混合不确定性下的结构可靠性分析方法
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摘要
在工程实际中,部件或者系统的失效是由多失效模式引起的。针对变量和失效模式间复杂非线性相关问题,采用Copula函数进行建模。为了最大限度避免人为主观信息等带来的误差,利用最大熵方法分别近似极值响应的概率密度函数,在此基础上确定各自失效模式失效概率的最大和最小值。采用仿真和最大似然估计法相结合确定Copula函数中参数的最大和最小值。为了近似求解系统失效概率的最大和最小值,给出了相应的优化模型。算例分析表明该模型为混合不确定性及多失效模式相关下的结构可靠性分析提供新途径。
Components or systems fails are usually caused by multiple failure models in practical engineering. Copula functions are used to model complicated nonlinear corrections between variables and failure modes. To avoid error from subjective hypothesis at utmost, maximum entropy approach is employed for approximating probability density functions of extreme value responses, and the lower and upper bounds of probability of failure can be determined according to the approximated probability density functions. Finally, both simulation and maximum likelihood estimation approaches are used for determining the lower and upper bounds of parameters in selected Copula functions. An optimization model is presented to calculate the lower and upper bounds of system probability of failure. Numerical example has demonstrated that the proposed method is available for structural systems with multiple failure modes under mixed uncertainties.
Components or systems fails are usually caused by multiple failure models in practical engineering. Copula functions are used to model complicated nonlinear corrections between variables and failure modes. To avoid error from subjective hypothesis at utmost, maximum entropy approach is employed for approximating probability density functions of extreme value responses, and the lower and upper bounds of probability of failure can be determined according to the approximated probability density functions. Finally, both simulation and maximum likelihood estimation approaches are used for determining the lower and upper bounds of parameters in selected Copula functions. An optimization model is presented to calculate the lower and upper bounds of system probability of failure. Numerical example has demonstrated that the proposed method is available for structural systems with multiple failure modes under mixed uncertainties.
引文
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[11]童玲,陈光?.测量数据处理中的Bayes理论与最大熵方法[J].电子科技大学学报,2007,36(1):77-78,85.TONG Ling,CHENG Guang-ju.Bayes theorem and maximum entropy principle in the measurement data processing[J].Journal of University of Electronic Science and Technology of China,2007,36(1):77-78,85.
[12]WU Xi-ming.Calculation of maximum entropy densities with application to income distribution[J].Journal of Econometrics,2003,115(2):347-354.
[13]XI Zhi-min,JING R,WANG Ping-feng,et al.Acopula-based sampling method for data-driven prognostics[J].Reliability Engineering and System Safety,2014,132(4):72-82.
[14]韦艳华,张世英.Copula理论及其在金融分析上的应用[M].北京:清华大学出版社,2008.WEI Yan-hua,ZHANG Shi-ying.Copula theory and its application in finance[M].Beijing:Tsinghua University Press,2008.
[2]MELCHERS R E.Structural reliability analysis and prediction[M].2nd ed.New York:Wiley,1999.
[3]HU Z,MAHADEVAN S,DU Xiao-ping.Uncertainty quantification of time-dependent reliability analysis in the presence of parametric uncertainty[J].ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems,Part B:Mechanical Engineering,2015,1(2):04015004.
[4]DITEVSEN O.Narrow reliability method bounds for structural systems[J].Journal of Structural Mechanics,ASCE,1979,7(4):453-472.
[5]YOUN B D,WANG Ping-feng.A generalized complementary intersection method for system reliability analysis[J].Journal of Mechanical Design,Transaction of the ASME,2011,133(7):74-82.
[6]DU Xiao-ping.System reliability analysis with saddlepoint approximation[J].Structural and Multidisciplinary Optimization,2010,42:193-208.
[7]TANG Xiao-song,ZHOU Chuang-bing,LI D Q,et al.Impact of copulas for modeling bivariate distributions on system reliability[J].Structural Safety,2013,44:80-90.
[8]韩文钦,周金宇.基于鞍点逼近的机械零件可靠性Copula分析方法[J].机械强度,2013,35(5):612-616.HAN Wen-qin,ZHOU Jin-yu.Copula analysis method of machine components reliability based on saddlepoint approximation[J].Journal of Mechanical Strength,2013,35(5):612-616.
[9]NOH Y J,CHOI K K,DU L.Reliability-based design optimization of problems with correlated input variables using a Gaussian copula[J].Structural and Multidisciplinary Optimization,2009,38:1-16.
[10]PARK C Y,KIM N H,HAFTKA RP.The effect of ignoring dependence between failure modes on evaluating system reliability[J].Structural and Multidisciplinary Optimization,2015,52:251-268.
[11]童玲,陈光?.测量数据处理中的Bayes理论与最大熵方法[J].电子科技大学学报,2007,36(1):77-78,85.TONG Ling,CHENG Guang-ju.Bayes theorem and maximum entropy principle in the measurement data processing[J].Journal of University of Electronic Science and Technology of China,2007,36(1):77-78,85.
[12]WU Xi-ming.Calculation of maximum entropy densities with application to income distribution[J].Journal of Econometrics,2003,115(2):347-354.
[13]XI Zhi-min,JING R,WANG Ping-feng,et al.Acopula-based sampling method for data-driven prognostics[J].Reliability Engineering and System Safety,2014,132(4):72-82.
[14]韦艳华,张世英.Copula理论及其在金融分析上的应用[M].北京:清华大学出版社,2008.WEI Yan-hua,ZHANG Shi-ying.Copula theory and its application in finance[M].Beijing:Tsinghua University Press,2008.