In practice, a model-based structural damage detection (SDD) method is helpful for locating and quantifying damages with the aid of reasonable finite element (FE) model. However, only limited information in single or two structural states is often used for model updating in existing studies, which is not reasonable enough to represent real structures. Meanwhile, as an output-only damage indicator, transmissibility function (TF) is proven to be effective for SDD, but it is not sensitive enough to change in structural parameters. Therefore, a multi-state strategy based on weighted TF (WTF) is proposed to improve sensitivity of TF to change in parameters and in order to further obtain a more reasonable FE model for SDD in this study. First, WTF is defined by TF weighted with element stiffness matrix, and relationships between WTFs and change in structural parameters are established based on sensitivity analysis. Then, a multi-state strategy is proposed to obtain multiple structural states, which is used to reasonably update the FE model and detect structural damages. Meanwhile, due to fabrication errors, a two-stage scheme is adopted to reduce the global and local discrepancy between the real structure and the FE model. Further, the l1-norm and the l1∕2-norm regularization techniques are, respectively, introduced for both model updating and SDD problems by considering the characteristics of problems. Finally, the effectiveness of the proposed method is verified by a simply supported beam in numerical simulations and a six-storey frame in laboratory. From the simulation results, it can be seen that the sensitivity to structural damages can be improved by the definition of WTF. For the experimental studies, compared with the FE model updated from the single structural state, the FE model obtained by the multi-state strategy has an ability to more reasonably describe the change of states in the frame. Moreover, for the given structural damages, the proposed method can detect damage locations and degrees accurately, which shows the validity of the proposed method and the reliability of the updated FE model.

中文翻译：

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一种基于加权传递函数灵敏度的结构损伤检测多态策略

在实践中，基于模型的结构损伤检测 (SDD) 方法有助于借助合理的有限元 (FE) 模型对损伤进行定位和量化。然而，现有研究中通常仅使用单一或两种结构状态的有限信息进行模型更新，这不足以代表真实结构。同时，作为一种仅输出的损伤指标，传递函数（TF）被证明对SDD有效，但它对结构参数的变化不够敏感。因此，提出了一种基于加权TF（WTF）的多状态策略，以提高TF对参数变化的敏感性，以进一步获得本研究中更合理的SDD有限元模型。首先，WTF 由单元刚度矩阵加权的 TF 定义，基于敏感性分析建立WTF与结构参数变化之间的关系。然后，提出了一种多状态策略来获取多个结构状态，用于合理更新有限元模型和检测结构损伤。同时，由于制造误差，采用两阶段方案来减少真实结构与有限元模型之间的全局和局部差异。此外，l1-规范和l1∕2考虑问题的特点，分别针对模型更新和SDD问题引入了范数正则化技术。最后，通过数值模拟中的简支梁和实验室中的六层框架验证了所提方法的有效性。从模拟结果可以看出，WTF的定义可以提高对结构损伤的敏感性。对于实验研究，与从单一结构状态更新的有限元模型相比，多状态策略得到的有限元模型能够更合理地描述框架内的状态变化。此外，对于给定的结构损伤，所提出的方法可以准确地检测损伤位置和程度，