A data-driven polynomial chaos method considering correlated random variables

2020 ◽  
Vol 62 (4) ◽  
pp. 2131-2147
Author(s):  
Qizhang Lin ◽  
Fenfen Xiong ◽  
Fenggang Wang ◽  
Xin Yang
Keyword(s):  
Polynomial Chaos ◽  
Random Variables ◽  
Data Driven

scholarly journals An Efficient Polynomial Chaos Method for Stiffness Analysis of Air Spring Considering Uncertainties

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Feng Kong ◽  
Penghao Si ◽  
Shengwen Yin
Keyword(s):  
Orthogonal Polynomial ◽  
Polynomial Chaos ◽  
Random Variables ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
Response Analysis ◽  
Air Spring ◽  
Stiffness Analysis ◽  
Orthogonal Polynomial Expansion ◽  
Sparse Quadrature

Traditional methods for stiffness analysis of the air spring are based on deterministic assumption that the parameters are fixed. However, uncertainties have widely existed, and the mechanic property of the air spring is very sensitive to these uncertainties. To model the uncertainties in the air spring, the interval/random variables models are introduced. For response analysis of the interval/random variables models of the air spring system, a new unified orthogonal polynomial expansion method, named as sparse quadrature-based interval and random moment arbitrary polynomial chaos method (SQ-IRMAPC), is proposed. In SQ-IRMAPC, the response of the acoustic system related to both interval and random variables is approximated by the moment-based arbitrary orthogonal polynomial expansion. To efficiently calculate the coefficient of the interval and random orthogonal polynomial expansion, the sparse quadrature is introduced. The proposed SQ-IRMAPC was employed to analyze the mechanic performance of an air spring with interval and/or random variables, and its effectiveness has been demonstrated by fully comparing it with the most recently proposed orthogonal polynomial-based interval and random analysis method.

scholarly journals Polynomial chaos expansions for dependent random variables

2019 ◽  
Vol 351 ◽  
pp. 643-666 ◽  
Author(s):  
John D. Jakeman ◽  
Fabian Franzelin ◽  
Akil Narayan ◽  
Michael Eldred ◽  
Dirk Plfüger
Keyword(s):  
Polynomial Chaos ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Polynomial Chaos Expansions
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