The deflection of the beam estimated from modal flexibility matrix (MFM) indirectly is used in structural damage detection due to the fact that deflection is less sensitive to experimental noise than the element in MFM. However, the requirement for mass-normalized mode shapes (MMSs) with a high spatial resolution and the difficulty in damage quantification restricts the practicability of MFM-based deflection damage detection. A damage detection method using the deflections estimated from MFM is proposed for beam structures. The MMSs of beams are identified by using a parked vehicle. The MFM is then formulated to estimate the positive-bending-inspection-load (PBIL) caused deflection. The change of deflection curvature (CDC) is defined as a damage index to localize damage. The relationship between the damage severity and the deflection curvatures is further investigated and a damage quantification approach is proposed accordingly. Numerical and experimental examples indicated that the presented approach can detect damages with adequate accuracy at the cost of limited number of sensors. No finite element model (FEM) is required during the whole detection process.

中文翻译：

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使用模态柔度矩阵估计的挠度对梁结构进行 FEM 自由损伤检测

从模态柔度矩阵 (MFM) 估计的梁的挠度间接用于结构损伤检测，因为挠度对实验噪声的敏感性低于 MFM 中的元素。然而，对具有高空间分辨率的质量归一化模式形状（MMS）的要求和损伤量化的难度限制了基于MFM的偏转损伤检测的实用性。提出了一种利用MFM估计的挠度对梁结构进行损伤检测的方法。通过使用停放的车辆来识别光束的 MMS。然后制定 MFM 以估计正弯曲检查负载 (PBIL) 引起的偏转。挠曲曲率的变化（CDC）被定义为定位损伤的损伤指标。进一步研究了损伤严重程度与挠度曲率之间的关系，并据此提出了损伤量化方法。数值和实验示例表明，所提出的方法可以以有限数量的传感器为代价以足够的精度检测损坏。在整个检测过程中不需要有限元模型（FEM）。