一种基于Kriging和Monte Carlo的主动学习可靠度算法

doi:10.7527/S1000-6893.2014.0361

固体力学与飞行器总体设计

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一种基于Kriging和Monte Carlo的主动学习可靠度算法

佟操¹, 孙志礼¹, 杨丽^1,2, 孙安邦¹

1. 东北大学机械工程与自动化学院, 沈阳 110819;
2. 沈阳理工大学装备工程学院, 沈阳 110159

收稿日期:2014-10-21 修回日期:2014-12-28 出版日期:2015-09-15 发布日期:2015-01-07
通讯作者: 孙志礼男, 博士, 教授, 博士生导师。主要研究方向: 机械可靠性工程, 摩檫学设计理论及应用。 Tel: 024-83679346 E-mail: zhlsun@mail.neu.edu.cn E-mail:zhlsun@mail.neu.edu.cn
作者简介:佟操男, 博士研究生。主要研究方向: 结构可靠性分析, 齿轮系统动力学。 E-mail: tongcao19@163.com
基金资助:
国家科技重大专项 (2013ZX04011-011)

An active learning reliability method based on Kriging and Monte Carlo

TONG Cao¹, SUN Zhili¹, YANG Li^1,2, SUN Anbang¹

1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, China;
2. School of Equipment Engineering, Shenyang Ligong University, Shenyang 110159, China

Received:2014-10-21 Revised:2014-12-28 Online:2015-09-15 Published:2015-01-07
Supported by:
National Science and Technology Major Project (2013ZX04011-011)

摘要/Abstract

摘要：

机械结构可靠性分析时,常常会采用代理模型拟合隐式功能函数来解决计算量大的问题,但由于试验设计方案需要同时考虑代理模型的拟合精度和可靠度计算精度的问题。因此,为了能够充分使用较少的样本信息,最大化可靠度计算精度,本文充分发挥Kriging预测的随机特性,提出一种主动学习可靠度计算方法。首先,类似于优化问题中改善函数的选点方式,提出一种基于Kriging预测的学习函数,基于Monte Carlo法生成大量的候选样本点,找出学习函数最小值对应的样本点作为最佳取样点。其次,推导和提出了一种学习停止的条件,保证了Monte Carlo样本点预测符号的正确性且学习次数明显减小。最后,通过2个数值算例分析结果表明,该算法相比其他方法需要更少的样本数量,得到的可靠度计算精度更高,验证了本文算法的正确性和高效性。

关键词: 可靠性, Monte Carlo, Kriging模型, 主动学习, 失效概率

Abstract:

In structural reliability analysis, surrogate models are usually used to approximate implicit performance function in order to solve the problem of large computation. However, selection of the design of numerical experiments should consider the accuracy of fitting surrogate model and the precision of calculating reliability simultaneously. Therefore, in order to make full use of the few sample information as little as possible and to maximize the accuracy of reliability calculation, an active learning reliability calculation method is proposed. Firstly, a learning function based on Kriging prediction is proposed similar to the improved function determining the selection of point in the optimization problem. And the best sampling point corresponding to the minimum of learning function is selected from the Monte Carlo population. Secondly, an iterative stopping criterion is proposed to ensure the correctness of Monte Carlo sample points' sign, and the iterations decrease dramatically. Finally, the correctness and efficiency of the proposed method are proved by two academic examples from literature; it is shown that the proposed method requires fewer calls to the performance function than other methods and the failure probability obtained from the proposed method is more accurate.

Key words: reliability, Monte Carlo, Kriging model, active learning, failure probability

中图分类号:

佟操, 孙志礼, 杨丽, 孙安邦. 一种基于Kriging和Monte Carlo的主动学习可靠度算法[J]. 航空学报, 2015, 36(9): 2992-3001.

TONG Cao, SUN Zhili, YANG Li, SUN Anbang. An active learning reliability method based on Kriging and Monte Carlo[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(9): 2992-3001.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

一种基于Kriging和Monte Carlo的主动学习可靠度算法

An active learning reliability method based on Kriging and Monte Carlo

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