Multifractal analysis and wavelet leaders for structural damage detection of structures subjected to earthquake excitation

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.