Reliability Estimate of Linear Oscillator with Uncertain Input Parameters
The first passage probability of a linear oscillator subjected to non-stationary uniformly-modulated seismic excitation is estimated considering the uncertainties of the parameters in the structure and input model. A geophysical model for the input power spectral density of the seismic excitation is used and the probability distributions of the assumed time-invariant parameters are estimated from regression analyses using actual accelerogram records. The statistics of the structural parameters are adopted from current literature. The time-variant reliability of the oscillator are estimated using a Markovian extreme point process model and two different methods of incorporating the uncertain input parameters, namely, the method of moments and the Advanced First-Order Second-Moment (AFOSM) method are presented. Using a numerical example it is shown that uncertainties in the input parameters affect the reliability significantly. The AFOSM is preferred and should be used when the probability distributions of the uncertain parameters can be reasonably approximated whereas the method of moments albeit simple is sensitive to the assumed distribution of the maximum peak of the response, S. It is further noted that the variabilities of geophysical model parameters contribute significantly to the variance of S compared to that of the structural parameters.
KeywordsPower Spectral Density Linear Oscillator Seismic Excitation Geophysical Model Fourier Amplitude Spectrum
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- 3.Ang, A.H-S.; Tang, W.H.: Probability concepts in engineering planning and design — volume 1. John Wiley and Sons 1975.Google Scholar
- 4.Hohenbichler, M.; Rackwitz, R.: Non-normal dependent vectors in structural safety. J. Eng. Mech. Div. ASCE 107 (EM6) (1981) 1227–1238.Google Scholar
- 5.Vanmarcke, E.H.; Lai, S-S.P.: Strong-motion duration and rms amplitude of earthquake records. Bull. Seism. Soc. Amer. 70 (1980) 1293–1307.Google Scholar
- 7.Anderson, J.G.; Hough, S.E.: A model for the shape of the Fourier amplitude spectrum of acceleration at high frequency. Bull. Seism. Soc. Amer. 74 (1984) 1969–1994.Google Scholar
- 8.Shinozuka, M.; Sato, Y.: Simulation of nonstationary random processes. J. Eng. Mech. Div. ASCE 93 (EM1) (1967) 11–40.Google Scholar
- 9.Trifunac, M.D.; Brady, A.G.: A study on the duration of strong earthquake ground motion. Bull. Seism. Soc. Amer. 65 (1975) 581–626.Google Scholar
- 10.McGuire, R.K.: A simple model for estimating Fourier amplitude spectra of horizontal ground acceleration. Bull. Seism. Soc. Amer. 68 (1978) 803–822.Google Scholar
- 11.IMSL User’s Manual, STAT/LIBRARY 1, Houston, USA.Google Scholar
- 13.Sues, R.H.; Wen, Y.K.; Ang A.H-S: Stochastic seismic performance evaluation of buildings. Struc. Res. Ser. 506, University of Illinois, Urbana 1983.Google Scholar