基于Kriging和MCMC的结构可靠性主动学习算法

doi:10.12068/j.issn.1005-3026.2021.10.011

东北大学学报（自然科学版） ›› 2021, Vol. 42 ›› Issue (10): 1444-1450.DOI: 10.12068/j.issn.1005-3026.2021.10.011

基于Kriging和MCMC的结构可靠性主动学习算法

张灏岩，毕秋实，李勃，郭广勇

(吉林大学机械与航空航天工程学院，吉林长春130025)

修回日期:2021-01-04 接受日期:2021-01-04 发布日期:2021-10-22
通讯作者: 张灏岩
作者简介:张灏岩(1996-)，女，满族，河北承德人，吉林大学硕士研究生.
基金资助:
国家自然科学基金资助项目(51775225).

Active Learning Algorithm of Structural Reliability Based on Kriging and MCMC

ZHANG Hao-yan， BI Qiu-shi， LI Bo， GUO Guang-yong

School of Mechanical and Aerospace Engineering， Jilin University， Changchun 130025， China.

Revised:2021-01-04 Accepted:2021-01-04 Published:2021-10-22
Contact: BI Qiu-shi
About author:-
Supported by:
-

摘要/Abstract

摘要： 在进行机械结构可靠性分析时，由于很多工程问题的性能函数较为复杂，计算成本很高，所以常采用代理模型拟合隐式性能函数来降低计算成本.为了能够利用较少的样本信息，获得较高的可靠度计算精度，将Kriging代理模型与学习函数相结合，提出一种主动学习可靠性分析计算方法.该方法找出学习效果最好的样本点对Kriging模型进行更新，提高了模型的拟合精度.用马尔科夫链蒙特卡洛(MCMC)方法对结构的可靠性进行了评估，加快了样本点的收敛速度，节约了样本空间.通过分析4个算例的结果表明与其他方法相比，该方法能通过较少的样本点得到精度更高的计算结果，降低了计算成本.

关键词: 可靠性;Kriging;MCMC;主动学习;失效概率

Abstract: Because the performance functions of many engineering problems are more complicated and the calculation cost is high in the reliability analysis of mechanical structures， the agent model is often used to fit the implicit performance function to reduce the calculation cost. In order to use less sample information and obtain higher reliability calculation accuracy， the Kriging agent model is combined with the learning function， and an active learning reliability analysis and calculation method is proposed. This method finds the sample points with the best learning effect to update the Kriging model， which improves the fitting accuracy of the model. Markov chain Monte Carlo(MCMC)method is used to evaluate the reliability of the structure， which speeds up the convergence speed of sample points and saves sample space. Analyzing the results of 4 calculation examples shows that compared with the other methods， this method can obtain higher precision calculation results with fewer sample points， and reduce the calculation cost.

Key words: reliability; Kriging; MCMC; active learning; failure probability

中图分类号:

TB114.3

张灏岩，毕秋实，李勃，郭广勇. 基于Kriging和MCMC的结构可靠性主动学习算法[J]. 东北大学学报（自然科学版）, 2021, 42(10): 1444-1450.

ZHANG Hao-yan， BI Qiu-shi， LI Bo， GUO Guang-yong. Active Learning Algorithm of Structural Reliability Based on Kriging and MCMC[J]. Journal of Northeastern University(Natural Science), 2021, 42(10): 1444-1450.

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基于Kriging和MCMC的结构可靠性主动学习算法

Active Learning Algorithm of Structural Reliability Based on Kriging and MCMC

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