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不确定性传播的混沌多项式方法研究进展

熊芬芬 陈江涛 任成坤 张立 李泽贤

熊芬芬, 陈江涛, 任成坤, 等. 不确定性传播的混沌多项式方法研究进展[J]. 中国舰船研究, 2021, 16(4): 19–36 doi: 10.19693/j.issn.1673-3185.02130
引用本文: 熊芬芬, 陈江涛, 任成坤, 等. 不确定性传播的混沌多项式方法研究进展[J]. 中国舰船研究, 2021, 16(4): 19–36 doi: 10.19693/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
Citation: 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

不确定性传播的混沌多项式方法研究进展

doi: 10.19693/j.issn.1673-3185.02130
基金项目: 国家数值风洞项目(NNW2020ZT7-B31);国防基础科研科学挑战专题资助项目(TZ2018001)
详细信息
    作者简介:

    熊芬芬,女,1982年生,博士,副教授。研究方向:不确定性量化和优化设计。E-mail:fenfenx@bit.edu.cn

    陈江涛,男,1983年生,博士,副研究员

    任成坤,男,1994年生,博士生。研究方向:不确定性量化和优化设计。E-mail:3120170071@bit.edu.cn

    张立,男,1997年生,硕士生。研究方向:不确定性量化和深度学习。E-mail:18811367828@163.com

    李泽贤,男,1998年生,硕士生。研究方向:不确定性量化和优化设计。E-mail:lzx_bit@163.com

    通信作者:

    熊芬芬

  • 中图分类号: U662.2

Recent advances in polynomial chaos method for uncertainty propagation

  • 摘要: 不确定性在工程设计中广泛存在,作为工程设计中的核心内容之一,不确定性传播和量化一直都是工程设计领域重要的理论课题之一。混沌多项式作为一种高效的不确定性传播方法近年来得到了广泛研究和应用,具有较大的工程应用潜力。为此,对混沌多项式方法的研究进展进行综述。首先,介绍该方法的应用场景和基本原理;其次,针对混沌多项式应用中面临的“维数灾难”、计算量大等难题,介绍基截断、稀疏重构、稀疏网格、多可信度建模等诸多解决策略;然后,对基于混沌多项式的全局和局部灵敏度分析方法进行介绍;最后,对混沌多项式的研究进行展望。
  • 图  1  概率不确定性传播示意图

    Figure  1.  Probabilistic uncertainty propagation

    图  2  不确定性传播在模型确认中的作用

    Figure  2.  UP in model validation

    图  3  确定性最优和稳健性最优

    Figure  3.  Deterministic and robust optimums

    图  4  确定性最优和可靠性最优

    Figure  4.  Deterministic and reliability-based optimums

    图  5  不确定性传播在不确定性优化中的地位

    Figure  5.  UP in design optimization under uncertainty

    图  6  不同稀疏因子下一元正交多项式的阶数组合

    Figure  6.  Order combinations of orthogonal polynomial with different sparse factors

    图  7  基于概率盒和混沌多项式的混合不确定性传播

    Figure  7.  Mixed UP with PC and P-box

    图  8  证据理论下输出响应y的CBF和CPF曲线

    Figure  8.  CBF and CPF of output response with Dempster-Shafer theory

    图  9  基于混沌多项式和模糊理论的混合不确定性传播

    Figure  9.  Mixed uncertainty propagation with PC and fuzzy theory

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出版历程
  • 收稿日期:  2020-09-29
  • 录用日期:  2021-06-09
  • 修回日期:  2021-01-28
  • 网络出版日期:  2021-06-09
  • 刊出日期:  2021-08-10

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