High dimensional structural reliability with dimension reduction. (November 2017)

• Record Type: Journal Article
• Authors: Jiang, Zhongming; Li, Jie
• Is Part Of: Structural safety. Volume 69(2017)
• Page Start: 35
• Page End: 46
• Publication Date: 2017-11
• Subjects: Uncertainty quantification -- Active subspace -- Kriging metamodel -- Probability density evolution method -- Bouc-Wen; Structural stability -- Periodicals; Safety factor in engineering -- Periodicals; Reliability (Engineering) -- Periodicals; Constructions -- Stabilité -- Périodiques; Coefficient de sécurité en ingénierie -- Périodiques; Fiabilité -- Périodiques; 620.86
• DOI: 10.1016/j.strusafe.2017.07.007
• Languages: English
• ISSNs: 0167-4730

Abstract

Highlights: ASK method is a reliability method based on Dimension Reduction technology and PDEM. A supervised dimension reduction technology for exploiting latent low dimensional subspace is employed with GF-discrepancy points. Numerical examples involving up to 20 random variables are reduced to one dimensional problem with fair efficiency and precision. Abstract: 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.