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High dimensional structural reliability with dimension reduction
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DOI：10.1016/j.strusafe.2017.07.007.png)
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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. (C) 2017 Elsevier Ltd. All rights reserved.
Keyword:
Uncertainty quantification
Active subspace
Kriging metamodel
Probability density evolution method
Bouc-Wen
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