一种基于Kriging和Monte Carlo的主动学习可靠度算法
收稿日期: 2014-10-21
修回日期: 2014-12-28
网络出版日期: 2015-01-07
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
Received date: 2014-10-21
Revised date: 2014-12-28
Online published: 2015-01-07
Supported by
National Science and Technology Major Project (2013ZX04011-011)
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
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 . DOI: 10.7527/S1000-6893.2014.0361
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
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