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The Use of ARMA Models in Earthquake Response Spectra

[+] Author Affiliations
Malek Brahimi, Sidi Berri

New York City College of Technology, Brooklyn, NY

Paper No. ICONE14-89023, pp. 7-13; 7 pages
  • 14th International Conference on Nuclear Engineering
  • Volume 3: Structural Integrity; Nuclear Engineering Advances; Next Generation Systems; Near Term Deployment and Promotion of Nuclear Energy
  • Miami, Florida, USA, July 17–20, 2006
  • Conference Sponsors: Nuclear Engineering Division
  • ISBN: 0-7918-4244-4 | eISBN: 0-7918-3783-1
  • Copyright © 2006 by ASME


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. ARMA models are developed for four major earthquakes after processing by a variance stabilizing transformation. Samples of acceleration records are generated for each event. In this earthquake modeling procedure, parameters describing the modulating function of the record and the stabilized series are estimated. Maximum displacement ductility demand and normalized hysteretic energy demand for linear and stiffness softening single degree of freedom system systems are computed for the samples generated for each event. The sensitivity and dependence of demand spectra on earthquake model characteristics are examined to develop a response prediction model. Non linear response analysis of the four events indicates that ARMA (2,1) process using samples of twenty simulated earthquakes provide a reliable description of the information contained within acceleration records. Empirical relationships for displacement ductility and Normalized hysteretic energy demand spectra are developed.

Copyright © 2006 by ASME



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