摘要
考虑随机变量间相关性的复杂工程结构整体可靠性分析仍然是一个挑战,特别是对于非线性相关问题.该文考虑到随机变量之间非线性相关的影响,提出了一种用于结构整体可靠性分析的增强型高阶矩方法.该文首先回顾了传统的Nataf变换,进而通过引入Copula理论提出了广义Nataf变换;其次,采用状态变量描述法统一描述整体可靠性问题对应的功能函数,并发展了基于GL_(2)-偏差点集的状态变量高阶矩估计和灵敏度分析方法;再次,通过改进的最大熵法准确估计了结构整体可靠度;最后,通过两个算例验证了所提方法的准确性和有效性以及考虑随机变量间的非线性相关性对结构整体可靠度影响的必要性.算例结果与蒙特卡洛模拟方法比较表明,随机变量间的非线性相关性对结构的整体可靠度有显著影响,所提方法对结构高阶矩估计和全局可靠度分析具有较高的精度和效率.
The global reliability analysis of complex engineering structures considering the correlations between basic random variables remains a challenge,especially for nonlinear correlation problems.In this work,to take into account the influence of nonlinear correlation between random variables,an enhanced high-order moment method is proposed for structural global reliability analysis.Firstly,the traditional Nataf transformation is reviewed,and the generalized Nataf transformation is presented by introducing the Copula theory.Secondly,the corresponding performance functions of global reliability problems are described uniformly by the state variable description method,and the GL_(2)-discrepancy point set is developed for the high-order moments estimation and sensitivity analysis of the state variable.Thirdly,the global reliability of the structures is accurately determined by using the improved maximum entropy method(IMEM).Finally,two examples,including one static and one dynamic,are investigated to demonstrate the accuracy and efficiency of the proposed method and the influence of nonlinear correlation between random variables on the global reliability of the structures,in which the results obtained from the proposed method are compared with Monte Carlo simulation(MCS)method.The results of the examples show the nonlinear correlation between random variables has a significant impact on the global reliability of structures,and the proposed method has fairly high accuracy and efficiency for structural high-order moments estimation and global reliability analysis.
作者
宋鹏彦
王涛
吕大刚
Pengyan Song;Tao Wang;Dagang Lu(College of Civil Engineering and Architecture,Hebei University,Baoding,071002,China;School of Transportation Science and Engineering,Harbin Institute of Technology,Harbin,150040,China;Chongqing Research Institute of Harbin Institute of Technology,Harbin Institute of Technology,Chongqing,401151,China;Key Lab of Structure Dynamic Behavior and Control of China Ministry of Education,Harbin Institute of Technology,Harbin,150090,China)
基金
supported by the National Key Research and Development Plan of China“Basic Theory and Methods for Resilience Assessment and Risk Control of Transportation Infrastructures”(Grant No.2021YFB2600500)
Natural Science Foundation of Chongqing CSTC(Grant No.2022NSCQ-MSX4037)
Advanced Talents Incubation Program of the Hebei University(Grant No.521000981082).
