Subdomain sampling methods – Efficient algorithm for estimating failure probability

Uncertainties in the solution model and its input parameters make it difficult to ascertain the performance of an engineering system. While Monte Carlo simulation methods may be used to model the uncertain performance of such system, computational efficiency is a great challenge. To this end, subdomain sampling method (SSM), an efficient algorithm for estimating the failure probability of a system, is proposed in this study. The SSM involves a few steps. First, the possible domain of uncertain input variables of the system of concern is partitioned into a set of subdomains. Then, samples of uncertain variables are generated in each and every domain separately. Among these generated samples, those that lead to failure of the system are identified through a deterministic analysis. Finally, the failure probability is estimated using the total probability theorem. This SSM approach is referred to as the coarse subdomain sampling method, which is a fast algorithm with a generally acceptable accuracy. To reduce the variation of the failure probability estimate, a refined SSM is further developed by combining the coarse SSM with the importance sampling method. The accuracy and the efficiency of the proposed subdomain sampling methods, the coarse and refined SSMs, are demonstrated with two supported excavation problems.