An Efficient Monte Carlo Reliability Analysis Using Global and Local Metamodels

Abstract

*† ‡ An accurate and efficient computational method is presented for reliability analysis of engineering systems. The method can handle implicit, nonlinear limit-state functions, with correlated or non-correlated random variables, which are described by any probabilistic distribution. It uses a global and a local metamodel of the limit state. Both metamodels serve as an indicator to determine the failure and safe regions. Sample points close to limit state define a transition region between the safe and failure regions. An accurate local metamodel of the actual limit state is generated and used to evaluate all samples in the transition region. A Monte Carlo simulation calculates the probability of failure using the global and local metamodels. The cross-validated moving least squares method, and a robust maximin “space-filling” sampling technique, are used to construct the metamodels. Also, a Principal Component Analysis reduces the problem dimensionality making therefore, the proposed method attractive for problems with a large number of random variables. Three numerical examples highlight the accuracy and efficiency of the method.