Long-distance high-precision optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral
By introducing a three-dimensional generalized Euler spiral model, the problem of insufficient reconstruction accuracy in existing fiber shape reconstruction methods is solved, and high-precision and efficient reconstruction of long-distance fiber shapes is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HARBIN ENG UNIV
- Filing Date
- 2026-01-16
- Publication Date
- 2026-05-12
AI Technical Summary
Existing fiber shape reconstruction methods suffer from insufficient reconstruction accuracy and low computational efficiency in long-distance sensing environments. This is mainly due to the step changes in the parameter information of the curve micro-segments during the continuous transformation process, which leads to insufficient accuracy of the reconstructed curve.
A three-dimensional generalized Euler spiral model is adopted, in which the ratio between curvature and torsion is expressed as the ratio of two linear functions. Through piecewise fitting and parameter optimization, a homogeneous linear equation system of infinitesimal segments is constructed, and numerical integration is performed to reconstruct the three-dimensional curve.
It significantly improves the continuous linearity of curve curvature and torsion between sensing points, enhances measurement accuracy and computational efficiency, and enables robust reconstruction of the shape of long-distance optical fibers.
Smart Images
Figure CN122020751A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of fiber optic shape sensing and curve shape reconstruction technology, and in particular to a long-distance fiber optic shape reconstruction method based on a three-dimensional generalized Euler spiral, which is applicable to shape detection and reconstruction systems. Background Technology
[0002] With the development of distributed fiber optic sensing technology, reconstructing the shape of an optical fiber in three-dimensional space based on information such as displacement, phase, scattering intensity, or fiber strain obtained along the fiber has become an important research direction. Existing reconstruction methods are based on the Frenet–Serret or Bishop framework of differential geometry. They obtain the spatial coordinates of the curve by piecewise integration using measured curvature and torsion or equivalent quantities, according to the relationship between points on the curve revealed by the Frenet–Serret or Bishop framework equations. (Reference: Q. Jiang, F. Wang and Y. Zhang, "Shape Reconstruction for Flexible Robot Using FBG Sensor," in IEEE Instrumentation & Measurement Magazine, vol.28, no. 3, pp. 44-51, May 2025, doi: 10.1109 / MIM.2025.10982090.) However, in practical engineering deployments and long-distance sensing environments, these methods still suffer from several core bottlenecks, limiting further improvements in reconstruction accuracy, robustness, and computational efficiency. One important reason is that during the curve reconstruction process, the existing curve segments are usually simplified to maintain the curvature parameter as the basic principle during the continuous transformation process. This principle leads to the parameter information of the segments deviating from the physical reality in a step-like change, resulting in insufficient accuracy of the reconstructed curve. Existing methods construct segments using a three-dimensional Euler spiral model. Compared with traditional methods, the curve constructed by this model has continuous linear characteristics in the changes of curvature and torsion, and more accurately restores the continuity of the connection points of the segments and the overall curve (Reference: YET, ZHU S, DUAN C, et al. Optical fiber shape reconstruction algorithm based on 3D Euler spiral model[J]. Measurement Science and Technology, 2024, 35(11): 115111.). However, since its use of the three-dimensional ordinary Euler spiral model is limited to the ordinary linear curvature-torsion relationship Euler spiral, there is still a deviation in the physical model from the actual curve distribution. Summary of the Invention
[0003] The purpose of this invention is to address the aforementioned prior art by providing a long-distance optical fiber shape reconstruction method based on a three-dimensional generalized Euler spiral. This method introduces a common definition of a three-dimensional generalized Euler spiral, which involves reconstructing the curvature of the fiber. With torsion The ratio between them is expressed as the ratio of two linear functions, that is... Alternatively, κ and τ can be considered as a family of functions that satisfy a certain linear / rational linear relationship. The three-dimensional ordinary Euler model can be regarded as a degenerate or special case of the three-dimensional generalized Euler model. The three-dimensional generalized Euler model brings a clear physical interpretation in differential geometry, indicating that κ and τ do not fluctuate arbitrarily and independently in real, smooth three-dimensional space curves, but often exhibit a coupling relationship with a low-order parameterized form.
[0004] This invention proposes a long-distance optical fiber shape reconstruction method based on a three-dimensional generalized Euler spiral, the core of which includes the following technical solutions:
[0005] A method for reconstructing the shape of long-distance optical fibers based on three-dimensional generalized Euler spirals includes the following steps:
[0006] Step 1: Obtain the raw strain data and preprocess it to obtain the preprocessed strain data sequence.
[0007] Step 2: Based on the preprocessed strain data sequence, perform discrete sampling for the multi-core optical fiber and calculate the curvature and deflection of each sampling point.
[0008] Step 3: Based on the curvature and torsion of each sampling point discretely sampled along the fiber arc length, perform piecewise three-dimensional generalized Euler spiral fitting to obtain the parameterized model to be fitted.
[0009] Step 4: Based on the parameterized model to be fitted, construct a matrix equation consisting of homogeneous linear equations corresponding to each infinitesimal segment and solve it to obtain the parameter vector.
[0010] Step 5: Determine whether the parameter vector exceeds the threshold. If so, perform weighted and constrained model processing to obtain the processed stable intra-segment model parameters; if not, perform intra-segment parameter optimization to obtain the optimized intra-segment curvature and torsion.
[0011] Step 6: Based on all the processed stable micro-segment model parameters and all the optimized micro-segment curvature and torsion, perform numerical integration, recursively calculate the reconstruction position and reference frame segment by segment, obtain the reconstructed 3D curve, and visualize it.
[0012] Furthermore, the method for calculating the curvature and torsion of each sampling point in step 2 specifically includes:
[0013] Step 2.1: Based on the geometric model of the multi-core optical fiber, obtain the strain values at each sampling point on the same cross-section. Calculate the curvature vector at each sampling point ;
[0014]
[0015] in, The number of sampling points, For the first The radial distance from each sampling point to the center of the multi-core optical fiber For the first The fixed angular offset between each sampling point and the optical fiber material coordinate system. These are the unit vectors in the y-axis and z-axis directions of the material coordinate system, respectively.
[0016] Step 2.2: Calculate the curvature scalar for each sampling point based on the curvature vector corresponding to each sampling point. and curvature components;
[0017]
[0018]
[0019]
[0020] in, These are all curvature components at each sampling point.
[0021] Step 2.3: Calculate the bending direction angle at each sampling point based on the curvature components. ;
[0022] .
[0023] Step 2.4: Calculate the arc length of each sampling point based on the bending direction angle of each sampling point. torsion ;
[0024]
[0025] in, The bending direction angle is relative to the arc length. The first derivative.
[0026] Furthermore, step 3, the generalized Euler spiral fitting, specifically includes the following steps:
[0027] Step 3.1: Calculate the characteristic ratio at each sampling point based on the curvature and torsion of each sampling point. ;
[0028] ;
[0029] Step 3.2: Divide the multi-core optical fiber into continuous micro-segments, and construct a parameterized model to be fitted for each micro-segment based on the feature ratio of each sampling point;
[0030]
[0031] in, These are all model parameters to be fitted.
[0032] Furthermore, the matrix equation described in step 4 Specifically:
[0033]
[0034] in, For the parameter matrix, For parameter vectors, This is for transpose calculation.
[0035] Furthermore, the parameter optimization within the micro-segment described in step 5 specifically includes:
[0036] Calculate the fitted value at the midpoint of the infinitesimal segment within which the parameter vector does not exceed the threshold. ;
[0037] Based on the fitted values, set the objective function. And minimize the objective function;
[0038]
[0039] in, As a scale factor, The midpoint curvature measurement value within the infinitesimal segment where the parameter vector does not exceed the threshold. The measured midpoint torsion value within the micro-segment where the parameter vector does not exceed the threshold.
[0040] The fitted value when the objective function is minimized The scale factor is the curvature within the infinitesimal segment where the optimized parameter vector does not exceed the threshold. The torsion within the infinitesimal segment that is not exceeded by the optimized parameter vector.
[0041] Furthermore, the weighted and constrained model processing specifically includes:
[0042] Each row in the parameter matrix is weighted according to the reliability of the torsion, thus weakening the influence of sampling points in the infinitesimal segments of the parameter vector that exceed the threshold.
[0043] For each sampling point in the infinitesimal segment where the parameter exceeds the threshold, a separate three-dimensional generalized Euler model is set. Then, the model was refitted to obtain the processed and stable intra-segment model parameters.
[0044] Furthermore, the three-dimensional generalized Euler model Specifically, it includes:
[0045]
[0046] in, All are weighting coefficients.
[0047] A computer device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method described above.
[0048] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.
[0049] A computer program product includes computer instructions that, when executed by a processor, implement the steps of the method described above.
[0050] The beneficial effects of this invention are as follows: it adopts a three-dimensional generalized Euler model to realize the connection of micro-segments, which significantly improves the continuous linearity of the curvature and torsion of the curve between sensing points compared with existing methods, and achieves a comprehensive improvement in measurement accuracy and computational efficiency. Attached Figure Description
[0051] Figure 1 This is a schematic diagram of an optical fiber sensing device according to an embodiment of the present invention.
[0052] Figure 2 This is a schematic diagram of the process of the present invention.
[0053] Figure 3 This is a schematic diagram of the curvature and torsion distribution of several typical three-dimensional generalized Euler curves according to embodiments of the present invention.
[0054] Figure 4 This is a schematic diagram of a random curve used for testing in an embodiment of the present invention.
[0055] Figure 5 This is an error analysis diagram of an embodiment of the present invention. Detailed Implementation
[0056] The following is in conjunction with the appendix Figure 2 The present invention will be further described below.
[0057] A method for reconstructing the shape of long-distance optical fibers based on three-dimensional generalized Euler spirals includes the following steps:
[0058] Step 1: Obtain the raw strain data and preprocess it to obtain the preprocessed strain data sequence.
[0059] Step 2: Based on the preprocessed strain data sequence, perform discrete sampling for the multi-core optical fiber and calculate the curvature and deflection of each sampling point.
[0060] The specific methods for calculating the curvature and torsion at each sampling point include:
[0061] Step 2.1: Based on the geometric model of the multi-core optical fiber, obtain the strain values at each sampling point on the same cross-section. Calculate the curvature vector at each sampling point ;
[0062]
[0063] in, The number of sampling points, For the first The radial distance from each sampling point to the center of the multi-core optical fiber For the first The fixed angular offset between each sampling point and the optical fiber material coordinate system. These are the unit vectors in the y-axis and z-axis directions of the material coordinate system, respectively.
[0064] Step 2.2: Calculate the curvature scalar for each sampling point based on the curvature vector corresponding to each sampling point. and curvature components;
[0065]
[0066]
[0067]
[0068] in, These are all curvature components at each sampling point.
[0069] Step 2.3: Calculate the bending direction angle at each sampling point based on the curvature components. ;
[0070] .
[0071] Step 2.4: Calculate the arc length of each sampling point based on the bending direction angle of each sampling point. torsion ;
[0072]
[0073] in, The bending direction angle is relative to the arc length. The first derivative.
[0074] Step 3: Based on the curvature and torsion of each sampling point discretely sampled along the fiber arc length, perform piecewise three-dimensional generalized Euler spiral fitting to obtain the parameterized model to be fitted.
[0075] The generalized Euler spiral fitting specifically includes the following steps:
[0076] Step 3.1: Calculate the characteristic ratio at each sampling point based on the curvature and torsion of each sampling point. ;
[0077] .
[0078] Step 3.2: Divide the multi-core optical fiber into continuous micro-segments, and construct a parameterized model to be fitted for each micro-segment based on the feature ratio of each sampling point;
[0079]
[0080] in, These are all model parameters to be fitted.
[0081] Step 4: Based on the parameterized model to be fitted, construct a matrix equation consisting of homogeneous linear equations corresponding to each infinitesimal segment and solve it to obtain the parameter vector.
[0082] The matrix equation Specifically:
[0083]
[0084] in, For the parameter matrix, For parameter vectors, This is for transpose calculation.
[0085] Step 5: Determine whether the parameter vector exceeds the threshold. If so, perform weighted and constrained model processing to obtain the processed stable intra-segment model parameters; if not, perform intra-segment parameter optimization to obtain the optimized intra-segment curvature and torsion.
[0086] The weighted and constrained model processing specifically includes:
[0087] Each row in the parameter matrix is weighted according to the reliability of the torsion, thus weakening the influence of sampling points in the infinitesimal segments of the parameter vector that exceed the threshold.
[0088] For each sampling point in the infinitesimal segment where the parameter exceeds the threshold, a separate three-dimensional generalized Euler model is set. Then, the model was refitted to obtain the stable intra-segment model parameters after processing.
[0089]
[0090] in, All are weighting coefficients.
[0091] The optimization of parameters within the micro-element segment specifically includes:
[0092] Calculate the fitted value at the midpoint of the infinitesimal segment within which the parameter vector does not exceed the threshold. ;
[0093] Based on the fitted values, set the objective function. And minimize the objective function;
[0094]
[0095] in, As a scale factor, The midpoint curvature measurement value within the infinitesimal segment where the parameter vector does not exceed the threshold. The parameter vector does not exceed the midpoint torsion measurement value within the micro-element segment of the threshold;
[0096] The fitted value when the objective function is minimized The scale factor is the curvature within the infinitesimal segment where the optimized parameter vector does not exceed the threshold. The torsion within the infinitesimal segment that is not exceeded by the optimized parameter vector.
[0097] Step 6: Based on all the processed stable micro-segment model parameters and all the optimized micro-segment curvature and torsion, perform numerical integration, recursively calculate the reconstruction position and reference frame segment by segment, obtain the reconstructed 3D curve, and visualize it.
[0098] Example
[0099] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.
[0100] This embodiment relates to an optical fiber shape reconstruction system based on fitting a three-dimensional generalized Euler spiral to a rational function. Its basic implementation framework includes:
[0101] The data acquisition and demodulation module is used to acquire and demodulate the backscattered Rayleigh or interferometric signals of the optical fiber into measurement data along the arc length direction of the fiber, obtaining data including the arc length vector. curvature With torsion The initial data sequence.
[0102] The algorithm processing module, connected to the data acquisition and demodulation module, is used to receive input data. , and The data sequence and initial reference frame and position, including the initial tangent vector T0, principal normal vector N0, double normal vector B0 and starting point coordinates, are processed by the algorithm to output the reconstructed coordinates and the corresponding TNB reference frame; the algorithm processing module includes at least the following sub-modules: (a) data preprocessing sub-module; (b) baseline generation sub-module; (c) ratio fitting sub-module; (d) midpoint parameter optimization sub-module; (e) numerical integration sub-module.
[0103] The output and verification module is used to save and output the reconstructed coordinates and the TNB reference frame, and to provide reconstruction accuracy evaluation and verification. Figure 4 The test uses a comparison of randomized patterns;
[0104] The system achieves stable and high-precision reconstruction of the shape of long-distance multi-core optical fibers through the collaborative work of the above sub-modules, and significantly reduces the impact of parameter abrupt changes caused by demodulation jumps or noise on the reconstruction results.
[0105] Data acquisition and demodulation module: Common implementations use a high-resolution optical demodulator as the front end, combined with an amplifier and a high-speed ADC to acquire complex amplitude / phase data along the optical fiber; real-time phase tracking, phase unwrapping, and primary denoising are performed using an FPGA, embedded processor, or other processing devices. The software converts the phase / amplitude values into physical quantities along the arc length according to the sensing model and estimates the curvature. With torsion This also includes outlier detection and interpolation, various filtering methods (moving average, spline, low-pass), resampling, or anti-aliasing processing to ensure... The module employs a monotonic step size that satisfies numerical integration requirements and incorporates temperature / reference fiber calibration procedures to compensate for environmental drift, outputting standardized data. The data acquired by this module is calculated from strain data obtained at different sensor placement points at the same measuring point under arbitrary bending curvature and angle directions. This is represented by the strain data measured from the i-th optical fiber. Indicates the fiber core spacing of each fiber. This represents the fixed angular offset between each fiber core and the optical fiber material coordinate system. Let be the unit vector along the y-axis and z-axis of the material coordinate system. The magnitude of the apparent curvature vector is determined by the strain value and the radial distance, while its direction is controlled by the calibrated angular offset. For an N-core fiber optic system, its apparent curvature vector can be expressed as:
[0106]
[0107] The curvature scalar is then:
[0108]
[0109] Further decomposition of curvature into components in the material coordinate system:
[0110]
[0111]
[0112] The bending angle and deflection are:
[0113]
[0114]
[0115] Therefore, with an N-core optical fiber, we can obtain all the necessary data through strain measurement. The sensor structure is based on... Figure 1 For example, this shows a typical structure of a three-core optical fiber.
[0116] Preferably, the data preprocessing submodule is characterized in that it is used for processing the data... , and The module performs validity checks, missing / distortion detection, and orthogonalization and normalization of the initial reference vector; the ratio fitting submodule is characterized by its use in constructing the curvature-to-torsion ratio. The intra-segment fitting model is derived, and a numerical method is used to solve for the form of a first-order rational function. The fitting parameters, the data preprocessing submodule further includes:
[0117] Step A-1 is an arc length verification step, used to detect and ensure that the input arc length vector s is strictly increasing. If necessary, s is resampled or interpolated to meet the numerical integration accuracy requirements.
[0118] Step A-2: Derivative estimation step, calculating the analytic derivative. , ;
[0119] Step A-3 is the initial vector orthogonalization step, which involves progressively orthogonalizing and normalizing the inputs T0, N0, and B0.
[0120] Step A-4 implements a noise suppression strategy to reduce the impact of measurement noise on subsequent fitting and integration.
[0121] Preferably, the baseline generation submodule is characterized by being used to generate a baseline within adjacent sampling point segments using an interpolation method and further fit a generalized Euler model; the baseline generation and ratio fitting submodule further includes:
[0122] Step B-1: Within each adjacent sampling segment, use interpolation to generate a baseline for the ratio of curvature to deflection within the segment, as shown in the following formula;
[0123]
[0124] Step B-2 involves solving for the characteristic fitting coefficients a, b, c, and d of the three-dimensional generalized Euler spiral in the form of a first-order rational function on the baseline within the segment. Here, a, b, c, and d are parameters of the generalized Euler model. Specifically, this is achieved by assuming that the segment satisfies a local ratio model in the form of a generalized Euler spiral. It can also be regarded as This runs within our segment Construct a homogeneous linear system at the sampling points .
[0125] Step B-3 uses SVD to solve for the parameter vector. The solution in the least squares sense is determined, and the impact of data on VBτ being very small (denominator approaching 0) is assessed. Set two thresholds: an absolute threshold (adjusted according to the physical magnitude of the data) and a relative threshold (representing the proportion relative to the median within a segment). At points exceeding these thresholds... exist When noise is very small, it is amplified, so each row of the M matrix is... The reliability is weighted to weaken the influence of sampling points with very small τ, and a restricted three-dimensional generalized Euler model is set separately for these points, that is, c=0, and a linear model is fitted. This eliminates the risk of extreme points in the denominator.
[0126]
[0127] Preferably, the intra-segment parameter optimization submodule of the micro-element segment is characterized by using the fitted value of the three-dimensional generalized Euler spiral within the segment, and analytically solving for the optimal solution to recover the curvature and deflection parameters evaluated within the segment, thereby suppressing parameter jumps between segments. The parameter optimization submodule further includes:
[0128] Step C-1 evaluates the interpolated curvature-to-deflection baseline at the midpoint of the segment and uses the first-order three-dimensional generalized Euler spiral characteristic rational function fitted within the segment. Update the value within the segment;
[0129] Step C-2 sets a scaling factor as a standard for measuring parameters, minimizing the objective function within the segment, and thereby solving for the parameter changes within the segment under the generalized Euler model, where the scaling factor... It is set as follows to measure the goodness or badness of the fit parameters to the actual situation. When the value is minimum, the curvature parameter within the segment is considered as The torsion parameter within the segment is considered as ;
[0130]
[0131] Preferably, the numerical integration submodule is characterized by its use of numerical integration methods such as fourth-order Runge-Kutta (RK4) within the Bishop or Frenet-Serret framework to recursively calculate the reconstructed position and reference frame segment by segment based on the recovered intra-segment parameters (endpoint and midpoint parameters). The Frenet-Serret frame in three-dimensional space can be represented as:
[0132]
[0133] The expression for the Bishop logo is:
[0134]
[0135] Combined with appendix Figure 5 The output and verification module is responsible for saving the reconstruction results, visualization, and accuracy evaluation. The visualization provides 3D curves, reference frames (T, N, B), and error plots; the evaluation indicators include point errors, such as RMSE, maximum error, tangent vector angle error, orthogonality deviation, etc., as the basis and standard for further optimization.
[0136] Preferably, this embodiment provides an electronic device including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of the shape reconstruction method based on a three-dimensional Euler spiral.
[0137] Preferably, this embodiment proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the shape reconstruction method based on a three-dimensional Euler spiral.
[0138] Preferably, the memory in this embodiment can be volatile memory or non-volatile memory, or a combination of both. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which serves as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct Memory Bus RAM (DRRAM). It should be noted that the memory used in the methods described in this invention is intended to include, but is not limited to, these and any other suitable types of memory.
[0139] Preferably, in this embodiment, it can be implemented entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state drives (SSDs)).
[0140] In implementation, this can be accomplished through integrated logic circuits in the processor's hardware or through software instructions. The steps described in this embodiment can be directly manifested as execution by the hardware processor, or as a combination of hardware and software modules within the processor. The software modules can reside in readily available storage media in the art, such as random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, or registers. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, further details are omitted here.
[0141] It should be noted that the processor in this embodiment can be an integrated circuit chip with signal processing capabilities. During implementation, each step of this embodiment can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The aforementioned processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams in this embodiment. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method in this embodiment can be directly manifested as execution by a hardware decoding processor, or execution by a combination of hardware and software modules in the decoding processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.
[0142] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for reconstructing the shape of long-distance optical fibers based on three-dimensional generalized Euler spirals, characterized in that, Includes the following steps: Step 1: Obtain the raw strain data and preprocess it to obtain the preprocessed strain data sequence; Step 2: Based on the preprocessed strain data sequence, perform discrete sampling for the multi-core optical fiber and calculate the curvature and deflection at each sampling point; Step 3: Based on the curvature and torsion of each sampling point discretely sampled along the fiber arc length, perform piecewise three-dimensional generalized Euler spiral fitting to obtain the parameterized model to be fitted; Step 4: Based on the parameterized model to be fitted, construct a matrix equation consisting of homogeneous linear equations corresponding to each infinitesimal segment and solve it to obtain the parameter vector; Step 5: Determine whether the parameter vector exceeds the threshold. If so, perform weighted and constrained model processing to obtain the processed stable intra-segment model parameters; if not, perform intra-segment parameter optimization to obtain the optimized intra-segment curvature and torsion. Step 6: Based on all the processed stable micro-segment model parameters and all the optimized micro-segment curvature and torsion, perform numerical integration, recursively calculate the reconstruction position and reference frame segment by segment, obtain the reconstructed 3D curve, and visualize it.
2. The method for reconstructing the shape of a long-distance optical fiber based on a three-dimensional generalized Euler spiral according to claim 1, characterized in that, The method for calculating the curvature and torsion of each sampling point in step 2 specifically includes: Step 2.1: Based on the geometric model of the multi-core optical fiber, obtain the strain values at each sampling point on the same cross-section. Calculate the curvature vector at each sampling point ; in, The number of sampling points, For the first The radial distance from each sampling point to the center of the multi-core optical fiber For the first The fixed angular offset between each sampling point and the optical fiber material coordinate system. These are the unit vectors in the y-axis and z-axis directions of the material coordinate system, respectively; Step 2.2: Calculate the curvature scalar for each sampling point based on the curvature vector corresponding to each sampling point. and curvature components; in, These are all curvature components at each sampling point; Step 2.3: Calculate the bending direction angle at each sampling point based on the curvature components. ; ； Step 2.4: Calculate the arc length of each sampling point based on the bending direction angle of each sampling point. torsion ; in, The bending direction angle is relative to the arc length. The first derivative.
3. The method for reconstructing the shape of a long-distance optical fiber based on a three-dimensional generalized Euler spiral according to claim 2, characterized in that, Step 3, the generalized Euler spiral fitting, specifically includes the following steps: Step 3.1: Calculate the characteristic ratio at each sampling point based on the curvature and torsion of each sampling point. ; ； Step 3.2: Divide the multi-core optical fiber into continuous micro-segments, and construct a parameterized model to be fitted for each micro-segment based on the feature ratio of each sampling point; in, These are all model parameters to be fitted.
4. The method for reconstructing the shape of a long-distance optical fiber based on a three-dimensional generalized Euler spiral according to claim 3, characterized in that, The matrix equation described in step 4 Specifically: in, For the parameter matrix, For parameter vectors, This is for transpose calculation.
5. The method for reconstructing the shape of a long-distance optical fiber based on a three-dimensional generalized Euler spiral according to claim 4, characterized in that, Step 5, the optimization of parameters within the micro-segment, specifically includes: Calculate the fitted value at the midpoint of the infinitesimal segment within which the parameter vector does not exceed the threshold. ; Based on the fitted values, set the objective function. And minimize the objective function; in, As a scale factor, The midpoint curvature measurement value within the infinitesimal segment where the parameter vector does not exceed the threshold. The parameter vector does not exceed the midpoint torsion measurement value within the micro-element segment of the threshold; The fitted value when the objective function is minimized The scale factor is the curvature within the infinitesimal segment where the optimized parameter vector does not exceed the threshold. The torsion within the infinitesimal segment that is not exceeded by the optimized parameter vector.
6. The method for reconstructing the shape of a long-distance optical fiber based on a three-dimensional generalized Euler spiral according to claim 5, characterized in that, The weighted and constrained model processing specifically includes: Each row in the parameter matrix is weighted according to the reliability of the torsion, thus weakening the influence of sampling points in the infinitesimal segments of the parameter vector that exceed the threshold. For each sampling point in the infinitesimal segment where the parameter exceeds the threshold, a separate three-dimensional generalized Euler model is set. Then, the model was refitted to obtain the processed and stable intra-segment model parameters.
7. The method for reconstructing the shape of a long-distance optical fiber based on a three-dimensional generalized Euler spiral according to claim 6, characterized in that, The three-dimensional generalized Euler model Specifically, it includes: in, All are weighting coefficients.
8. A computer device comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method of claim 7.
9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, it implements the steps of the method of claim 7.
10. A computer program product comprising computer instructions, characterized in that: When the computer instructions are executed by the processor, they implement the steps of the method of claim 7.