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基于改进的动态Kriging模型的结构可靠度算法

魏娟 张建国 邱涛

魏娟, 张建国, 邱涛等 . 基于改进的动态Kriging模型的结构可靠度算法[J]. 北京航空航天大学学报, 2019, 45(2): 373-380. doi: 10.13700/j.bh.1001-5965.2018.0301
引用本文: 魏娟, 张建国, 邱涛等 . 基于改进的动态Kriging模型的结构可靠度算法[J]. 北京航空航天大学学报, 2019, 45(2): 373-380. doi: 10.13700/j.bh.1001-5965.2018.0301
WEI Juan, ZHANG Jianguo, QIU Taoet al. Structural reliability algorithm based on improved dynamic Kriging model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(2): 373-380. doi: 10.13700/j.bh.1001-5965.2018.0301(in Chinese)
Citation: WEI Juan, ZHANG Jianguo, QIU Taoet al. Structural reliability algorithm based on improved dynamic Kriging model[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(2): 373-380. doi: 10.13700/j.bh.1001-5965.2018.0301(in Chinese)

基于改进的动态Kriging模型的结构可靠度算法

doi: 10.13700/j.bh.1001-5965.2018.0301
基金项目: 

国家自然科学基金 51675026

详细信息
    作者简介:

    魏娟  女, 硕士研究生。主要研究方向:机械产品可靠性分析与设计

    张建国  男, 博士, 教授, 博士生导师。主要研究方向:机械可靠性与安全性

    通讯作者:

    张建国, E-mail: zjg@buaa.edu.cn

  • 中图分类号: TB114.3

Structural reliability algorithm based on improved dynamic Kriging model

Funds: 

National Natural Science Foundation of China 51675026

More Information
  • 摘要:

    对于复杂航空航天机械产品,极限状态方程往往表现出隐式、高度非线性的特点,而且通常需要调用有限元分析,从而耗费大量时间。将混合粒子群-模拟退火(PSOSA)算法应用到Kriging模型中相关参数的寻优过程,提高了预测精度。同时结合动态更新机制,逐渐加入样本点,尽可能减少函数的调用次数,从而提高了计算效率,并将该算法应用到结构可靠性分析中。通过案例分析,和传统蒙特卡罗模拟方法、响应面等经典方法进行对比,所提算法与蒙特卡罗模拟方法计算结果更加接近,计算时间大大缩短,效率和精度都明显改进。

     

  • 图 1  PSOSA算法示意图

    Figure 1.  Sketch map of PSOSA algorithm

    图 2  改进的动态Kriging模型流程图

    Figure 2.  Flowchart of improved dynamic Kriging model

    图 3  极限状态函数

    Figure 3.  Limit state function

    图 4  算法说明图

    Figure 4.  Illustration of algorithm

    图 5  应力和应变计算结果

    Figure 5.  Calculation results of stress and strain

    图 6  θ*的迭代过程

    Figure 6.  Iteration process of θ*

    表  1  不同方法结果对比(算例1)

    Table  1.   Comparison of results of different methods (Example 1)

    方法 样本点 βr 失效概率/10-3
    MCS 108 6.3
    RSM 65 2.392 7 8.3
    经典Kriging 40 2.475 1 6.7
    PSO-Kriging 40 2.480 5 6.56
    本文 40 2.489 3 6.4
    下载: 导出CSV

    表  2  不同方法结果对比(算例2)

    Table  2.   Comparison of results of different methods (Example 2)

    方法 函数调用次数 βr 失效概率/10-3
    MCS 106 4.16
    RSM 5 1.472 9 70.39
    经典Kriging 30 2.624 5 4.30
    PSO-Kriging 30 2.630 7 4.26
    本文 30 2.639 6 4.15
    下载: 导出CSV

    表  3  涡轮盘参数

    Table  3.   Parameters of turbine disk

    参数 涡轮盘的转速ω 弹性模量(轮盘)E1 泊松比(轮盘)ε1 密度(轮盘)ρ1 弹性模量(销轴)E2 泊松比(销轴)ε2 密度(销轴)ρ2 均布载荷P
    均值 9 550 r/min 123 GPa 0.33 4.48 g/cm3 219 GPa 0.3 7.76 g/cm3 24 925 N
    变异系数 0.1 0.015 0.01 0.02 0.015 0.01 0.002 0.1
    下载: 导出CSV

    表  4  计算结果对比

    Table  4.   Comparison of calculation results

    方法 函数调用次数 样本点 失效概率/10-3
    MCS方法 105 3.300
    本文算法 15 40 3.352
    下载: 导出CSV
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出版历程
  • 收稿日期:  2018-05-28
  • 录用日期:  2018-08-24
  • 刊出日期:  2019-02-20

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