摘要
针对工程中概率信息不全的可靠性问题,利用Copula理论逼近基本变量的联合分布函数和联合概率密度函数,建立Copula逼近基础上可靠性分析的自适应截断抽样法,并建立Copula逼近基础上基本变量对失效概率影响的重要测度分析的自适应截断抽样法。在所建模型中,基于Spearman相关系数的Copula函数被用来描述模型的相关性部分,其本身不受各个变量边缘分布的限制,比传统的Pearson相关系数具有更强的实用性。而建立在Copula逼近基础上的自适应截断抽样,可以利用自适应寻找设计点过程中的信息来计算失效概率,提高可靠性分析和基本变量重要性分析方法的效率和稳健性。在详细给出建模原理和求解流程方法后,算例用于说明模型的合理性和算法的可行性。
For engineering reliability problem under incomplete probability information,Copula theory is employed to approximate joint distribution function and joint probability density function of basic variables,on which an adaptive truncated sampling method is established to analyze the reliability and the importance measure about effect of the basic variables on failure probability.In the established model,the Spearman＇s correlation coefficient based model is used to describe the correlation part in the Copula function,and it is not restricted by marginal distribution function of the basic variable,and it＇s more practical than traditional Pearson correlation coefficient.The adaptive truncated sampling on the Copula approximation can compute the failure probability by use of the information from process of adaptively searching design point,as a result,the efficiency and the robustness of the reliability method are both enhanced.After the model concepts and the implementation are given,several examples are presented to demonstrate the rationality of the model and the feasibility of the solutions.
出处
《机械强度》
CAS
CSCD
北大核心
2012年第1期58-63,共6页
Journal of Mechanical Strength
基金
国家自然科学基金(10572117
50875213)
新世纪优秀人才支持计划(NCET-05-0868)
航空基金(2007ZA53012)
国家863计划课题(2007AA04Z401)资助~~
