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Heuristic spectral estimation of bivariate nonstationary processes

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Abstract

A heuristic technique is developed for the estimation of auto-spectra and cross-spectra of multivariate nonstationary random processes which are used as models of earthquake accelerograms. The spectra are estimated by considering the statistical moments of the energy of linear systems (filters) excited by the stochastic seismic processes. The usefulness of the proposed technique is demonstrated by examples.

Sommario

Si propone una tecnica euristica per la determinazione degli spettri di processi aleatori non-stazionari multivariati, che vengono usati come modelli di accelerogrammi sismici. Gli spettri sono valutati considerando i momenti statistici dell'energia di sistemi lineari (filtri) eccitati dai processi sismici aleatori. Alcuni esempi dimostrano l'utilità della tecnica proposta.

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References

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    Spanos, P.D., Donley, M., and Roesset, J., ‘Evolutionary power spectrum estimation of September 19, 1985 Mexico earthquake accelerograms’, in: Y.K. Lin, and R.M. Mina (eds) Proceedings of the U.S.-Japan Seminar on Stochastic Approaches in Earthquake Engineering, Springer-Verlag, New York, 1987, pp. 322–333.

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    Priestley, M. B. and Tong, H., ‘On the analysis of bivariate non-stationary processes’, Royal Statistical Society (1973) 153–166.

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    Tein, W.Y., An Engineering Approach for Estimating Seismic Power Spectra, Thesis submitted in partial fulfillment of the PhD degree, Rice University, Houston, March 1992.

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    Lin, Y.K., and Cai, G.O., Probabilistic Structural Dynamics, MacGraw-Hill, New York, 1995.

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    Sawada, T. and Kameda, H., ‘Modeling of nonstationary cross-spectrum for multivariate earthquake motions by multifilter technique’, Proceedings of Ninth World Conference on Earthquake Engineering, Japan, Vol. II, August, 1988 pp.795–800.

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    Walter, J.C., Wavelets and Other Orthonormal Systems with Applications, CRC Press, Boca Raton, FL, 1994.

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Spanos, P.D., Tein, W.-. & Ghanem, R.G. Heuristic spectral estimation of bivariate nonstationary processes. Meccanica 31, 207–218 (1996). https://doi.org/10.1007/BF00426261

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Key words

  • Random processes
  • Spectral estimation
  • Nonstationarity
  • Earthquake inputs
  • Structural dynamics