基于NSGA-Ⅱ传感位置优化的曲面重构及误差补偿方法

Surface Reconstruction and Error Compensation Method Based on NSGA-II Sensing Position Optimization

通过优化光纤布拉格光栅形状传感技术中传感点位置和补偿重构结果来提高薄层合金板三维形状重构精度。通过ANSYS workbench建立合金板仿真模型,提取应变和位移模态振型,根据模态置信准则、转换矩阵稳定性和模态振型相似性分别设计了三个目标函数,采用快速和精英机制的多目标遗传算法优化传感器位置。将镍钛合金板弯曲成不同曲率半径的弧形,利用光纤布拉格光栅中心波长漂移量和线性插值算法计算得出不同形状下的结构应变,重构合金板形状,均方根误差和最大误差相较于单目标优化算法分别减小30%和15%。利用粒子群优化径向基函数神经网络算法拟合误差与位移的关系实现误差补偿,均方根误差和最大误差比无补偿时分别减小了90%和70%,最大相对百分比误差仅为5%,提高了三维形状重构算法精度。

In order to improve the accuracy of shape sensing,this paper optimizes the sensing position based on the Non-dominated Sorting Genetic Algorithm-II(NSGA-II),and uses the Radial Basis Function-Particle Swarm Optimization(PSO-RBF)neural network algorithm to improve the accuracy of structural reconstruction.In this study,the goal was to reconstruct the shape of a 150 mm×150 mm×0.5 mm nitinol version.Firstly,the finite element model of the nitinol version was established by using ANSYS workbench software.After a series of operations such as meshing,adding constraints,adding materials,and modal analysis,the surface strain modal matrix and displacement modal matrix of the model were extracted.According to the modal analysis results and the principle of modal reconstruction,8 sensing points can be selected to realize the shape reconstruction of the model.The strain mode matrix is used as the input matrix of the NSGA-II algorithm.According to the modal confidence criterion,the conditional number criterion and the modal mode shape similarity criterion,three objective functions were obtained.The NSGA-II multi-objective optimization algorithm,which introduces fast non-dominance sequences,business strategies and congestion operators,was used to select the best sensing location.It not only reduces the computational complexity of the algorithm,but also better retains the excellent individuals.Then,the wavelength of the center of the Fiber Bragg Grating(FBG)was demodulated by the SM125 interrogator,and the linear relationship between the wavelength change and curvature of the eight FBG centers was obtained by linear fitting.Since epoxy resin has a high strain transfer rate,the FBG was glued to the selected optimal sensing position.The nitinol plate was bent into different arcs to obtain FBG strain data.The displacement and shape of the nitinol plate at this time were recorded.The strain-mode mode shape,displacement mode mode and FBG strain data were input into the reconstruction algorithm.According to the modal reconstruction algorithm,the shape reconstruction was preliminarily realized,and the best sensing position point reconstruction results obtained by the K-means++algorithm were compared.Finally,the PSO-RBF neural network algorithm was used to fit the nonlinear relationship between the reconstruction error and the reconstruction displacement.The PSO-RBF neural network algorithm has strong nonlinear fitting ability,which can avoid falling into local optimum.The ratio of the training,validation,and test sets is 6∶2∶2.In this way,the prediction of the reconstruction error can be realized,and the accuracy of the shape reconstruction can be improved.The NSGA-II algorithm was used to optimize the sensing position,and the FBG strain information was collected to reconstruct the structure shape,and the reconstruction effect was better than that of the K-means++algorithm,and the root mean square error was reduced by 30%and the maximum error was reduced by 15%compared with the Kmeans++algorithm.After fitting the nonlinear relationship between the reconstruction error and the reconstruction displacement by PSO-RBF,the root mean square error and the maximum error are reduced by 90%and 70%respectively compared with the non-error compensation,and the reconstruction shape is almost the same as the structural shape,which can achieve high-precision reconstruction of the structural shape.This paper successfully realizes the high-precision shape reconstruction of the nitinol version.By optimizing the optimal sensing position,the root mean square errors are 0.500 mm,0.561 mm and 0.636 mm,and the maximum errors are 2.102 mm,2.315 mm and 2.561 mm,respectively,when the bending curvature radius of the nitinol plate is 200 mm,180 mm and 160 mm,respectively.When the bending curvature radius is 180 mm and 160 mm,the root mean square error is 0.038 mm and 0.046 mm,and the maximum error is 0.686 mm and 0.778 mm,respectively.