Recent advances in polynomial chaos method for uncertainty propagation

XIONG Fenfen; CHEN Jiangtao; REN Chengkun; ZHANG Li; LI Zexian

doi:10.19693/j.issn.1673-3185.02130

Volume 16 Issue 4

Aug. 2021

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Chinese Journal of Ship Research > 2021 > 16(4): 19-36. > DOI: 10.19693/j.issn.1673-3185.02130 CSTR: 32390.14.j.issn.1673-3185.02130

XIONG F F, CHEN J T, REN C K, et al. Recent advances in polynomial chaos method for uncertainty propagation[J]. Chinese Journal of Ship Research, 2021, 16(4): 19–36. DOI: 10.19693/j.issn.1673-3185.02130

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Recent advances in polynomial chaos method for uncertainty propagation

1.
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
2.
China Aerodynamics Research and Development Center, Mianyang 621000, China

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Received Date: September 28, 2020
Revised Date: January 27, 2021
Accepted Date: June 08, 2021
Available Online: March 29, 2021

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

Abstract

Uncertainty exists widely in engineering design. As one of the key components of engineering design, uncertainty propagation and quantification has always been an important research topic. Polynomial chaos (PC) is a highly efficient uncertainty propagation method which has been widely studied and applied. Therefore, this paper reviews recent advances in the PC method. First, the fundamentals of PC are introduced, including the construction of an orthogonal polynomial basis and the calculation of PC coefficients. Second, strategies such as basis truncation, sparse reconstruction, sparse grid and multi-fidelity modeling are described to address the "curse of dimensionality" issue of PC. Local and global sensitivity analyses based on PC are then introduced. Finally, the research prospects of PC are given.
- uncertainty propagation,
- polynomial chaos,
- curse of dimensionality,
- multi-fidelity modeling,
- sensitivity analysis

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