An efficient stratified sampling scheme for the simultaneous estimation of small failure probabilities in wind engineering applications

With the advent of performance-based engineering frameworks for extreme winds, greater efficiency in the estimation of failure probabilities associated with multiple limit states at ultimate load levels, including collapse, is required. To meet this demand, an optimal stratified sampling-based simulation scheme is proposed that shares several meritorious characteristics of standard Monte Carlo simulation (MCS), including the capability to deal with high-dimensional uncertain spaces and multiple limit state functions. The optimality of the scheme is governed by the allocation of MCS samples among the strata as well as the strata division itself. A constrained optimization problem is formulated to address efficient sample allocation which is an extension of the Neyman allocation. Details for the practical implementation of the scheme within wind engineering reliability assessment applications are discussed. It is observed that the proposed methodology can reduce the variance by several orders of magnitude compared to MCS, which is illustrated on a wind-excited steel structure for the limit states of member/system first yield and collapse. The applicability of Latin hypercube sampling within stratified sampling-based simulation and the resulting efficiency gains are also critically studied. The results show promise in the wider applicability of the proposed scheme in performance-based wind engineering.