Advertisement

Reliability Estimate of Linear Oscillator with Uncertain Input Parameters

  • S. T. Quek
  • Y. P. Teo
  • T. Balendra
Conference paper

Abstract

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.

Keywords

Power Spectral Density Linear Oscillator Seismic Excitation Geophysical Model Fourier Amplitude Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yang, J.N.: First-excursion probability in nonstationary random vibration. J. Sound & Vib. 27 (2) (1973) 165–182.CrossRefzbMATHADSGoogle Scholar
  2. 2.
    Quek, S.T.; Teo, Y.P.; Balendra, T.: Nonstationary structural response with evolutionary spectra using seismological input model. Earthq. Eng. & Struc. Dyn. 19 (1990) 275–288.CrossRefGoogle Scholar
  3. 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. 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. 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
  6. 6.
    Boore, D.M.: Stochastic simulation of high-frequency ground motions based on seismological models of the radiated spectra. Bull. Seism. Soc. Amer. 73 (1983) 1865–1894.ADSGoogle Scholar
  7. 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. 8.
    Shinozuka, M.; Sato, Y.: Simulation of nonstationary random processes. J. Eng. Mech. Div. ASCE 93 (EM1) (1967) 11–40.Google Scholar
  9. 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. 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. 11.
    IMSL User’s Manual, STAT/LIBRARY 1, Houston, USA.Google Scholar
  12. 12.
    O’Connor, J.M.; Ellingwood, B.: Reliability of nonlinear structures with seismic loading. J. Struc. Eng. ASCE 113 (5) (1987) 1011–1028.CrossRefGoogle Scholar
  13. 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
  14. 14.
    Wen, Y.K.; Chen, H.C.: On fast integration for time variant structural reliability. Prob. Eng. Mech. 2 (3) (1987) 156–162.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • S. T. Quek
    • 1
  • Y. P. Teo
    • 1
  • T. Balendra
    • 1
  1. 1.Department of Civil EngineeringNational University of SingaporeRepublic of Singapore

Personalised recommendations