Abstract This work is an effort to join, for the first-time, multifractal analysis and damage detection in civil structures subjected to strong ground seismic motions. Specifically, based on the singularity spectrum quantitative and qualitative criteria are proposed. The qualitative criteria are based on the concave of singularity spectrum of damage and undamaged structure. The proposed quantitative criterion is based on calculation of damage index taken the parameters of singularity spectrum. In order to achieve the above goal, a robust signal processing method, which is known as multifractal wavelet leader (MFWL) is used. The multifractal analysis is a tool to calculate fractal properties as well as scaling behavior of the structural response excited by an earthquake. The singularity spectrum is obtained from the Legendre-transformation to Holder exponents. In this paper, a parameter which is based on the shape of singularity spectrum and can identify the damage in the structure is proposed. The proposed method is an output-only approach for damage detection. Considering that the dynamic behavior of an inelastic system subjected to strong ground motion appears to be a non-stationary process, the above procedure of multifractal wavelet leader is suitable to retrieve the simulation response data. The findings from the analysis show that the MFWL is an appropriate scheme for structural damage detection.

中文翻译：

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多重分形分析和小波前导用于地震激发结构的结构损伤检测

摘要 这项工作是首次将多分形分析和损伤检测结合在遭受强烈地面地震运动的土木结构中。具体而言，提出了基于奇异性谱的定量和定性标准。定性标准基于损坏和未损坏结构的奇异谱的凹面。提出的量化准则是基于奇异谱参数计算损伤指数。为了实现上述目标，使用了称为多重分形小波前导 (MFWL) 的稳健信号处理方法。多重分形分析是一种计算分形特性以及地震激发的结构响应的标度行为的工具。奇点谱是从勒让德变换到霍尔德指数获得的。本文提出了一种基于奇异谱形状的结构损伤识别参数。所提出的方法是用于损伤检测的仅输出方法。考虑到非弹性系统在强地震动作用下的动力学行为似乎是一个非平稳过程，上述多重分形小波前导过程适合于反演模拟响应数据。分析结果表明，MFWL 是一种合适的结构损伤检测方案。所提出的方法是用于损伤检测的仅输出方法。考虑到非弹性系统在强地震动作用下的动力学行为似乎是一个非平稳过程，上述多重分形小波前导过程适合于反演模拟响应数据。分析结果表明，MFWL 是一种合适的结构损伤检测方案。所提出的方法是用于损伤检测的仅输出方法。考虑到非弹性系统在强地震动作用下的动力学行为似乎是一个非平稳过程，上述多重分形小波前导过程适合于反演模拟响应数据。分析结果表明，MFWL 是一种合适的结构损伤检测方案。