Wavelet transform is one of the mathematical concepts for studying the frequency content of waves. It can be divided into two groups, continuous and discrete. In general, the continuous wavelet transform is used to examine the time-frequency relationship, whereas the discrete wavelet transform is used 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. The Fourier spectrum and the diagram of five of the dominant frequency of the earthquake are plotted in the next step. 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 was to find the best stage of a discrete wavelet filter based on frequency content to reduce computations by more than 80%. The time of the strong ground motion, the structural response of a single degree of freedom, and the dynamical response of the timing of the structure of a degree of freedom are all investigated in the following step. By examining the above parameters, the best-performing wavelet transformation step is inferred. (c) 2022 Sharif University of Technology. All rights reserved.

Gypsum mortar is a common building material that can be used especially for plastering the walls. This mortar has three important weaknesses which can limit the gypsum mortar for building and statue construction. First; it has low compressive strength. Second; it has high water absorption, and third; it has low setting time. In the current study, cement, Nano silica, and a superplasticizer with polycarboxylate ether were used for solving the problems. The results showed that using cement with providing C-S-H can improve the mortar strength trend line. The results showed significant growth of 28t h day compressive strength (from 9 MPa to 45 MPa). Using Nano silica increases the compressive strength by making C-S-H dense and decreases the water absorption to 1/3 of the control sample. Consuming polycarboxylate ether causes the uniform dispersion of Nanoparticles through mortar. This even diffusion blocks the pores and reduces their mean dimensions. The ANOVA test was used to find the main effective parameters on the 28t h day compressive strength, water absorption, and setting time. In this regard, Nano silica (49.82% contribution), cement content (56.68% contribution), and superplasticizer (73.10 degrees/0 contribution) have the main roles in compressive strength, water absorption, and setting time, respectively.

The current study focuses on two main goals. First, with the use of construction and demolition (C&D) of building materials, a new aggregate was produced and it was utilized for green concrete production. The compressive strength test confirmed the good function of C&DW aggregate concrete. This concrete did not show significant differences with natural sand concrete. Second, Backpropagation neural network (BNN) was adjusted for C&DW concrete strength prediction at different curing times. Although BNN has good accuracy for strength prediction, due to the importance of 28th day of concrete strength the need to improve the accuracy was felt. So discrete wavelet transform (DWT) was used on BNN and a hybrid network was produced. DWT by filtering the noises can improve the homogeneity of the dataset. The results of DWT-BNN showed that the regression can increase to 98% and the MSE index reduces to 0.001. Continued research has shown that increasing the number of filters to four steps leads to reduced accuracy and increased computational cost. So using DWT-BNN as a hybrid network with one filter can improve prediction ability to the desired level but adding up the number of filters not recommended.

In this paper, strong ground mot (SGM) parameters are calculated using discrete wavelet transform (DWT) in different kinds of soils with different magnitudes. The main earthquake record (MER) is divided into approximation and detailed signals using wavelet transform with denoising. The high and low frequencies of MER are separated from each other. Previous studies showed that the approximation signal has the greatest effect on dynamic response and it is very similar to the main signal. Then SGM parameters of the new signal are calculated by DWT decomposition. This process continues over five levels and, in each level, SGM parameters are calculated and compared with the MER and its error percentage is presented. In DWT with the denoising method, the curve becomes softer such that the calculation time reduces. Results show that the error percentage in the first two levels is less than 1% and for the third level, this index is less than 3%. In addition, the reduction percentage of calculation time is 1%, 4%, and 8%, respectively, in the first to third levels. The best result is relative to the third decomposition level in which error value as well as computational time reduction is nearly 3% and 8%.

Dynamic analysis of shear building structures (SBS) is achieved using fast wavelet transform (FWT). The loads are considered as acceleration of earthquake record. for the analysis, A time history dynamic analysis is carried out. A fast wavelet transform is used by which the number of points in the earthquake record is reduced by filter bank. In the filter bank method, the low-pass and high-pass filters are used for the decomposition of earthquake record into two parts. One part contains the low frequency, and the other part contains the high frequency of the record. The low frequency is the most important part; therefore, this part of the record is used for dynamic analysis of structures. A shear building structure is analyzed and the results are compared with exact dynamic analysis (EDA) and fast Fourier transform method. It is concluded that the best choice for approximation record was the second and third stage of decomposition. Also, overall time for dynamic analysis was reduced using Fwt.

Wavelet analysis is a new mathematical technique and in the recent years enormous interest in application of engineering has been observed. This new technique is particularly suitable for non-stationary processes as in contrast to the Fourier transform. The wavelet transform allows exceptional localization, both in time and frequency domains. The application of the wavelet transform to earthquake engineering is rare. In this paper the wavelet transform capability to give a full time-frequency representation of the earthquake record is demonstrated. In this method, the time series of the earthquake record, breaking at the tropical coral reefs and mechanically generated waves in the wave flume demonstrates the ability of the wavelet transform technique to detect a complex variability of these signals in the time-frequency domain. Various spectral representations resulting from the wavelet transform are discussed and their application for earthquake record is shown.

Approximate dynamic analysis of structures is achieved by fast wavelet transform (FWT). The loads are considered as time history earthquake loads. To reduce the computational work, FWT is used by which the number of points in the earthquake record are reduced. For this purpose, the theory of wavelets together with filter banks are used. The low and high pass filters are used for the decomposition of earthquake records in the high and low frequency of the records. The low frequency content is the most important part; therefore this part of the record is used for dynamic analysis. A number of structures are analysed and the results are compared with exact dynamic analysis and the Fast Fourier method (FFT).

Dynamic analysis of structures is achieved by wavelet transforms and filter banks. The method reduces the computational burden of the large-scale dynamic analysis. A time history analysis is carried out for a seismic analysis. To reduce the computational work, fast wavelet transform is used. To compute fast wavelet transforms, the Mallat and the Shensa algorithms are used. These two methods are used for wavelet theory together with filter banks. The low and high pass filters are used for the decomposition of accelerogram ground acceleration into two parts. The first part contains the low frequency of the record, and the other contains the high frequency of the record. The low frequency content is the most important part; therefore this part of the record is used for dynamic analysis. A number of structures are analysed and the results are compared with dynamic analysis using the original earthquake record.

Optimum design of structures for earthquake is achieved by simulated annealing. To reduce the computational work, a fast wavelet transform is used by means of which the number of points in the earthquake record is decreased. The record is decomposed into two parts. One part contains the low frequency of the record, and the other contains the high frequency of the record. The low-frequency content is the effective part, since most of the energy of the record is contained in this part of the record. Thus, the low-frequency part of the record is used for dynamic analysis. Then, using a wavelet neural network, the dynamic responses of the structures are approximated. By such approximation, the dynamic analysis of the structure becomes unnecessary in the process of optimization. The wavelet neural networks have been employed as a general approximation tool for the time history dynamic analysis. A number of structures are designed for optimal weight and the results are compared to those corresponding to the exact dynamic analysis. Copyright © 2004 John Wiley & Sons, Ltd.

Optimum design of structures is achieved by a modified genetic algorithm. Some features of the simulated annealing are used to control various parameters of the genetic algorithm. The loads are considered as earthquake loads. A time history analysis is carried out for the dynamic analysis. To decrease the computational work of analysis, a discrete wavelet transform is used by which the number of points in the earthquake record is reduced. Then in the optimization process, the structures are analysed with these points. To reconstruct the actual responses of structures from the responses of these points, a reverse wavelet transform is employed. A number of structures are designed for minimum weight and the results are compared with optimal solution using exact dynamic analysis. Copyright (c) 2005 John Wiley & Sons, Ltd.

Optimum design of structures against earthquake is achieved by a modified genetic algorithm. Some features of the simulated annealing are used to control various parameters of the genetic algorithm. To reduce the computational work, a fast wavelet transform is used by which the number of points in the earthquake record is decreased. For this purpose, the record is decomposed into two parts. One part contains the low frequency and the other possesses the high frequency of the record. The low-frequency part is used for dynamic analysis. Then, by using a wavelet network, the dynamic responses of the structures are approximated. By such approximation, the dynamic analysis of the structure is not necessary during the optimisation process. Thus, wavelet neural networks have been employed as a general approximation tool for the time-history dynamic analysis and estimation of the dynamic responses in the process of optimisation. A number of structures are designed for optimal weight against El Centro earthquake and the results are compared with those of the exact approach.