The problem of the time-variant reliability/safety analysis of nonlinear hysteretic structural systems with system parameter uncertainty and subjected to stochastic dynamic loading is the object of this paper. A computatinal method based o nthe first-order reliabiltiy method, FORM, to obtain an upper bound of the probability of the system exiting or out-crossing a safe domain within a given time interval is applied to the Bouc-Wen single-degree-of-freedom (SDOF) hysteretic oscillator subjected to base excitation. An algorithm to compute the exact gradient of the numerical response of the oscillator with respect to both loading and system parameters is developed and used as part of the time-variant reliability method. The effects and relative impoertance of loading stochasticity and system parameter uncertainty are investigated. Valuable insight into the behavior of the SDOF system under conditions of loading and system uncertainty is provided by the design point. Upper bound time-variant failure probabilities obtained for both the determinsitic and uncertain Bouc-Wen oscillators are verified through Monte Carlo simulation.
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