Identifying structural damage can usually be modeled as a problem with the use of linear equations. Due to measurement noise and spatial incompleteness of the measured mode shapes, these linear equations are usually ill conditioned, which will significantly reduce the accuracy of subsequent damage assessment. This study develops an iterative total least squares (TLS) based estimation method, which can effectively mitigate such ill conditioning and avoid propagating noise into estimates of structural damage severity. In particular, a procedure, called the δ–p curve method, is proposed to choose the effective rank of a TLS estimation. Further, an iterative approach of TLS‐based estimation is proposed to eliminate spurious damage estimates due to modal expansion and measurement noise. To investigate the effectiveness of the proposed iterative TLS‐based estimation method, detailed numerical studies of damage assessment are first conducted on a simulated 3D frame structure, in which both noise pollution and spatial incompleteness of the mode shapes are considered. Additionally, experimental tests with a laboratory structure are performed to validate the proposed method. Results indicate that the proposed iterative TLS‐based method can accurately identify the structural damage, even with noise‐polluted and spatially incomplete modes.

中文翻译：

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3D框架结构的结构损伤识别的基于总最小二乘的迭代估计方法

使用线性方程式通常可以将识别结构损坏建模为问题。由于测量噪声和所测量模态的空间不完整性，这些线性方程通常状况不佳，这将大大降低后续损伤评估的准确性。这项研究开发了一种基于迭代总最小二乘（TLS）的估算方法，该方法可以有效缓解这种病态，并避免将噪声传播到结构破坏严重性的估算中。特别是，一个程序，称为δ - p建议采用曲线法选择TLS估计的有效等级。此外，提出了一种基于TLS的迭代估算方法，以消除由于模态扩展和测量噪声引起的虚假损害估算。为了研究所提出的基于TLS的迭代估计方法的有效性，首先在模拟的3D框架结构上进行了损伤评估的详细数值研究，其中考虑了噪声污染和模式形状的空间不完整性。此外，还进行了具有实验室结构的实验测试，以验证所提出的方法。结果表明，即使采用噪声污染和空间不完整的模式，所提出的基于TLS的迭代方法也可以准确识别结构损伤。