基于改进加权响应面的结构可靠度计算方法

吴洁; 张建国; 游令非; 叶楠

doi:10.13700/j.bh.1001-5965.2020.0251

基于改进加权响应面的结构可靠度计算方法

doi: 10.13700/j.bh.1001-5965.2020.0251

吴洁^{1, 2},
张建国^{1, 2, ,},
游令非^{1, 2},
叶楠^{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国防科技重点实验室, 北京 100083

基金项目:

国家自然科学基金 51675026

详细信息

通讯作者:
张建国. E-mail: zjg@buaa.edu.cn

中图分类号: TB114.3
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- 文章访问数: 616
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- PDF下载量: 87
- 被引次数: 0
出版历程
- 收稿日期: 2020-06-11
- 录用日期: 2020-08-07
- 网络出版日期: 2021-08-20

Structural reliability calculation method based on improved weighted response surface

WU Jie^{1, 2},
ZHANG Jianguo^{1, 2
, ,},
YOU Lingfei^{1, 2},
YE Nan^{1, 2}

1.
School of Reliability and System Engineering, Beihang University, Beijing 100083, China
2.
Science and Technology on Reliability and 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:
在结构可靠度分析中，响应面法由于具有良好的适用性和可操作性，是目前广泛使用的基于代理模型的分析方法。针对响应面法的计算效率和精度难以平衡兼顾等难点问题，提出一种基于改进加权响应面的结构可靠度计算方法。首先，在迭代过程中，同时考虑样本点与验算点距离、极限状态函数值、联合概率密度函数值3个权重因子对样本点进行赋权，采用加权回归并重复利用已有样本点更新不含交叉项的二次多项式响应面函数。其次，在迭代收敛后，选取已有样本点中权重较大的样本点加权拟合含有交叉项的二次多项式响应面函数。最后，结合数值算例和工程案例，通过与传统抽样方法和其他响应面法进行对比，验证了改进加权响应面法的可行性。结果表明所提方法具有较高效率的同时也保证了精度。
- 结构可靠度 /
- 响应面法 /
- 响应面函数 /
- 加权回归 /
- 样本重用
Abstract:
Response surface method is a widely used agent model analysis method for structural reliability analysis because of its good applicability and maneuverability. Aimed at the difficulties of the response surface method, such as balancing the efficiency and accuracy, a structural reliability calculation method based on improved weighted response surface is proposed. In the iterative process, three weighting factors, including the distance between the sample point and the design point, the absolute value of limit state function and the value of joint probability density function, are considered to weight the sample points. The quadratic polynomial response surface function without cross term is updated by weighted regression and reusing all known sample points. After the iterative convergence, the sample points with the larger weight among the existing sample points are selected to fit the quadratic polynomial response surface function with cross terms. Finally, with numerical examples and engineering cases, the feasibility of the proposed method is verified by comparing with traditional sampling methods and other response surface methods. The results show that the proposed method has higher efficiency and meanwhile guarantees accuracy.
- structural reliability /
- response surface method /
- response surface function /
- weighted regression /
- sample points reused

HTML全文

图 1 非线性加权响应面法流程^[22]

Figure 1. Flowchart of weighted nonlinear response surface method^[22]

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图 2 改进加权响应面法流程

Figure 2. Flowchart of improved weighted response surface method

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图 3 算例1求解过程

Figure 3. Solving process of Example 1

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图 4 带有集中力的悬臂梁

Figure 4. A cantilever beam with concentrated force

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图 5 算例2求解过程

Figure 5. Solving process of Example 2

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图 6 十杆桁架结构

Figure 6. Ten-bar truss structure

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图 7 十杆桁架ANSYS仿真结果

Figure 7. ANSYS simulation results of ten-bar truss

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图 8 算例3求解过程

Figure 8. Solving process of Example 3

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表 1 算例1计算结果比较

Table 1. Comparison of calculation results of Example 1

方法	失效概率	误差/%	结构分析次数	计算时间/s
蒙特卡罗法	0.003 622	0	10 000 000
经典响应面法	0.003 369	6.985 09	30	0.061
线性加权响应面法	0.003 362	7.178 36	20	0.023
单加权响应面法	0.003 366	7.067 92	20	0.026
双加权响应面法	0.003 393	6.322 37	20	0.034
改进加权响应面法	0.003 689	1.849 81	15	0.048

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表 2 算例2计算结果比较

Table 2. Comparison of calculation results of Example 2

方法	失效概率	误差/%	结构分析次数	计算时间/s
蒙特卡罗法	0.005 959	0	10 000 000
经典响应面法	0.005 691	4.497 40	56	0.026
线性加权响应面法	0.005 691	4.497 40	28	0.021
单加权响应面法	0.005 689	4.530 96	49	0.031
双加权响应面法	0.005 861	1.644 57	21	0.030
改进加权响应面法	0.005 967	0.134 25	21	0.052

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表 3 算例3计算结果比较

Table 3. Comparison of calculation results of Example 3

方法	失效概率	误差/%	结构分析次数
蒙特卡罗法^[23]	0.844 20	0	100 000
经典响应面法	0.836 41	0.922 77	196
线性加权响应面法	0.879 58	4.199 10	21
单加权响应面法	0.838 17	0.714 29	28
双加权响应面法	0.836 32	0.933 43	49
改进加权响应面法	0.848 89	0.555 56	21

下载: 导出CSV

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