Influence line (IL) has emerged as very promising damage indices for bridge damage detection. This study proposed a method to localize and quantify damage in beam structures by estimating section flexibility change from deflection IL (DIL) change. To this end, the relationship between second derivative of DIL change and flexibility change was established. To remove noise interference in measurement, piecewise quadratic functions were used to fit and replace noisy DIL change curves, wherein the coefficients of quadratic function were determined via a sparse regularization method, considering the sparsity nature of damage that typically takes place in only a limited number of elements. The feasibility and accuracy of the proposed method are verified through numerical examples and laboratory experiments. Through four hypothetical damage scenarios of a simply supported beam with one or two damaged locations, its ability to quantify minor damage and its anti-noise robustness were well verified. Finally, a laboratory experiment on a simply supported aluminum beam illustrated that the location and extent of damage could be successfully identified in the single-damage and double-damage cases. The numerical and experimental results indicate that the proposed method is promising for future damage localization and quantification of bridge structures.

影响线（IL）已成为桥梁检测中非常有希望的损伤指标。这项研究提出了一种方法，可以通过估计由挠度IL（DIL）变化引起的截面挠性变化来定位和量化梁结构中的损伤。为此，建立了DIL变化的二阶导数和柔韧性变化之间的关系。为了消除测量中的噪声干扰，使用分段二次函数拟合并替换了嘈杂的DIL变化曲线，其中二次函数系数是通过稀疏正则化方法确定的，考虑到通常仅在有限数量内发生的损坏的稀疏性的元素。通过数值算例和实验室实验验证了该方法的可行性和准确性。通过具有一个或两个损坏位置的简单支撑梁的四种假设损坏场景，可以很好地验证其量化轻微损坏的能力和抗噪声的鲁棒性。最后，在简单支撑的铝梁上进行的实验室实验表明，在单损坏和双损坏情况下，损坏的位置和程度可以成功识别。数值和实验结果表明，所提出的方法对桥梁结构的损伤定位和量化具有广阔的前景。在简单支撑的铝梁上进行的实验室实验表明，在单损坏和双损坏情况下，损坏的位置和程度可以成功识别。数值和实验结果表明，所提出的方法对桥梁结构的损伤定位和量化具有广阔的前景。在简单支撑的铝梁上进行的实验室实验表明，在单损坏和双损坏情况下，损坏的位置和程度可以成功识别。数值和实验结果表明，所提出的方法对桥梁结构的损伤定位和量化具有广阔的前景。