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Identification of Localized Damage in Structures Using Highly Incomplete Modal Information

机译：使用高度不完整的模态信息识别结构的局部损坏

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The objective of this paper is to provide a new theoretical basis to localize and quantify sparse damage in a structure based on highly incomplete modal information. Although a large number of papers have been written on the subject, this paper offers a new perspective on the problem by proposing the L-l norm minimization criteria, in contrast to the more traditional L-2 (Euclidean) norm minimization criterion. The proposed L-l norm approach enables accurate and robust examination of a number of potential damage locations much larger than the number of frequencies used in the formulation of the modal sensitivity matrix. In addition, it is shown that L-l minimization leads to sparse solutions, this is in contrast with the L-2 criteria, which leads to disperse solutions. The computational effort necessary to solve the L-1 optimization is significantly larger than in the traditional Euclidean norm and requires the use of convex optimization algorithms. However, given the results that can be obtained, the computational effort is justified. The efficacy of the proposed framework is demonstrated in detecting sparse damage in a simulated 21 degree of freedom shear building structure.
机译：本文的目的是为基于高度不完整的模态信息提供新的理论基础，以定位和量化结构中的结构稀疏损坏。虽然已经在该主题上写了大量论文，但是通过提出L-L标准最小化标准，据对比更传统的L-2（Euclidean）规范最小化标准，本文提供了对该问题的新视角。所提出的L-L规范方法可以精确且鲁棒地检查许多潜在的损坏位置，大于模态灵敏度矩阵配方中使用的频率的数量。此外，显示L-L最小化导致稀疏解决方案，这与L-2标准相反，这导致分散解决方案。解决L-1优化所需的计算工作明显大于传统欧几里德规范，并且需要使用凸优化算法。但是，鉴于可以获得的结果，计算工作是合理的。在模拟21自由剪切建筑结构中检测稀疏损坏，证明了所提出的框架的功效。

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