An efficient numerical method for estimating reliabilities of linear structures under fully nonstationary earthquake

The Conte–Peng’s equations for a fully nonstationary model of an earthquake are reformulated as modulated filtered white-noise processes so that the reliabilities of a linear structure under the fully nonstationary earthquake model can be estimated through calculating the first passage time probabilities of several time-varying linear systems subjected to independent white-noise processes. Each time-varying linear system consists of a second-order single-degree-of-freedom (SDOF) linear oscillator, a deterministic time-modulating function applied at the stationary oscillator’s responses and the linear structure considered. The unit impulse response functions of these time-varying linear systems are derived, from which the useful spectral characteristics of system responses in estimating the crossing rates and limiting decay rates can be numerically calculated. To save computation time, efficient matrix procedures in the time domain are proposed. The reliability analysis of a moment-resisting steel frame subjected to El-Centro-like earthquake demonstrates the effectiveness, accuracy and application of the numerical method.