Updating finite element dynamic models using an element-by-element sensitivity methodology
Updating finite element dynamic models using an element-by-element sensitivity methodology
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DOI：
10.2514/3.11833
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发表时间：
1993-09
期刊：
影响因子：
2.5
通讯作者：
C. Farhat;F. Hemez
中科院分区：
文献类型：
--
作者：
C. Farhat;F. Hemez
提出了一种基于灵敏度的方法，用于利用测试模态数据和少量传感器改进给定结构的有限元模型。所提出的方法搜索的质量和刚度误差的位置和来源，并不干扰有限元模型背后的理论，同时纠正这些错误。修正算法是通过两步交错迭代过程，从无约束最小化模态动态残差的平方ε 2范数导出的。在每次迭代中，首先假设模型是无误差的，扩展测量的振型，然后假设扩展的振型是精确的，校正模型参数。数值算法是在一个元素的元素的方式来实现，并能够“缩放”检测到的错误位置。几个模拟的例子，证明所提出的方法的潜力进行了讨论。I.介绍E VEN虽然结构动力问题的有限元分析领域在过去的二十年里取得了巨大的进展，但仍然对实验数据有更大的信心。因此，给定结构的有限元模型经常被更新以反映特定实验的结果。通常，计算的本征模与测量的频率和模态形状进行比较。如果两个集合不一致，则通过两步更新过程来细化有限元模型，该两步更新过程：1）定位误差，2）校正误差。显然，第一步是两个步骤中最具挑战性的。一旦知道错误的位置，就相对容易纠正它们，特别是如果可以识别错误源。然而，由于以下原因，定位和识别这些错误可能是一项困难的任务。一般来说，只有少数几个实验模式是可用的，这些可能会受到随机和系统测量误差的污染。此外，仅可监测有限元模型中的自由度（DOF）的子集;并且出于实用和经济的原因，仅可利用少数传感器。
A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared £2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of "zooming" on the detected error locations. Several simulation examples which demonstrate the potential of the proposed methodology are discussed. I. Introduction E VEN though the field of finite element analysis of structural dynamic problems has witnessed tremendous progress in the last two decades, greater confidence is still placed in experimental data. Therefore, the finite element model of a given structure is often updated to reflect the results of a particular experiment. Usually, the computed eigenmodes are compared with the measured frequencies and mode shapes. If both sets are not in agreement, the finite element model is refined via a two-step updating procedure which: 1) locates the errors and 2) corrects them. Clearly, the first step is the most challenging of the two. Once the location of the errors is known, it is relatively easy to correct them, especially if the error sources can be identified. However, locating and identifying these errors can be a difficult task for the following reasons. In general, only a few experimental modes are available, and these may be contaminated with random and systematic measuring errors. Moreover, only a subset of the degrees of freedom (DOF) in the finite element model can be monitored; and as for practical and economical reasons, only a few sensors can be utilized.