一种基于Galerkin映射减基法的结构参数反求方法

针对结构特性参数识别问题,提出了一种基于Galerkin映射减基法的参数反求方法。采用该方法对结构进行有限元建模,在观测点位置通过对向量子空间的夹角进行评判，构造出非奇异的观测点基矩阵及相应的整体基矩阵。通过使向量离散L2范数最小化途径构建结构参数的减基识别模型,进而利用信赖域优化技术求解得出问题的结构参数。算例表明，该方法在反求精度和总体计算效率方面优于传统方法。

An Identifying Structural Parameter Technique Based on Galerkin Mappingreduced Basis Method

An effective parameter identification technique  which was based on the Galerkin mappingreduced basis method was proposed for dealing with parameterized structural problems. The investigated structure was firstly discretized by the finite element method. And then using the angle of vector subspace, the nonsingular monitoring basis matrix and corresponding whole basis matrix were constructed in the positions of monitoring points. Subsequently, the identification model of structural parameters in the reduced basis model was constructed by minimizing discrete L2 norm of vector. Finally, the parameters of original problem were identified using the corresponding trust region optimization technique. An example herein demonstrates the presented method has higher computational accuracy and total efficiency than that of the existing classical methods.