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

doi:10.13700/j.bh.1001-5965.2018.0301

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

魏娟^{1, 2},
张建国^{1, 2, ,},
邱涛^{1, 2}

1.
北京航空航天大学可靠性与系统工程学院, 北京 100083
2.
北京航空航天大学可靠性与环境工程技术重点实验室, 北京 100083

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
计量
- 文章访问数: 702
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- PDF下载量: 484
- 被引次数: 0
出版历程
- 收稿日期: 2018-05-28
- 录用日期: 2018-08-24
- 网络出版日期: 2019-02-20

Structural reliability algorithm based on improved dynamic Kriging model

WEI Juan^{1, 2},
ZHANG Jianguo^{1, 2
, ,},
QIU Tao^{1, 2}

1.
School of Reliability and Systems Engineering, Beihang University, Beijing 100083, China
2.
Science and Technology on Reliability and Environment Engineering Laboratory, Beihang University, Beijing 100083, China

Funds:

National Natural Science Foundation of China 51675026

More Information

Corresponding author: ZHANG Jianguo, E-mail: zjg@buaa.edu.cn

摘要

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。
- 极限状态函数 /
- 动态更新 /
- Kriging模型 /
- 粒子群-模拟退火(PSOSA)算法 /
- 可靠性
Abstract:
For complex aerospace machinery products, the limit state functions are often implicit and highly nonlinear, and the reliability calculation usually requires time-consuming finite element analysis. In this paper, the particle swarm optimization-simulated annealing (PSOSA) algorithm is applied to the optimization of the correlation parameters of the dynamic Kriging model, which improves the prediction accuracy. At the same time, with the dynamic update mechanism, sample points are gradually added to reduce the number of function callsas much as possible, thereby improving the calculation efficiency. The algorithm is applied to the structural reliability analysis. The Monte Carlo method, response surface and other classic algorithms are compared, and the results of the proposed algorithm are closer to those of Monte Carlo method, and the calculation time is greatly shortened, which shows that the efficiency and accuracy of the algorithm are improved significantly.
- limit state function /
- dynamic update /
- Kriging model /
- particle swarm optimization-simulated annealing (PSOSA) algorithm /
- reliability

HTML全文

图 1 PSOSA算法示意图

Figure 1. Sketch map of PSOSA algorithm

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图 2 改进的动态Kriging模型流程图

Figure 2. Flowchart of improved dynamic Kriging model

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图 3 极限状态函数

Figure 3. Limit state function

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图 4 算法说明图

Figure 4. Illustration of algorithm

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图 5 应力和应变计算结果

Figure 5. Calculation results of stress and strain

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图 6 θ^*的迭代过程

Figure 6. Iteration process of θ^*

下载: 全尺寸图片幻灯片

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	β_r	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

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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	β_r	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

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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

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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

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