A cubature collocation based sparse polynomial chaos expansion for efficient structural reliability analysis

2018 ◽  
Vol 74 ◽  
pp. 24-31 ◽  
Author(s):  
Jun Xu ◽  
Fan Kong
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Structural Reliability Analysis ◽  
Sparse Polynomial ◽  
Sparse Polynomial Chaos Expansion

Adaptive-Sparse Polynomial Chaos Expansion for Reliability Analysis and Design of Complex Engineering Systems

2009 ◽  
Author(s):  
Chao Hu ◽  
Byeng D. Youn
Keyword(s):  
Reliability Analysis ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Nonlinear Correlation ◽  
Analysis And Design ◽  
Decomposition Scheme ◽  
Reduction Techniques ◽  
Sparse Polynomial ◽  
Sparse Polynomial Chaos Expansion

This paper presents an adaptive-sparse polynomial chaos expansion (adaptive-sparse PCE) method for performing engineering reliability analysis and design. The proposed method leverages three ideas: (i) an adaptive scheme to build sparse PCE with the minimum number of bivariate basis functions, (ii) a new projection method using dimension reduction techniques to effectively compute the expansion coefficients of system responses, and (iii) an integration of copula to handle nonlinear correlation of input random variables. The proposed method thus has three distinct features for reliability analysis and design: (a) no need of response sensitivities, (b) no extra cost to evaluate probabilistic sensitivity for design, and (c) capability to handle a nonlinear correlation. Besides, an error decomposition scheme of the proposed method is presented to help analyze error sources in probability analysis. Several engineering problems are used to demonstrate the effectiveness of the adaptive-sparse PCE method.

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