基于优化Kriging模型和重要抽样法的结构可靠度混合算法
收稿日期: 2012-07-24
修回日期: 2013-01-03
网络出版日期: 2013-01-09
基金资助
国家"973"计划(2013CB733000)
Hybrid Structure Reliability Method Combining Optimized Kriging Model and Importance Sampling
Received date: 2012-07-24
Revised date: 2013-01-03
Online published: 2013-01-09
Supported by
National Basic Research Program of China (2013CB733000)
结构可靠度分析计算通常采用多项式响应面拟合隐式极限状态函数,但对于复杂航空航天机械结构产品极限状态方程往往表现出高度非线性,此时多项式响应面的模拟精度不够就会造成计算不收敛。为了提高结构可靠度计算的精度、效率和收敛性,提出了基于优化Kriging模型和重要抽样法的结构可靠度计算方法。首先,利用人工蜂群算法对Kriging模型的参数进行优化;再用优化后的模型模拟隐式极限状态函数,结合重要抽样法不断修正抽样重心,逐步提高模拟精度以达到给定要求;最后,结合一阶矩法(FORM)/二阶矩法(SORM)经典算法求解结构可靠度。该方法提高了高度非线性隐式极限状态方程可靠度计算的精度和收敛性,并且具有较高的计算效率。
刘瞻 , 张建国 , 王灿灿 , 谭春林 , 孙京 . 基于优化Kriging模型和重要抽样法的结构可靠度混合算法[J]. 航空学报, 2013 , 34(6) : 1347 -1355 . DOI: 10.7527/S1000-6893.2013.0235
In structural reliability analysis, a polynomial function is usually used to approach the implicit limit state function. But the limit state function is likely to be implicit and highly nonlinear for complex aeronautic and astronautic structures. The calculation may not converge if the simulation of the polynomial function is not accurate enough. In order to improve the accuracy, efficiency, and convergency, a reliability method combining the approved Kriging model and importance sampling is proposed in this paper. Firstly, the parameter of Kriging model is optimized using the artificial bee colony algorithm. Then the implicit limit state function is fitted with the optimized Kriging model, and the sampling center is revised constantly by importance sampling to improve gradually the fitting accuracy. Finally, the reliability is solved combining the Kriging model and the parsing algorithm such as the first order reliability method (FORM) or second order reliability method (SORM). This method improves the accuracy and convergency of reliability calculations with highly nonlinear limit state functions, and has high computing efficiency.
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