基于FBG的薄板空间形状重构误差分析

茶映鹏; 蔡建军; 彭星玲

doi:10.13756/j.gtxyj.2025.240164

您当前的位置：

首页 >

文章列表页 >

基于FBG的薄板空间形状重构误差分析

光纤光缆技术与应用 | 更新时间：2025-10-15

- 基于FBG的薄板空间形状重构误差分析
- Error Analysis of Spatial Shape Reconstruction of FBG-based Thin Plate
- 光通信研究 2025年第5期
- 作者机构：
  
  江西水利电力大学　精密驱动与装备江西省重点实验室，南昌　330099
- 作者简介：
  
  茶映鹏（1988-），男，云南凤庆人。工程师，硕士，主要研究方向为光纤传感技术。
  彭星玲，副教授。E-mail：pengxingling0223@163.com
- 基金信息：
  
  江西省教育厅科技资助项目(GJJ211911);江西省2023年度大学生创新创业训练计划资助项目(S202311319014)
- DOI：10.13756/j.gtxyj.2025.240164
  中图分类号： TP212;TN253
- 收稿：2024-08-01，
  
  修回：2024-08-15，
  
  纸质出版：2025-10-10
- 稿件说明：
移动端阅览
茶映鹏，蔡建军，彭星玲. 基于FBG的薄板空间形状重构误差分析[J]. 光通信研究，2025(5): 240164.

Cha Y P, Cai J J, Peng X L. Error Analysis of Spatial Shape Reconstruction of FBG-based Thin Plate[J]. Study on Optical Communications, 2025(5): 240164.
茶映鹏，蔡建军，彭星玲. 基于FBG的薄板空间形状重构误差分析[J]. 光通信研究，2025(5): 240164. DOI： 10.13756/j.gtxyj.2025.240164.

Cha Y P, Cai J J, Peng X L. Error Analysis of Spatial Shape Reconstruction of FBG-based Thin Plate[J]. Study on Optical Communications, 2025(5): 240164. DOI： 10.13756/j.gtxyj.2025.240164.

摘要

【目的】

为实现板状结构空间形状快速和准确地检测和重构，将4点光纤布拉格光栅（FBG）串封装到高锰钢薄板表面制成形状传感单元，利用FBG质轻、径细、灵敏度高、抗电磁干扰和可波分复用等优点，文章结合重构算法实现了薄板结构的形状传感和可视化重构。

【方法】

文章分析了温度修正后的薄板曲率传感与空间形状重构原理，进行了基于FBG薄板结构的温度和曲率标定实验。根据拟合温度灵敏度、曲率灵敏度以及曲率与波长变化量的表达式得到6种情况下的曲率组合，再利用线性插值、二次函数插值或三次样条曲率插值算法对曲率进行插值，得到更多的离散曲率点。通过对曲率进行坐标变换得到薄板的坐标信息后，利用B样条曲面重构薄板的空间形状。

【结果】

实验测得薄板的曲率灵敏度分别为-0.154、-0.248、-0.257和-0.235 nm/mm，经温度修正显著降低了曲面重构误差，线性插值、二次函数插值和三次样条插值的平均相对误差

mean

分别为2.47%、2.60%和2.21%，其中三次样条插值在单曲率（1.86%）和变曲率（2.04%）曲面重构中误差最小，表现最优。

【结论】

该方法通过温度修正可有效削弱环境干扰，结合三次样条插值算法能有效提升曲面重构精度，实现薄板结构位移、曲率和形状的同步预测。

Abstract

【Objective】

In order to realize the rapid and accurate detection and reconstruction of the spatial shape of the plate structure

a 4-point Fiber Bragg Grating (FBG) string is surface-mounted on a high-manganese steel thin plate to form a shape-sensing unit. Leveraging the advantages of FBGs-lightweight

compact size

high sensitivity

immunity to electromagnetic interference

and wavelength-division multiplexing-the system integrates a reconstruction algorithm to achieve shape sensing and visual reconstruction of thin-plate structures.

【Methods】

The principle of curvature sensing and spatial shape reconstruction of thin plate after temperature correction is analyzed. The temperature and curvature calibration experiments of thin plate structure based on FBG are carried out. By fitting temperature sensitivity

curvature sensitivity

and the relationship between curvature and wave-length shift

six curvature combinations are derived. Then the curvature interpolation algorithm of linear interpolation

quadratic function interpolation or cubic spline curvature interpolation is used to interpolate the curvature

and more discrete curvature points are obtained. After the coordinate information of the thin plate is obtained by the coordinate transformation of the curvature

the spatial shape of thin plate is reconstructed by using B-spline surface fitting.

【Results】

The curvature sensitivity of the sheet metal is experimentally measured as -0.154

-0.248

-0.257 and -0.235 nm/mm

respectively. The error of surface reconstruction is significantly reduced by temperature correction. Among these methods

cubic spline interpolation achieve the lowest error in both single-curvature (1.86%) and variable-curvature (2.04%) surface reconstruction

thus exhibiting the superior performance.

【Conclusion】

The proposed method effectively mitigates environmental interference through temperature correction and enhances the surface reconstruction accuracy by employing a cubic spline interpolation algorithm

thereby enabling simultaneous prediction of displacement

curvature

and shape in thin plate structures.

关键词

Keywords

references

黄文恺 , 梁智洪 , 王明华 , 等 . 数字孪生在航空航天结构设计、制造和运维中的应用与展望 [J ] . 图学学报 , 2024 , 45 ( 2 ): 241 - 249 .

Huang W K , Liang Z H , Wang M H , et al . Application and Prospect of Digital Twin in the Design, Manufacturing, and Operation of Aerospace Structures [J ] . Journal of Graphics , 2024 , 45 ( 2 ): 241 - 249 .

田婧 , 祝连庆 , 姚霁峰 , 等 . 低损耗超声波金属化光纤布拉格光栅传感特性研究 [J ] . 红外与激光工程 , 2024 , 53 ( 6 ): 168 - 174 .

Tian J , Zhu L Q , Yao J F , et al . Sensing Characteristics of Low-Loss Metallized Fiber Bragg Grating by Ultrasonic Welding [J ] . Infrared and Laser Engineering , 2024 , 53 ( 6 ): 168 - 174 .

丁宝艳 , 赵强 , 陈东营 , 等 . 光纤布拉格光栅压力传感技术与应用进展 [J ] . 光通信研究 , 2024 ( 3 ): 230018 .

Ding B Y , Zhao Q , Chen D Y , et al . Technology and Application Progress of Fiber Bragg Grating Pressure Sensing [J ] . Study on Optical Communications , 2024 ( 3 ): 230018 .

Xu L , Ge J , Patel J H , et al . Dual-layer Orthogonal Fiber Bragg Grating Mesh based Soft Sensor for 3-Dimensional Shape Sensing [J ] . Optics Express , 2017 , 25 ( 20 ): 24727 - 24734 .

Jäckle S , Strehlow J , Heldmann S . Shape Sensing with Fiber Bragg Grating Sensors [C ] // Bildverarbeitung für die Medizin 2019 . Wiesbaden, Germany : Springer Fachmedien Wiesbaden , 2019 : 258 - 263 .

张旭 , 侯茂盛 , 刘智超 , 等 . 基于光纤布拉格光栅传感器的板壳结构曲面重构算法 [J ] . 激光与光电子学进展 , 2020 , 57 ( 9 ): 090603 .

Zhang X , Hou M S , Liu Z C , et al . Surface Reconstruction Algorithm of Plate-Shell Structure based on Fiber Bragg Grating Sensor [J ] . Laser & Optoelectronics Progress , 2020 , 57 ( 9 ): 090603 .

殷礼鑫 , 刘智超 , 刘春辉 . 基于FBG阵列的曲面结构状态感知系统 [J ] . 中国激光 , 2021 , 48 ( 24 ): 2406001 .

Yin L X , Liu Z C , Liu C H . Surface Structure State Perception System based on FBG Array [J ] . Chinese Journal of Lasers , 2021 , 48 ( 24 ): 2406001 .

王彦 , 徐浩雨 , 汪俊亮 , 等 . 环形布设光纤布拉格光栅的三维曲面形状重构 [J ] . 中国光学(中英文) , 2024 , 17 ( 2 ): 398 - 408 .

Wang Y , Xu H Y , Wang J L , et al . Three-Dimensional Surface Shape Reconstruction of Fiber Bragg Gratings in a Ring Arrangement [J ] . Chinese Optics , 2024 , 17 ( 2 ): 398 - 408 .

黎敏 , 廖延彪 . 光纤传感器及其应用技术 [M ] . 北京 : 科学出版社 , 2018 .

Li M , Liao Y B . Optical Fiber Sensor and Its Application Technology [M ] . Beijing, China : Science Press , 2018 .

Peng X , Cai J , Gong Z , et al . Design and Measurement of a Parallel-dual FBG Shape Sensor for Elastic Cantilever Beam Structure Shape Reconstruction [J ] . Optical Fiber Technology , 2024 , 86 : 103849 .

He L , Rong F , Wang Z . A New α Algorithm based on Lagrange Linear Interpolating Power Prediction for Photovoltaic Systems [J ] . IEICE Electronics Express , 2024 , 21 ( 16 ): 20240267 .

Hu S , Li F , Li X . Weight Hierarchies of a Class of Three-Weight P-ary Linear Codes from Inhomogeneous Quadratic Functions [J ] . Applicable Algebra in Engineering, Communication and Computing , 2025 , 36 ( 5 ): 877 - 896 .

Sun M , Lan L , Zhu C G , et al . Cubic Spline Interpolation with Optimal End Conditions [J ] . Journal of Computational and Applied Mathematics , 2023 , 425 : 115039 .

Wang Q , Li P , Rocca P , et al . Interval-based Tolerance Analysis Method for Petal Reflector Antenna with Random Surface and Deployment Errors [J ] . IEEE Transactions on Antennas and Propagation , 2023 , 71 ( 11 ): 8556 - 8569 .

Lynch K M , Park F C . Modern Robotics [M ] . Cambridge, UK : Cambridge University Press , 2017 .

Jiang X , Lin Y . Reparameterization of B-spline Surface and Its Application in Ship Hull Modeling [J ] . Ocean Engineering , 2023 , 286 : 115535 .

Feng D , Zhou W , Qiao X , et al . Compact Optical Fiber 3D Shape Sensor based on a Pair of Orthogonal Tilted Fiber Bragg Gratings [J ] . Scientific Reports , 2015 , 5 : 17415 .

Chen S , Huang J , Liu W , et al . Spectrum Characteristics and Temperature Measurement Error of FBG Sensor based on Rotor Temperature Monitoring System [J ] . Optical Fiber Technology , 2023 , 78 : 103306 .

浏览量

下载量

CSCD

CNKI被引量

文章被引用时，请邮件提醒。

提交

工具集

关联资源

基于光纤光栅的锂电池表面物理场监测

基于改进LSTM的FBG传感网络光谱基线校正方法

面向光纤光栅传感线性拟合度的PSO-GPR算法

光纤布拉格光栅压力传感技术与应用进展

飞秒激光制备光纤布拉格光栅研究进展