Spectral analysis of structures using wavelet theory and concept of time of strong ground motion

In this paper, for the first time, the simultaneous analysis of wavelet transformation and the concept of the time of strong ground motion in spectral analysis of structures has been used. The purpose of this research is to optimize the calculations related to the main earthquake spectrum. Accordingly, the earthquake is filtered up to 5 steps. At each stage, the filter provides two waves of approximations and details. Because the wave of approximations is closer to the original earthquake, this wave is used for calculations. For this reason, at each stage of the filter, the number of earthquake records is half past. Subsequently, based on the concept of the time of strong ground motion in the wave of the main earthquake and the wave obtained from the wavelet filter, part of the earthquake that has a strong movement is separated. So at this stage, there was a reduction in earthquake records. After that, the spectrum of each of the waveforms is plotted. At the end, a two-dimensional 10-story structure and a three-dimensional five-story structure with each spectrum obtained from two discrete wavelet concepts and the duration of a strong ground motion are analyzed. The results show that by reducing the computation of the spectrum by more than 93%, the structure can be analyzed with an error less than 4%. It can be said that the proposed technique is one of the best techniques presented in the optimization of calculations related to spectral analysis of structures.