Error Analysis of Spatial Shape Reconstruction of FBG-based Thin Plate

CHA Yingpeng; CAI Jianjun; PENG Xingling

doi:10.13756/j.gtxyj.2025.240164

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Error Analysis of Spatial Shape Reconstruction of FBG-based Thin Plate

更新时间：2025-10-15

- Error Analysis of Spatial Shape Reconstruction of FBG-based Thin Plate
- Study on Optical Communications Issue 5, (2025)
- 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：
- 基金信息：
- DOI：10.13756/j.gtxyj.2025.240164
  CLC： TP212;TN253
- Received：01 August 2024，
  
  Revised：2024-08-15，
  
  Published：10 October 2025
- 稿件说明：
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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

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Related Institution

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School of Computer and Information Engineering, Shanghai Polytechnic University

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