Response spectra of earthquakes using ARMA model

Abstract

This study is concerned with calculating hysteretic energy using ARMA coefficient models. We know that: For any random time series we can write a model of ARMA(p,q) detailed by Box and Jenkins [2]. Any movement generates energy, regardless of its form or type, negative or positive, so how do we deal with it or reduce its danger? This is possible through ARMA models that have proven their efficiency through several procedures such as earthquakes and accelerometer time series that are generated from random models in the time domain or frequency domain. Extensive reviews of time series process models for acceleration in the frequency and times domain have been presented by [1], [12], and [4]. A number of papers have reported on ARMA models. ARMA models are discussed in detail by Box and Jenkins [4]. Here we generally found the hysteretic energy NH in terms of the ARMA(2,1) coefficients, but the ARMA(2,1) model can be considered the most appropriate in this case for the regions of northern Algeria, from which we took the Boumerdes earthquake. When taking the AIC RITERIA criterion, we found that it is in fact ARMA. (2,1) which is what we studied The use of mathematical relationships, including some results of nodal integration, such as relationship [7] , which conforms to the definition of a stationary time series, which is that the mean and standard deviation are constant.