Multicut‐High Dimensional Model Representation for Structural Reliability Bounds Estimation Under Mixed Uncertainties

Abstract

In reliability analysis of structural systems involving both aleatory and epistemic uncertainties, in conjunction with multiple design points, every configuration of the interval variables is to be explored to determine the bounds on reliability. To reduce the computational cost involved, this article presents a novel uncertain analysis method for estimating the bounds on reliability of structural systems involving multiple design points in the presence of mixed uncertain (both random and fuzzy) variables. The proposed method involves Multicut‐High Dimensional Model Representation (MHDMR) technique for the limit state/performance function approximation, the transformation technique to obtain the contribution of the fuzzy variables to the convolution integral and fast Fourier transform for solving the convolution integral. The limit state function approximation is obtained by linear and quadratic approximations of the first‐order HDMR component functions at the most probable point. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by the sample points, as compared to full‐scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability estimation involving any number of fuzzy variables and random variables with any kind of distribution. The accuracy and efficiency of the proposed method is demonstrated through four examples involving explicit/implicit performance functions.

Improved non-intrusive polynomial chaos for reliability analysis under hybrid uncertainty

“…And the limit state functions of these systems are covered by codes, thus are implicit [1]. In this case, the most widely used reliability analysis methods such as First Order Reliability Method (FORM) and Second Order Reliability Method (SORM) are not applicable [2]. To mitigate this issue, various surrogate models such as Response Surface Method (RSM) are employed to approximate the computational expensive black-box functions [3].…”

Probability and interval hybrid reliability analysis based on adaptive local approximation of projection outlines using support vector machine

“…Aleatory and epistemic uncertainties exist in most engineering problems simultaneously (Alvarez, Uribe, & Hurtado, 2018;Balu & Rao, 2012;Der Kiureghian & Ditlevsen, 2009;Liu, Kuang, Yin, & Hu, 2017;Wang, Gao, Zhou, & Zhang, 2018;Zhang & Huang, 2010). Aleatory uncertainty is objective and irreducible, which is often described by the classical probability theory.…”

Stochastic free vibration analysis of laminated composite plates using polynomial correlated function expansion

“…NSA that are popular among researchers include but are not limited to polynomial chaos expansion (PCE) [18][19][20][21], Kriging [22][23][24], radial basis function (RBF) [25,26], conventional response surface method (RSM) [27,28], moving least square [29,30] and high dimensional model representation [31][32][33].…”