High dimensional structural reliability with dimension reduction

For the uncertainty quantification in structural dynamics, random simulate methods such as Monte Carlo Simulation, Probability Density Evolution Method (Le and Chen, 2009) and metamodel method (Hastie et al., 2005) [2] are extensively used because of their usability and universality. Unfortunately, the required computational resource for structural stochastic analysis is still a burdensome task especially structures are involved in nonlinearity and high dimensional uncertainty. The so called “curse of dimension” problem means the cost of performing a reliable reliability analysis increases exponentially with the dimension. In present paper, a supervised dimension reduction methodology named Active Subspace Method (Constantine, 2015) is introduced to deal with the high dimension problem of structural reliability. GF-discrepancy based point set is employed to exploit the hidden low-dimensional structure in the mapping from input to the quantity of interest (QOI), a kriging metamodel (Kaymaz, 2005) with higher accuracy and efficiency can be constructed on the low-dimensional subspace. Further, the extreme-value reliability of structure is calculated effectively by incorporating into probability density evolution method based extreme-value system reliability (Li et al., 2007). The proposed approach is then applied to a theoretical four branches system with two-dimensional random variable and a 6-DOF Bouc-Wen nonlinear numerical model with 20-dimension random variable. The results show that the Active Subspace Kriging (ASK) method significantly improved the result of extreme-value reliability analysis for stochastic nonlinear structures, in which high dimensional randomness problem is involved.