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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.

Keywords:
multifractal wavelet leader, damage detection, singularity spectrum, earthquake engineering, structural safety

Abstract:
This paper deals with the application of wavelet analysis on damage detection in mixed concrete/steel frame structures subjected to earthquake excitation. Such buildings are typically the result of a building initially constructed as a reinforced concrete building and, at a later time, more storeys were added as steel moment resisting frames. These structures consist of rein-forced concrete frames at the lower storeys and steel frames at the upper storeys. They are characterized by the material inconsistency in height. The proposed method of wavelet analysis of structural response is an output-only damage detection method. Non-linear dynamic analysis has been performed and response data at each story are obtained which are used as simulation data. Damage in the frame is due to hysteretic behaviour of columns and beams. Since the dynamic behaviour of an inelastic structure subjected to an earthquake excitation is a non-stationary process, discrete and continuous wavelet analysis were performed in order to re-trieve the simulation response data. The proposed method is based on the assumption that there is a correlation between structural damage, due to non-linear behaviour of structural elements and spikes that can be clearly detected in the wavelet details. This is supported by the fact that at the time when the spikes are recorded, structural damage occurs as well. The numerical results indicate that the discrete wavelet analysis is a promising method for the detection of damage in structures without the need for visual inspection.

Keywords:
Mixed concrete/steel frame, Damage detection, Discrete wavelet analysis, Continues wavelet analysis, Structural dynamics, Earthquake engineering