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb are connected in series in this order. As a result, in the shape sensing system 100H, the strain measuring device 20 can measure the amount of strain at each position in the longitudinal direction of these six optical fibers.

[0149] Next, the computing device 30H calculates the curvature vector and twist ratio at each position in the longitudinal direction of the optical fiber cable 10H based on the difference or sum of the strain amounts, and can calculate the three-dimensional coordinates of the central axis of the optical fiber cable 10H at each position in the longitudinal direction based on the curvature vector and twist ratio. The calculation of the three-dimensional coordinates can be performed, for example, by using a three-dimensional shape calculation method for multicore fibers, similar to Embodiment 2.

[0150] Figure 33 is a diagram showing an example of a flowchart illustrating the data processing process performed by the strain measuring device 20 and the calculation device 30H of the shape sensing system 100H according to Embodiment 4. Specifically, Figure 33 uses the difference in strain amount.

[0151] First, in step S201, the strain measuring device 20 measures the distribution of strain in the longitudinal direction of the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb. The data of the strain distribution is transmitted to the arithmetic unit 30H.

[0152] Next, in step S202, the arithmetic unit 30H calculates the difference in strain amounts between optical fibers 11Fc1aa and 11Fc1ab, the difference in strain amounts between optical fibers 11Fc1ba and 11Fc1bb, and the difference in strain amounts between optical fibers 11Fc1ca and 11Fc1cb at each position in the longitudinal direction.

[0153] Next, in step S203, the calculation unit 30H converts the difference in the calculated strain amounts at each position in the longitudinal direction into a value (converted value) obtained by raising the absolute value of the value to the power of 1 / m, while keeping the sign of the value unchanged.

[0154] Next, in step S204, the arithmetic unit 30H applies the transformed values ​​at each position in the longitudinal direction to a sine function as a function of position in the longitudinal direction and calculates the phase angle at each position. Specifically, for example, it can be fitted with a function A sin(Bz + C) + D to determine the parameters A, B, C, and D. This allows the phase angle (Bz + D) in the z direction to be calculated.

[0155] Next, in step S205, the arithmetic unit 30H raises the sine function applied in step S204 to the power of (m-1).

[0156] Next, in step S206, the arithmetic unit 30H divides the difference in strain by the values ​​at each position in the longitudinal direction of the function obtained in step S205 to obtain the division value.

[0157] Next, in step S207, the curvature vector and torsion ratio in the longitudinal direction are calculated using the division values ​​obtained for each of the two optical fibers, using either the JP. Moore method or the vector projection method.

[0158] Next, in step S208, the three-dimensional coordinates are calculated according to the Freinet-Serret formula, using the longitudinal curvature vector and torsion ratio calculated in step S207.

[0159] The flowchart in Figure 33 will be explained using mathematical formulas. Below, we will explain using the case where the strain confinement coefficient m is 2. First, by rearranging equation (1-2) above, the following equation (2-2) holds for the difference in strain ε. Note that η ｂ Let k = 1 and k = 4.

[0160] If the converted value obtained in step S203 is ε', then the following equation (3-2) holds for ε'. Alternatively, before step S204, a bandpass filter that transmits components centered around the angular frequency 2π / p may be used to remove low-frequency and high-frequency noise from the converted value ε' obtained in step S203.

[0161] In step S204, the value of the phase angle 2πz / p+φ at position z in the longitudinal direction is obtained from the data shown in equation (3-2). In step S205, sin(2πz / p+φ) is obtained using the value of the phase angle 2πz / p+φ at position z in the longitudinal direction of the optical fiber. In step S206, the relation in equation (2-2) is divided by sin(2πz / p+φ) to obtain the following equation (4-2).

[0162] From the relationship in equation (4-2), it can be seen that the relationship between 1 / R (curvature) and ε (strain) with respect to position z can be determined.

[0163] When applied to optical fiber cables, from the relationship in equation (4-2), the phase angle of the sine function 2πz / p + φ is expressed as the sum of the angle change 2πz / p due to the twisting of the cable slot and the angle change φ due to other changes in the cable shape. Therefore, in order to calculate the cable shape from step S207 onward, subtract the angle change 2πz / p due to the twisting of the cable slot from the phase angle 2πz / p + φ. This can be applied to equation (11) in the form shown.

[0164] As described above, the shape sensing system 100H according to Embodiment 4 can calculate the three-dimensional coordinates of each position in the longitudinal direction of the central axis of the optical fiber cable 10H.

[0165] The inventor constructed a shape sensing system according to the configuration of the shape sensing system 100H according to Embodiment 4, bent a certain optical fiber cable, measured the distribution of the difference in strain in the longitudinal direction, and conducted an experiment to calculate the three-dimensional coordinates of the central axis of the optical fiber cable 10H at each position in the longitudinal direction based on this. The optical fiber cable is η ｂ A fiber with a length of 1, a length of 2, a p of 0.5m, and a d of 3mm was used. As a result, the difference in strain at each position along the longitudinal direction of the three sets of optical fibers was determined, as shown in Figure 34. In Figure 34, the horizontal axis represents the position from the input end, and the vertical axis represents the difference in strain. Based on the determined difference in strain, it was possible to calculate the three-dimensional coordinates of the central axis of the optical fiber cable at each position along the longitudinal direction, as shown in Figure 35.

[0166] Figure 36 is a diagram showing another example of a flowchart illustrating the data processing process performed by the strain measuring device 20 and the calculation device 30H of the shape sensing system 100H according to Embodiment 4. Specifically, Figure 36 uses the sum of the measured strain amounts.

[0167] First, in step S301, the strain measuring device 20 measures the distribution of strain in the longitudinal direction of the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb. The data of the strain distribution is transmitted to the arithmetic unit 30B.

[0168] Next, in step S302, the arithmetic unit 30H calculates the sum of the strain amounts of optical fibers 11Fc1aa and 11Fc1ab, the sum of the strain amounts of optical fibers 11Fc1ba and 11Fc1bb, and the sum of the strain amounts of optical fibers 11Fc1ca and 11Fc1cb at each position in the longitudinal direction.

[0169] Next, in step S303, the calculation unit 30H converts the sum of the calculated strain amounts at each position in the longitudinal direction into a value (converted value) obtained by raising the absolute value of the value to the power of 1 / m, while keeping the sign of the value unchanged.

[0170] Next, in step S304, the arithmetic unit 30H applies the transformed values ​​at each position in the longitudinal direction to the cosine function as a function of position in the longitudinal direction and calculates the phase angle at each position.

[0171] Next, in step S305, the arithmetic unit 30H raises the cosine function applied in step S304 to the power of (m-1).

[0172] Next, in step S306, the arithmetic unit 30H divides the sum of the strain amounts by the values ​​at each position in the longitudinal direction of the function obtained in step S305 to obtain the division value.

[0173] Next, in step S307, the curvature vector and bending angle in the longitudinal direction are calculated using the division values ​​obtained for each of the two optical fibers, either by JP. Moore's method or a vector projection method.

[0174] Next, in step S308, the three-dimensional coordinates are calculated according to the Freinet-Serret formula using the longitudinal curvature vector and torsion ratio calculated in step S307.

[0175] The flowchart in Figure 36 will be explained using mathematical formulas. Below, we will explain using the case where the strain confinement coefficient m is 2. First, by rearranging equation (1-3) above, the following equation (2-3) holds for the sum of strains ε. Note that k = 4.

[0176] If the conversion value obtained in step S303 is denoted as ε', then the following equation (3-3) holds for ε.

[0177] In step S304, the value of the phase angle 2πz / p+φ at position z in the longitudinal direction is obtained from the data shown in equation (3-3). In step S305, cos(2πz / p+φ) is obtained using the value of the phase angle 2πz / p+φ at position z in the longitudinal direction of the optical fiber. In step S306, the relationship in equation (2-2) is divided by cos(2πz / p+φ) to obtain the following equation (4-3).

[0178] From the relationship in equation (4-3), it can be seen that the relationship between 1 / R (curvature) and ε (strain) with respect to position z can be determined.

[0179] When applied to optical fiber cables, from the relationship in equation (4-3), the phase angle of the cosine function 2πz / p + φ is expressed as the sum of the angle change 2πz / p due to the twisting of the cable slot and the angle change φ due to other changes in the cable shape. Therefore, in order to calculate the cable shape from step S307 onward, subtract the angle change 2πz / p due to the twisting of the cable slot from the phase angle 2πz / p + φ. This can be applied to equation (11) in the form shown.

[0180] (Modification 1 of Embodiment 4) Figures 37 and 38 are schematic configuration diagrams of a shape sensing system according to Modification 1 of Embodiment 4. The shape sensing system 100I has a configuration in which the optical fiber cable 10H of the shape sensing system 100H is replaced with an optical fiber cable 10I. The optical fiber cable 10I has a configuration in which the input end 12H of the optical fiber cable 10H is replaced with an input end 12I, and the far end 13H is replaced with a far end 13I.

[0181] The input terminal 12I is equipped with a 1x6 optical switch 12h. One port of the optical switch 12h is connected to the connecting optical fiber 40. Each of the six ports of the optical switch 12h is connected to the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb, respectively.

[0182] The far end 13I is equipped with six non-reflective ends 13a. At the far end 13I, each of the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb is terminated by a non-reflective end 13a.

[0183] In the shape sensing system 100I, the optical switch 12h selectively outputs probe light from the strain measuring device 20 to one of the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb. In this case, the backscattered light from that one optical fiber is input to the strain measuring device 20 via the optical switch 12h and the connecting optical fiber 40. Furthermore, the optical switch 12h can switch the optical fiber that receives the probe light and generates the backscattered light. As a result, the strain measuring device 20 can measure the amount of strain at each position in the longitudinal direction of the six optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb. Furthermore, the computing unit 30H can calculate the three-dimensional coordinates of each position along the longitudinal direction of the central axis of the optical fiber cable 10I.

[0184] (Modification 2 of Embodiment 4) Figure 39 is a schematic configuration diagram of a shape sensing system according to Modification 2 of Embodiment 4. The shape sensing system 100J has a configuration in which the optical fiber cable 10H of the shape sensing system 100H is replaced with an optical fiber cable 10J, and the strain measuring device 20 is replaced with a strain measuring device 20A. The optical fiber cable 10J has a configuration in which the input end 12H of the optical fiber cable 10H is replaced with an input end 12J. That is, the optical fiber cable 10J has a far end 13H.

[0185] Unlike the input end 12H shown in Figure 31, at the input end 12J, the optical fiber 11Fc1cb is not connected to the non-reflective end, but is connected to the strain measuring device 20A via the connecting optical fiber 40.

[0186] The strain measuring device 20A sends probe light to the optical fiber 11Fc1aa and pump light to the optical fiber 11Fc1cb. As a result, the pump light and probe light are transmitted in opposite directions in the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb. This generates backscattered light from the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb, which is received by the strain measuring device 20A.

[0187] With the configuration described above, in the shape sensing system 100J, the strain measuring device 20A can measure the amount of strain at each position in the longitudinal direction of the six optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb. Furthermore, the calculation device 30H can calculate the three-dimensional coordinates of each position in the longitudinal direction of the central axis of the optical fiber cable 10J.

[0188] (Modification 3 of Embodiment 4) Figure 40 is a schematic diagram of the shape sensing system according to Modification 3 of Embodiment 4. The shape sensing system 100K has a configuration in which the optical fiber cable 10H of the shape sensing system 100H is replaced with an optical fiber cable 10K. The optical fiber cable 10K has a configuration in which the input end 12H of the optical fiber cable 10H is replaced with an input end 12K. That is, the optical fiber cable 10J has a far end 13H.

[0189] The input terminal 12K is equipped with 1x3 optical switches 12i and 12j. One port of optical switch 12i is connected to the connecting optical fiber 40. Each of the three ports of optical switch 12i is connected to the optical fibers 11Fc1aa, 11Fc1ba, and 11Fc1ca, respectively. One port of optical switch 12j is connected to the connecting optical fiber 41. Each of the three ports of optical switch 12j is connected to the optical fibers 11Fc1ab, 11Fc1bb, and 11Fc1cb, respectively.

[0190] In the shape sensing system 100K, with the above configuration, the optical switch 12i selectively outputs probe light from the strain measuring device 20A to the optical fiber 11Fc1aa and the optical fiber 11Fc1ab connected in series with it, or the optical fiber 11Fc1ba and the optical fiber 11Fc1bb connected in series with it, or the optical fiber 11Fc1ca and the optical fiber 11Fc1cb connected in series with it. In this case, scattered light from the series-connected optical fibers is input to the strain measuring device 20A via the optical switch 12i and the connecting optical fiber 40. On the other hand, the optical switch 12j selectively outputs pump light from the strain measuring device 20A to the optical fiber 11Fcab and the optical fiber 11Fc1aa connected in series with it, or the optical fiber 11Fc1bb and the optical fiber 11Fc1ba connected in series with it, or the optical fiber 11Fc1cb and the optical fiber 11Fc1ca connected in series with it. As a result, in the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb, the pump light and probe light are transmitted in opposite directions. Consequently, backscattered light is generated in the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb, and is received by the strain measuring device 20A. The strain measuring device 20A can measure the amount of strain at each position in the longitudinal direction of the optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb. Furthermore, the calculation device 30H can calculate the three-dimensional coordinates of the central axis of the optical fiber cable 10K at each position in the longitudinal direction.

[0191] (Embodiment A2) As a system for calculating the three-dimensional coordinates at each position in the longitudinal direction of an optical fiber cable, the curvature vector and torsion ratio in the longitudinal direction can be calculated using a method different from JP. Moore's method or the vector projection method, with the same configuration as in Embodiment 4 (Figures 31 and 32).

[0192] Similar to Embodiment 4, the strain amounts of the six optical fibers 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, and 11Fc1cb in the optical fiber cable 10H shown in Figures 31 and 32 are measured by the strain measuring device 20.

[0193] Next, the calculation unit 30H calculates the curvature vector and torsion ratio at each position in the longitudinal direction of the optical fiber cable 10H based on the difference or sum of the strain amounts. The calculation process is the same up to step S203 in the flowchart (Figure 33) showing the data processing process in Embodiment 4 when the difference in strain amounts is used. When the sum of strain amounts is used, the process is the same up to step S303 in the flowchart (Figure 36) showing the data processing process in Embodiment 4.

[0194] Then, the radius of curvature at each position in the longitudinal direction of the cable body 11F is calculated using equation (1-2) or (1-3) from the difference or sum of the measured strain amounts of the optical fiber at position z obtained in step S203 or S303.

[0195] When using the difference in the amount of strain of the optical fiber, the radius of curvature R can be determined by the same procedure as in [First example of calculating the radius of curvature: Calculation based on the difference in the amount of strain] in Embodiment 3.

[0196] When using the sum of the strain amounts of the optical fibers, the radius of curvature R can be determined by the same procedure as in [Second example of calculating the radius of curvature: Calculation based on the sum of strain amounts] in Embodiment 3.

[0197] The curvature vector κ(z) can be simply determined using the relationship with the radius of curvature shown in equation (A1).

[0198] Next, the phase angle θ(z) at each position in the longitudinal direction of the optical fiber is calculated using the same method as shown in Embodiment 4.

[0199] When using the difference in the amount of strain of the optical fiber, the phase angle is obtained in step S204 in the flowchart (Figure 33) showing the data processing process in Embodiment 4.

[0200] When using the sum of the strain amounts of the optical fibers, the phase angle is obtained in step S304 in the flowchart (Figure 36) showing the data processing process in Embodiment 4.

[0201] The calculated phase angle includes the rotation angle due to the twisting of the cable slot. Therefore, the bending angle θb(z) of the optical fiber cable at each position in the longitudinal direction of the optical fiber is given by equation (A2).

[0202] Similar to Embodiment 2, the torsion ratio τ is the derivative of the angle in the fiber bending direction (bending angle) with respect to the fiber longitudinal direction, and equation (17) holds.

[0203] The obtained curvature vector and torsion ratio can be introduced into the Freinet-Serret relation shown in equation (16), and the three-dimensional coordinates at each position in the longitudinal direction can be calculated in the same manner as in Embodiment 2.

[0204] (Embodiment A3) As a system for calculating three-dimensional coordinates at each position in the longitudinal direction of an optical fiber cable, a more precise three-dimensional coordinate can be calculated with the same configuration as in Embodiments 2, 4, A1, and A2.

[0205] If the cable itself is twisted in the circumferential direction, the calculated phase angle θ(z) at each position in the longitudinal direction of the optical fiber will include the amount of angle change due to the twisting of the cable itself.

[0206] Therefore, in order to more accurately determine the three-dimensional shape of the cable, it is necessary to subtract the amount of angle change due to the twisting of the cable itself from the phase angle θ(z).

[0207] We investigated what kind of strain occurs in the optical fibers within the ribbon core housed in the slot when twisting occurs in the circumferential direction of the slot cable.

[0208] The amount of strain generated in the optical fiber within the ribbon core mounted in the slot was measured when the slot cable was kept straight and twisted in the same direction as the slot's twisting direction, and when twisted in the opposite direction. The results showed that when the cable was twisted in the same direction as the slot's twisting direction, the amount of strain increased uniformly along the entire longitudinal length, while when it was twisted in the opposite direction, the amount of strain tended to decrease uniformly along the entire longitudinal length.

[0209] This indicates that the change in the torsional angle of the slot due to external force is reflected in the amount of strain on the optical fiber.

[0210] Quantitatively, the relationship between the twist angle Φ(z) when a slot cable is twisted in a straight state and the amount of strain ε(z) generated at the following points along the longitudinal direction of the optical fiber is given by equation (A3). Here, d: distance from the center of the optical fiber cable to the center of the optical fiber ribbon core, and P: twist pitch of the slots.

[0211] Considering the cable's longitudinal direction, the accumulation of the angle Φ(z) corresponding to the strain generated at each point along the longitudinal direction over its entire length influences the phase change.

[0212] The strain caused by the circumferential twisting of this slotted cable is due to a different factor than the strain caused by bending. Therefore, when both bending and twisting occur, the optical fiber will have a value that is the sum of the strains from both.

[0213] The distortion that occurs when a slotted cable is bent appears as a component whose value changes with a period corresponding to the twist pitch of the slots, but the distortion that occurs due to twisting does not have a specific periodic component and is unrelated to the period of the twist pitch of the slots.

[0214] Generally, when considering cases where a slotted cable deforms, it is rare for the cable to experience twisting equal to or greater than the twist pitch of the slots. If such twisting were to occur, the cable would likely break.

[0215] Therefore, the strain generated by the circumferential twisting of this slot cable is thought to appear as a component with a period longer than the period of the slot twist pitch.

[0216] Taking the above results into consideration, the angular change due to twisting of the slot cable in the circumferential direction is determined from the calculated longitudinal phase angle using the following procedure, and then the phase angle θ(z) is corrected using that value.

[0217] The strain generated by the circumferential twisting of the slot cable is determined from the longitudinal strain distribution calculated to determine the phase angle θ(z) and the radius of curvature R(z) or the curvature vector κ. Here, the longitudinal strain distribution of the optical fiber in the ribbon core of the slot cable is the strain distribution calculated in each embodiment of Embodiments 2, 4, A1, or A2.

[0218] In the strain distribution along the longitudinal direction, period f １ The period f is determined by ≤ 1 / 10P (where P is the twist pitch of the slots). １ The following fluctuating components are extracted. For example, the extraction method involves setting the cutoff frequency to f. １ A low-pass filter can be used, as set to [this value].

[0219] The calculated period f １ From the following strain distribution, the longitudinal distribution of the torsional angle Φ(z) is determined using the relationship in equation (A3).

[0220] The calculated twist angles Φ(z) are added together along the longitudinal direction to determine the angle change ξ(z) due to cable twisting in the longitudinal direction. Here, z, which represents the longitudinal direction of the optical fiber, is equal to z at intervals of dz. ｌ from z ｎ Let n be the values ​​up to z. ｉ ξ(z) for (i is between 1 and n, inclusive) ｉ ) can be expressed by the following formula.

[0221] In embodiments 2, 4, and A2, where the strain distribution of two or more optical fibers is measured, it is also possible to determine ξ(z) for all optical fibers and calculate and use the average value in the longitudinal direction.

[0222] By subtracting ξ(z) from the phase angle θ(z) at each point along the longitudinal direction, a phase angle distribution that reflects the deformation of the cable, while eliminating the effects of cable twisting, can be obtained.

[0223] (Implementation Form A4) The following method can also be used to calculate the amount of strain due to twisting in the circumferential direction of the cable itself.

[0224] In the strain distribution along the longitudinal direction, f １ The period f is determined by ≤ 1 / 10P (where P is the twist pitch of the slots). １ and period f ２ <f １ The period f is determined by ２ f is determined by ２ f １ Extract the fluctuating component in the interval up to f. ２ For example, the value of f ２ =f １ / 10 can be used. As an extraction method, for example, the cutoff frequency on the low-frequency side is f ２ Set to f, and set the high-frequency cutoff wavelength to f １ Set to f ２ f １ A bandpass filter can be used to extract components in the frequency band between these two points.

[0225] (Embodiment A5) The following method can also be used to calculate the amount of strain due to twisting in the circumferential direction of the cable itself.

[0226] Referring to Figures 22A, 22B, and 22C, the optical fibers to be measured in the slotted cable are described in order to calculate the amount of strain due to the twisting of the cable itself in the circumferential direction. In this embodiment, in addition to the optical fiber ribbon core 11Fca, the optical fiber ribbon core 11Fca5 is measured as an example of an optical fiber ribbon core located in the same slot as the optical fiber ribbon core 11Fca, but at a different distance from the center of the cable than 11ca.

[0227] The optical fiber used to measure the amount of strain in the optical fiber ribbon core 11Fca5 is the optical fiber located in the same arrangement position within the ribbon core as the optical fiber being measured within the optical fiber ribbon core 11Fca. For example, when measuring optical fiber 11Fc1aa in the optical fiber ribbon core 11Fca, optical fiber 11Fc5aa in the optical fiber ribbon core 11Fca5 is added for measurement, and when measuring optical fiber 11Fc1ab, optical fiber 11Fc5ab in the optical fiber ribbon core 11Fca5 is added for measurement.

[0228] When adding a new optical fiber for measurement, the shape sensing systems 100B, 100C, 100D, 100E, 100H, 100I, 100J, 100K and their associated strain measuring devices 20, 20A and calculation devices 30B, 30H can also be used to calculate the three-dimensional coordinates of the cable.

[0229] Here, we consider a configuration similar to the shape sensing system 100J shown in Modification 2 of Embodiment 4. Additionally, the optical fibers to be measured are optical fibers 11Fc5aa and 11Fc5ab in the optical fiber ribbon fiber 11Fca5 located in the same slot as the optical fiber ribbon fiber 11Fca5, which is positioned to correspond to optical fibers 11Fc1aa and 11Fc1ab in the optical fiber ribbon fiber 11Fca5 within the same slot 11b1.

[0230] In this configuration, the optical fiber to be measured is configured such that at the input end 12H, the connecting optical fiber 12f connected to the optical fiber 11Fc1ab is connected to the optical fiber 11Fc5aa, the optical fiber 11Fc5ab and the optical fiber 11Fc1ba are connected with a new connecting optical fiber, and at the far end 13H, the optical fiber 11Fc5aa and the optical fiber 11Fc5ab are connected with a new connecting optical fiber, thereby enabling the measurement of the strain distribution of the added optical fibers 11Fc5aa and 11Fc5ab.

[0231] Figure 41 is a diagram showing an example of a flowchart illustrating the data processing process performed by the strain measurement device and calculation device of the shape sensing system according to Embodiment A5.

[0232] First, in step S401, the strain measuring device 20 measures the distribution of strain in the longitudinal direction of the optical fibers 11Fc1aa, 11Fc1ab, 11Fc5aa, and 11Fc5ab. The data of the strain distribution is transmitted to the arithmetic unit 30H.

[0233] Next, in step S402, the computing unit 30H extracts a fluctuation component with a period longer than the twist pitch of the slot from the measured strain amount at each position in the longitudinal direction of each optical fiber. As an extraction method, for example, a specific period f １ A low-pass filter that transmits the following fluctuating components (which will be the cutoff period) can be used.

[0234] Here, the period f １ For example, f １ It can be set to ≤ 1 / 10P (where P is the twist pitch of the slot).

[0235] Next, in step S403, the arithmetic unit 30H calculates the difference in strain amounts between the two optical fiber ribbon cores 11Fca and 11Fca5 measured in the same slot. If multiple optical fibers are measured for each optical fiber ribbon, the average value of the strain distribution of each optical fiber ribbon core is calculated and then the difference is taken. Here, the average value of the longitudinal strain distribution of optical fibers 11Fc1aa and 11Fc1ab is calculated, and the average value of the longitudinal strain distribution of optical fibers 11Fc5aa and 11Fc5ab is calculated, and the difference in strain amounts between the two, Δε, is calculated.

[0236] Next, in step S404, the calculation unit 30H converts the difference in strain amounts Δε calculated at each position in the longitudinal direction into the longitudinal torsion angle distribution Δφ of the cable using the relation shown in equation (A3).

[0237] Here, we introduce the relaxation coefficient ω (0 < ω < 1) of the optical fiber ribbon core within the slot when the cable is twisted. The relationship between the measured value Δε and the theoretical value Δε' which can be theoretically determined from the twisting angle of the cable is expressed by equation (A5).

[0238] The specific value of ω can be determined experimentally. For example, it can be determined by applying a known torsional angle to a cable that is straight and free of torsional distortion, finding the amount of strain generated in the fibers at a desired position within the cable, and comparing it with the theoretical amount of torsional distortion for the given angle. Since this relaxation coefficient is characterized by the cable structure, if ω is determined in advance using the method described above, that value can be used in shape sensing using cables of the same structure.

[0239] Theoretically, the torsional strain ε generated in the optical fiber within the optical fiber ribbon core 11Fca is calculated using the theoretical value Δε'. r1 This can be written as shown in the following equation (A6). Here, d1 and d5 are the distances from the center of the cable to the optical fiber ribbon cores 11Fca and 11Fca5.

[0240] Using ω and expressing it in terms of the measured value Δε, we get the following equation.

[0241] Required torsional strain ε r1 By substituting this into equation (A3), the torsional angle Φ(z) can be determined.

[0242] In the example above, two optical fibers are measured for each of the two optical fiber ribbon cores in the same slot, but it is also acceptable to measure only one optical fiber for each optical fiber ribbon core.

[0243] Furthermore, in the example above, two different optical fiber ribbon cores within a single slot in the cable were measured, but similar measurements could also be performed on multiple slots to obtain the averaged torsional angle distribution Δφ.

[0244] (Correction by measuring temperature distribution) The shape sensing system according to the above embodiment may include a temperature distribution measuring device that measures the temperature distribution in the longitudinal direction of the optical fiber contained in the optical fiber ribbon core, and the calculation device may be configured to correct the measured amount of strain based on the measured temperature distribution.

[0245] Figures 42A and 42B are schematic diagrams of a shape sensing system equipped with a temperature distribution measuring device. The shape sensing system 100L shown in Figure 42A has a configuration that adds a connecting optical fiber 42 and a temperature distribution measuring device 50 to the shape sensing system 100 shown in Figure 1.

[0246] The connecting optical fiber 42 connects the temperature distribution measuring device 50 to an optical fiber other than the optical fiber 11c1a (referred to as the temperature measuring optical fiber) included in the optical fiber cable 10.

[0247] The temperature distribution measuring device 50 is, for example, a temperature distribution measuring device that uses the R-OTDR (Raman OTDR) method, which uses changes in Raman scattered light in a temperature measuring optical fiber, but is not particularly limited. When the temperature distribution measuring device 50 is a device that uses the R-OTDR method, the temperature distribution measuring device 50 sends probe pulse light to the temperature measuring optical fiber. The temperature distribution measuring device 50 receives Stokes light and anti-Stokes light from the Raman scattered light generated by the probe pulse light, and can calculate the temperature distribution in the temperature measuring optical fiber from the ratio of their intensities.

[0248] The shape sensing system 100M shown in Figure 42B has a configuration that adds a connecting optical fiber 42 and a temperature distribution measuring device 50 to the shape sensing system 100A shown in Figure 8.

[0249] The connecting optical fiber 42 connects the temperature distribution measuring device 50 to optical fibers other than optical fibers 11c1a and 11c1a' (temperature measuring optical fibers) included in the optical fiber cable 10A.

[0250] Generally, optical fibers expand and contract with changes in temperature. Therefore, when measuring the strain distribution of an optical fiber, changes in the temperature of the optical fiber affect the strain measurement. To address this, the computing device 30 uses the temperature distribution measuring device 50 to determine the temperature distribution in the longitudinal direction of the optical fiber cable 10 or 10A, and corrects the amount of strain measured by the strain measuring device 20 or 20A based on the temperature distribution.

[0251] Here, in measuring the strain distribution of an optical fiber, the strain due to deformation of the optical fiber and the expansion / contraction due to temperature changes are determined by adding the effects of both. The amount of change due to deformation of the optical fiber is ε f ε t Therefore, the value ε measured in the strain distribution measurement of the optical fiber is given by the following equation (18). c is the coefficient of thermal expansion of the optical fiber, and t is the temperature. For silica glass optical fibers, c is 5 × 10⁻⁶. ―７ It is known to be around / °C. From the relationship in equation (18), the amount of strain can be corrected based on the temperature distribution in the longitudinal direction of the optical fiber obtained by the temperature distribution measuring device 50.

[0252] (Modified Cable Body 1 and 2) In the cable body 11 or 11F according to the above embodiment, the optical fiber ribbon core 11c or 11Fc is not fixed within the slot. However, as shown in Modified Cable Body 1 and 2 below, the optical fiber ribbon core may be fixed or loosely fixed.

[0253] Figures 43A and 43B are schematic diagrams of modified versions 1 and 2 of the cable body. The cable body 11N shown in Figure 43A has a configuration in which a plurality of fixing members 11e are added to the cable body 11 or 11F to intermittently fix the optical fiber ribbon core to the slot in the longitudinal direction. In the figure, the fixing members 11e are provided inside the slot 11b1, but they may be provided in other slots or outside the slot.

[0254] The cable body 11O shown in Figure 43B has a configuration in which jelly 11f is added to the cable body 11 or 11F to fill the slots. In the figure, the jelly 11f is intermittently filled in the slot 11b1, but it may also be filled in other slots or continuously.

[0255] If the cable body is configured as cable body 11N or 11O, the strain on the optical fiber ribbon core is mitigated, reducing the possibility of optical fiber breakage, while also allowing sufficient strain to be retained during deformation of the optical fiber, which is necessary for realizing the shape sensing function.

[0256] (Suitable Examples of Optical Fibers to be Measured) As the optical fiber included in the optical fiber ribbon core of the optical fiber cable in the above embodiment, a single-mode optical fiber conforming to G. 652, G. 653, G. 654, G. 655, G. 656, and G. 657 specified by the International Telecommunication Union (ITU) can be used. These are known optical fibers used in optical communication. However, when using an OFDR, TW-OTDR, or DAS that detects Rayleigh scattered light as a strain measurement device, an FBG optical fiber having a fiber Bragg grating core in which the refractive index of the core changes periodically in the longitudinal direction may be used as the optical fiber to be measured. By using an FBG optical fiber, light of a specific wavelength can be efficiently scattered backward. This can increase the intensity of backscattered light in the core, thereby improving the sensitivity of sensing (see Non-Patent Literature 3). Such an FBG optical fiber is an example of an optical fiber having a scattered light increasing function.

[0257] Furthermore, when using BOTDR, BOCDR, BOTDA, or BOCDA as strain measurement devices that detect Brillouin scattered light, it is effective to use a highly nonlinear optical fiber with a high nonlinear refractive index as the optical fiber to be measured. Increasing the nonlinearity of an optical fiber can be achieved by increasing the amount of germanium added to the core or by reducing the core diameter to increase the optical density within the core. Such highly nonlinear optical fibers are an example of optical fibers that have a function of increasing scattered light.

[0258] Furthermore, when using BOTDR, BOCDR, BOTDA, or BOCDA as strain measurement devices that detect Brillouin scattered light, it is effective to use an optical fiber with a high Brillouin scattering coefficient as the optical fiber to be measured, such as an optical fiber with a core made of pure silica. A high Brillouin scattering coefficient improves the detection accuracy of the detected Brillouin scattering frequency shift. Moreover, with an optical fiber core made of pure silica, since the core does not contain impurities other than silica, the transmission loss of light is reduced, and the loss of light propagating through the optical fiber during strain measurement is also reduced, thereby improving measurement performance.

[0259] (Application to Offshore Wind Power Generation Systems) The shape sensing systems according to the above embodiments can be applied to a variety of systems. Figure 44 is a schematic diagram of an offshore wind power generation system to which the shape sensing system according to the embodiments is applied.

[0260] In the SYS1000 offshore wind power generation system, the offshore platform 10055 is connected to the offshore substation 1006 by a dynamic cable 1001a. The offshore platform 1005 is a tension-moored platform, for example, called a TLP (Tension Leg Platform). The offshore platform 1005 consists of a floating body 1051, a tower 1052, a nacelle 1053, a rotor 1054, blades 1054a, a tendon 1055, and a foundation 1056. The offshore platform 1005 is moored by the tension force generated by buoyancy, with the floating body 1051 being forcibly semi-submerged and the foundation 1056 installed on the seabed connected by a tendon 1055. The nacelle 1053 is located on top of the tower 1052, which is installed on the floating body 1051. A yaw drive device is provided at the joint between the nacelle 1053 and the tower 1052 to rotate the nacelle 1053 around the central axis of the tower 1052 according to the wind direction. The nacelle 1053 supports a main shaft (not shown), and a rotor 1054 having blades 1054a is attached to this main shaft. A generator (not shown) is housed inside the nacelle 1053, and the main shaft of the rotor 1054 is connected to the rotating shaft of the generator via a speed increaser. The nacelle 1053 also houses power equipment for supplying power obtained from the generator to the dynamic cable 1001a, as well as a wind direction and speed meter, and a computer device for communicating with onshore monitoring equipment that monitors the offshore platform 1005. The offshore platform 1005 supplies power to the offshore substation 1006 via the dynamic cable 1001a at a voltage of, for example, 22kV.

[0261] The offshore substation 1006 is equipment that boosts the power transmitted from the offshore platform 1005 at 22kV to 66kV. The power boosted to 66kV at the offshore substation 1006 is supplied to the shore switch station 1007 via the dynamic cable 1001b, the submarine joint 1003, and the submarine cable 1002.

[0262] The dynamic cables 1001a and 1001b are fitted with multiple buoyant intermediate buoys 1004 to ensure a sufficient length between the floating body 1051 and the seabed, so that excessive tension is not generated in the dynamic cables 1001a and 1001b when they are moving around in the sea.

[0263] The submarine joint 1003 is a joint that connects the dynamic cable 1001b, which is connected to the offshore substation 1006, to the submarine cable 1002. The submarine cable 1002 is installed on the seabed and connects the shore switch station 1007 to the submarine joint 1003, and transmits the power sent via the submarine joint 1003 to the shore switch station 1007. The shore switch station 1007 is a facility that opens and closes the power circuit using switches (not shown). The switches in the shore switch station 1007 are connected to overhead power lines, and the power supplied from the offshore substation 1006 is transmitted via the overhead power lines.

[0264] Figure 45 is a cross-sectional view perpendicular to the longitudinal direction of a dynamic cable 1001a, which is an example of a power cable in which an optical fiber cable 10 is housed. The dynamic cable 1001a mainly consists of a power line unit 1110, a sheath 1127 that covers the power line unit 1110 from the outside, and an optical fiber cable 10 in the shape sensing system 100. The power line unit 1110 is a three-core power cable formed by twisting together three power lines 1103. However, the power line unit 1110 may also be a single-core configuration consisting of one power line 1103. The power line 1103 consists of, in order from the center, a conductor 1107, an internal semiconducting layer 1109 provided on the outer circumference of the conductor 1107, an insulating layer 1111 provided on the outer circumference of the internal semiconducting layer 1109, an external semiconducting layer 1113 provided on the outer circumference of the insulating layer 1111, a metal sheath 1115 provided on the outer circumference of the external semiconducting layer 1113, and an internal sheath 1117 provided on the outer circumference of the metal sheath 1115. The dynamic cable 1001a is an example of a power cable in which an optical fiber cable and a power line are integrated.

[0265] Furthermore, the covering 1127 includes a retaining tape 1121, an iron wire armor 1123 made of iron wire, and an outer sheath 1125. Note that the configuration of the power line 1103 and the covering 1127 is not limited to the illustrated example, and some of the illustrated components may be omitted, or other components may be added. For example, the power line 1103 only needs to have at least the conductor 1107 covered with an insulator (including an internal semiconducting layer 1109, an insulating layer 1111, and an outer semiconducting layer 1113).

[0266] A spacer member 1129 is placed in the gap formed between the power line unit 1110 and the sheath 1127. The spacer member 1129 is a member formed, for example, by extrusion molding of resin, and is twisted with the power line unit 1110. The spacer member 1129 is flexible and can be easily bent and twisted. For this reason, it can be easily twisted together with the power line 1103 when manufacturing the dynamic cable 1001a. Furthermore, although the manufactured dynamic cable 1001a is flexible, the spacer member 1129 can easily follow the flexibility of the dynamic cable 1001a. In addition, the spacer member 1129 fills the gap between the power line 1103 and the sheath 1127, maintaining the outer shape of the dynamic cable 1001a. At this time, the spacer member 1129 is resistant to lateral pressure on the dynamic cable 1001a and is less likely to be crushed. Therefore, deformation of the dynamic cable 1001a can be suppressed.

[0267] The spacer member 1129 may be placed in one location as shown in Figure 45, but is not limited to the example shown in Figure 45. It may also be placed in three locations, in each of the gaps between the three power lines 1103. In the gap formed between the power line unit 1110 and the covering 1127, the portion where the spacer member 1129 is not placed may be left empty without other members being placed. For example, an intervening made of polypropylene string may be placed to fill the gap.

[0268] The optical fiber cable 10 of the shape sensing system 100 is placed in the gap 1130a provided by the spacer member 1129. The optical fiber cable 10 is connected to a strain measuring device 20 (not shown). The strain measuring device 20 is connected to a calculation device 30 (not shown). If the dynamic cable 1001a has multiple spacer members 1129, the optical fiber cable 10 may be placed in each of the gaps 1130a of the spacer member 1129, or the optical fiber cable 10 may be placed in at least one gap 1130a. The optical fiber cable 10 may be housed in the gap 1130b between the spacer member 1129 and the power line unit 1110, or in the gap 1130c in the center of the three twisted power lines 1103. Alternatively, the gap between the retaining tape 1121 and the power line unit 1110 may be filled with an intervening made of resin fibers such as polyethylene, and the optical fiber cable 10 may be housed in this intervening, thereby twisting the power line unit 1110 and the optical fiber cable 10 together.

[0269] Note that the dynamic cable 1001b may have the same configuration as the dynamic cable 1001a. Also, the dynamic cables 1001a and 1001b may be the dynamic cable 1001c shown in Figure 46. Figure 46 is a cross-sectional view perpendicular to the longitudinal direction of another example of the dynamic cable 1001c.

[0270] The dynamic cable 1001c consists of a power line unit 1110 and a sheath 1127A that covers the power line unit 1110 from the outside. The dynamic cable 1001c does not have a spacer member 1129, and has iron wire armor 1123a, intervening 1131, base 1132, and base 1133, and differs from the dynamic cable 1001a in that the sheath 1127A has a retaining tape 1121, base 1132, iron wire armor 1123, base 1133, iron wire armor 1123a, and an outer sheath 1125.

[0271] The intervening material 1131 is made of, for example, a polypropylene string and is filled in the gap between the power line unit 1110 and the retaining tape 1121. In the dynamic cable 1001c, the optical fiber cable 10 is arranged inside the intervening material 1131, and the optical fiber cable 10 is twisted with the power line unit 1110. The base 1132 is made of, for example, a plastic string and covers the outer circumference of the retaining tape 1121. Iron wire armor 1123 is arranged on the outer circumference side of the base 1132, and the base 1133 is provided on the outer circumference side of the iron wire armor 1123. The base 1133 is made of, for example, a plastic string. Iron wire armor 1123a made of iron wire is arranged on the outer circumference side of the base 1133. That is, in the dynamic cable 1001c, the iron wire armor is doubled with the base 1133 in between. The outer periphery of the wire armor 1123a is covered with an outer sheath 1125.

[0272] The dynamic cable 1001c may also be configured to include a spacer member 1129, similar to the dynamic cable 1001a. When the dynamic cable 1001c includes a spacer member 1129, the optical fiber cable 10 is placed in the gap 1130a provided by the spacer member 1129.

[0273] In Figures 45 and 46, the optical fiber cable 10 is positioned inside the sheath 1127, but the position in which the optical fiber cable 10 is positioned is not limited to the positions shown. Figure 47 shows an example of the position in which the optical fiber cable 10 is positioned. For example, as shown in Figure 47, the optical fiber cable 10 may be positioned outside the outer sheath 1125. Alternatively, as shown in Figure 47, the optical fiber cable 10 may be positioned between the outer and inner surfaces of the outer sheath 1125. Furthermore, as shown in Figure 47, the optical fiber cable 10 may be positioned between the retaining tape 1121 and the outer sheath 1125.

[0274] In the offshore wind power generation system SYS1000 shown in Figure 44, the radius of curvature at each position in the longitudinal direction of the optical fiber cable 10 can be determined using the optical fiber cable 10 arranged in dynamic cables 1001a and 1001b.

[0275] Note that since the optical fiber cable 10 is twisted together with three power line units 1110 by the dynamic cable 1001a, the bending radius at the center of the dynamic cable 1001a is different from the bending radius of the optical fiber cable 10. The maximum bending radius of the optical fiber cable 10 associated with the twisting in the dynamic cable 1001a, that is, the maximum bending radius of the optical fiber cable 10 when the dynamic cable 1001a is in a straight state, is denoted as R ｍｕ , the bending radius of the dynamic cable 1001a is denoted as R ｃ , the maximum bending radius of the optical fiber cable 10 caused by the bending of the dynamic cable 1001a is denoted as R ｍｕｃ . Then, approximately, the following formula (19) holds. Also, by transforming formula (19), formula (20) can be obtained.

[0276]

[0277] Also, by using the optical fiber cables 10 arranged in the dynamic cables 1001a and 1001b, the three-dimensional coordinates at each position in the longitudinal direction of the optical fiber cable 10 can be obtained.

[0278] Note that since the optical fiber cable 10 is twisted together with three power line units 1110 by the dynamic cable 1001a, the three-dimensional coordinates at the center of the dynamic cable 1001a are different from the three-dimensional coordinates of the optical fiber cable 10. However, by the following calculation method, the three-dimensional coordinates of the central axes of the dynamic cables 1001a and 1001b can be uniquely determined from the three-dimensional coordinates of the optical fiber cable 10.

[0279] Let a point on the central axis of the dynamic cable 1001a at one end, that is, one end of the optical fiber cable 10 (position z = 0, and this point is denoted as Z0), be C0, and assume that the three-dimensional coordinates are known. Also, let the distance from the central axis of the dynamic cable 1001c to the central axis of the optical fiber cable 10 be d ｆｃLet's assume that this is constant along the entire length of the dynamic cable 100a. At this time, let's consider the next data point Z1 in the longitudinal direction of the optical fiber cable 10 from Z0. As shown in the calculation method in Embodiment 2, at measurement points in the longitudinal direction of the optical fiber cable 10, the normal vector N and binormal vector B at that position, along with the three-dimensional coordinates, can be obtained from the relationship in equation (16). Therefore, on the two-dimensional plane formed by the normal vector N and binormal vector B at data point Z1, let's consider a distance d from data point Z1. ｆｃ Consider the circumference of the circle. Then, find the distance from data point Z0 to this circumference and select the point with the shortest distance. This point can be determined as point C1 on the central axis of the dynamic cable at data point Z1. By repeating this process from the next data point Z2 onwards, the coordinates of points on the central axis of the dynamic cable can be determined up to the end of the dynamic cable. Then, calculate the three-dimensional coordinates of the central axis of the dynamic cables 1001a and 1001b corresponding to the position on the central axis of the optical fiber cable 10, and the radius of curvature at that position (coordinate).

[0280] (Application to a seabed exploration system) Figure 48 is a schematic diagram of a seabed exploration system to which the shape sensing system according to the embodiment is applied.

[0281] The SYS2000 seabed exploration system is a seabed exploration system that explores the seabed of the ocean Se, comprising a shape sensing system 100, power cables 2010a and 2010b, an ocean exploration vessel 2020, an unmanned exploration vehicle launcher 2030, and a sub-vehicle vehicle 2040.

[0282] The strain measuring device 20 and the calculation device 30 of the shape sensing system 100 are mounted on the ocean exploration vessel 2020. The power cable 2010a is connected to the strain measuring device 20. The power cable 2010a is also called the primary cable and is relatively long, for example, 10 km in length.

[0283] Launcher 2030 is connected to the ocean exploration vessel 2020 by power cable 2010a. Launcher 2030 is equipped with various exploration devices and has a mechanism for housing, guiding, and recovering vehicle 2040.

[0284] Power cable 2010b is connected to power cable 2010a via launcher 2030. Power cable 2010b is also called a secondary cable and is relatively short in length, for example, 200m.

[0285] Vehicle 2040 is connected to launcher 2030 by power cable 2010b. Vehicle 2040 launches from launcher 2030 and travels near the seabed. Vehicle 2040 is equipped with various exploration devices.

[0286] Power cables 2010a and 2010b are composite cables that have the function of supplying power from the ocean exploration vessel 2020 to the launcher 2030 and vehicle 2040, as well as facilitating communication.

[0287] Figure 49 is a cross-sectional view perpendicular to the longitudinal direction of power cable 2010a in the submarine exploration system SYS2000. Power cable 2010b has the same configuration as power cable 2010a. Power cable 2010a is a composite cable with a circular cross-section and comprises power lines 2011a, 201b, and 2011c, a ground wire 2012, optical fiber lines 2013a and 2013b, an optical fiber cable 10 of the shape sensing system 100, an internal covering layer 2015, a plurality of tension members 2016, an external covering layer 2017, and a filler material 2018. The power lines 2011a, 2011b, 2011c, the ground wire 2012, the optical fiber wires 2013a, 2013b, the inner covering layer 2015, the tension member 2016, the outer covering layer 2017, and the filler material 2018 are structural materials that constitute the structure of the power cable 2010a.

[0288] The power lines 2011a, 2011b, 2011c and the ground wire 2012 are each composed of a stranded wire made of a conductor and an insulating coating made of resin or the like that covers the outer circumference of the stranded wire. The three power lines 2011a, 2011b, and 2011c are twisted spirally in the longitudinal direction. The optical fiber wires 2013a and 2013b are each composed of a glass optical fiber coated with resin or the like, consisting of an optical fiber core and a cladding. Note that the optical fiber wires 2013a and 2013b may each contain multiple coated glass optical fibers.

[0289] The optical fiber cable 10 is arranged spirally around the central axis of the power cable 2010a in the longitudinal direction. The optical fiber cable 10 is also fixed in the longitudinal direction to at least one of the structural materials, such as the power lines 2011a, 2011b, and the internal covering layer 2015, by a filler material 2018.

[0290] In the submarine exploration system SYS2000 shown in Figure 48, the radius of curvature at each longitudinal position of the optical fiber cable 10 contained in the power cables 2010a and 2010b can be determined by the shape sensing system 100.

[0291] Furthermore, since the optical fiber cable 10 is twisted together with three power lines 2011a, 2011b, and 2011c in the power cables 2010a and 2010b, the bending radius of the central axis of the power cables 2010a and 2010b will be different from the bending radius of the optical fiber cable 10. However, even in this case, the radius of curvature of the power cables 2010a and 2010b can be determined from the relationship in equation (20) described above.

[0292] Furthermore, the SYS2000 seabed exploration system can use the shape sensing system 100 to determine the three-dimensional coordinates of each longitudinal position of the optical fiber cable 10 contained in the power cables 2010a and 2010b.

[0293] Since the optical fiber cable 10 is twisted with three power lines 2011a, 2011b, and 2011c in the power cables 2010a and 2010b, the three-dimensional coordinates of the central axes of the power cables 2010a and 2010b are different from the three-dimensional coordinates of the optical fiber cable 10. However, using the same method as in the case of the offshore wind power generation system SYS1000 described above, the three-dimensional coordinates of the central axes of the power cables 2010a and 2010b can be uniquely determined from the three-dimensional coordinates of the optical fiber cable 10.

[0294] Furthermore, the optical fiber cable 10 can also be installed so as to coincide with the central axis of the power cables 2010a and 2010b in the longitudinal direction. In this case, the optical fiber cable 10 will always be located in a position that coincides with the central axis of the power cables 2010a and 2010b in the longitudinal direction. In this case, since the central axes of the power cables 2010a and 2010b coincide with the optical fiber cable 10, the radius of curvature and three-dimensional coordinates of the optical fiber cable 10 will coincide with the radius of curvature and three-dimensional coordinates of the central axes of the power cables 2010a and 2010b.

[0295] In Embodiment 1 described above, the number of optical fibers included in the optical fiber ribbon is 5, but any other number is acceptable, and one optical fiber at the center in the width direction of the optical fiber ribbon can be used as the target for strain measurement. Similarly, in Embodiment 3 described above, the number of optical fibers included in the optical fiber ribbon is 4, but any other number is acceptable, and two optical fibers located symmetrically with respect to the center in the width direction of the optical fiber ribbon can be used as the targets for strain measurement.

[0296] Furthermore, the present invention is not limited by the embodiments described above. Configurations that appropriately combine the above-described components are also included in the present invention. Moreover, further effects and modifications can be easily derived by those skilled in the art. Therefore, broader aspects of the present invention are not limited to the embodiments described above, and various modifications are possible.

[0297] 10, 10A, 10B, 10C, 10D, 10E, 10F, 10G, 10H, 10I, 10J, 10K: Fiber optic cable 11, 11F, 11N, 11O: Cable body 11a, 2016: Tension member 11b: Slot material 11b1, 11b2, 11b3, 11b4, 11b5: Slot 11c, 11ca, 11cb, 11cc, 11Fc, 11Fca, 11Fcb, 11Fcc: Fiber optic ribbon core 11c1, 11c1a, 11c1a', 11c1aa, 11c1ab, 11c1b, 11c1c, 11c1c', 11Fc1, 11Fc1aa, 11Fc1ab, 11Fc1ba, 11Fc1bb, 11Fc1ca, 11Fc1cb, 11Fcab: Optical fiber 11c2: Tape coating 11d, 2017: Outer coating layer 11e: Fixing member 11f: Jelly 12, 12A, 12B, 12C, 12D, 12E, 12F, 12G, 12H, 12I, 12J, 12K: Input end 12a, 12f, 12g, 13b, 13c, 13d, 13e, 40, 41, 42: Connecting optical fiber 12b, 12c, 12d, 12h, 12i, 12j: Optical switches 12e, 13a: Non-reflective ends 13, 13A, 13B, 13C, 13D, 13F, 13H, 13I: Far ends 20, 20A: Strain measurement devices 30, 30B, 30F, 30H: Calculation units 50: Temperature distribution measurement devices 100, 100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I, 100J, 100K, 100L, 100M: Shape sensing systems 100a, 1001a, 1001b, 1001c: Dynamic cables 201b, 1103, 2011a, 2011b, 2011c: Power lines 1002: Submarine cable 1003: Submarine joint 1004: Intermediate buoy 1005,10055: Offshore platform 1006: Offshore substation 1007: Land switch station 1051: Floating body 1052: Tower 1053: Nacelle 1054: Rotor 1054a: Blade 1055: Tendon 1056: Foundation 1107: Conductor 1109: Internal semiconducting layer 1110: Power line unit 1111: Insulating layer 1113: External semiconducting layer 1115: Metal sheath 1117: Internal sheath 1121: Retaining tape 1123, 1123a: Iron wire armor 1125: External sheath 1127, 1127A: Covering 1129: Spacer member 1130a, 1130b, 1130c: Gap 1131: Interposition 1132, 1133: Seat 2010a, 2010b: Power cable; 2012: Grounding wire; 2013a, 2013b: Optical fiber wire; 2015: Inner sheathing layer; 2018: Filling material; 2020: Ocean exploration vessel; 2030: Launcher; 2040: Vehicle; SYS1000: Offshore wind power generation system; SYS2000: Seabed exploration system.

Claims

1. A cable shape sensing system comprising: an optical fiber cable comprising an optical fiber ribbon core containing a plurality of optical fibers and a slot material formed such that the slots are twisted in the longitudinal direction, wherein the optical fiber ribbon core is housed in the slots; a strain measuring device for measuring the amount of strain at each position in the longitudinal direction of one optical fiber located at the center in the width direction or two optical fibers located symmetrically with respect to the center in the width direction among the plurality of optical fibers contained in the optical fiber ribbon core; and a calculation device for calculating the radius of curvature at each position in the longitudinal direction of the optical fiber cable based on the measured amount of strain.

2. The cable shape sensing system according to claim 1, wherein the strain measuring device measures the amount of strain at each position in the longitudinal direction of the single optical fiber, and the calculation device calculates the radius of curvature at each position in the longitudinal direction of the optical fiber cable using the following formula (1-1). However, ηa: strain reduction coefficient (0 ≤ ηa ≤ 1) m: strain confinement coefficient p: slot twist pitch d: distance from the center of the optical fiber cable to the center of the optical fiber ribbon core z: position in the longitudinal direction of the optical fiber cable n: integer ε(z): measured amount of strain in the optical fiber at position z R(z): radius of curvature of the optical fiber cable at position z 3. The cable shape sensing system according to claim 2, wherein the strain measuring device measures the amount of strain at each position in the longitudinal direction of the single optical fiber, the calculation device calculates the curvature vector and twist ratio at each position in the longitudinal direction of the optical fiber cable using formula (1-1) based on the measured amount of strain, and calculates the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction based on the curvature vector and the twist ratio.

4. The optical fiber cable comprises a plurality of optical fiber ribbon cores and a slot material having a plurality of slots formed on it at different positions in the circumferential direction of the slot material, the strain measuring device measures the amount of strain at each position in the longitudinal direction of one optical fiber contained in each of two or more optical fiber ribbon cores housed in different slots, the calculation device calculates a curvature vector and a twist ratio at each position in the longitudinal direction of the optical fiber cable based on the measured amount of strain, and calculates the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction based on the curvature vector and the twist ratio, the cable shape sensing system according to claim 2.

5. The cable shape sensing system according to claim 1, wherein the strain measuring device measures the amount of strain at each position in the longitudinal direction of the two optical fibers, and the calculation device calculates the radius of curvature at each position in the longitudinal direction of the optical fiber cable using the following formula (1-2). However, k: the number of optical fibers in the optical fiber ribbon, i: the position of one of the optical fibers to be measured within the optical fiber ribbon (i = 1 for the outermost optical fiber: 1 ≤ i ≤ k) η b　　　　 : Strain reduction coefficient (0 ≤ η) b ≤1) m: strain confinement coefficient p: twist pitch of slots z: position in the longitudinal direction of the optical fiber cable d ｆ　　　　 : Distance between adjacent optical fibers within the optical fiber ribbon core n: Integer ε(z): Difference in the amount of strain of the optical fiber measured at position z R(z): Radius of curvature of the optical fiber cable at position z 6. The cable shape sensing system according to claim 1, wherein the strain measuring device measures the amount of strain at each position in the longitudinal direction of the two optical fibers, and the calculation device calculates the radius of curvature at each position in the longitudinal direction of the optical fiber cable using the following formula (1-3). However, k: the number of optical fibers in the optical fiber ribbon, i: the position of one of the optical fibers to be measured within the optical fiber ribbon (i = 1 for the outermost optical fiber: 1 ≤ i ≤ k) η a　　　　 : Strain reduction coefficient (0 ≤ η) a ≤1) m: strain confinement coefficient p: twist pitch of slots z: position in the longitudinal direction of the optical fiber cable d: distance from the center of the optical fiber cable to the center of the optical fiber ribbon core d ｆ　　　　 : Distance between adjacent optical fibers in the optical fiber ribbon core n: Integer ε(z): Sum of the measured strain amounts of the optical fibers at position z R(z): Radius of curvature of the optical fiber cable at position z 7. The cable shape sensing system according to claim 5 or 6, wherein the strain measuring device measures the amount of strain at each position in the longitudinal direction of the two optical fibers, the calculation device calculates the curvature vector and twist ratio at each position in the longitudinal direction of the optical fiber cable using formula (1-2) or (1-3) based on the measured amount of strain, and calculates the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction based on the curvature vector and the twist ratio.

8. The optical fiber cable comprises a plurality of optical fiber ribbon cores and a slot material having a plurality of slots formed on it at different positions in the circumferential direction of the slot material, the strain measuring device measures the amount of strain at each longitudinal position of the two optical fibers contained in each of the two or more optical fiber ribbon cores housed in different slots, the calculation device calculates the curvature vector and twist ratio at each longitudinal position of the optical fiber cable based on ε(z), and calculates the three-dimensional coordinates of the central axis of the optical fiber cable at each longitudinal position based on the curvature vector and twist ratio, the cable shape sensing system according to claim 5 or 6.

9. The cable shape sensing system according to any one of claims 3, 4, 7, and 8, wherein the computing device calculates the curvature vector at each position in the longitudinal direction of the optical fiber cable and the twist angle of the cable itself based on the measured amount of strain, and calculates the three-dimensional coordinates of the central axis of the optical fiber cable at each position in the longitudinal direction based on the twist ratio corrected by the twist angle.

10. The calculation device calculates f based on the measured amount of strain. １ The period f is determined by ≤ 1 / 10P (where P is the twist pitch of the slots). １ The cable shape sensing system according to claim 9, which extracts the following fluctuating components and converts the fluctuating components of the strain amount into the twist angle of the cable itself.

11. The arithmetic unit extracts a variation component in a section from f １ to f determined by f ≦ 1 / 10P (where P is the twist pitch of the slot), and f １ to f determined by f < f ２ and converts the variation component of the amount of strain into the twist angle of the cable itself. The cable shape sensing system according to claim 9 １ wherein the variation component of the amount of strain is converted into the twist angle of the cable itself. The cable shape sensing system according to claim 9 ２ wherein the variation component of the amount of strain is converted into the twist angle of the cable itself. The cable shape sensing system according to claim 9 ２ to f １ and converts the variation component of the amount of strain into the twist angle of the cable itself. The cable shape sensing system according to claim 9 12. The cable shape sensing system according to claim 9, wherein the strain measuring device measures the amount of strain at each longitudinal position of an optical fiber in another tape core in a slot containing the optical fiber to be measured, and the calculation device calculates the twist angle of the cable itself based on the difference in the amount of strain measured in optical fibers in different tape cores in the same slot.

13. The optical fiber cable is further comprising a plurality of fixing members that intermittently fix the optical fiber ribbon cores in the slots in the longitudinal direction, as described in claim 1.

14. The cable shape sensing system according to claim 1, wherein the optical fiber cable comprises jelly that fills the slot.

15. The cable shape sensing system according to claim 1, comprising a temperature distribution measuring device for measuring the temperature distribution in the longitudinal direction of the optical fiber contained in the optical fiber ribbon core, wherein the computing device corrects the measured amount of strain based on the measured temperature distribution.

16. The cable shape sensing system according to claim 15, wherein the strain measuring device or the temperature distribution measuring device performs measurements using light scattering in the optical fiber to be measured, and the optical fiber to be measured has a scattered light increasing function.

17. The cable shape sensing system according to any one of claims 1 to 16, wherein the strain measuring device detects Brillouin scattered light generated in the optical fiber, and the optical fiber to be measured has a core made of pure silica.

18. The optical fiber cable is housed in a power cable, and the computing device calculates the radius of curvature at each position in the longitudinal direction of the power cable based on the calculated radius of curvature of the optical fiber cable. The cable shape sensing system according to any one of claims 1, 2, 5, 6, 11, 12, 13, 14, and 15.

19. The optical fiber cable is housed in a power cable, and the computing device calculates the three-dimensional coordinates of the central axis of the power cable at each longitudinal position based on the three-dimensional coordinates of the optical fiber cable calculated above, the cable shape sensing system according to any one of claims 3, 4, 7, 8, 9, 10, 11, and 12.

20. A power cable comprising an optical fiber ribbon core containing multiple optical fibers and a slot material formed such that the slots are twisted in the longitudinal direction, wherein the optical fiber ribbon core is housed in the slots and the power cable is integrated with the optical fiber cable and power line.

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