Abstract Summary
In this paper a novel approach is developed for the estimation of evolutionary cross-spectral density functions of bivariate nonstationary random processes that can be used as models of earthquake accelerograms. Specifically, the spectra are estimated by determining the statistical moments of an energy-like quantity of lightly damped single degree-of-freedom (SDOF) linear systems (filters) excited by the stochastic seismic processes [1]. This sequence of SDOF filters is characterized by a varying natural frequency, thus providing a resolution of the bivariate processes along the frequency domain [2]. Notably, an appropriate smoothing procedure is also incorporated, relying on the use of the so-called Savitzky-Golay moving average filter [3]. This is done for obtaining reliable spectra based on a relatively small number of available records. Further, an appropriate model is introduced to capture the shape of the energy-like quantities associated with the output of the filters, leading to enhanced accuracy in the estimated spectra. Finally, several examples involving both simulated and measured data are used to assess the usefulness and reliability of the proposed approach. References [1] Spanos, P.D., 1980, Probabilistic Earthquake Energy Spectra Equations. Journal of the Engineering Mechanics Division, 106: 147-159. [2] Spanos, P.D., Tein, W.Y., Ghanem, R.G., 1996, Heuristic Spectral Estimation of Bivariate nonstationary processes. Meccanica, 31: 207-218. [3] Savitzky, A., and Golay, M.J.E., 1964, Smoothing and Differentiation of Data by Simplified Least Squares Procedures. Analytical Chemistry, 36: 1627–1639.
