Abstract In order to obtain a precise dynamic structural FE model for dynamic analysis, FE model updating is usually used to correct uncertainty parameters for an initial FE model using incomplete measured data. Despite numerous studies concerning FE model updating, the computational cost is still a challenging issue for the repeated eigenvalue structures. Firstly, an improved modal assurance criterion is proposed to evaluate the similarity of mode shapes for the repeated eigenvalue structures in this paper. And then, a novel ROM-based FE model updating framework consisting of an off-line phase and an on-line phase is proposed. In the off-line phase, a reduced-order basis is constructed by extracting primary components of a snapshot matrix using a proper orthogonal decomposition technique. The snapshot matrix represents a collection of static displacement vectors of the FE model under radial nodal loads, which are determined by incomplete measured mode shapes. In the on-line phase, FE model updating is performed via a reduced-order model with much cheaper computational cost. Finally, a numerical example and an experimental example demonstrate the accuracy and efficiency of the proposed framework. The results indicate that the proposed ROM-based FE model updating framework is more efficient and stable than the FOM-based FE model updating framework.

中文翻译：

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使用不完全测量模式通过降阶模型更新重复特征值结构的有限元模型

摘要 为了获得用于动力分析的精确动力结构有限元模型，有限元模型更新通常用于使用不完整的测量数据校正初始有限元模型的不确定性参数。尽管对有限元模型更新进行了大量研究，但对于重复特征值结构而言，计算成本仍然是一个具有挑战性的问题。首先，本文提出了一种改进的模态保证准则来评估重复特征值结构的模态形状的相似性。然后，提出了一种新的基于 ROM 的有限元模型更新框架，包括离线阶段和在线阶段。在离线阶段，通过使用适当的正交分解技术提取快照矩阵的主要成分来构建降阶基础。快照矩阵表示在径向节点载荷下有限元模型的静态位移矢量的集合，这些矢量由不完整的测量模态形状确定。在在线阶段，有限元模型更新是通过降阶模型执行的，计算成本要低得多。最后，一个数值例子和一个实验例子证明了所提出框架的准确性和效率。结果表明，所提出的基于 ROM 的有限元模型更新框架比基于 FOM 的有限元模型更新框架更有效和稳定。一个数值例子和一个实验例子证明了所提出框架的准确性和效率。结果表明，所提出的基于 ROM 的有限元模型更新框架比基于 FOM 的有限元模型更新框架更有效和稳定。一个数值例子和一个实验例子证明了所提出框架的准确性和效率。结果表明，所提出的基于 ROM 的有限元模型更新框架比基于 FOM 的有限元模型更新框架更有效和稳定。