北京航空航天大学学报 ›› 2018, Vol. 44 ›› Issue (6): 1156-1163.doi: 10.13700/j.bh.1001-5965.2017.0664

• 论文 • 上一篇    下一篇

结构输出响应概率密度估计中分数矩求解方法

李宝玉1,2, 张磊刚2, 师娇2, 余雄庆1   

  1. 1. 南京航空航天大学 航空宇航学院, 南京 210016;
    2. 中国运载火箭技术研究院, 北京 100076
  • 收稿日期:2017-10-25 出版日期:2018-06-20 发布日期:2018-06-28
  • 通讯作者: 张磊刚.E-mail:leigang_zhang@163.com E-mail:leigang_zhang@163.com
  • 作者简介:李宝玉 男,博士研究生,高级工程师。主要研究方向:飞行器设计、结构可靠性设计及结构优化;张磊刚 男,硕士,工程师。主要研究方向:飞行器结构可靠性设计、重要性分析及结构优化。
  • 基金资助:
    军委装备发展部“十三五”装备预研领域基金(6140244010216HT15001)

Solution method of fractional moments involved in probability density estimation of structural output response

LI Baoyu1,2, ZHANG Leigang2, SHI Jiao2, YU Xiongqing1   

  1. 1. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
    2. China Academy of Launch Vehicle Technology, Beijing 100076, China
  • Received:2017-10-25 Online:2018-06-20 Published:2018-06-28

摘要: 鉴于概率不确定性背景下基于分数矩极大熵准则的结构可靠性分析方法具有较大的效率与精度优势,综合研究并给出了可以用于极大熵准则中约束条件输出响应分数矩求解的3种分数矩求解方法,包括降维积分(DRI)方法、稀疏网格积分(SGI)方法和无迹变换(UT)方法。阐述了分数矩求解原理及过程,给出了方法的计算效率,并分析了方法的适用性。3种分数矩求解方法在确保计算精度的同时可以很大程度减少结构输入-输出模型的调用次数,大幅提高统计分析效率。通过与Monte Carlo仿真分析法对比,验证了3种分数矩求解方法的正确性与高效性。

关键词: 极大熵准则, 分数矩, 降维积分(DRI), 稀疏网格积分(SGI), 无迹变换(UT)

Abstract: For the fact that the fractional moment based principle of maximum entropy for structural reliability analysis has some advantages in computational efficiency and precision, in this paper, three computational methods for accurately estimating the fractional moments of constraint condition output response involved in the principle of maximum entropy, are studied and presented, including the dimension reduction integration (DRI) method, the sparse gird integration (SGI) method and the unscented transformation (UT) method. The computational theory and process are expounded, the calculation efficiency of each method is given, and the applicability of each method is analyzed in the paper. The presented three methods can greatly reduce the number of structural input-output model estimates and ensure the accuracy of calculation at the same time, so the efficiency of statistical analysis can be greatly improved. Besides, compared with the Monte Carlo simulation method, the accuracy and efficiency of the presented methods are verified according to the applied examples.

Key words: principle of maximum entropy, fractional moments, dimension reduction integration (DRI), sparse grid integration (SGI), unscented transformation (UT)

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