Evaluation of wavelet decomposition level to enhance numerical analysis of seismic responses

In this study, the discrete wavelet transform (DWT) is used to enhance the efficiency of numerical analysis by decomposing earthquake excitation signals into low- and high-frequency components. The low-frequency components, considered as the main damaging factor in earthquake waves, stored in approximation coefficients have been used to perform time response analysis. In the selection of the ground motions, the special attention is given to the ratio of peak ground acceleration (PGA) to peak ground velocity (PGV). An ensemble of nine earthquake records have been selected and used. For each earthquake, displacement response spectra have been generated for both the original signal and its approximations at different DWT levels. To determine the most accurate decomposition level, the normalized root-mean-squared error (NRMSE) of wavelet energy has been computed in spectral displacement responses. The outcomes reveal a dependency of the decomposition level on the specific characteristics of each earthquake. Subsequently, structural analyses are conducted on base-isolated structures with varying story numbers, to examine the accuracy of decomposed signals. Employing both the original signal and its approximations to the structures, base mat displacements and roof accelerations are computed. The findings of the seismic analyses demonstrate the effectiveness of the proposed decomposition levels.