Structures 29 (2021) 863–882 2352-0124/© 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved. Seismic response evaluation of structures using discrete wavelet transform through linear analysis Reza Kamgar a , Masoud Dadkhah a , Hosein Naderpour b, * a Department of Civil Engineering, Shahrekord University, Shahrekord, Iran b Faculty of Civil Engineering, Semnan University, Semnan, Iran A R T I C L E INFO Keywords: Discrete wavelet transform OpenSees Elastic response spectrum Time history analysis ABSTRACT In this article, the discrete wavelet transform (DWT) has been used to construct the wavelet response spectrum analysis (WRSA) of structures in the linear elastic zone. For this purpose, the elastic response spectra of different single degree of freedom (SDOF) systems are studied for different beam-to-column stiffness ratios. Initially, using the DWT, the records of near- and far-feld earthquakes are decomposed into three levels. Finally, the linear response spectra of the SDOF systems are constructed subjected to the main and decomposed earthquakes. In the end, the error values for different levels of decompositions are computed using the considered error estimation criteria. The results show that using WRSA, the computational volume of time history analysis has reduced since the consuming time to perform the analysis has signifcantly reduced (e.g., it reduces the computational cost by almost 50% in the frst decomposition level). In addition, the results indicate that the highest error values occur for the structures with a beam-to-column stiffness ratio equal to one. However, for the structures with ratios of greater than one, the values of error reduced. For the conventional structures where the ratio is less than one and the natural period is in the range of 0.5 s and 10 s, the error values are <10%. Results also revealed that, except for the structures with beam-to-column stiffness ratio equal to one, in all the other cases, the values of error for the structure subjected to the near-feld earthquakes are less than those of the far-feld ones. Furthermore, the results obtained from the SDOF system analysis were investigated for several multi-degree-of-freedom structures with a linear behavior. 1. Introduction Using some mathematical transforms such as Wavelet and Fourier, the signal information can be transferred from the time domain to do- mains like the frequency domain or the time-frequency domain. In this way, the information hidden in the signal can be more clearly displayed. The wavelet transform is a newer method whose mathematical basis dates back to the theory of Joseph Fourier in the nineteenth century. By presenting his frequency analysis theory, Joseph Fourier showed that each iterative function could be expressed as a fnite sum of sine and cosine waves with different frequencies. In other words, Fourier was able to convert a time-dependent function into a frequency-dependent one [1]. The next step towards the current wavelet concept was taken by Alfred Hare in 1910 [2]. In 1981, Grossman and Morlet realized that a wavelet transform signal could be returned to its original coeffcients without destroying its information. Grossman and Morlet contended that they need a dual integral to convert the wavelet coeffcients back to the original signal state since wavelets were dependent on two variables of time and frequency. Finally, in 1984, they further realized that the wavelet coeffcients were required to be returned with only one integral. They also found that a small change in the wavelet coeffcients caused only a slight change in the initial signal. The waves made of their wavelet components were better than those generated by the Fourier transform [3]. In 1989, Mallat showed that wavelets were implicitly involved in the decomposition process, reducing the computational volume of wavelet transform [4]. In addition to these, Daubechies introduced a new group of wavelets called Daubechies wavelets using the idea of multiple analysis. These wavelets could be implemented with simple digital fltering and being orthogonal and orderly [5,6]. In recent years, researchers have used wavelet transforms in various sciences related to engineering. In so doing, [7] predicted the quantity of daily sewage sludge using different models such as wavelet-model tree and wavelet-evolutionary polynomial regression. In another research, [8] used the six-mother wavelet functions to increase the accuracy level * Corresponding author at: Faculty of Civil Engineering, Semnan University, Semnan 3513119111, Iran. E-mail address: naderpour@semnan.ac.ir (H. Naderpour). Contents lists available at ScienceDirect Structures journal homepage: www.elsevier.com/locate/structures https://doi.org/10.1016/j.istruc.2020.11.012 Received 6 August 2020; Received in revised form 6 November 2020; Accepted 9 November 2020