An approximate analytical method for evaluating the first-crossing probability of base-isolated structures subjected to stochastic pulse-like ground motions

This study presents an efficient method for evaluating the first-crossing probability of base-isolated structures (BIS) subjected to stochastic pulse-like ground motions (PLGMs), with emphasis on the inherent randomness of the excitation.First, the PLGMs are modeled as non-zero-mean random processes, consisting of a deterministic pulse component and a stochastic component characterized by its power spectral density.Consequently, the corresponding stochastic structural response also exhibits a non-zero mean and is approximated using a novel analytical approach, termed SLT-RKA (statistical linearization technique combined with the Runge-Kutta algorithm).Subsequently, a generalized closed-form expression for the decay rates is derived to account for the time-varying mean of the response.Finally, the decay rates are utilized to estimate the first-crossing probability based on the Poisson out-crossing assumption.The accuracy and computational efficiency of the proposed method are validated through comparisons with Monte Carlo simulation (MCS) results in representative numerical examples.