A Monte Carlo Reliability Assessment for Multiple Failure Region Problems Using Approximate Metamodels

An efficient Monte Carlo reliability assessment methodology is presented for engineering systems with multiple failure regions and potentially multiple most probable points. The method can handle implicit, nonlinear limit-state functions, with correlated or non-correlated random variables, which can be described by any probabilistic distribution. It uses a combination of approximate or “accurate-on-demand,” global and local metamodels which serve as indicators to determine the failure and safe regions. Samples close to limit states define transition regions between safe and failure domains. A clustering technique identifies all transition regions which can be in general disjoint, and local metamodels of the actual limit states are generated for each transition region. A Monte Carlo simulation calculates the probability of failure using the global and local metamodels. A robust maximin “space-filling” sampling technique is used to construct the metamodels. Also, a principal component analysis addresses the problem dimensionality making therefore, the proposed method attractive for problems with a large number of random variables. Two numerical examples highlight the accuracy and efficiency of the method.