基于轴向应变误差修正的FBG形状重构算法

针对轴向应变误差影响光纤布拉格光栅(FBG)形状传感器的重构精度问题，提出了一种基于轴向应变误差修正的形状重构算法。纤芯位置偏差是造成轴向应变误差的主要因素，为了获取光纤形状传感器的纤芯位置偏差，提出了三芯光纤形状传感器的误差理论模型。通过ANSYS Workbench对误差理论模型进行有限元建模仿真，将纤芯位置偏差和标定偏差代入误差理论模型，对存在位置偏差的纤芯轴向应变数据进行修正，并与理想纤芯位置处的轴向应变数据进行对比，证明了该理论模型对存在误差的轴向应变数据具有良好的修正效果。为了计算每个检测点的纤芯位置偏差，根据提出的误差理论模型，提出了一种基于二分法逐次逼近的FBG形状传感器纤芯位置偏差计算方法。仿真结果表明，纤芯位置偏差修正前后重构曲线的最大位置误差从1.74 mm减小到0.10 mm。对于自封装的FBG形状传感器，使用纤芯位置偏差修正前后，重构空间曲线的最大位置误差从19.81 mm减小到7.66 mm。

FBG Shape Reconstruction Algorithm Based on Axial Strain Error Correction

To solve the problem that axial strain error affects the reconstruction accuracy of optical fiber grating shape sensor, a shape reconstruction algorithm based on axial strain error correction is proposed. Core position deviation is the main factor that causes axial strain error. In order to obtain the core position deviation of fiber shape sensor, an error theoretical model of three-core fiber shape sensor is proposed. Finite element modeling and simulation were carried out by ANSYS Workbench. The core position deviation and calibration deviation were substituted into the error theoretical model, the axial strain data of the core with the position deviation was corrected, and it was compared with the axial strain data at the ideal core position. It was proved that the theoretical model has a good correction effect on the axial strain data with errors. In order to calculate the core position deviation of each detection point, a method of calculating the core position deviation of FBG shape sensor based on dichotomous successive approximation was proposed according to the proposed error theoretical model. The simulation results show that before and after the core position deviation correction, the maximum position error of the reconstructed curve is increased from 1.74mm to 0.10mm. And for the self-encapsulated FBG shape sensor, the maximum position error of the reconstructed space curve is increased from 19.81mm to 7.66mm.