Structural reliability analysis on the basis of small samples: An interval quasi-Monte Carlo method

In practice, reliability analysis of structures is often performed on the basis of limited data. Under, this circumstance, there are practical difficulties in identifying unique distributions as input for a probabilistic analysis. But the selection of realistic probabilistic input is critical for the quality of the results of the reliability analysis. This problem can be addressed using an entire set of plausible distribution functions rather than one single distribution for random variables based on limited data. The uncertain nature of the available information is then reflected in the probabilistic input. An imprecise probability distribution can be modeled by a probability box, i.e., the bounds of the cumulative distribution function for the random variable. Sampling-based methods have been proposed to perform reliability analysis with probability boxes. However, direct sampling of probability boxes requires a large number of samples. The computational cost can be very high as each simulation involves an interval analysis (a range-finding problem). This study proposes an interval quasi-Monte Carlo simulation methodology to efficiently compute the bounds of structure failure probabilities. The methodology is based on deterministic low-discrepancy sequences, which are distributed more regularly than the (pseudo) random points in direct Monte Carlo simulation. The efficiency and accuracy of the present method is illustrated using two examples. The reliability implications of different approaches for construction of probability boxes are also investigated through the example. Crown Copyright (C) 2012 Published by Elsevier Ltd. All rights reserved.