Probabilistic hazard model of inelastic oscillator based on semi-theoretical solutions of first passage problem Mori, Yasuhiro; Takashima, Masato; Kojima, Sayo; Ozaki, Fuminobu
In this study, an approximate method of estimating the exceedance probability of the maximum ductility factor of an inelastic oscillator is proposed based on the equivalent linearization technique using the capacity spectrum (CS) method. The CS method seeks to determine the first point at which the demand spectrum crosses the CS. Because the auto-correlation function of the response spectrum is only a function of the difference between the logarithms of two natural periods, the CS method can be interpreted as the first passage problem of a stationary standard normal stochastic process. Because the auto-correlation function is not continuous when the difference is equal to zero, and because the crossing event cannot be modeled as a Poisson process when the CS is close to the horizontal axis, the mean crossing rate is semi-theoretically estimated based on Monte Carlo simulation. The results are further modified to create a general model. The accuracy of the proposed method is demonstrated by using numerical examples.
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