Time Series Modeling of Earthquake Ground Motions Using ARMA-GARCH Models

2013 ◽  
Vol 470 ◽  
pp. 240-243 ◽  
Author(s):  
Jeng Hsiang Lin
Keyword(s):  
Ground Motion ◽  
Moving Average ◽  
Ground Motions ◽  
Structural Response ◽  
Earthquake Ground Motion ◽  
Response Analysis ◽  
Practical Implementation ◽  
Autoregressive Moving Average ◽  
Arma Models ◽  
Earthquake Models

Engineers are well aware that, due to the stochastic nature of earthquake ground motion, the information obtained from structural response analysis using scant records is quite unreliable. Thus, providing earthquake models for specific sites or areas of research and practical implementation is essential. This paper presents a procedure for the modeling strong earthquake ground motion based on autoregressive moving average (ARMA) models. The Generalized autoregressive conditional heteroskedasticity (GARCH) model is used to simulate the time-varying characteristics of earthquakes.

STOCHASTIC SEISMIC RESPONSE OF BASE-ISOLATED BUILDINGS

2013 ◽  
Vol 05 (01) ◽  
pp. 1350006 ◽  
Author(s):  
C. JACOB ◽  
K. SEPAHVAND ◽  
V. A. MATSAGAR ◽  
S. MARBURG
Keyword(s):  
Seismic Response ◽  
Ground Motion ◽  
Probability Distributions ◽  
Ground Motions ◽  
Earthquake Ground Motion ◽  
Response Analysis ◽  
Motion Model ◽  
Stochastic Response ◽  
Ground Motion Model ◽  
Stochastic Seismic Response

The stochastic response of base-isolated building considering the uncertainty in the characteristics of the earthquakes is investigated. For this purpose, a probabilistic ground motion model, for generating artificial earthquakes is developed. The model is based upon a stochastic ground motion model which has separable amplitude and spectral non-stationarities. An extensive database of recorded earthquake ground motions is created. The set of parameters required by the stochastic ground motion model to depict a particular ground motion is evaluated for all the ground motions in the database. Probability distributions are created for all the parameters. Using Monte Carlo (MC) simulations, the set of parameters required by the stochastic ground motion model to simulate ground motions is obtained from the distributions and ground motions. Further, the bilinear model of the isolator described by its characteristic strength, post-yield stiffness and yield displacement is used, and the stochastic response is determined by using an ensemble of generated earthquakes. A parametric study is conducted for the various characteristics of the isolator. This study presents an approach for stochastic seismic response analysis of base-isolated building considering the uncertainty involved in the earthquake ground motion.

A Stochastic Approach to Nonlinear Seismic Design Spectra

2010 ◽  
Author(s):  
Malek Brahimi
Keyword(s):  
Yield Strength ◽  
Ground Motion ◽  
Nonlinear Response ◽  
Moving Average ◽  
Response Spectra ◽  
Stochastic Approach ◽  
Earthquake Ground Motion ◽  
Autoregressive Moving Average ◽  
Design Spectra ◽  
Nonlinear Design

The purpose of this study is to examine the effects of yield strength ratios and damping values on the nonlinear response of Single Degree of Freedom Systems (S.D.F.S) subjected to earthquake ground motion. A stochastic approach to constructing design response spectra and period dependent strength reduction factors for current existing nonlinear design spectra is then proposed. Non-stationary stochastic models are adopted to characterize earthquake ground motion. Twenty simulated earthquakes accelerograms are generated for each of eight historical events using Autoregressive Moving Average (ARMA) techniques. The average of nonlinear response spectra for a given Structural period from a sample of twenty records for each event are calculated to obtain the response spectra. These response spectra are used to examine the effects of structural strength factors such as the yield strength ratio and damping value, and the effects of nonlinear stiffness models including the elastoplasic model, a stiffness degrading model and a stiffness softening model.

Analysis and Simulation of Strong Earthquake Ground Motions Using ARMA Models

2011 ◽  
Vol 418-420 ◽  
pp. 1786-1795
Author(s):  
Abderrazak Menasri ◽  
Malek Brahimi ◽  
Abderrahmane Bali
Keyword(s):  
Ground Motion ◽  
Strong Earthquake ◽  
General Procedure ◽  
Ground Motions ◽  
Gaussian White Noise ◽  
Soil Layer ◽  
Earthquake Ground Motion ◽  
Frequency Content ◽  
Arma Models ◽  
Earthquake Ground Motions

The acceleration record of an earthquake ground motion is a nonstationary process with both amplitude and frequency content varying in time. The paper presents a general procedure for the analysis and simulation of strong earthquake ground motions based on parametric ARMA models. Structural design spectra are based on smoothed linear response spectra obtained from different events scaled by their peak values. Such an approach does not incorporate other characteristics of the excitation represented by measured data. This study investigate the use of non-stationary models which can be considered characteristic and representative of specific historical earthquakes. An earthquake record is regarded as a sample realization from a population of such samples, which could have been generated by the stochastic process characterized by an Autoregressive Moving Average (ARMA) model. This model is capable of reproducing the nonstationary amplitude as well as the frequency content of the earthquake ground accelerations. The moving time-window technique is applied to synthesize the near field earthquakes, Boumerdes-1, Boumerdes -2, and Boumerdes -3 2003 recorded on dense soils in Algeria. This model, is based on a low-order, time-invariant ARMA process excited by Gaussian white noise and amplitude modulated using a simple envelope function to account for the non-stationary characteristics. This simple model gives a reasonable fit to the observed ground motion. It is shown that the selected ARMA (2,1) model and the algorithm used for generating the accelerograms are able to preserve the features of the real earthquake records with different frequency content. In this evaluation, the linear and non linear responses of a given soil layer have been adopted. This study suggests the ability to characterize the earthquake by a minimum number of parameters.

An Ensemble of Ground Motions Simulation Based on Discrete Stationary Wavelet Transform

2012 ◽  
Vol 166-169 ◽  
pp. 2408-2411
Author(s):  
Quan Bai ◽  
Liang Hua Fu ◽  
Wen Bo Bao ◽  
Sheng Ji Jin ◽  
Da Sheng Zhang
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Ground Motion ◽  
Ground Motions ◽  
Earthquake Ground Motion ◽  
Response Analysis ◽  
Discrete Wavelet ◽  
Superposition Method ◽  
Stationary Characteristic ◽  
Simulation Based

Simulation of earthquake ground motion was a hot topic for structure seismic response analysis. According to the problems in simulating ground motion history with harmony superposition method, such as more interference of human factors and simulated ground motion history didn’t have frequency non-stationary characteristic, a novel method of ground motion simulation based on stationary discrete wavelet transform was presented. Using stationary discrete wavelet transform, the parent ground motion history was decomposed into different frequency bands, and the coefficients were modified. Using inverse stationary discrete wavelet transform, an ensemble of ground motions were simulated whose statistics closely resemble those of the parent history. Through a numerical example, the statistic characteristics of simulated histories were compared with the original values, and the feasibility and correctness of presented method was illustrated.

Evaluation of Earthquake Response Spectra Directionality Using Stochastic Simulations

2021 ◽  
Author(s):  
Alan Poulos ◽  
Eduardo Miranda ◽  
Jack W. Baker
Keyword(s):  
Stochastic Process ◽  
Ground Motion ◽  
Ground Motions ◽  
Gaussian White Noise ◽  
Response Spectra ◽  
Orientation Dependence ◽  
Stochastic Simulations ◽  
Earthquake Ground Motion ◽  
Significant Duration ◽  
Simulated Ground Motions

ABSTRACT For earthquake-resistant design purposes, ground-motion intensity is usually characterized using response spectra. The amplitude of response spectral ordinates of horizontal components varies significantly with changes in orientation. This change in intensity with orientation is commonly known as ground-motion directionality. Although this directionality has been attributed to several factors, such as topographic irregularities, near-fault effects, and local geologic heterogeneities, the mechanism behind this phenomenon is still not well understood. This work studies the directionality characteristics of earthquake ground-motion intensity using synthetic ground motions and compares their directionality to that of recorded ground motions. The two principal components of horizontal acceleration are sampled independently using a stochastic model based on finite-duration time-modulated filtered Gaussian white-noise processes. By using the same stochastic process to sample both horizontal components of motion, the variance of horizontal ground acceleration has negligible orientation dependence. However, these simulations’ response spectral ordinates present directionality levels comparable to those found in real ground motions. It is shown that the directionality of the simulated ground motions changes for each realization of the stochastic process and is a consequence of the duration being finite. Simulated ground motions also present similar directionality trends to recorded earthquake ground motions, such as the increase of average directionality with increasing period of vibration and decrease with increasing significant duration. These results suggest that most of the orientation dependence of horizontal response spectra is primarily explained by the finite significant duration of earthquake ground motion causing inherent randomness in response spectra, rather than by some physical mechanism causing polarization of shaking.

Autoregressive Moving Average (ARMA) Models of Neuromuscular System

1982 ◽  
Vol 15 (4) ◽  
pp. 1205-1210
Author(s):  
G.C. Agarwal ◽  
S.M. Goodarzi ◽  
W.D. O'Neill ◽  
G.L. Cottlieb
Keyword(s):  
Moving Average ◽  
Autoregressive Moving Average ◽  
Neuromuscular System ◽  
Arma Models

Modeling nonlinear site effects in physics-based ground motion simulations of the 2010–2011 Canterbury earthquake sequence

2020 ◽  
Vol 36 (2) ◽  
pp. 856-879 ◽  
Author(s):  
Christopher A de la Torre ◽  
Brendon A Bradley ◽  
Robin L Lee
Keyword(s):  
Wave Propagation ◽  
Ground Motion ◽  
Site Effects ◽  
Ground Motions ◽  
Site Amplification ◽  
Earthquake Sequence ◽  
Response Analysis ◽  
Site Specific ◽  
Ground Motion Simulations ◽  
Empirical Ground

This study examines the performance of nonlinear total stress one-dimensional (1D) wave propagation site response analysis for modeling site effects in physics-based ground motion simulations of the 2010–2011 Canterbury, New Zealand earthquake sequence. This approach explicitly models three-dimensional (3D) ground motion phenomena at the regional scale, and detailed site effects at the local scale. The approach is compared with a more commonly used empirical VS30-based method of computing site amplification for simulated ground motions, as well as prediction via an empirical ground motion model. Site-specific ground response analysis is performed at 20 strong motion stations in Christchurch for 11 earthquakes with 4.7≤ MW≤7.1. When compared with the VS30-based approach, the wave propagation analysis reduces both overall model bias and uncertainty in site-to-site residuals at the fundamental period, and significantly reduces systematic residuals for soft or “atypical” sites that exhibit strong site amplification. The comparable performance in ground motion prediction between the physics-based simulation method and empirical ground motion models suggests the former is a viable approach for generating site-specific ground motions for geotechnical and structural response history analyses.

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