面向混合不确定性的可靠性设计优化方法研究
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摘要
针对可靠性设计优化过程中,模型受到不确定性参数的影响而使计算可靠度困难的问题,提出一种面向设计变量和参数同时存在不确定性情况下的可靠性指标计算方法.基于克里金响应面进行估值,计算数据分布特征,拟合数据分布的概率密度函数,形成混合不确定性的统一量化表达形式,根据可靠性理论的应力强度干涉模型,使用联合概率积分法计算得到设计点的可靠度.在此基础上构建基于克里金响应面的可靠性设计优化流程,实现设计变量和参数同时存在不确定性时的可靠性设计优化.通过典型算例进行分析,计算结果表明:与只含有设计变量不确定性的情况相比,该方法可有效应对参数不确定性造成的影响.
To solve the realiability-based design optimization problem with uncertain parameters effect which makes it more difficult to calculate the realiability,a reliability index calculation method was proposed for the uncertainty of design variables and parameters at the same time.In this method,the estimation was made based on the Kriging model,the distribution characteristics of the data was calculated,the probability density function was fitted based on sample points,and a unified quantitative expression of the mixed uncertainty was formed.In each itertion of the optimization design,based on the stress-strength interference model of the reliability theory,the reliability of the design point was calculated by the joint probability integral method.And then a reliability based optimiztion design(RBDO) process was built based on the Kriging model for the uncertainty of design variables and the uncertainty of parameters existed at the same time.The calculation results of the typical example show that this method can effectively cope with the impact of parameter uncertainty compared with the case when only exist design variable uncertainty.
To solve the realiability-based design optimization problem with uncertain parameters effect which makes it more difficult to calculate the realiability,a reliability index calculation method was proposed for the uncertainty of design variables and parameters at the same time.In this method,the estimation was made based on the Kriging model,the distribution characteristics of the data was calculated,the probability density function was fitted based on sample points,and a unified quantitative expression of the mixed uncertainty was formed.In each itertion of the optimization design,based on the stress-strength interference model of the reliability theory,the reliability of the design point was calculated by the joint probability integral method.And then a reliability based optimiztion design(RBDO) process was built based on the Kriging model for the uncertainty of design variables and the uncertainty of parameters existed at the same time.The calculation results of the typical example show that this method can effectively cope with the impact of parameter uncertainty compared with the case when only exist design variable uncertainty.
引文
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[5]ELDRED M S,SWILER L P,TANG G.Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation[J].Reliability Engineering and System Safety,2011,96(9):1092-1113.
[6]ZHANG X,HUANG H Z.Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties[J].Structural and Multidisciplinary Optimization,2010,40(1):165-175.
[7]DU L,CHOI K K,YOUN B D,et al.Possibility-based design optimization method for design problems with both statistical and fuzzy input data[J].Journal of Mechanical Design,2006,128(4):928-935.
[8]MOURELATOS Z P,ZHOU J.A design optimization method using evidence theory[J].Journal of Mechanical Design,2006,128(4):901-908.
[9]DU X,CHEN W.Sequential optimization and reliability assessment method for efficient probabilistic design[J].Journal of Mechanical Design,2004,126(2):225-233.
[10]陈小前,姚雯,欧阳琦.飞行器不确定性多学科设计优化理论与应用[M].北京:科学出版社,2013.
[11]JIANG C,LONG X Y,HAN X,et al.Probability-interval hybrid reliability analysis for cracked structures existing epistemic uncertainty[J].Engineering Fracture Mechanics,2013,112:148-164.
[12]KIM C,CHOI K K.Reliability-based design optimization using response surface method with prediction interval estimation[J].Journal of Mechanical Design,2008,130(12):121401.
[13]ZAMAN K,RANGAVAJHALA S,MCDONALD M P,et al.A probabilistic approach for representation of interval uncertainty[J].Reliability Engineering and System Safety,2011,96(1):117-130.
[14]CHEN Z,QIU H,GAO L,et al.A local adaptive sampling method for reliability-based design optimization using Kriging model[J].Structural and Multidisciplinary Optimization,2014,49(3):401-416.
[15]孙靖民,梁迎春.机械优化设计[M].北京:机械工业出版社,2006.
[2]ADDURI P R,PENMETSA R C.System reliability analysis for mixed uncertain variables[J].Structural Safety,2009,31(5):375-382.
[3]ZHANG X,HUANG H Z,XU H.Multidisciplinary design optimization with discrete and continuous variables of various uncertainties[J].Structural and Multidisciplinary Optimization,2010,42(4):605-618.
[4]DU X.Unified uncertainty analysis by the first order reliability method[J].Journal of Mechanical Design,2008,130(9):091401.
[5]ELDRED M S,SWILER L P,TANG G.Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation[J].Reliability Engineering and System Safety,2011,96(9):1092-1113.
[6]ZHANG X,HUANG H Z.Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties[J].Structural and Multidisciplinary Optimization,2010,40(1):165-175.
[7]DU L,CHOI K K,YOUN B D,et al.Possibility-based design optimization method for design problems with both statistical and fuzzy input data[J].Journal of Mechanical Design,2006,128(4):928-935.
[8]MOURELATOS Z P,ZHOU J.A design optimization method using evidence theory[J].Journal of Mechanical Design,2006,128(4):901-908.
[9]DU X,CHEN W.Sequential optimization and reliability assessment method for efficient probabilistic design[J].Journal of Mechanical Design,2004,126(2):225-233.
[10]陈小前,姚雯,欧阳琦.飞行器不确定性多学科设计优化理论与应用[M].北京:科学出版社,2013.
[11]JIANG C,LONG X Y,HAN X,et al.Probability-interval hybrid reliability analysis for cracked structures existing epistemic uncertainty[J].Engineering Fracture Mechanics,2013,112:148-164.
[12]KIM C,CHOI K K.Reliability-based design optimization using response surface method with prediction interval estimation[J].Journal of Mechanical Design,2008,130(12):121401.
[13]ZAMAN K,RANGAVAJHALA S,MCDONALD M P,et al.A probabilistic approach for representation of interval uncertainty[J].Reliability Engineering and System Safety,2011,96(1):117-130.
[14]CHEN Z,QIU H,GAO L,et al.A local adaptive sampling method for reliability-based design optimization using Kriging model[J].Structural and Multidisciplinary Optimization,2014,49(3):401-416.
[15]孙靖民,梁迎春.机械优化设计[M].北京:机械工业出版社,2006.