Reconstruction method of seven-core fiber distributed sensing shape sensor based on weighted average update framework

Abstract

The seven-core fiber optic distributed sensing shape sensor reconstruction method based on a weighted average update framework belongs to the field of precision instrument manufacturing and measurement technology. This method, based on a weighted average of reconstructed coordinate points, utilizes redundant information to adjust the minimum rotation frame, unifying the minimum rotation frame at each reconstruction point. This reduces the impact of the fiber optic sensing system on coordinate point reconstruction and the reconstruction frame, thereby improving the accuracy of shape sensing. Furthermore, this invention achieves accuracy improvement through data processing alone without changing the hardware, offering significant economic benefits.

Description

Technical Field

[0001] This invention belongs to the field of precision instrument manufacturing and measurement technology, and relates to a reconstruction method for a seven-core fiber optic distributed sensing shape sensor based on a weighted average update framework. Background Technology

[0002] In recent years, online testing technology for curves and surfaces has received increasing attention in fields such as medicine, aerospace, soft robotics, and smart structures. To achieve accurate shape control and high-precision spatial positioning, precise measurement of the three-dimensional shape and curve coordinates of the structure is required. Therefore, there is an urgent need for a sensing technology capable of efficiently measuring the shape of three-dimensional curves. Shape sensors based on multi-core optical fibers are characterized by their small size and high precision, but they are susceptible to the measurement accuracy and noise of fiber optic sensing systems, and their shape measurement accuracy needs improvement.

[0003] Currently, the main methods for 3D curve reconstruction include the following:

[0004] 1. Jason P. Moore of NASA Research Center first used the Frenet frame for the reconstruction of three-dimensional curves in space. He used the rate of change of the bending direction as the torsion and combined it with the curvature as the input parameter of the Frenet frame. By solving the differential equation, he obtained the three-dimensional tangent vector, normal vector and binormal vector of each small fiber segment. Then he integrated the tangent vector to obtain the three-dimensional spatial coordinates of the fiber.

[0005] 2. Zeng Jie et al. from Nanjing University of Aeronautics and Astronautics proposed using a minimum rotation frame to reconstruct three-dimensional curves in space. They used curvature and curvature direction to describe the tangent vector, the first normal vector, and the second normal vector, eliminating the need for torsion calculation. Compared with the Frenet frame, the minimum rotation frame has higher curve reconstruction accuracy and does not have the reconstruction fallacy caused by zero curvature.

[0006] In summary, shape sensors based on the multi-core fiber principle have advantages such as strong applicability, high accuracy, and long sensing distance, and have been widely used. However, some problems still exist:

[0007] 1. The accuracy and noise of fiber optic sensing systems directly affect the accuracy of shape sensing. Conventional methods can only suppress the influence of Gaussian noise, and the error on the frame accumulates continuously with the sensing length.

[0008] 2. The Frenet framework cannot overcome the problem of the principal normal vector being instantly reversed due to the curvature being zero, which will result in a reconstruction error and cause the shape reconstruction after the reconstruction error to be completely wrong. Summary of the Invention

[0009] The purpose of this invention is to propose a high-precision, noise-resistant shape reconstruction method based on a multi-core fiber optic shape sensor, suppressing the impact of fiber optic sensing system noise on shape reconstruction accuracy. This invention proposes a seven-core fiber optic distributed sensing shape sensor reconstruction method based on a weighted average update framework. Utilizing the redundant sensing information inherent in the seven-core fiber, it employs a weighted point-by-point averaging approach to continuously update the minimum rotation framework, suppressing the impact of fiber optic sensing system noise on shape reconstruction accuracy. This method more effectively suppresses noise and reduces accumulated errors than traditional shape reconstruction methods. Without altering the existing multi-core fiber optic shape sensing system, this method significantly improves the shape sensing accuracy of the seven-core fiber optic sensor through data processing alone.

[0010] The working principle of this invention is to accurately solve the reconstructed coordinates by using the redundant sensing information of the seven-core optical fiber and the weighted average of the reconstructed three-dimensional coordinate points, and then re-solve the T vector of the minimum rotation frame using the accurate reconstructed coordinates. Based on the rotation angle and rotation axis between the T vector and the T vector in the previous iteration, the N1 and N2 vectors of the minimum rotation frame are adjusted in real time, thereby improving the accuracy of the reconstructed frame, reducing the influence of noise in the optical fiber sensing system, and realizing the unification of the redundant minimum rotation frames at each reconstruction point, which can achieve high-precision shape sensing.

[0011] The technical solution of this invention is: a reconstruction method for a seven-core fiber optic distributed sensing shape sensor based on a weighted average update framework. The seven-core fiber optic shape sensor contains seven fiber cores: fiber core 1, fiber core 2, fiber core 3, fiber core 4, fiber core 5, fiber core 6, and fiber core 7. Fiber cores 1, 2, 3, 4, 5, and 6 are evenly distributed in a 60° ring on the cross-section of the seven-core fiber optic shape sensor, with a consistent fiber spacing. If the angle of fiber core 1 is taken as 0°, then the angles of fiber cores 2, 3, 4, and 5 are 60°, 120°, and 120°, respectively. At 180°, 240°, and 300°, fiber core seven is located at the center of the cross-section of the seven-core fiber shape sensor. The seven-core fiber shape sensor is divided into three components based on its length region: a non-shape sensing part, a shape sensing initiation end, and a shape sensing part. During sensing, the seven-core fiber shape sensor near the shape sensing initiation end must be a straight line. The Z-axis of the initial coordinate frame for shape reconstruction coincides with the straight line, with its positive direction pointing from the shape sensing initiation end to the shape sensing part. The X-axis of the initial coordinate frame for shape reconstruction points from fiber core seven to fiber core one. The Y-axis of the initial coordinate frame for shape reconstruction... The initial minimum rotation frame is perpendicular to the X-axis and Z-axis respectively and satisfies a right-handed coordinate system. It coincides with the initial coordinate frame of the shape reconstruction, with the T vector of the initial minimum rotation frame being a unit vector in the Z-axis direction, the N1 vector of the initial minimum rotation frame being a unit vector in the X-axis direction, and the N2 vector of the initial minimum rotation frame being a unit vector in the Y-axis direction. The non-shape sensing part of the seven-core fiber optic shape sensor is connected to a seven-channel optical frequency domain distributed fiber optic sensing device. The seven-channel optical frequency domain distributed fiber optic sensing device acquires the distributed strain data of the seven fiber cores within the shape sensing part of the seven-core fiber optic shape sensor. Wherein, distributed strain data 1 corresponds to fiber core 1, distributed strain data 2 corresponds to fiber core 2, distributed strain data 3 corresponds to fiber core 3, distributed strain data 4 corresponds to fiber core 4, distributed strain data 5 corresponds to fiber core 5, distributed strain data 6 corresponds to fiber core 6, and distributed strain data 7 corresponds to fiber core 7. The spatial resolution of the sensing points of the seven-channel optical frequency domain distributed fiber optic sensing device is the length interval of each sensing point on the seven-core fiber optic shape sensor. Then, the data is processed according to the following steps to reconstruct the sensing shape of the shape sensing part of the seven-core fiber optic shape sensor, thereby realizing the shape sensing of the seven-core fiber optic shape sensor:

[0012] Step 1: Group the distributed strain data 1, 2, 3, 4, 5, 6, and 7 into a total of nine distributed strain combinations, as follows:

[0013] Distributed strain combination one: Strain data one, strain data three, strain data five.

[0014] Distributed strain combination two: strain data two, strain data four, strain data six.

[0015] Distributed strain combination three: Strain data one, strain data two, strain data three.

[0016] Distributed strain combination four: Strain data two, strain data three, strain data four.

[0017] Distributed strain combination five: Strain data three, strain data four, strain data five.

[0018] Distributed strain combination six: Strain data four, strain data five, strain data six.

[0019] Distributed strain combination seven: Strain data one, strain data five, strain data six.

[0020] Distributed strain combination eight: Strain data one, strain data two, strain data six.

[0021] Distributed strain combination nine: Strain data one, strain data two, strain data three, strain data four, strain data five, strain data six.

[0022] Calculate the apparent curvature vector K at each sensing point for each of the nine sets of distributed strain combinations. ij The apparent curvature vector K ij =[K1 ij K2 ij ], i = 1, 2, 3…N, where N is the number of sensing points for distributed strain data, j = 1, 2, 3…9, corresponding to nine distributed strain combinations. Distributed strain combination one to distributed strain combination eight are calculated according to the following formula:

[0023]

[0024] Among them, e iα e iβ e iΓ For the three fiber core strain data at the i-th sensing point in the corresponding combination, α, β, and γ are the distribution angles of the three corresponding fiber cores on the cross-section of the seven-core fiber shape sensor, r is the fiber core pitch, and e i7 The strain data at the i-th sensing point is shown in Figure 7.

[0025] The distributed strain combination nine is calculated using the following formula:

[0026]

[0027] Among them, e i1 e i2 e i3 …e i7 For strain data one to strain data seven, r is the fiber core distance;

[0028] Step 2: Utilize T of the i-th sensing point ij Vector and reconstructed coordinates R(x) i ,y i ,z i The reconstructed coordinates of the nine distributed strain combinations at the (i+1)th sensing point were obtained:

[0029] R(x (i+1)j ,y (i+1)j ,z (i+1)j ) = T ij Δs+R(x i ,y i ,z i ),

[0030] Where Δs is the spatial resolution of the sensing points, i = 1, 3…N, and N is the number of sensing points for the distributed strain data. In the first iteration, the T vector of the initial minimum rotating frame is used as T. 1j j = 1, 2...9, corresponding to nine strain distribution combinations, R(x i ,y i ,z i Let R(x1,y1,z1) be the reconstructed coordinates of the i-th sensing point. In the first iteration, R(x1,y1,z1) = [0,0,0].

[0031] Step 3: Calculate the reconstructed coordinates R(x) of the nine strain distribution combinations for the i-th sensing point in Step 2. (i+1)j ,y (i+1)j ,z (i+1)j (Average) The reconstructed coordinates R(x) of the (i+1)th sensing point obtained in step 2 are obtained from the nine distribution strain combinations. (i+1)j ,y (i+1)j ,z (i+1)j The average value of the reconstructed coordinates of the (i+1)th sensing point and the nine distributed strain combinations. Calculate the magnitude ΔR of the reconstructed coordinate error (i+1)j The calculation method is as follows: Where i = 1, 2...N, N is the number of sensing points for distributed strain data, and j = 1, 2...9, corresponding to nine combinations of distributed strain;

[0032] Step 4: Calculate the magnitude ΔR of the reconstructed coordinate error from Step 3. (i+1)j Sort from largest to smallest, the new sequence order is I. (i+1)s The magnitude of the corresponding reconstructed coordinate error is ΔR. (i+1)s Where s = 1, 2...9, then a weighted average of the reconstructed coordinates is performed, in the new sequence order I. (i+1)s Select the sequence order corresponding to the third to ninth positions from I. (i+1)ss = 3, 4...9, and calculate the weighted average of the reconstructed coordinates of the (i+1)th sensing point. And The reconstructed coordinates R(x) of the (i+1)th sensing point i+1 ,y i+1 ,z i+1 ):

[0033]

[0034] Where i = 1, 2...N, and N is the number of sensing points for the distributed strain data.

[0035] Step 5: Reconstruct the coordinates R(x) using the (i+1)th sensor point. i+1 ,y i+1 ,z i+1 The reconstructed coordinates R(x) of the i-th sensing point and the reconstructed coordinates of the i-th i ,y i ,z i ), recalculate the minimum rotation frame [T'] for the i-th sensing point. i N1' i N2' i First calculate Then, Tadj is calculated using the vector cross product. i To T' i rotation angle α i and rotation axis c i , N1adj i With N2adj i Respectively around the axis of rotation c i Rotation angle α i Obtain N1' i and N2' i , where i = 1, 2...N, and N is the number of sensing points for distributed strain data. In the first iteration, the initial minimum rotating frame (205) is used as the adjusted minimum rotating frame [Tadj1, N1adj1, N2adj1].

[0036] Step 6: Resolve the minimum rotation frame [T] for the (i+1)th sensing point using the differential equation form of the minimum rotation frame. (i+1)j N1 (i+1)j N2 (i+1)j ], and recalculate the minimum rotating frame [T'] using the i-th sensing point. i N1' i N2' i As the initial value for the differential equation, the differential equation of the minimum rotating frame is in the form of:

[0037]

[0038] Where i = 1, 2...N, N is the number of sensing points for distributed strain data, and j = 1, 2...9, corresponding to nine combinations of distributed strain;

[0039] Step 7: Utilize the new sequence order I from step 4. (i+1)s For the minimum rotation frame [T] of the (i+1)th sensing point in step 6 (i+1)j N1 (i+1)j N2 (i+1)j Sort the sequences, and the new sequence is [T]. (i+1)s N1 (i+1)s N2 (i+1)s ], in the new sequence order I (i+1)s The minimum rotating frame [T] corresponding to the (i+1)th sensing point from the seventh to the ninth position is selected. (i+1)s N1 (i+1)s N2 (i+1)s ], where s = 7, 8, 9, calculate the average value of the minimum rotating frame for the (i+1)th sensing point:

[0040]

[0041] Where i = 1, 2…N, and N is the number of sensing points for distributed strain data. The minimum rotation frame after adjustment of the (i+1)th sensing point [Tadj] i+1 N1adj i+1 N2adj i+1 ];

[0042] Step 8: Repeat steps 2 through 7 until the reconstructed coordinates R(x) of all sensor points are obtained. i ,y i ,z i ), where i = 1, 2...N, and N is the number of sensing points for distributed strain data.

[0043] The advantages of this invention are:

[0044] 1. This invention can achieve averaging of the reconstructed coordinate frame and adjust the minimum rotation frame using redundant information, thereby unifying the minimum rotation frame of each reconstructed point, reducing the impact of the fiber optic sensing system on coordinate point reconstruction and the reconstructed frame, and thus improving the accuracy of shape sensing.

[0045] 2. This invention achieves improved accuracy through data processing alone without changing the hardware, resulting in significant economic benefits. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of a seven-core fiber optic distributed sensing shape sensing system based on a weighted average update framework.

[0047] In the figure: 101. Seven-core fiber shape sensor, 102. Fiber core one, 103. Fiber core two, 104. Fiber core three, 105. Fiber core four, 106. Fiber core five, 107. Fiber core six, 108. Fiber core seven, 109. Fiber core pitch, 110. Non-shape sensing part, 111. Shape sensing start end, 112. Shape sensing part, 113. Straight line, 114. Seven-channel optical frequency domain distributed fiber optic sensing device.

[0048] Figure 2 This is a schematic diagram of the initial coordinate frame and the initial minimum rotation frame for shape reconstruction;

[0049] In the figure: 201. Initial coordinate frame for shape reconstruction, 202. Z-axis, 203. X-axis, 204. Y-axis, 205. Initial minimum rotation frame, 206. T vector, 207. N1 vector, 208. N2 vector.

[0050] Figure 3 This is a schematic diagram of the strain distribution data of the seven fiber cores inside a seven-core fiber shape sensor.

[0051] In the figure: 301. Distributed strain data one, 302. Distributed strain data two, 303. Distributed strain data three, 304. Distributed strain data four, 305. Distributed strain data five, 306. Distributed strain data six, 307. Distributed strain data seven. Detailed Implementation

[0052] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings:

[0053] A reconstruction method for a seven-core fiber optic distributed sensing shape sensor based on a weighted average update framework is presented. The seven-core fiber optic shape sensor 101 contains seven fiber cores: fiber core 102, fiber core 103, fiber core 104, fiber core 105, fiber core 106, fiber core 107, and fiber core 108. Fiber cores 102, 103, 104, 105, 106, and 107 are evenly distributed in a 60° ring on the cross-section of the seven-core fiber optic shape sensor 101, with a consistent fiber core spacing of 109. If the angle of fiber core 102 is taken as 0°, then the angles of fiber cores 103, 104, 105, 106, and 108 are 60°, 120°, 109, 100° ... At 80°, 240°, and 300°, fiber core 7 108 is located at the center of the cross-section of the seven-core fiber shape sensor 101. The seven-core fiber shape sensor 101 is divided into three parts according to its length region: a non-shape sensing part 110, a shape sensing start end 111, and a shape sensing part 112. During sensing, the seven-core fiber shape sensor 101 near the shape sensing start end 111 must be a straight line 113. The Z-axis 202 of the initial coordinate frame 201 for shape reconstruction coincides with the straight line 113, and its positive direction is from the shape sensing start end 111 to the shape sensing part 112. The X-axis 203 of the initial coordinate frame 201 for shape reconstruction is from fiber core 7 108 to fiber core 102. The Y-axis 204 direction is perpendicular to the X-axis 203 and Z-axis 202 respectively and satisfies the right-hand coordinate system. The initial minimum rotation frame 205 coincides with the initial coordinate frame 201 of shape reconstruction, and the T vector 206 of the initial minimum rotation frame 205 is a unit vector in the Z-axis 202 direction. The N1 vector 207 of the initial minimum rotation frame 205 is a unit vector in the X-axis 203 direction, and the N2 vector 208 of the initial minimum rotation frame 205 is a unit vector in the Y-axis 204 direction. The non-shape sensing part 110 of the seven-core fiber shape sensor 101 is connected to the seven-channel optical frequency domain distributed fiber optic sensing device 114. The seven-channel optical frequency domain distributed fiber optic sensing device 114 collects data from the shape sensing part 112 inside the seven-core fiber shape sensor 101. The distributed strain data of the seven fiber cores are as follows: distributed strain data 1 (301) corresponds to fiber core 1 (102), distributed strain data 2 (302) corresponds to fiber core 2 (103), distributed strain data 3 (303) corresponds to fiber core 3 (104), distributed strain data 4 (304) corresponds to fiber core 4 (105), distributed strain data 5 (305) corresponds to fiber core 5 (106), distributed strain data 6 (306) corresponds to fiber core 6 (107), and distributed strain data 7 (307) corresponds to fiber core 7 (108). The spatial resolution 115 of the sensing points of the seven-channel optical frequency domain distributed optical fiber sensing device 114 is the length interval of each sensing point on the seven-core optical fiber shape sensor 101. Then, data processing is performed according to the following steps to reconstruct the sensing shape of the shape sensing part 112 of the seven-core optical fiber shape sensor 101.Achieving shape sensing using the seven-core fiber optic shape sensor 101:

[0054] Step 1: Group the distributed strain data 1 (301), distributed strain data 2 (302), distributed strain data 3 (303), distributed strain data 4 (304), distributed strain data 5 (305), distributed strain data 6 (306), and distributed strain data 7 (307) into a total of nine distributed strain combinations, as follows:

[0055] Distributed strain combination one: strain data one 301, strain data three 303, strain data five 305,

[0056] Distributed strain combination two: strain data two 302, strain data four 304, strain data six 306.

[0057] Distributed strain combination three: strain data one 301, strain data two 302, strain data three 303.

[0058] Distributed strain combination four: strain data two 302, strain data three 303, strain data four 304.

[0059] Distributed strain combination five: strain data three 303, strain data four 304, strain data five 305.

[0060] Distributed strain combination six: strain data four 304, strain data five 305, strain data six 306.

[0061] Distributed strain combination seven: strain data one 301, strain data five 305, strain data six 306.

[0062] Distributed strain combination eight: Strain data one 301, strain data two 302, strain data six 306.

[0063] Distributed strain combination nine: Strain data one 301, strain data two 302, strain data three 303, strain data four 304, strain data five 305, strain data six 306.

[0064] Calculate the apparent curvature vector K at each sensing point for each of the nine sets of distributed strain combinations. ij The apparent curvature vector K ij =[K1 ij K2 ij ], i = 1, 2, 3…N, where N is the number of sensing points for distributed strain data, j = 1, 2, 3…9, corresponding to nine distributed strain combinations. Distributed strain combination one to distributed strain combination eight are calculated according to the following formula:

[0065]

[0066] Among them, e iα eiβ e iΓ For the three fiber core strain data at the i-th sensing point position in the corresponding combination, α, β, and γ are the distribution angles of the three corresponding fiber cores on the cross section of the seven-core fiber shape sensor 101, r is the fiber core pitch 109, and e i7 The strain data at the i-th sensing point is 7307.

[0067] The distributed strain combination nine is calculated using the following formula:

[0068]

[0069] Among them, e i1 e i2 e i3 …e i7 For strain data 1-301 to strain data 7-307, r is the fiber core distance 109;

[0070] Step 2: Utilize T of the i-th sensing point ij Vector and reconstructed coordinates R(x) i ,y i ,z i The reconstructed coordinates of the nine distributed strain combinations at the (i+1)th sensing point were obtained:

[0071] R(x (i+1)j ,y (i+1)j ,z (i+1)j ) = T ij Δs+R(x i ,y i ,z i ),

[0072] Where Δs is the spatial resolution of the sensing points (115), i = 1, 3...N, and N is the number of sensing points for the distributed strain data. In the first iteration, the T vector (206) of the initial minimum rotating frame (205) is used as T. 1j j = 1, 2...9, corresponding to nine strain distribution combinations, R(x i ,y i ,z i Let R(x1,y1,z1) be the reconstructed coordinates of the i-th sensing point. In the first iteration, R(x1,y1,z1) = [0,0,0].

[0073] Step 3: Calculate the reconstructed coordinates R(x) of the nine strain distribution combinations for the i-th sensing point in Step 2. (i+1)j ,y (i+1)j ,z (i+1)j (Average) The reconstructed coordinates R(x) of the (i+1)th sensing point obtained in step 2 are obtained from the nine distribution strain combinations. (i+1)j ,y (i+1)j ,z(i+1)j The average value of the reconstructed coordinates of the (i+1)th sensing point and the nine distributed strain combinations. Calculate the magnitude ΔR of the reconstructed coordinate error (i+1)j The calculation method is as follows: Where i = 1, 2...N, N is the number of sensing points for distributed strain data, and j = 1, 2...9, corresponding to nine combinations of distributed strain;

[0074] Step 4: Calculate the magnitude ΔR of the reconstructed coordinate error from Step 3. (i+1)j Sort from largest to smallest, the new sequence order is I. (i+1)s The magnitude of the corresponding reconstructed coordinate error is ΔR. (i+1)s Where s = 1, 2...9, then a weighted average of the reconstructed coordinates is performed, in the new sequence order I. (i+1)s Select the sequence order corresponding to the third to ninth positions from I. (i+1)s s = 3, 4...9, and calculate the weighted average of the reconstructed coordinates of the (i+1)th sensing point. And The reconstructed coordinates R(x) of the (i+1)th sensing point i+1 ,y i+1 ,z i+1 ):

[0075]

[0076] Where i = 1, 2...N, and N is the number of sensing points for the distributed strain data.

[0077] Step 5: Reconstruct the coordinates R(x) using the (i+1)th sensor point. i+1 ,y i+1 ,z i+1 The reconstructed coordinates R(x) of the i-th sensing point and the reconstructed coordinates of the i-th i ,y i ,z i ), recalculate the minimum rotation frame [T'] for the i-th sensing point. i N1' i N2' i First calculate Then, Tadj is calculated using the vector cross product. i To T' i rotation angle α i and rotation axis c i , N1adj i With N2adj i Respectively around the axis of rotation c i Rotation angle α i Obtain N1' i and N2' i, where i = 1, 2...N, and N is the number of sensing points for distributed strain data. In the first iteration, the initial minimum rotating frame (205) is used as the adjusted minimum rotating frame [Tadj1, N1adj1, N2adj1].

[0078] Step 6: Resolve the minimum rotation frame [T] for the (i+1)th sensing point using the differential equation form of the minimum rotation frame. (i+1)j N1 (i+1)j N2 (i+1)j ], and recalculate the minimum rotating frame [T'] using the i-th sensing point. i N1' i N2' i As the initial value for the differential equation, the differential equation of the minimum rotating frame is in the form of:

[0079]

[0080] Where i = 1, 2...N, N is the number of sensing points for distributed strain data, and j = 1, 2...9, corresponding to nine combinations of distributed strain;

[0081] Step 7: Utilize the new sequence order I from step 4. (i+1)s For the minimum rotation frame [T] of the (i+1)th sensing point in step 6 (i+1)j N1 (i+1)j N2 (i+1)j Sort the sequences, and the new sequence is [T]. (i+1)s N1 (i+1)s N2 (i+1)s ], in the new sequence order I (i+1)s The minimum rotating frame [T] corresponding to the (i+1)th sensing point from the seventh to the ninth position is selected. (i+1)s N1 (i+1)s N2 (i+1)s ], where s = 7, 8, 9, calculate the average value of the minimum rotating frame for the (i+1)th sensing point:

[0082]

[0083] Where i = 1, 2…N, and N is the number of sensing points for distributed strain data. The minimum rotation frame after adjustment of the (i+1)th sensing point [Tadj] i+1 N1adj i+1 N2adj i+1 ];

[0084] Step 8: Repeat steps 2 through 7 until the reconstructed coordinates R(x) of all sensor points are obtained. i ,y i ,z i), where i = 1, 2...N, and N is the number of sensing points for distributed strain data.

[0085] The working process of this invention is as follows:

[0086] The seven-channel optical frequency domain distributed fiber optic sensing device 114 acquires the distributed strain data of the seven fiber cores inside the shape sensing part 112 of the seven-core fiber optic shape sensor 101. Distributed strain data 1 (301) corresponds to fiber core 1 (102), distributed strain data 2 (302) corresponds to fiber core 2 (103), distributed strain data 3 (303) corresponds to fiber core 3 (104), distributed strain data 4 (304) corresponds to fiber core 4 (105), distributed strain data 5 (305) corresponds to fiber core 5 (106), distributed strain data 6 (306) corresponds to fiber core 6 (107), and distributed strain data 7 (307) corresponds to fiber core 7 (108). The spatial resolution 115 of the sensing points of the seven-channel optical frequency domain distributed fiber optic sensing device 114 is the length interval of each sensing point on the seven-core fiber optic shape sensor 101. Then, the data is processed according to the following steps to reconstruct the sensing shape of the shape sensing part 112 of the seven-core fiber optic shape sensor 101, thereby realizing the shape sensing of the seven-core fiber optic shape sensor 101:

[0087] Step 1: Group the distributed strain data 1 (301), 2 (302), 3 (303), 4 (304), 5 (305), 6 (306), and 7 (307) into nine groups, resulting in a total of nine distributed strain combinations. Calculate the apparent curvature vector K for each sensing point in each of the nine groups of distributed strain combinations. ij The apparent curvature vector K ij =[K1 ij K2 ij ], i = 1, 2, 3…N, where N is the number of sensing points for distributed strain data, j = 1, 2, 3…9, corresponding to nine distributed strain combinations. Distributed strain combination one to distributed strain combination eight are calculated according to the following formula:

[0088]

[0089] The distributed strain combination nine is calculated using the following formula:

[0090]

[0091] Step 2: Utilize T of the i-th sensing point ij Vector and reconstructed coordinates R(x) i ,y i ,z i The reconstructed coordinates of the nine distributed strain combinations at the (i+1)th sensing point were obtained:

[0092] R(x (i+1)j ,y (i+1)j,z (i+1)j ) = T ij Δs+R(x i ,y i ,z i ),

[0093] Where Δs is the spatial resolution of the sensing points, i = 1, 3…N, and N is the number of sensing points for the distributed strain data. In the first iteration, the T vector of the initial minimum rotating frame is used as T. 1j j = 1, 2...9, corresponding to nine strain distribution combinations, R(x i ,y i ,z i Let R(x1,y1,z1) be the reconstructed coordinates of the i-th sensing point. In the first iteration, R(x1,y1,z1) = [0,0,0].

[0094] Step 3: Calculate the reconstructed coordinates R(x) of the nine strain distribution combinations for the i-th sensing point in Step 2. (i+1)j ,y (i+1)j ,z (i+1)j (Average) The reconstructed coordinates R(x) of the (i+1)th sensing point obtained in step 2 are obtained from the nine distribution strain combinations. (i+1)j ,y (i+1)j ,z (i+1)j The average value of the reconstructed coordinates of the (i+1)th sensing point and the nine distributed strain combinations. Calculate the magnitude ΔR of the reconstructed coordinate error (i+1)j Calculation method:

[0095]

[0096] Where i = 1, 2...N, N is the number of sensing points for distributed strain data, and j = 1, 2...9, corresponding to nine combinations of distributed strain;

[0097] Step 4: Calculate the magnitude ΔR of the reconstructed coordinate error from Step 3. (i+1)j Sort from largest to smallest, the new sequence order is I. (i+1)s The magnitude of the corresponding reconstructed coordinate error is ΔR. (i+1)s Where s = 1, 2...9, then a weighted average of the reconstructed coordinates is performed, in the new sequence order I. (i+1)s Select the sequence order corresponding to the third to ninth positions from I. (i+1)s s = 3, 4...9, and calculate the weighted average of the reconstructed coordinates of the (i+1)th sensing point. And The reconstructed coordinates R(x) of the (i+1)th sensing point i+1 ,y i+1 ,z i+1 ):

[0098]

[0099] Where i = 1, 2...N, and N is the number of sensing points for the distributed strain data.

[0100] Step 5: Reconstruct the coordinates R(x) using the (i+1)th sensor point. i+1 ,y i+1 ,z i+1 The reconstructed coordinates R(x) of the i-th sensing point and the reconstructed coordinates of the i-th i ,y i ,z i ), recalculate the minimum rotation frame [T'] for the i-th sensing point. i N1' i N2' i First calculate Then, Tadj is calculated using the vector cross product. i To T' i rotation angle α i and rotation axis c i , N1adj i With N2adj i Respectively around the axis of rotation c i Rotation angle α i Obtain N1' i and N2' i , where i = 1, 2...N, and N is the number of sensing points for distributed strain data. In the first iteration, the initial minimum rotating frame (205) is used as the adjusted minimum rotating frame [Tadj1, N1adj1, N2adj1].

[0101] Step 6: Resolve the minimum rotation frame [T] for the (i+1)th sensing point using the differential equation form of the minimum rotation frame. (i+1)j N1 (i+1)j N2 (i+1)j ], and recalculate the minimum rotating frame [T'] using the i-th sensing point. i N1' i N2' i As the initial value for the differential equation, the differential equation of the minimum rotating frame is in the form of:

[0102]

[0103] Where i = 1, 2...N, N is the number of sensing points for distributed strain data, and j = 1, 2...9, corresponding to nine combinations of distributed strain;

[0104] Step 7: Utilize the new sequence order I from step 4. (i+1)sFor the minimum rotation frame [T] of the (i+1)th sensing point in step 6 (i+1)j N1 (i+1)j N2 (i+1)j Sort the sequences, and the new sequence is [T]. (i+1)s N1 (i+1)s N2 (i+1)s ], in the new sequence order I (i+1)s The minimum rotating frame [T] corresponding to the (i+1)th sensing point from the seventh to the ninth position is selected. (i+1)s N1 (i+1)s N2 (i+1)s ], where s = 7, 8, 9, calculate the average value of the minimum rotating frame for the (i+1)th sensing point:

[0105]

[0106] Where i = 1, 2…N, and N is the number of sensing points for distributed strain data. The minimum rotation frame after adjustment of the (i+1)th sensing point [Tadj] i+1 N1adj i+1 N2adj i+1 ];

[0107] Step 8: Repeat steps 2 through 7 until the reconstructed coordinates R(x) of all sensor points are obtained. i ,y i ,z i ), where i = 1, 2...N, and N is the number of sensing points for distributed strain data.

[0108] The technological innovations and beneficial effects of the seven-core fiber optic distributed sensing shape sensing reconstruction method based on weighted point-by-point averaging frame updates are as follows: Conventional point-by-point averaging algorithms only average the coordinates of the reconstructed points, while this invention averages the reconstructed coordinate frame and uses redundant information to adjust the minimum rotation frame, achieving uniformity of the minimum rotation frame for each reconstructed point. This reduces the impact of the fiber optic sensing system on coordinate point reconstruction and the reconstructed frame, thereby improving the accuracy of shape sensing. Furthermore, this invention achieves accuracy improvement through data processing alone without changing the hardware, offering significant economic benefits.

Claims

1.A reconstruction method of a seven-core fiber distributed sensing shape sensor based on a weighted average update framework, the seven-core fiber shape sensor (101) comprising seven cores, namely core one (102), core two (103), core three (104), core four (105), core five (106), core six (107), and core seven (108), wherein the core one (102), the core two (103), the core three (104), the core four (105), the core five (106), and the core six (107) are uniformly distributed in a ring shape at an angle of 60° on a cross section of the seven-core fiber shape sensor (101) with a consistent core distance (109), and if the angle direction of the core one (102) is 0°, the angle directions of the core two (103), the core three (104), the core four (105), the core five (106), and the core six (107) are 60°, 120°, 180°, 240°, and 300°, respectively, and the core seven (108) is at the center of the cross section of the seven-core fiber shape sensor (101), the seven-core fiber shape sensor (101) is divided into three parts according to length regions, namely a non-shape sensing part (110), a shape sensing starting end (111), and a shape sensing part (112), and when the sensor is implemented, the seven-core fiber shape sensor (101) near the shape sensing starting end (111) needs to be a straight line (113), a Z-axis (202) of an initial coordinate frame (201) of shape reconstruction coincides with the straight line (113) and a positive direction is that the shape sensing starting end (111) points to the shape sensing part (112), an X-axis (203) of the initial coordinate frame (201) of shape reconstruction is a direction in which the core seven (108) points to the core one (102), a Y-axis (204) of the initial coordinate frame (201) of shape reconstruction is perpendicular to the X-axis (203) and the Z-axis (202) and satisfies a right-hand coordinate system, an initial minimum rotation frame (205) coincides with the initial coordinate frame (201) of shape reconstruction, a T-vector (206) of the initial minimum rotation frame (205) is a unit vector in the direction of the Z-axis (202), an N1-vector (207) of the initial minimum rotation frame (205) is a unit vector in the direction of the X-axis (203), and an N2-vector (208) of the initial minimum rotation frame (205) is a unit vector in the direction of the Y-axis (204), the non-shape sensing part (110) of the seven-core fiber shape sensor (101) is connected with a seven-channel optical frequency domain distributed fiber sensing device (114), the seven-channel optical frequency domain distributed fiber sensing device (114) collects distributed strain data of the seven cores in the shape sensing part (112) of the seven-core fiber shape sensor (101), wherein a distributed strain data one (301) corresponds to the core one (102), a distributed strain data two (302) corresponds to the core two (103), a distributed strain data three (303) corresponds to the core three (104), a distributed strain data four (304) corresponds to the core four (105),The distributed strain data five (305) corresponds to the fiber core five (106), the distributed strain data six (306) corresponds to the fiber core six (107), the distributed strain data seven (307) corresponds to the fiber core seven (108), and the spatial resolution (115) of the sensing points of the seven-channel optical frequency domain distributed optical fiber sensing device (114) is the length interval of each sensing point on the seven-core optical fiber shape sensor (101). After the data processing is performed in the following steps, the reconstruction of the sensing shape is implemented on the shape sensing part (112) of the seven-core optical fiber shape sensor (101), and the shape sensing of the seven-core optical fiber shape sensor (101) is realized: Step 1, group the distribution strain data one (301), distribution strain data two (302), distribution strain data three (303), distribution strain data four (304), distribution strain data five (305), distribution strain data six (306), distribution strain data seven (307), a total of nine distribution strain combinations, respectively: distribution strain combination one: strain data one (301), strain data three (303), strain data five (305), distribution strain combination two: strain data two (302), strain data four (304), strain data six (306), distribution strain combination three: strain data one (301), strain data two (302), strain data three (303), distribution strain combination four: strain data two (302), strain data three (303), strain data four (304), distribution strain combination five: strain data three (303), strain data four (304), strain data five (305), distribution strain combination six: strain data four (304), strain data five (305), strain data six (306), distribution strain combination seven: strain data one (301), strain data five (305), strain data six (306), distribution strain combination eight: strain data one (301), strain data two (302), strain data six (306), distribution strain combination nine: strain data one (301), strain data two (302), strain data three (303), strain data four (304), strain data five (305), strain data six (306), The apparent curvature vector K of each sensing point of the nine groups of distributed strain combinations is calculated respectively ij Wherein the apparent curvature vector K ij =[K1 ij , K2 ij ], i=1, 2, 3…N, N is the number of sensing points of distributed strain data, j=1, 2, 3…9, corresponding to nine distributed strain combinations, distributed strain combination one to distributed strain combination eight are calculated according to the following formula: wherein e iα 、e iβ 、e iΓ is the strain data of the i-th sensing point position in the corresponding combination, α, β, γ are the distribution angles of the corresponding three cores on the cross section of the seven-core optical fiber shape sensor (101), r is the core distance (109), e i7 is the strain data seven (307) of the i-th sensing point position Distribution strain combination nine is calculated according to the following formula: wherein e i1 , e i2 , e i3 …e i7 are strain data one (301) through strain data seven (307), and r is the core distance (109). Step 2, T ij vector sum of the reconstructed coordinates R(x i ,y i ,z i ) of the nine distributed strain combinations of the i+1th sensor point is solved. R(x (i+1)j ,y (i+1)j ,z (i+1)j ) = T ij Δs+R(x i ,y i ,z i ), where Δs is the spatial resolution of the sensor points (115), i = 1, 3,... N, N is the number of sensor points for which strain data is distributed, and in the first iteration T is the T vector (206) of the initial minimum rotation frame (205) 1j , j = 1, 2,... 9, corresponding to nine strain distribution combinations, R(x i ,y i ,z i ) is the reconstructed coordinate of the i-th sensor point, and in the first iteration R(x1, y1, z1) = [0, 0, 0]. Step 3, calculate the average of the reconstructed coordinates R(x (i+1)j ,y (i+1)j ,z (i+1)j ) of the nine distributed strain combinations of the i-th sensor point in step 2: Using the reconstructed coordinates R(x (i+1)j ,y (i+1)j ,z (i+1)j ) of the nine distributed strain combinations of the i+1-th sensor point obtained in step 2 and the average of the reconstructed coordinates of the nine distributed strain combinations of the i+1-th sensor point Calculate the modulus of the reconstructed coordinate error ΔR (i+1)j , the calculation method is: Wherein, i=1, 2…N, N is the number of sensing points of distribution strain data, j=1, 2…9, corresponding to nine distribution strain combinations; Step 4, the module of the reconstructed coordinate error of step 3 is ΔR (i+1)j The new sequence order is I (i+1)s , and the corresponding module of the reconstructed coordinate error is ΔR (i+1)s , wherein s = 1, 2…9, and then the weighted average of the reconstructed coordinates is taken, and the sequence order I (i+1)s corresponding to the third to ninth positions is selected in the new sequence order I (i+1)s , s = 3, 4…9, and the weighted average value of the reconstructed coordinates of the i+1th sensing point is calculated as the reconstructed coordinates R(x i+1 ,y i+1 ,z i+1 ) of the i+1th sensing point.​ wherein i = 1, 2…N, N is the number of sensing points of distributed strain data, Step 5, using the reconstructed coordinates R(x i+1 ,y i+1 ,z i+1 ) of the i+1th sensing point and the reconstructed coordinates R(x i ,y i ,z i ) of the ith sensing point, re-calculate the minimum rotation frame [T' i , N1' i , N2' i ] of the ith sensing point, first calculate Then calculate the rotation angle a i and the rotation axis c i from Tadj i to T' i , rotate N1adj i and N2adj i by the rotation angle a i around the rotation axis c i to obtain N1' i and N2' i , wherein i = 1, 2…N, N is the number of sensing points of distributed strain data, and the initial minimum rotation frame (205) is taken as the adjusted minimum rotation frame [Tadj1, N1adj1, N2adj1] in the first iteration. Step 6, re-solve the minimum rotation frame of the (i+1)th sensor point using the differential equation form of the minimum rotation frame [T (i+1)j , N1 (i+1)j , N2 (i+1)j ], and re-calculate the minimum rotation frame [T' i , N1' i , N2' i ] of the ith sensor point as the initial value of the differential equation, and the differential equation form of the minimum rotation frame is: Wherein, i=1, 2…N, N is the number of sensing points of distribution strain data, j=1, 2…9, corresponding to nine distribution strain combinations; Step 7, the new sequence order I (i+1)s , the minimum rotation frame [T (i+1)j , N1 (i+1)j , N2 (i+1)j ] of the i+1th sensing point in step 6 is sorted, and the new sequence is [T (i+1)s , N1 (i+1)s , N2 (i+1)s ], the minimum rotation frame [T (i+1)s , N1 (i+1)s , N2 (i+1)s ] of the i+1th sensing point corresponding to the seventh to ninth positions in the new sequence order I (i+1)s is selected, wherein s=7, 8, 9, and the average value of the minimum rotation frame of the i+1th sensing point is calculated: Wherein, i = 1, 2…N, N is the number of sensing points of distributed strain data, will The minimum rotating frame [Tadj i+1 , N1adj i+1 , N2adj i+1 ] adjusted as the i+1th sensing point ; Step 8, repeat steps 2 to 7 until the reconstructed coordinates R(x i ,y i ,z i ) of all sensing points are obtained, where i = 1, 2…N, N is the number of sensing points distributed with strain data.

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