基于模糊的框架变形重构的应变测量修正

针对三维(three-dimensional,简称3-D)框架结构弹性变形重构中存在的应变测量误差问题,提出了一种应变测量修正的方法。通过逆有限元法(inverse finite element method,简称iFEM)推导出结构表面应变量与测量点位移量之间的应变-位移关系,实测位移量代入应变-位移的转化关系得到相应的逆解应变。由于测量应变中含有安装、测量误差等,测量应变量与逆解应变量之间非线性数学关系模型难以准确得到。基于模糊网络对任意映射关系的无限逼近特性,采用模糊网络(fuzzy network,简称FN)逼近测量应变与逆解应变的关系。在确定模糊网络后,调用网络完成测量应变的修正,利用修正后应变量求解框架的变形位移。最后在三维框架模型上进行实验验证,实验结果表明结构变形重构的误差普遍减小了60%以上,说明该测量应变修正方法能够有效提高变形重构的精度。

Updating Measurement Strain for the Elastic Deformation of 3-D Frame Structure Using Fuzzy Method

For the elastic deformation reconstruction of the 3-D frame structure, this paper proposes a measurement strain correction method to solve the strain measurement error problem. The transformation relationship between the surface strain and the deformation of measurement points is derived by the inverse finite element method. The measured deformation values are substituted into the transformation relationship to obtain the corresponding inverse solution of strain. According to the strain measurement error introduced by the installation of the framework model and measuring operation, the nonlinear relationship between the measured strain and inverse strain of the corresponding measurement point is difficult to get. Based on the fuzzy network (FN) with universal approximation ability for arbitrarily functional relation, the FN is attempted to approach this unknown relationship. After the fuzzy network is fixed, the measured strain is modified by the network. The deformation of framework structure is determined by using the modified strain. Finally, the accuracy of the method is verified by conducting the experiment on the 3-D frame structure. The results show that the error of deformation reconstruction generally decreases by more than 60%. This also illustrates that the measured strain modification method can improve the accuracy of deformation reconstruction effectively.