Strain Energy of the structure can be changed with the damage at the damage location. The accurate detection of the damage location using this index in a force system is dependent on the degree of accuracy in determining the structure deformation function before and after damage. The use of modal-based methods to identify damage in complex bridges is always associated with problems due to the need to consider the effects of higher modes and the adverse effect of operational conditions on the extraction of structural modal parameters. In this paper, the deformation of the structure was determined by the concept of influence line using the Betti-Maxwell theory. Then two damage detection indicators were developed based on strain energy variations. These indices were presented separately for bending and torsion changes. Finite element analysis of a five-span concrete curved bridge was done to validate the stated methods. Damage was simulated by decreasing stiffness at different sections of the deck. The response regarding displacement of a point on the deck was measured along each span by passing a moving load on the bridge at very low speeds. Indicators of the strain energy extracted from displacement influence line and the strain energy extracted from the rotational displacement influence line (SERIL) were calculated for the studied bridge. The results show that the proposed methods have well identified the location of the damage by significantly reducing the number of sensors required to record the response. Also, the location of symmetric damages is detected with high resolution using SERIL.

中文翻译：

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基于单点测量提取的应变能的复杂桥梁多重损伤检测

结构的应变能可以随损坏位置的损坏而改变。在力系统中使用该指标对损坏位置进行精确检测取决于确定损坏前后结构变形函数的准确性。由于需要考虑较高模态的影响以及操作条件对结构模态参数的提取的不利影响，使用基于模态的方法来识别复杂桥梁中的损伤始终伴随着问题。在本文中，利用贝蒂-麦克斯韦理论通过影响线的概念确定了结构的变形。然后根据应变能的变化建立了两个损伤检测指标。这些指数是分别针对弯曲和扭转变化而提出的。对五跨混凝土弯桥进行了有限元分析，以验证所述方法。通过降低甲板不同部分的刚度来模拟损坏。通过以非常低的速度在桥上传递移动的载荷，沿着每个跨度测量关于甲板上的点的位移的响应。计算了所研究桥梁从位移影响线提取的应变能和从旋转位移影响线提取的应变能的指标。结果表明，所提出的方法通过显着减少记录响应所需的传感器数量，已经很好地确定了损坏的位置。另外，使用SERIL可以高分辨率检测对称损伤的位置。