基于 ELM 算法的柔性 FBG 形状重构末端分析

为了提高光纤光栅(FBG)柔性结构采用正交曲率三维重构方法的末端精度，通过神经网络将重构后的曲率末端坐标与实际空间坐标建立映射关系。首先利用COMSOL仿真软件对聚氨酯胶棒建立模型，将两根光纤光栅串共8支光栅正交排布，采用递推角算法建立动态坐标系进行三维重构。对重构的末端点坐标利用误差逆传播(BP)神经网络算法与极限学习机(ELM)神经网络算法进行训练检测，结果表明，BP神经网络和ELM神经网络训练平均误差分别为0.443 6和0.008 2。最后搭建实验平台，对聚氨酯胶棒在受力情况下进行形状重构，并代入ELM模型中进行训练，训练结果相关系数R²=0.985 8,均方根误差(RMSE)为1.363 0,相较于BP神经网络方法有效提高了形状重构的末端坐标精度。

Terminal analysis of flexible FBG shape reconstruction based on ELM algorithm

To improve the end precision of fiber Bragg grating ( FBG) flexible structure by using the orthogonal curvature 3Dreconstruction method, a mapping relationship is established in the reconstructed curvature end coordinates and actual spatial coordinatesthrough neural network. Firstly, the model of polyurethane glue rod is established by COMSOL simulation software. Two fiber Bragggrating strings are orthogonal arranged with 8 gratings, and a dynamic coordinate system is established by the recursive angle algorithmfor three-dimensional reconstruction. The reconstructed end point coordinates are trained by back propagation (BP) neural network andextreme learning machine (ELM) neural network. The results show that the average training errors of BP neural network and ELM neuralnetwork are 0. 443 6 and 0. 008 2, respectively. Finally, an experimental platform is established to reconstruct the shape of thepolyurethane glue stick under stress, and it is substituted into the ELM model for training. The correlation coefficient R2of the trainingresults is 0. 985 8, and the root mean square error is 1. 363 0, which effectively improve the precision of the end coordinates of the shapereconstruction compared with the BP neural network.