doi:10.3850/978-981-08-7619-7_P029

ABSTRACT

In this paper the problem of deriving non-stationary stochastic processes defined by a parametric evolutionary power spectrum (EPS) compatible with a given (target) design spectrum is addressed. An inverse stochastic dynamics problem is formulated and solved in a least-square sense to determine the requisite EPS. This involves the incorporation of a "peak factor" which is used to relate statistically the target spectrum to the EPS. Special attention is focused on deriving design spectrum compatible processes of specific ëffective duration" as commonly defined in the field of earthquake engineering. Specifically, the design spectrum of the Chinese GB 50011 aseismic code is considered as a paradigm of a target spectrum. Comprehensive Monte Carlo analyses are undertaken to numerically estimate GB 50011-compatible median peak factor spectra, given in a polynomial form. These spectra are associated with the first passage problem for linear oscillators excited by uniformly modulated colored non-stationary processes of various durations. The derived peak factor spectra used in conjunction with the herein adopted stochastic formulation yield an excellent level of agreement between the GB 50011 spectrum and the ensemble average response spectra of simulated EPS-compatible accelerograms of different effective durations. Additional numerical results pertaining to the design spectra of the European EC8 code and the GB 50011 code are included to show how the behavior of the target spectrum in the range of long periods affects the choice of the assumed spectral form of the EPS. It is envisioned that the herein derived stochastic processes can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo-based or random vibration-based context of analysis.

Keywords: Non-stationary process, Design spectrum compatible accelerograms, Inverse problem, Monte Carlo simulation, Peak factors.

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