Local Domain Monte Carlo Simulation

In this contribution, a novel procedure denoted as ‘Local Domain Monte Carlo Simulation’ (LD-MCS) is studied for its potential use in structural reliability analysis. Instead of points as used in Monte Carlo sampling, small local domains surrounding these points are used to explore the failure domain and to estimate the associated occurrence probability. The suggested generalization of Direct Monte Carlo Simulation (D-MCS) is attractive in cases where the performance function within the specified local domains can be approximated by a simple analytical expression for which the conditional failure probability can be obtained without further structural response evaluations. It is shown that the LD-MCS approach significantly reduces the variance of the estimated failure probability when compared with Direct Monte Carlo Simulation (D-MCS). The proposed LD-MCS procedure is applied for non-linear performance functions g(x)g(x) in high dimensions where the gradient ∇g(x)∇g(x) depends strongly on the position x within the uncertain parameter space.