Reliability analysis using high dimensional model representation for mixed uncertain variables

The reliability estimation of a structural system depends on the type of uncertain parameters considered. If all the uncertain parameters are defined as random variables, then the reliability can be estimated by using probability theory. However, when modeling uncertain variables with limited information as intervals with upper and lower bounds, the entire range of these bounds should be explored. When dealing with the combination of both random and interval variables, as every combination of interval variables demands one probabilistic based analysis, the computational cost involved in estimating the reliability of the system increases exponentially. Therefore in this paper, high dimensional model representation (HDMR) is used to approximate the failure function accurately, and fast Fourier transform techniques are applied to solve the convolution integral. The proposed methodology demonstrates the improvement in computational efficiency and accuracy in the estimation of the reliability bounds using numerical examples.