CN-122020751-A - Long-distance high-precision optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral

CN122020751ACN 122020751 ACN122020751 ACN 122020751ACN-122020751-A

Abstract

The invention discloses a long-distance optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral, and relates to the technical field of optical fiber shape sensing and curve shape reconstruction. The method comprises the steps of firstly collecting and demodulating optical fiber sensing signals to obtain strain data along the arc length of an optical fiber, calculating curvature and deflection rate of each sampling point according to a multi-core optical fiber geometric model, constructing an in-segment fitting model of a ratio of the curvature to the deflection rate, obtaining generalized Euler spiral parameters by solving a matrix equation, respectively carrying out in-segment parameter optimization or weighted limited processing according to a deflection rate reliability threshold judgment result to inhibit parameter jump, and finally reconstructing the three-dimensional shape of the optical fiber segment by segment based on Frenet-Serset or Bishop frame numerical integration. The invention improves the continuity between micro-segments through generalized Euler spiral fitting, effectively solves the problem of insufficient precision in long-distance reconstruction of the traditional method, and realizes high-precision and high-robustness optical fiber shape sensing.

Inventors

TIAN YE
ZHANG HENGXU
ZHU SHICHENG
LI ZHUOHONG
ZHOU ZIJING
ZHANG GONGQI
XU JUN
ZHANG JIANZHONG

Assignees

哈尔滨工程大学

Dates

Publication Date: 20260512
Application Date: 20260116

Claims (10)

1. The long-distance optical fiber shape reconstruction method based on the three-dimensional generalized Euler spiral is characterized by comprising the following steps of: step 1, acquiring original strain data, and preprocessing the original strain data to obtain a preprocessed strain data sequence; step 2, performing discrete sampling on the multi-core optical fiber according to the preprocessed strain data sequence, and calculating the curvature and deflection of each sampling point; Step 3, performing piecewise three-dimensional generalized Euler spiral fitting according to the curvature and the deflection rate of each sampling point along the discrete sampling of the arc length of the optical fiber to obtain a parameterized model to be fitted; Step 4, constructing a matrix equation consisting of homogeneous linear equations corresponding to each micro-element segment according to the parameterized model to be fitted, and solving to obtain a parameter vector; Step 5, judging whether the parameter vector exceeds a threshold value, if so, carrying out weighting and limited model processing to obtain a processed stable in-segment model parameter, and if not, carrying out parameter optimization in the micro-segment to obtain an optimized internal curvature and flexibility rate of the micro-segment; And 6, carrying out numerical integration according to all the processed stable model parameters in the micro-element section and all the optimized internal curvature and flexibility rate of the micro-element section, calculating a reconstruction position and a reference system in a segment-by-segment recursive manner to obtain a reconstruction three-dimensional curve, and carrying out visual operation on the reconstruction three-dimensional curve.
2. The method for reconstructing a long-distance optical fiber shape based on three-dimensional generalized euler spiral according to claim 1, wherein the method for calculating curvature and flexibility of each sampling point in step 2 specifically comprises: Step 2.1, according to the geometric model of the multi-core optical fiber, the strain value of each sampling point of the same section Calculating curvature vector of each sampling point ; Wherein, the For the number of sampling points, Is the first The radial distance from the sampling point to the center of the multi-core fiber, Is the first Fixed angular offsets between the sample points and the fiber material coordinate system, The unit vectors are respectively in the y-axis direction and the z-axis direction of the material coordinate system; Step 2.2, calculating the curvature scalar of each sampling point according to the curvature vector corresponding to each sampling point And a curvature component; Wherein, the The curvature component of each sampling point; Step 2.3, calculating the bending direction angle of each sampling point according to the curvature component ; ; Step 2.4, calculating the arc length along each sampling point according to the bending direction angle of each sampling point Flexible rate of (a) ; Wherein, the Is the angle of the bending direction to the arc length Is a first derivative of (a).
3. The method for reconstructing the shape of the long-distance optical fiber based on the three-dimensional generalized Euler spiral according to claim 2, wherein the generalized Euler spiral fitting in the step 3 specifically comprises the following steps: Step 3.1, calculating the characteristic ratio at each sampling point according to the curvature and the flexibility ratio of each sampling point ; ; Step 3.2, dividing the multi-core optical fiber into continuous micro-element sections, and constructing a parameterized model to be fitted of each micro-element section according to the characteristic ratio of each sampling point; Wherein, the Are all model parameters to be fitted.
4. A method for reconstructing a long-distance optical fiber shape based on three-dimensional generalized euler spiral according to claim 3, wherein the matrix equation in step4 The method comprises the following steps: Wherein, the As a matrix of parameters, As a vector of the parameters, Is a transposed calculation.
5. The method for reconstructing the shape of the long-distance optical fiber based on the three-dimensional generalized Euler spiral according to claim 4, wherein the parameter optimization in the micro-segment in step 5 specifically comprises: calculating a fit value at a midpoint within a bin for which the parameter vector does not exceed a threshold ; Setting an objective function according to the fitting value And minimizing the objective function; Wherein, the As a scale factor of the dimensions of the device, For midpoint curvature measurements within the micro-segment where the parameter vector does not exceed the threshold, A midpoint flex rate measurement in a micro-segment where the parameter vector does not exceed a threshold; The fitting values when the objective function is minimized As the optimized parameter vector does not exceed the curvature in the micro-element section of the threshold value, the scale factor And the flexibility rate in the micro-element section which is used as the optimized parameter vector and does not exceed the threshold value.
6. The method for reconstructing a long-distance optical fiber shape based on three-dimensional generalized euler spiral according to claim 5, wherein the weighting and limiting model processing specifically comprises: Weighting each row in the parameter matrix according to the reliability of the flexible rate, and weakening the influence of sampling points in the micro-element section of which the parameter vector exceeds a threshold value; setting independent three-dimensional generalized Euler models for sampling points in the micro-element section with the parameters exceeding the threshold value And fitting again to obtain the processed stable intra-segment model parameters.
7. The long-distance optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral of claim 6, wherein the three-dimensional generalized Euler model is characterized in that The method specifically comprises the following steps: Wherein, the Are weight coefficients.
8. A computer device comprising a memory, a processor and a computer program stored on the memory, characterized in that the processor executes the computer program to carry out the steps of the method according to claim 7.
9. A computer-readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method as claimed in claim 7.
10. A computer program product comprising computer instructions which, when executed by a processor, implement the steps of the method of claim 7.

Description

Long-distance high-precision optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral Technical Field The invention relates to the technical field of optical fiber shape sensing and curve shape reconstruction, in particular to a long-distance optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral, which is suitable for a shape detection and reconstruction system. Background With the development of distributed optical fiber sensing technology, reconstructing the shape of an optical fiber in a three-dimensional space based on information such as displacement, phase, scattering intensity, or optical fiber strain obtained along the optical fiber has become an important research direction. The existing reconstruction method is based on a Frenet-Serset or Bishop frame of differential geometry, and the spatial coordinates of the curve are obtained by integrating segment by segment according to the relation between the measured curvature and the deflection rate or equivalent quantity and the points of the curve disclosed by the Frenet-Serset or Bishop frame equation. (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, such methods still present several core bottlenecks in actual engineering deployment and long-distance sensing environments, limiting further improvements in reconstruction accuracy, robustness and computational efficiency, one of the important reasons is that during curve reconstruction, existing curve micro-segments are generally simplified in a serialization process without changing curvature parameters as a fundamental principle, which results in that parameter information of the micro-segments during curve reconstruction deviates from physical reality to present step changes, thereby resulting in insufficient accuracy of the reconstructed curve. Disclosure of Invention The invention aims at providing a long-distance optical fiber shape reconstruction method based on a three-dimensional generalized Euler spiral, wherein one common definition of introducing the three-dimensional generalized Euler spiral is to make curvatureAnd flexibility ratio ofThe ratio between is expressed as the ratio of two linear functions, i.eOr equivalently, the kappa and the tau are regarded as a function family meeting a certain linear/rational linear relation, the three-dimensional common Euler model can be regarded as a degradation or special case of the three-dimensional generalized Euler model, and the three-dimensional generalized Euler model brings clear physical interpretation on differential geometry, which means that the kappa and the tau do not fluctuate independently in a real and smooth three-dimensional space curve, but often present a coupling relation with a low-order parameterized form. The invention provides a long-distance optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral, which comprises the following technical scheme: A long-distance optical fiber shape reconstruction method based on three-dimensional generalized Euler spiral comprises the following steps: And step 1, acquiring original strain data, and preprocessing the original strain data to obtain a preprocessed strain data sequence. And 2, performing discrete sampling on the multi-core optical fiber according to the preprocessed strain data sequence, and calculating the curvature and deflection of each sampling point. And 3, performing piecewise three-dimensional generalized Euler spiral fitting according to the curvature and the deflection rate of each sampling point along the optical fiber arc length in a discrete sampling manner to obtain a parameterized model to be fitted. And 4, constructing a matrix equation consisting of homogeneous linear equations corresponding to each micro-element segment according to the parameterized model to be fitted, and solving to obtain a parameter vector. And 5, judging whether the parameter vector exceeds a threshold value, if so, carrying out weighting and limited model processing to obtain a processed stable in-segment model parameter, and if not, carrying out parameter optimization in the micro-segment to obtain the optimized curvature and flexibility rate in the micro-segment. And 6, carrying out numerical integration according to all the processed stable model parameters in the micro-element section and all the optimized internal curvature and flexibility rate of the micro-element section, calculating a reconstruction position and a reference system in a segment-by-segment recursive manner to obtain a reconstruction three-dimensional curve, and carrying out visual operation on the reconstruction three-dimensional curve. Further, the method for calculating the curvature and the flexibility ratio of each samplin