随机变量和非独立区间变量下的可靠性序列迭代算法

摘要/Abstract

摘要：

针对机械系统中输入变量存在随机变量和区间变量混合的情况，考虑区间变量的非独立性，提出高效混合可靠性分析方法。区间变量使可靠性分析问题变为双层优化问题。为降低双层优化和非独立区间变量对可靠性计算效率的影响，提出了高效序列迭代计算策略，基于椭球模型描述的非独立区间变量，提出将非独立区间变量转换为独立区间变量的方法，并利用二次泰勒近似方法，将区间分析问题转换为易求解的二次规划问题。算例结果表明，所提出的可靠性序列迭代算法具有较高的计算效率和精度；可靠性分析结果受区间变量独立性假设的影响，区间变量独立可导致较保守的可靠性分析结果。

关键词: 可靠性分析, 椭球模型, 非独立区间变量, 序列迭代算法

Abstract:

Focusing on the mixed conditions of both random variables and dependent interval variables,an efficient hybrid reliability analysis method was proposed.Interval variables made the reliability analysis problem become a double-loop optimization problem.In order to reduce the impacts on the reliability analysis efficiency by the double-loop optimization and dependent interval variables,
an efficient sequentially iterative strategy was proposed,and a formula to transform the dependent interval variables modelled by ellipsoid model was developed into independent interval variables,and the limit-state function was approximated during the inner loop in the second order form to make the optimization problem become a more solvable quadratic programming problem.The results show that the proposed sequential iteration algorithm has good efficiency and accuracy, and that the reliability analysis results are affected by the assumption of dependence between interval variables; results under the assumption of independence between interval variables
can be more conservative than that of dependence.

Key words: reliability analysis;ellipsoid , model;dependent interval variable;sequentially iterative algorithm

中图分类号:

TH122

潘柏松1;谢少军1;Du Xiaoping2;梁利华1. 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): 1569-1575,1583.

Pan Baisong1;Xie Shaojun1;Du Xiaoping2;Liang Lihua1. A Sequential Iteration Algorithm for Reliability Analysis with Random and Dependent Interval Variables[J]. China Mechanical Engineering, 2015, 26(12): 1569-1575,1583.

参考文献

[1]Elishakoff I.Uncertainties in Mechanical Structures:AMF Reudenthal's Criticisms and Modern Convex Models[J].Journal of Applied Mechanics,1999,63(1):683-692.
[2]Nikolaidis E,Ghiocel D M.Singhal S.Engineering Design Reliability Handbook[M].New York:CRC Press,2004.
[3]Dubois D,Prade H.A   Synthetic View   of    Belief   Revision with Uncertain Inputs in the Framework of Possibility Theory[J].International   Journal of   Approximate Reasoning,1997,17(2):295-324.
[4]Shafer G.A Mathematical Theory   of   Evidence[M].Princeton: Princeton University Press,1976.
[5]Yakov   B,Elishakoff I.Convex Models of Uncertainty in Applied Mechanics[M].Amsterdam:Elsevier,1990.
[6]Wang P,Youn B D,Xi Z,et al.Bayesian Reliability Analysis with Evolving,Insufficient and Subjective Data Sets[J].Journal of Mechanical Design,2009,131(11):111008.
[7]Moore R E.Methods and Applications of Interval Analysis[M].Philadelphia:Siam,1979.
[8]Du X,Sudjianto A,Huang B.Reliability-based Design with the Mixture of Random and Interval Variables[J].Journal of Mechanical Design,2005,127:1068.
[9]江涛,陈建军,姜培刚,等.区间模型非概率可靠性指标的一维优化算法[J].工程力学,2007,24(7):23-27.
Jiang Tao,Chen Jianjun,Jiang Peigang,et al.A   One-dimensional Optimization Algorithm for Non-probabilstic Reliability Index[J].Engineering Mechanics,2007,24(7):23-27.
[10]姜潮,黄新萍, 韩旭,等.含区间不确定性的结构时变可靠度分析方法[J].机械工程学报,2013,49(10):186-193.
Jiang Chao,Huang Xinping,Han Xu,et al.Time-dependent Structural Reliability Analysis Method with Interval Uncertainty[J].Journal of Mechanical Engineering,2013,49(10):186-193.
[11]Du X.Unified Uncertainty Analysis by the First Order Reliability Method[J].Journal of Mechanical Design,2008,130(9):091401.
[12]Jiang C,Han X,Liu G P.A Sequential   Nonlinear Interval Number Programming Method for Uncertain Structures[J].Computer Methods in Applied Mechanics and Engineering,2008,197(49/50):4250-4265.
[13]Du X.Reliability-based   Design Optimization with Dependent   Interval Variables[J].International Journal for Numerical Methods in   Engineering,2012,91(2):218-228.
[14]Jiang C,Zhang Z,Zhang Q,et al.A New Nonlinear Interval Programming Method for   Uncertain Problems with Dependent Interval Variables[J].European Journal of Operational Research,2014,238(1):245-253.
[15]Ben-Haim Y.Convex   Models   of   Uncertainty:Applications and Implications[J].Erkenntnis,1994,41(2):139-156.
[16]Kreinovich V,Beck J,Nguyen H T.Ellipsoids and Ellipsoid-shaped Fuzzy Sets as Natural Multi-variate Generalization of Intervals and Fuzzy Numbers: How   to   Elicit Them from Users, and How to   Use   Them in Data Processing[J].Information Sciences,2007,177(2):388-407.
[17]Kreinovich V,Hajagos J G,Tucker W T,et al.Propagating Uncertainty through a Quadratic Response Surface Model[R].Albuquerque,New Mexico:Sandia National Laboratories,2008.
[18]Zhang Y,Kiureghian A.Two Improved Algorithms for Reliability Analysis[C]//Proceedings of the Sixth IFIP WG7.5 Working Conference on Reliability and Optimization of Structural Systems.Springer US,1995:297-304.
[19]Nocedal J,Wright S.Numerical Optimization[M].New York:Springer,2006.