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.
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