一种耦合区间-随机混合可靠性分析方法
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摘要
考虑区间变量的耦合性,基于多椭球模型提出了一种高效的耦合区间-随机混合可靠性分析方法。为解决耦合区间变量导致的可靠性分析计算效率低的问题,采用序列迭代分析方法,将混合可靠性分析的双层耦合循环分解为概率分析与区间分析,并结合多项式插值法提出了一种适用于极限状态函数关于耦合区间变量单调与非单调两种工况的高效区间分析算法。算例结果表明,所提的混合可靠性分析方法具有较好的计算精度与计算效率。
Considering the dependence between interval variables, an efficient hybrid reliability analysis method with the mixture of random and dependent interval variables was proposed based on the multi-ellipsoid model. To resolve the inefficiency of the hybrid reliability analysis due to dependent interval variables, a sequentially iterative strategy was adopted for decoupling the double-nest loop of the hybrid reliability analysis into the probability analysis and interval analysis. And an efficient interval analysis algorithm was developed by using polynomial interpolation, which was capable of efficiently handling the cases where the limit-state functions were monotonic or non-monotonic with respect to dependent interval variables.The results of numerical examples show that the proposed hybrid reliability analysis method has good accuracy and efficiency.
Considering the dependence between interval variables, an efficient hybrid reliability analysis method with the mixture of random and dependent interval variables was proposed based on the multi-ellipsoid model. To resolve the inefficiency of the hybrid reliability analysis due to dependent interval variables, a sequentially iterative strategy was adopted for decoupling the double-nest loop of the hybrid reliability analysis into the probability analysis and interval analysis. And an efficient interval analysis algorithm was developed by using polynomial interpolation, which was capable of efficiently handling the cases where the limit-state functions were monotonic or non-monotonic with respect to dependent interval variables.The results of numerical examples show that the proposed hybrid reliability analysis method has good accuracy and efficiency.
引文
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[3]刘海波,姜潮,郑静,等.含概率与区间混合不确定性的系统可靠性分析方法[J].力学学报,2017,49(2):456-466.LIU Haibo,JIANG Chao,ZHENG Jing,et al.ASystem Reliability Analysis Method for Structures with Probability and Interval Mixed Uncertainty[J].Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):456-466.
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[5]潘柏松,谢少军,DU Xiaoping,等.随机变量和非独立区间变量下的可靠性序列迭代算法[J].中国机械工程,2015,26(12):1569-1575.PAN Baisong,XIE Shaojun,DU Xiaoping,et al.ASequential Iteration Algorithm for Reliability Analysis with Random and Dependent Interval Variables[J].China Mechanical Engineering,2015,26(12):1569-1575.
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[9]HASOFER A M,LIND N C.Exact and Invariant Second-moment Code Format[J].Journal of Engineering Mechanics Division,1974,100(1):111-121.
[10]BEN-HAIM Y.Convex Models of Uncertainty:Applications and Implications[J].Erkenntnis,1994,41(2):139-156.
[11]BEN-HAIM Y,ELISHAKOFF I.Convex Models of Uncertainty in Applied Mechanics[M].Amsterdam:Elsevier,1990.
[12]潘柏松,谢少军,蒋立正.非独立区间变量和随机变量下的单步可靠性计算方法[J].中国机械工程,2016,27(18):2430-2436.PAN Baisong,XIE Shaojun,JIANG Lizheng.An One-step Reliability Analysis Method with Random and Dependent Interval Variables[J].China Mechanical Engineering,2016,27(18):2430-2436.
[13]GONG Jinxin,YI Ping.A Robust Iterative Algorithm for Structural Reliability Analysis[J].Structural and Multidisciplinary Optimization,2011,43(4):519-527.
[2]刘帅杰,段宝岩,杨东武.利用区间与概率的星载可展天线齿轮防卡分析[J].西安电子科技大学学报(自然科学版),2016,43(3):61-66.LIU Shuaijie,DUAN Baoyan,YANG Dongwu.Interval and Probability Based Analysis of Seizurepreventing for Synchronous Gears of the Astromesh Deployable Satellite Antenna[J].Journal of Xidian University(Natural Science),2016,43(3):61-66.
[3]刘海波,姜潮,郑静,等.含概率与区间混合不确定性的系统可靠性分析方法[J].力学学报,2017,49(2):456-466.LIU Haibo,JIANG Chao,ZHENG Jing,et al.ASystem Reliability Analysis Method for Structures with Probability and Interval Mixed Uncertainty[J].Chinese Journal of Theoretical and Applied Mechanics,2017,49(2):456-466.
[4]LUO Y,KANG Z,LI A.Structural Reliability Assessment Based on Probability and Convex Set Mixed Model[J].Computers&Structures,2009,87(21/22):1408-1415.
[5]潘柏松,谢少军,DU Xiaoping,等.随机变量和非独立区间变量下的可靠性序列迭代算法[J].中国机械工程,2015,26(12):1569-1575.PAN Baisong,XIE Shaojun,DU Xiaoping,et al.ASequential Iteration Algorithm for Reliability Analysis with Random and Dependent Interval Variables[J].China Mechanical Engineering,2015,26(12):1569-1575.
[6]HOHENBICHLER M,RACKWITZ R.Non-normal Dependent Vectors in Structural Safety[J].Journal of Engineering Mechanics Division,1981,107(6):1127-1138.
[7]DITLEVSEN O.Principle of Normal Tail Approximation[J].Journal of Engineering Mechanics Division,1981,107(6):1191-1209.
[8]RACKWITZ R,FLESSLER B.Structural Reliability under Combined Random Load Sequences[J].Computers&Structures,1978,9(5):489-494.
[9]HASOFER A M,LIND N C.Exact and Invariant Second-moment Code Format[J].Journal of Engineering Mechanics Division,1974,100(1):111-121.
[10]BEN-HAIM Y.Convex Models of Uncertainty:Applications and Implications[J].Erkenntnis,1994,41(2):139-156.
[11]BEN-HAIM Y,ELISHAKOFF I.Convex Models of Uncertainty in Applied Mechanics[M].Amsterdam:Elsevier,1990.
[12]潘柏松,谢少军,蒋立正.非独立区间变量和随机变量下的单步可靠性计算方法[J].中国机械工程,2016,27(18):2430-2436.PAN Baisong,XIE Shaojun,JIANG Lizheng.An One-step Reliability Analysis Method with Random and Dependent Interval Variables[J].China Mechanical Engineering,2016,27(18):2430-2436.
[13]GONG Jinxin,YI Ping.A Robust Iterative Algorithm for Structural Reliability Analysis[J].Structural and Multidisciplinary Optimization,2011,43(4):519-527.