吉林大学学报(工学版) ›› 2021, Vol. 51 ›› Issue (6): 1975-1981.doi: 10.13229/j.cnki.jdxbgxb20200613

• 车辆工程·机械工程 • 上一篇    

新型结构可靠性分析自适应加点策略

李国发1,2(),陈泽权1,2,何佳龙1,2()   

  1. 1.吉林大学 数控装备可靠性教育部重点实验室 长春 130022
    2.吉林大学 机械与航空航天工程学院 长春 130022
  • 收稿日期:2020-08-11 出版日期:2021-11-01 发布日期:2021-11-15
  • 通讯作者: 何佳龙 E-mail:ligf@jlu.edu.cn;hejl@jlu.edu.cn
  • 作者简介:李国发（1970-），男，教授，博士. 研究方向：数控装备可靠性理论及其全生命周期工程. E-mail：ligf@jlu.edu.cn
  • 基金资助:
    国家自然科学基金项目(51905209);吉林省中青年科技创新领军人才及团队项目(20190101015JH);吉林大学高层次科技创新团队项目（JLUSTIRT）

New adaptive sampling strategy for structural reliability analysis

Guo-fa LI1,2(),Ze-quan CHEN1,2,Jia-long HE1,2()   

  1. 1.Key Laboratory of CNC Equipment Reliability，Ministry of Education，Jilin University，Changchun 130022，China
    2.College of Mechanical and Aerospace Engineering，Jilin University，Changchun 130022，China
  • Received:2020-08-11 Online:2021-11-01 Published:2021-11-15
  • Contact: Jia-long HE E-mail:ligf@jlu.edu.cn;hejl@jlu.edu.cn

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摘要：

为了在进行结构可靠性分析时，能够构建高精度、高效率的代理模型，提出了一种面向多种代理模型的基于通用学习函数（GLF）的结构可靠性分析自适应加点策略。该策略被视为一个多目标优化过程，GLF考虑了样本点间的平均距离和最小距离、是否分布在极限状态函数的附近以及联合概率密度函数等因素，使得自适应添加的样本点能稳健、高效地提升代理模型对失效概率的估计精度。数值案例和工程案例结果表明，针对不同的代理模型，GLF能够利用少量的样本点，高精度、高效率地估计出结构的失效概率。

关键词: 结构可靠性, 可靠性分析, 代理模型, 自适应加点, 学习函数

Abstract:

In structural reliability analysis, choosing an appropriate adaptive sampling strategy is the key to constructing a high-precision and high-efficiency surrogate model. An adaptive sampling strategy for structural reliability analysis based on General Learning Function (GLF) for multiple surrogate models is proposed. The adaptive sampling strategy is regarded as a multi-objective optimization process, so the average and the minimum distance between the sample points, whether they are distributed near the limit state function, and the probability density function are all considered by the GLF to ensure that the new sample points can robustly and efficiently improve the surrogate model estimation accuracy of failure probability. Numerical cases and engineering case show that for different surrogate models, the GLF can use a small number of sample points to estimate the structural failure probability with high accuracy and efficiency.

Key words: structural reliability, reliability analysis, surrogate model, adaptive sampling, learning function

中图分类号: 

  • TB114.3

图1

自适应结构可靠性分析流程图"

图2

基于GLF的代理模型与真实极限状态函数的对比"

表1

本文方法指导的代理模型与MCS的对比"

分析方法代理模型样本量失效概率相对误差/%
MCS-1050.014 63-
本文方法kriging模型10+290.014 550.55
RBF神经网络10+560.014 690.41

图3

无阻尼单自由度振荡系统"

表2

变量的分布信息"

变量均值标准差分布类型
m10.05正态分布
c110.1正态分布
c20.10.01正态分布
r0.050.05正态分布
F110.2正态分布
t110.2正态分布

表3

本文方法指导的代理模型与MCS的对比"

分析方法代理模型样本量失效概率相对误差/%
MCS-1050.028 57-
本文方法kriging模型10+270.028 390.63
RBF神经网络10+130.028 540.11

图4

GLF学习函数指导的代理模型的失效概率收敛图"

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