عنوان مقاله [English]
Wavelet transform is a mathematical tool which indicates the time variations of frequency in a signal. On the other hand, the endurance time method is a new dynamic pushover procedure where the performance is assessed based on the length of the time interval needed to satisfy required performance objectives. In this paper, endurance time acceleration functions (ETAF) are generated for the compatible design spectrum of standard No. 2800 for soil type (II) with wavelet transform and optimization algorithms. To generate endurance time functions, in the first step, wavelet analysis is performed to decompose a series of random data to several levels, each level covering a special range of frequencies. Each level is then divided into a number of equal time intervals and each interval of time is multiplied by a variable. Unconstrained optimization algorithms are used to calculate the variables and minimize the error between the response and the target spectra. The method applied is a modification of the data in the time and frequency domain. For this purpose, the efficiency of the heuristic algorithm (GA), the classic algorithm (quasi-Newton algorithm) and their combination, for the simplified objective function (duration of this objective function is 5.12 seconds, which consist of 512 acceleration points in 0.01s time steps) is evaluated. The algorithm which determines the minimum error in the specified iteration is selected as the best method to optimize. Employing this optimization method, the main acceleration function (duration of this objective function is 20.48 seconds, which consist of 2048 acceleration points in 0.01s time steps) is produced. Finally, error values of the acceleration functions produced are compared with ETA20d acceleration functions. The target time of the functions is 10th of a second when the response of a SDOF system with a damping ratio of 5\% equals the codified template design spectrum.