Multi-core optical cable shape reconstruction method based on four-order step integration and GOC compensation

Abstract

The invention discloses a multi-core optical cable shape reconstruction method based on fourth-order step integral and GOC compensation, and belongs to the technical field of structure health monitoring, and the technical key points are that the method comprises the steps: solving a curvature vector through the central wavelength change data of a fiber grating sensor in a multi-core optical cable; obtaining a geometric information matrix of the multi-core optical cable; constructing a multi-core optical cable shape reconstruction algorithm, carrying out numerical solution on a nonlinear differential equation of a tangent vector by adopting a four-order step integration method, substituting the obtained tangent vector into a geometric information matrix of the multi-core optical cable, and combining curvature information of the multi-core optical cable to obtain an ideal shape of the multi-core optical cable; and constructing a fiber core position geometrical optical compensation model, analyzing a geometrical relationship between an actual deviation fiber core position and a fiber core position of an ideal multi-core optical cable shape, and correcting a multi-core optical cable wavelength variation error caused by fiber core position deviation, so as to at least have the technical effect of improving the shape reconstruction precision of the multi-core optical cable.

Description

Technical Field

[0001] This application relates to the field of structural health monitoring technology, and in particular to a method for reconstructing the shape of multi-core optical cables based on fourth-order step integral and GOC compensation. Background Technology

[0002] In modern industry, aerospace, and marine engineering, shape monitoring and reconstruction technologies for complex structures are crucial for ensuring system safety, optimizing performance, and extending service life. Especially under extreme environments or dynamic service conditions, traditional sensor technologies often struggle to meet the demands for high-precision, real-time, and long-distance monitoring. Multi-core optical cables, with their resistance to electromagnetic interference, high sensitivity, and multi-parameter sensing capabilities, have become one of the cutting-edge technologies in structural health monitoring.

[0003] However, existing shape reconstruction methods still suffer from limitations such as insufficient accuracy and low computational efficiency in handling complex curvature changes, multimodal coupling, and dynamic responses. Furthermore, the fabrication of multi-core optical cables inevitably introduces fiber core position deviations, causing the wavelength change of the fiber Bragg grating sensor in the multi-core cable to not correspond to the actual deformation shape of the cable, resulting in significant shape reconstruction errors. Summary of the Invention

[0004] The embodiments of this application provide a method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation, which at least has the technical effect of improving the accuracy of multi-core optical cable shape reconstruction.

[0005] To address the aforementioned technical problems, according to one aspect of this application, a method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation is provided. The method includes the following steps:

[0006] By using the center wavelength change data of the fiber optic grating sensor in the multi-core optical cable, and combining the center wavelength change-curvature relationship, the curvature vector is solved by matrix operations.

[0007] The geometric information matrix X(s) of the multi-core optical cable is obtained by calculating the differential operation relationship between the curvature corresponding to the position of each fiber grating sensor in the core optical cable and its tangent vector T(s) and two orthogonal vectors M1(s) and M2(s).

[0008] A multi-core optical cable shape reconstruction algorithm is constructed. The nonlinear differential equation of the tangent vector T(s) is numerically solved by the fourth-order step integral method. The obtained tangent vector T(s) is substituted into the geometric information matrix X(s) of the multi-core optical cable and combined with the curvature information of the multi-core optical cable to obtain the ideal multi-core optical cable shape.

[0009] A geometric optical compensation model for fiber core position is constructed to analyze the geometric relationship between the actual deviation fiber core position and the fiber core position of the ideal multi-core optical cable shape, and to correct the error in the wavelength variation of the multi-core optical cable caused by the fiber core position deviation.

[0010] Preferably, in a multi-core optical cable, each FBG sensor group contains three gratings with the same center. A local orthogonal coordinate system is set in each FBG sensor group, with its x-axis and y-axis located at the cross-section of the optical fiber and its z-axis pointing to the axis of the multi-core optical cable. When a multi-core optical cable is bent and deformed, the FBG sensor grating in the fiber core will produce a wavelength change. This wavelength change is proportional to the distance from the grating to the central bending axis. Therefore, the wavelength change-curvature relationship of the multi-core optical cable is expressed as: (1) In equation (1), s represents the arc length coordinate of each FBG sensor grating along the axis of the multi-core optical cable, and Δλ i (s) represents the wavelength change generated by the FBG sensor grating, and i∈{a, b, c} represents the three fiber cores in the multi-core optical cable. The curvature corresponding to the fiber core, y i (s) represents the distance from the grating to the central bending axis, r i (s) represents the distance from the i-th fiber core to the center of the multi-core optical cable, θ i (s) represents the angle between the fiber core and the bending direction; Substituting the angles between the three fiber cores and the bending direction, as well as the angles between the fiber cores, into equation (1), we get: (2) (3) (4) In equations (3) and (4), θ ba θ represents the angle between fiber cores a and b. ca The angle r represents the angle between fiber cores a and c. a r b r c r represents the distance from the three fiber core gratings to the central bending axis. i (s) represents the distance from the grating to the center of the multi-core optical cable. Using the trigonometric sum formula, equations (2) to (4) are transformed into matrix equations: (5) In equation (5), Let C be a column vector representing the wavelength variations of the three fiber cores, and let C be a 3×2 coefficient matrix determined by the fiber core spacing and the angle between the fiber cores. It is a column vector composed of curvature-related components; The wavelength variation data of the multi-core optical cable is obtained by demodulation equipment, and the matrix is ​​obtained by substituting it into equation (6). Then, according to the matrix Definition of calculating fiber core curvature : (7) (8) Where κ(s) is the magnitude of the curvature of the optical cable at the arc length coordinate s, and θ a (s) is the angle between the bending direction of the optical cable and the reference axis of the local coordinate system. Together, they constitute the curvature vector corresponding to a set of FBG sensor gratings at the arc length coordinate s of the optical fiber. v1 and v2 are... The amount.

[0011] Preferably, the step of numerically solving the nonlinear differential equation of the tangent vector T(s) using a fourth-order step integral method, substituting the obtained tangent vector T(s) into the geometric information matrix X(s) of the multi-core optical cable, and combining it with the curvature information of the multi-core optical cable to obtain the ideal shape of the multi-core optical cable includes: At the initial position s of the multi-core optical cable i At that point, use the initial tangent vector T i (s) Calculate the initial slope k1: (16), At the middle position of the multi-core optical cable i +k1 / 2 and s i At +k2 / 2, use the tangent vector T i+1 / 2 (s) Calculate the slopes k2 and k3 at that point: (17) In the formula, d s It is the step size parameter, T i (s) is the initial tangent vector, T i+1 / 2 (s) represents the middle position of the multi-core optical cable. i +k1 / 2 and s i The tangent vector at +k2 / 2; At position s in a multi-core optical cable i At +k3, use the tangent vector T i+1 (s) Calculate the slope k4 at this point: (18) In the formula, It is the step size parameter, T i+1 (s) represents the middle position of the multi-core optical cable. i The tangent vector at +k3; By using weighted slopes k1, k2, k3, and k4, and calculating the average value, update the geometric information matrix X(s) at the next location of the multi-core optical cable: (19) In the formula, X si+1 (s) is the geometric information matrix at the next location of the multi-core optical cable, X si (s) is the geometric information matrix of the initial position of the multi-core optical cable, where k1, k2, k3, and k4 represent the initial position and the intermediate position of the multi-core optical cable, respectively. i +k1 / 2, s i +k2 / 2, and s i The slope at +k3.

[0012] Preferably, the step of analyzing the geometric relationship between the actual deviation fiber core position and the fiber core position of the ideal multi-core optical cable shape, and correcting the error in the wavelength variation of the multi-core optical cable caused by the fiber core position deviation, includes: Assume θ ai θ bi θ ci Let θ' represent the three ideal positions of the fiber cores in the cross-section of the i-th FBG sensor. ai ,θ' bi ,θ' ci This represents the actual positions of the three fiber cores in the cross-section of the i-th FBG sensor. Let represent the positional deviations of the three fiber cores of the i-th FBG sensor cross-section, then The calculation method is as follows: (20).

[0013] Calculate the i-th grating on fiber core a, assuming the distance between the FBG sensor grating and the neutral axis of the multi-core optical cable bend is... The angle between the bending direction of the multi-core optical cable and the x-axis is... Then, based on the geometric relationship between the core and the central skeleton, we can obtain: (twenty one) In the formula, r a =r b =r c =r; Meanwhile, the strain relationship between the ideal core position a and the actual core position aa is: (twenty two) In the formula, For the strain at the ideal core position a, Let be the bending radius of the multi-core optical cable corresponding to the ideal fiber core position 'a'. The vertical distance from the ideal fiber core position 'a' to the bending neutral axis of the multi-core optical cable; The strain at the actual fiber core position aa This represents the bending radius of the multi-core optical cable corresponding to the actual fiber core position aa. This is the vertical distance from the actual fiber core position aa to the bending neutral axis of the multi-core optical cable; When a multi-core optical cable is bent and deformed, the bending radius R of the ideal fiber core position a and the actual fiber core position aa is... θai and R θ’ai The relational expression is expressed as: (twenty three) In the formula, This represents the ideal position of fiber core a in the cross section of the i-th FBG sensor; Because the core diameter of the fiber Bragg grating sensor is extremely small, it can be simplified as follows: (twenty four).

[0014] Combining equations (20), (21), (22), and (24), we get: (25) in, Let be the wavelength change of the i-th grating on fiber core a. Strain at the ideal core position a; Similarly, the relationship between the wavelength changes at the actual and ideal positions of fiber cores b and c can be obtained: (26) (27) Where, Δλ b Let be the wavelength change of the i-th grating on fiber core b. The strain at the ideal core position b; Δλ c Let be the wavelength change of the i-th grating on fiber core c. Strain at the ideal core position c; The core position deviation is solved iteratively.

[0015] Preferably, the step of iteratively solving for the core position deviation includes:

[0016] Set the initial guessed core position deviation and the maximum angular deviation range;

[0017] Substituting the calculated ideal position strain into the multi-core optical cable shape reconstruction algorithm, the algorithm obtains the multi-core optical cable shape position coordinates.

[0018] Extract the actual shape and position coordinates of the multi-core optical cable obtained from simulation or experiment, and calculate the difference between them and the position coordinates obtained by the algorithm;

[0019] The obtained error is returned to update the fiber core position deviation until the position coordinates obtained by the algorithm and the position coordinates of the actual shape of the multi-core optical cable obtained by simulation or experiment are within the preset range.

[0020] Preferably, the maximum angular deviation range is set to [-30°, 30°].

[0021] This application has the following beneficial effects:

[0022] By utilizing the center wavelength variation data of fiber optic grating sensors in multi-core optical cables and combining the center wavelength variation-curvature relationship, the curvature vector is solved using matrix operations, thus addressing the shape reconstruction error problem caused by the need for structural strain information in traditional shape sensing methods. A fourth-order step integral method is proposed to numerically solve the nonlinear differential equation of the tangent vector T(s). Adaptive control of the integration step size effectively suppresses the divergence and oscillation of the numerical solution, solving the problems of insufficient accuracy and error accumulation of traditional low-order integral methods under complex curvature variations or high dynamic loads. Simultaneously, by analyzing the geometric relationship between the actual deviation fiber core position and the ideal fiber core position, a geometric optical compensation (GOC) model is constructed to correct the wavelength variation error in multi-core optical cables caused by fiber core position deviation, thereby further improving the shape reconstruction accuracy of multi-core optical cables. Attached Figure Description

[0023] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments of this application and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0024] Figure 1 This is a schematic diagram of the overall process of the method of the present invention.

[0025] Figure 2 This is a schematic diagram of the application of simulation constraints according to an embodiment of the present invention.

[0026] Figure 3 This is a schematic diagram comparing the shapes of multi-core optical cables identified and simulated by the method of this invention.

[0027] Figure 4 This is a schematic diagram illustrating the relative error of the multi-core optical cable shape obtained by the method of this invention for identification and simulation. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0029] This embodiment provides a method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation. It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions. Also, although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in a different order than that shown here.

[0030] To enable those skilled in the art to better understand the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0031] like Figure 1 As shown, this embodiment provides a method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation, including the following steps:

[0032] S1, using the center wavelength change data of the fiber optic grating sensor in the multi-core optical cable, combined with the center wavelength change-curvature relationship, the curvature vector is solved by matrix operation;

[0033] S2, calculate the differential operation relationship between the curvature corresponding to the position of each fiber optic grating sensor in the core optical cable and its tangent vector T(s) and two orthogonal vectors M1(s) and M2(s) to obtain the geometric information matrix X(s) of the multi-core optical cable;

[0034] S3. Construct a multi-core optical cable shape reconstruction algorithm. Use the fourth-order step integral method to numerically solve the nonlinear differential equation of the tangent vector T(s). Substitute the obtained tangent vector T(s) into the geometric information matrix X(s) of the multi-core optical cable and combine it with the curvature information of the multi-core optical cable to obtain the ideal multi-core optical cable shape.

[0035] S4. Construct a geometric optical compensation model for the fiber core position, analyze the geometric relationship between the actual deviation fiber core position and the fiber core position of the ideal multi-core optical cable shape, and correct the error in the wavelength variation of the multi-core optical cable caused by the deviation of the fiber core position.

[0036] It should be noted that this method uses the center wavelength change data of fiber optic grating sensors in multi-core optical cables, combined with the center wavelength change-curvature relationship, to solve for the curvature vector using matrix operations. Based on this, according to differential geometry theory, the differential operation relationship between the curvature corresponding to each fiber optic grating sensor position in the multi-core optical cable and its tangent vector T(s) and two orthogonal vectors M1(s) and M2(s) is derived, thus obtaining the multi-core optical cable geometric information matrix X(s). This matrix addresses the shape reconstruction error problem caused by the need for structural strain information in traditional shape sensing methods. A fourth-order step integral method is used to numerically solve the nonlinear differential equation of the tangent vector T(s). The obtained tangent vector T(s) is then substituted into the multi-core optical cable geometric information matrix X(s) to reconstruct the shape of the multi-core optical cable, thus solving the problem of insufficient accuracy and error accumulation of low-order integrals under complex curvature or high dynamic conditions.

[0037] Based on this, considering that fiber core position deviations are inevitable during the manufacturing process of multi-core optical cables, this invention analyzes the geometric relationship between the actual deviation fiber core position and the ideal fiber core position, and constructs a fiber core position geometric optical compensation (GOC) model to correct the error in the wavelength variation of multi-core optical cables caused by fiber core position deviations, thereby further improving the shape reconstruction accuracy of multi-core optical cables.

[0038] refer to Figures 2-3 In one embodiment, step S1 includes:

[0039] In S11, each FBG sensor group in a multi-core optical cable contains three gratings that are concentric. Each FBG sensor group is set up with a local orthogonal coordinate system, with its x and y axes located at the cross-section of the optical fiber and its z axis pointing towards the axis of the multi-core optical cable.

[0040] When a multi-core optical cable is bent and deformed, the FBG sensor grating in the fiber core will produce a wavelength change. This wavelength change is proportional to the distance from the grating to the central bending axis. Therefore, the wavelength change-curvature relationship of the multi-core optical cable can be expressed as:

[0041] (1)

[0042] In equation (1), s represents the arc length coordinate of each FBG sensor grating along the axis of the multi-core optical cable, and Dl i (s) represents the wavelength change generated by the FBG sensor grating, i∈{a, b, c} represents the three fiber cores in the multi-core optical cable, k(s) represents the curvature corresponding to the fiber core, and y i (s) represents the distance from the grating to the central bending axis, r i (s) represents the distance from the grating to the center of the multi-core optical cable, θ i (s) represents the angle between the fiber core and the bending direction.

[0043] S12, substituting the angles between the three fiber cores and the bending direction, as well as the angles between the fiber cores, into equation (1), we can obtain:

[0044] (2)

[0045] (3)

[0046] (4)

[0047] In equations (3) and (4), θ ba θ represents the angle between fiber cores a and b. ca Let represent the angle between fiber core a and fiber core c. Using the trigonometric sum formula, equations (2) to (4) are transformed into matrix equations:

[0048] (5)

[0049] In equation (5), Let C be a column vector representing the wavelength variations of the three fiber cores, and let C be a 3×2 coefficient matrix determined by the fiber core spacing and the angle between the fiber cores. It is a column vector composed of curvature-related components.

[0050]

[0051] From equation (5), we can see that the matrix The components can be solved by the pseudo-inverse of matrix C:

[0052] (6)

[0053] S13, obtain the wavelength change data of the multi-core optical cable through demodulation equipment, and substitute it into equation (6) to obtain matrix n. Then, based on matrix n Definition of calculating fiber core curvature :

[0054] (7)

[0055] (8)

[0056] in, Let θ be the magnitude of the curvature of the optical cable at the arc length coordinate s. a (s) is the angle between the bending direction of the optical cable and the reference axis of the local coordinate system, and the two together constitute the curvature vector at the arc length coordinate s.

[0057] Formulas (7) and (8) give the curvature vectors corresponding to a set of FBG sensor gratings at the arc length position s of the optical fiber.

[0058] In one embodiment, step S2 includes:

[0059] S21, Assuming Let be the position vector of the multi-core optical cable. Three orthogonal vectors T(s), M1(s), and M2(s) are defined at the arc length position s.

[0060] (9)

[0061] (10)

[0062] (11)

[0063] (12)

[0064] in, Let be the position vector of the multi-core optical cable at the arc length coordinate s. Let be the derivative of the position vector with respect to the arc length s, representing the tangent direction of the multi-core optical cable axis at s; The primary / secondary normal vectors of the multi-core optical cable, together with T(s), M1(s), and M2(s), form an orthogonal coordinate system. Let M1(s) be the rate of change of the vector as the multi-core optical cable bends, M2(s) be the first normal vector of the multi-core optical cable at the arc length coordinate s, and M2(s) be the second normal vector of the optical cable at the arc length coordinate s. Let T(s) be the rate of change of the normal vector as the multi-core optical cable bends, and let T(s) be the tangent vector of the multi-core optical cable at the arc length coordinate s. This is also the rate of change of the normal vector as the multi-core optical cable bends.

[0065] In equations (10) to (12), The two components of the curvature vector on the x-axis and y-axis can be obtained by equation (13):

[0066] (13)

[0067] Where v1 and v2 are The amount, This is a column vector composed of curvature-related components. The total curvature θ of a multi-core optical cable at arc length s a (s) is the angle between the bending direction of the optical cable and the reference axis of the local coordinate system, and the two together constitute the curvature vector at the arc length coordinate s.

[0068] S22, To obtain the curvature distribution along the arc length of the multi-core optical cable, regularized spline interpolation is needed only for the curvature corresponding to the cross-section of each FBG sensor group. The interpolated curvature is expressed as follows: and Then the position vector g(s) of the multi-core optical cable and the three orthogonal vectors T(s), M1(s), and M2(s) can be obtained by equation (14):

[0069] (14)

[0070] in, Let X(s) be the rate of change of the entire local orthogonal coordinate system as the optical cable axis bends, X(s) be the column vector formed by the geometric vector system of the multi-core optical cable, and A(s) be the curvature matrix of the multi-core optical cable.

[0071]

[0072] in, T(s) is the position vector of the multi-core optical cable at arc length coordinate s; T(s) is the tangent vector of the multi-core optical cable at arc length coordinate s; M1(s) is the first normal vector of the multi-core optical cable at arc length coordinate s; M2(s) is the second normal vector of the optical cable at arc length coordinate s, which is orthogonal to both the tangent vector T(s) and the first normal vector M1(s); and They are respectively and Curvature after regularized spline interpolation.

[0073] S23, assuming the curvature matrix A(s) lies in two continuous sets of... and If the relationship remains unchanged, then equation (12) can be discretized as follows:

[0074] (15)

[0075] Where X(s+Δs) is the geometric vector system matrix at the arc length position s+Δs, which is the result of X(s) advancing Δs along the optical cable axis; exp(A(s)Δs) is the matrix exponential function, which transforms the curvature change within the small arc length Δs into the rigid body motion of the local coordinate system, realizing the coordinate transformation from s to s+Δs; Δs is the small arc length.

[0076] In equation (13), the initial assumptions are:

[0077]

[0078] in, Let be the position vector of the multi-core optical cable at arc length coordinate s; T be the tangent vector of the optical cable at arc length coordinate s; M1 be the first normal vector of the optical cable at arc length coordinate s; and M2 be the second normal vector of the optical cable at arc length coordinate s, which is orthogonal to both the tangent vector T and the first normal vector M1. This is the matrix transpose symbol.

[0079] In one embodiment, step S3 includes:

[0080] The steps of numerically solving the nonlinear differential equation of the tangent vector T(s) using a fourth-order step integral method, substituting the obtained tangent vector T(s) into the geometric information matrix X(s) of the multi-core optical cable, and combining it with the curvature information of the multi-core optical cable to obtain the ideal shape of the multi-core optical cable include: S31, at the initial position of the multi-core optical cable s i At that point, use the initial tangent vector T i (s) Calculate the initial slope k1: (16), S32, located in the middle of the multi-core optical cable. i +k1 / 2 and s i At +k2 / 2, use the tangent vector T i+1 / 2 (s) Calculate the slopes k2 and k3 at that point: (17) In the formula, d s It is the step size parameter, T i (s) is the initial tangent vector, T i+1 / 2 (s) represents the middle position of the multi-core optical cable. i +k1 / 2 and s i The tangent vector at +k2 / 2; S33, at position s in the multi-core optical cable i At +k3, use the tangent vector T i+1 (s) Calculate the slope k4 at this point: (18) In the formula, It is the step size parameter, T i+1 (s) represents the middle position of the multi-core optical cable. i The tangent vector at +k3; S34, by weighting the slopes k1, k2, k3, and k4 and calculating the average value, update the geometric information matrix X(s) at the next location of the multi-core optical cable: (19) In the formula, X si+1 (s) is the geometric information matrix at the next location of the multi-core optical cable, X si(s) is the geometric information matrix of the initial position of the multi-core optical cable, where k1, k2, k3, and k4 represent the initial position and the intermediate position of the multi-core optical cable, respectively. i +k1 / 2, s i +k2 / 2, and s i The slope at +k3.

[0081] refer to Figures 3-4 This is a comparative schematic diagram of the actual application of the embodiments of this application. In one embodiment, step S4 includes:

[0082] The step of analyzing the geometric relationship between the actual deviation fiber core position and the fiber core position of the ideal multi-core optical cable shape, and correcting the error in the wavelength variation of the multi-core optical cable caused by the fiber core position deviation, includes: S41, Assume θ ai θ bi θ ci Let θ' represent the three ideal positions of the fiber cores in the cross-section of the i-th FBG sensor. ai ,θ' bi ,θ' ci This represents the actual positions of the three fiber cores in the cross-section of the i-th FBG sensor. Let represent the positional deviations of the three fiber cores of the i-th FBG sensor cross-section, then The calculation method is as follows: (20).

[0083] With fiber core a The first i Taking a single grating as an example, calculate the i-th grating on fiber core a, assuming the distance between the FBG sensor grating and the bending neutral axis of the multi-core optical cable is y. θai The angle between the bending direction of the multi-core optical cable and the x-axis is... Then, based on the geometric relationship between the core and the central skeleton, we can obtain: (twenty one) In the formula, since the diameter of the optical fiber core is very small, the radius of the center polyurethane thin-diameter cable is generally taken as r. a =r b =r c =r; Meanwhile, the strain relationship between the ideal core position a and the actual core position aa is: (twenty two) In the formula, For the strain at the ideal core position a, Let be the bending radius of the multi-core optical cable corresponding to the ideal fiber core position 'a'. The vertical distance from the ideal fiber core position 'a' to the bending neutral axis of the multi-core optical cable; The strain at the actual fiber core position aa The radius of curvature of the multi-core optical cable corresponding to the actual fiber core position 'a'. This is the vertical distance from the actual fiber core position aa to the bending neutral axis of the multi-core optical cable; S42, When a multi-core optical cable is bent and deformed, the bending radius R of the ideal fiber core position a and the actual fiber core position aa is... θai and R θ’ai The relational expression is expressed as: (twenty three) In the formula, This represents the ideal position of fiber core a in the cross section of the i-th FBG sensor; Because the core diameter of the fiber Bragg grating sensor is extremely small, it can be simplified as follows: (twenty four).

[0084] S43, combining equations (20), (21), (22), and (24), we get: (25) in, Let be the wavelength change of the i-th grating on fiber core a. Strain at the ideal core position a; Similarly, the relationship between the wavelength changes at the actual and ideal positions of fiber cores b and c can be obtained: (26) (27) Where, Δλ b Let be the wavelength change of the i-th grating on fiber core b. The strain at the ideal core position b; Δλ c Let be the wavelength change of the i-th grating on fiber core c. Strain at the ideal core position c; S44, the core position deviation is solved iteratively.

[0085] It should be noted that since the wavelength change at the ideal position cannot be obtained directly in practice, it is necessary to solve for the core position deviation through iteration.

[0086] In one embodiment, the specific solution process for step S44 is as follows:

[0087] S441, Set the initial guessed core position deviation, with a maximum angular deviation range of [-30°, 30°];

[0088] S442, Next, the calculated ideal position strain is substituted into the multi-core optical cable shape reconstruction algorithm to obtain the multi-core optical cable shape position coordinates obtained by the algorithm.

[0089] S443: Extract the actual shape and position coordinates of the multi-core optical cable obtained from simulation or experiment, and calculate the difference between them and the position coordinates obtained by the algorithm.

[0090] S444 returns the obtained error to the fiber core position deviation guessing function to update the fiber core position deviation until the error between the position coordinates obtained by the algorithm and the actual shape position coordinates of the multi-core optical cable obtained by simulation or experiment is within an acceptable range.

[0091] The above description is only a preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this application, and these improvements and modifications should also be considered within the scope of protection of this application.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation, characterized in that, Includes the following steps: By using the center wavelength change data of the fiber optic grating sensor in the multi-core optical cable, and combining the center wavelength change-curvature relationship, the curvature vector is solved by matrix operations. The geometric information matrix X(s) of the multi-core optical cable is obtained by calculating the differential operation relationship between the curvature corresponding to the position of each fiber grating sensor in the core optical cable and its tangent vector T(s) and two orthogonal vectors M1(s) and M2(s). A multi-core optical cable shape reconstruction algorithm is constructed. The nonlinear differential equation of the tangent vector T(s) is numerically solved by the fourth-order step integral method. The obtained tangent vector T(s) is substituted into the geometric information matrix X(s) of the multi-core optical cable and combined with the curvature information of the multi-core optical cable to obtain the ideal multi-core optical cable shape. A geometric optical compensation model for fiber core position is constructed to analyze the geometric relationship between the actual deviation fiber core position and the fiber core position of the ideal multi-core optical cable shape, and to correct the error in the wavelength variation of the multi-core optical cable caused by the fiber core position deviation.

2. The method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation according to claim 1, characterized in that, The step of using the center wavelength change data of the fiber optic grating sensor in the multi-core optical cable, combined with the center wavelength change-curvature relationship, and using matrix operations to solve for the curvature vector is as follows: In a multi-core optical cable, each FBG sensor group contains three gratings with the same center. A local orthogonal coordinate system is set in each FBG sensor group, with its x-axis and y-axis located at the cross-section of the optical fiber and its z-axis pointing to the axis of the multi-core optical cable. When a multi-core optical cable is bent and deformed, the FBG sensor grating in the fiber core will produce a wavelength change. This wavelength change is proportional to the distance from the grating to the central bending axis. Therefore, the wavelength change-curvature relationship of the multi-core optical cable is expressed as: (1) In equation (1), s represents the arc length coordinate of each FBG sensor grating along the axis of the multi-core optical cable, and Δλ i (s) represents the wavelength change generated by the FBG sensor grating, and i∈{a, b, c} represents the three fiber cores in the multi-core optical cable. The curvature corresponding to the fiber core, y i (s) represents the distance from the grating to the central bending axis, r i (s) represents the distance from the i-th fiber core to the center of the multi-core optical cable, θ i (s) represents the angle between the fiber core and the bending direction; Substituting the angles between the three fiber cores and the bending direction, as well as the angles between the fiber cores, into equation (1), we get: (2) (3) (4) In equations (3) and (4), θ ba θ represents the angle between fiber cores a and b. ca The angle r represents the angle between fiber cores a and c. a r b r c r represents the distance from the three fiber core gratings to the central bending axis. i (s) represents the distance from the grating to the center of the multi-core optical cable. Using the trigonometric sum formula, equations (2) to (4) are transformed into matrix equations: (5) In equation (5), Let C be a column vector representing the wavelength variations of the three fiber cores, and let C be a 3×2 coefficient matrix determined by the fiber core spacing and the angle between the fiber cores. It is a column vector composed of curvature-related components; The wavelength variation data of the multi-core optical cable is obtained by demodulation equipment, and the matrix is ​​obtained by substituting it into equation (6). Then, according to the matrix Definition of calculating fiber core curvature : (7) (8) Where κ(s) is the magnitude of the curvature of the optical cable at the arc length coordinate s, and θ a (s) is the angle between the bending direction of the optical cable and the reference axis of the local coordinate system. Together, they constitute the curvature vector corresponding to a set of FBG sensor gratings at the arc length coordinate s of the optical fiber. v1 and v2 are... The amount.

3. The method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation according to claim 2, characterized in that, The steps of numerically solving the nonlinear differential equation of the tangent vector T(s) using a fourth-order step integral method, substituting the obtained tangent vector T(s) into the geometric information matrix X(s) of the multi-core optical cable, and combining it with the curvature information of the multi-core optical cable to obtain the ideal shape of the multi-core optical cable include: At the initial position s of the multi-core optical cable i At that point, use the initial tangent vector T i (s) Calculate the initial slope k1: (16) At the middle position of the multi-core optical cable i +k1 / 2 and s i At +k2 / 2, use the tangent vector T i+1 / 2 (s) Calculate the slopes k2 and k3 at that point: (17) In the formula, d s It is the step size parameter, T i (s) is the initial tangent vector, T i+1 / 2 (s) represents the middle position of the multi-core optical cable. i +k1 / 2 and s i The tangent vector at +k2 / 2; At position s in a multi-core optical cable i At +k3, use the tangent vector T i+1 (s) Calculate the slope k4 at this point: (18) In the formula, It is the step size parameter, T i+1 (s) represents the middle position of the multi-core optical cable. i The tangent vector at +k3; By using weighted slopes k1, k2, k3, and k4, and calculating the average value, update the geometric information matrix X(s) at the next location of the multi-core optical cable: (19) In the formula, X si+1 (s) is the geometric information matrix at the next location of the multi-core optical cable, X si (s) is the geometric information matrix of the initial position of the multi-core optical cable, where k1, k2, k3, and k4 represent the initial position and the intermediate position of the multi-core optical cable, respectively. i +k1 / 2, s i +k2 / 2, and s i The slope at +k3.

4. The method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation according to claim 3, characterized in that, The step of analyzing the geometric relationship between the actual deviation fiber core position and the fiber core position of the ideal multi-core optical cable shape, and correcting the error in the wavelength variation of the multi-core optical cable caused by the fiber core position deviation, includes: Assume θ ai θ bi θ ci Let θ' represent the three ideal positions of the fiber cores in the cross-section of the i-th FBG sensor. ai ,θ' bi ,θ' ci This represents the actual positions of the three fiber cores in the cross-section of the i-th FBG sensor. Let represent the positional deviations of the three fiber cores of the i-th FBG sensor cross-section, then The calculation method is as follows: (20)， Calculate the i-th grating on fiber core a, assuming the distance between the FBG sensor grating and the neutral axis of the multi-core optical cable bend is y. θai The angle between the bending direction of the multi-core optical cable and the x-axis is... Then, based on the geometric relationship between the core and the central skeleton, we can obtain: (21) In the formula, r a =r b =r c =r; Meanwhile, the strain relationship between the ideal core position a and the actual core position aa is: (22) In the formula, For the strain at the ideal core position a, Let be the bending radius of the multi-core optical cable corresponding to the ideal fiber core position 'a'. The vertical distance from the ideal fiber core position 'a' to the bending neutral axis of the multi-core optical cable; The strain at the actual fiber core position aa This represents the bending radius of the multi-core optical cable corresponding to the actual fiber core position aa. This is the vertical distance from the actual fiber core position aa to the bending neutral axis of the multi-core optical cable; When a multi-core optical cable is bent and deformed, the bending radius R of the ideal fiber core position a and the actual fiber core position aa is... θai and R θ’ai The relational expression is expressed as: (23) In the formula, This represents the ideal position of fiber core a in the cross section of the i-th FBG sensor; Because the core diameter of the fiber Bragg grating sensor is extremely small, it can be simplified as follows: (24)， Combining equations (20), (21), (22), and (24), we get: (25) in, Let be the wavelength change of the i-th grating on fiber core a. Strain at the ideal core position a; Similarly, the relationship between the wavelength changes at the actual and ideal positions of fiber cores b and c can be obtained: (26) (27) Where, Δλ b Let be the wavelength change of the i-th grating on fiber core b. The strain at the ideal core position b; Δλ c Let be the wavelength change of the i-th grating on fiber core c. Strain at the ideal core position c; The core position deviation is solved iteratively.

5. The method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation according to claim 4, characterized in that, The step of iteratively solving for the fiber core position deviation includes: Set the initial guessed core position deviation and the maximum angular deviation range; Substituting the calculated ideal position strain into the multi-core optical cable shape reconstruction algorithm, the algorithm obtains the multi-core optical cable shape position coordinates. Extract the actual shape and position coordinates of the multi-core optical cable obtained from simulation or experiment, and calculate the difference between them and the position coordinates obtained by the algorithm; The obtained error is returned to update the fiber core position deviation until the position coordinates obtained by the algorithm and the position coordinates of the actual shape of the multi-core optical cable obtained by simulation or experiment are within the preset range.

6. The method for reconstructing the shape of a multi-core optical cable based on fourth-order step integral and GOC compensation according to claim 5, characterized in that, The maximum angular deviation range is set to [-30°, 30°].

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