Estimation of earthquake frequency content and its effect on dynamic analysis using continuous and discrete wavelet transform

Abstract

Wavelet transform is one of the mathematical concepts for studying the frequency content of waves. It is divided into two groups of continuous and discrete. Generally, continuous wavelet transform is used to check the time-frequency and the discrete wavelet transform for filtering and noise reduction in waves. In this paper, for the first time, the combination of these two concepts is used for the earthquake acceleration wave. For this purpose, eight earthquakes from four different locations in the world have been selected. Initially, each earthquake is filtered up to 5 stages using a discrete wavelet transform. At each stage of the filter, two waves of approximations and details are obtained. Due to the close approximation of the frequency content of the wave to the original earthquake, the approximate wave is used for subsequent calculations. In the next stage, the spectrum of Fourier and the diagram of five of the frequency of dominant of the earthquake are plotted. Also, using the continuous wavelet transform, the time-frequency curves of the main earthquakes and the time-frequency curves of the wave obtained from the discrete wavelet transform are investigated. The goal is to find the best stage of a discrete wavelet filter based on frequency content to reduce computations to over 80%. In the next step, the study examines the time of the strong ground motion, the structure response of a single degree of freedom, and the dynamical response of the timing of the structure of a degree of freedom. By examining the above parameters, the best-performing wavelet transformation step is inferred.

Combining Discrete Wavelet Transform and Strong Ground Motion Duration to Reduce Computational Costs in Dynamic Analysis of Structures

“…In each stage, the number of new wave points is half the number of wave points in the previous stage. Since, according to previous studies, clearly that the approximate wave is more similar to the original wave [15,23,25,28,29], therefore, this wave section is used for dynamic analysis. At each stage of the frequency separation, the maximum acceleration of the approximate wave equates to the maximum acceleration of the original earthquake.…”