基于区间有限元的结构广义可靠度分析
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摘要
相对于只考虑随机性的狭义(或经典)结构可靠度理论,进一步考虑随机性、模糊性、未确知性的结构可靠度理论称为"结构广义可靠度",最早由王光远院士于20世纪80年代提出.本文介绍了作者所在团队近年来在结构广义可靠度理论方面所取得的一些成果.首先介绍了区间数学和区间有限元的基本概念,然后以区间有限元为工具,重点研究了3种类型不确定性情况下结构广义可靠度分析方法:第一种情况同时考虑基本变量的随机性与未确知性,未确知性以区间变量形式体现在随机变量的参数中;第二种情况为随机性与模糊性处于分离状态,即基本变量是随机的,而失效准则是模糊的;第三种情况为随机性与模糊性处于耦合状态,模糊性以模糊数形式体现在随机变量的参数中.采用区间蒙特卡罗模拟(IntMCS)技术和区间一次可靠度方法(IntFORM),提出并发展了上述3种情况下结构广义可靠度的分析方法.以一个平面桁架结构为例,展示了上述方法的适用性和有效性.
Relative to the special structure reliability theory only considering randomness, the advanced theory is called generalized reliability which considers randomness, fuzziness and unascertainty at the same time. This theory was first proposed by Wang GuangYuan academician in 1980 s. In this thesis, some research results of the team of authors are introduced.Fuzziness is considered by the fuzzy mathematics and unascertainty is reckoned with the interval mathematics. First,some basic conceptions of interval math and interval finite element are introduced. Then generalized reliability analysis methods of three kinds of uncertainty conditions are discussed with the tool of interval finite element. In the first condition,both randomness and unascertainty are considered and the parameters of the random variables are interval variables. The second condition is that randomness and fuzziness are separated. The basic variables are random and the failure criterion is fuzzy. Randomness and fuzziness are coupling in the third condition. The parameters of the random variables are fuzzy numbers to reflect fuzziness. Finally, authors propose and develop the generalized reliability analysis methods of this three cases using the interval Monte Carlo Simulation(IntMCS) and the interval First Order Reliability Method(IntFORM). By means of a plane truss example, the applicability and effectiveness of these methods are shown. After a series of research,some conclusions can be summarized. The IntFORM proposed in this thesis has enough computational accuracy and more computational efficiency than IntMCS. Therefore, this method can be used in the reliability analysis of large-scale structures.
Relative to the special structure reliability theory only considering randomness, the advanced theory is called generalized reliability which considers randomness, fuzziness and unascertainty at the same time. This theory was first proposed by Wang GuangYuan academician in 1980 s. In this thesis, some research results of the team of authors are introduced.Fuzziness is considered by the fuzzy mathematics and unascertainty is reckoned with the interval mathematics. First,some basic conceptions of interval math and interval finite element are introduced. Then generalized reliability analysis methods of three kinds of uncertainty conditions are discussed with the tool of interval finite element. In the first condition,both randomness and unascertainty are considered and the parameters of the random variables are interval variables. The second condition is that randomness and fuzziness are separated. The basic variables are random and the failure criterion is fuzzy. Randomness and fuzziness are coupling in the third condition. The parameters of the random variables are fuzzy numbers to reflect fuzziness. Finally, authors propose and develop the generalized reliability analysis methods of this three cases using the interval Monte Carlo Simulation(IntMCS) and the interval First Order Reliability Method(IntFORM). By means of a plane truss example, the applicability and effectiveness of these methods are shown. After a series of research,some conclusions can be summarized. The IntFORM proposed in this thesis has enough computational accuracy and more computational efficiency than IntMCS. Therefore, this method can be used in the reliability analysis of large-scale structures.
引文
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2 Wang G Y,Wang W Q.Fuzzy reliability anaysis of aseismic structures(in Chinese).Acta Mech Sin,1986,18:448-455[王光远,王文泉.抗震结构的模糊可靠性分析.力学学报,1986,18:448-455]
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7 Zhang A L,Zhao G F,Wang G Y.Practical method for the fuzzy dynamic reliability assessment of existing structures(in Chinese).J Basic Sci Eng,1998,6:83-90[张爱林,赵国藩,王光远.现役结构模糊动态可靠度评估实用方法.应用基础与工程科学学报,1998,6:83-90]
8 Wang G Y,Zhang P.Reliability analysis for engineering systems with intermediate state(in Chinese).China Civil Eng J,2001,34:13-17[王光远,张鹏.具有中介状态的工程系统的可靠性分析.土木工程学报,2001,34:13-17]
9 Liu Y B,Wang G Y.Generalized Reliability Theory of Engineering Structures.Beijing:Science Press,2005[刘玉彬,王光远.工程结构广义可靠性理论.北京:科学出版社,2005]
10 Cai K Y,Wen C Y,Zhang M L.Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context.Fuzzy Sets Syst,1991,42:145-172
11 Huang H Z.Research on the method of reliability analysis in the presence of fuzziness attached to the operating time(in Chinese).Chin J Mech Eng,1993,29:1-8[黄洪钟.关于模糊可靠性若干基本问题的讨论——将清晰工作时间拓广到模糊工作时间.机械工程学报,1993,29:1-8]
12 Guo S X,Lu Z Z.Procedure for computing the fuzzy probability of failure of mechanical structures when parameters of probabilistic models are fuzzy(in Chinese).J Mech Strength,2003,25:527-529[郭书详,吕震宙.概率模型含模糊分布参数时的模糊失效概率计算方法.机械强度,2003,25:527-529]
13 Ben-Haim Y,Elishakoff I.Convex of Uncertainty in Applied Mechanics.Amsterdam:Elsevier,1990
14 Jiang C,Ni B Y,Han X,et al.Non-probabilistic convex model process:A new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems.Comput Meth Appl Mech Eng,2014,268:656-676
15 Bi R G.Non-probabilistic Uncertainty Convex Model and Reliability Analysis Method Incorporating Correlation(in Chinese).Dissertation for Doctoral Degree.Changsha:Hunan University,2015[毕仁贵.考虑相关性的不确定凸集模型与非概率可靠性分析方法.博士学位论文.长沙:湖南大学,2015]
16 Ferson S,Kreinovich V,Ginzburg L,et al.Constructing probability boxes and Dempster-Shafer structures.Reprot,Sandia National Laboratories,Sand2002-4015,2003
17 Zhang H,Mullen R L,Muhanna R L.Interval Monte Carlo methods for structural reliability.Struct Saf,2010,32:183-190
18 Qiu Z,Yang D,Elishakoff I.Probabilistic interval reliability of structural systems.Int J Solids Struct,2008,45:2850-2860
2 Wang G Y,Wang W Q.Fuzzy reliability anaysis of aseismic structures(in Chinese).Acta Mech Sin,1986,18:448-455[王光远,王文泉.抗震结构的模糊可靠性分析.力学学报,1986,18:448-455]
3 Wang G Y,Wang W Q,Ou J P.Generalized reliability of system(in Chinese).Syst Eng Theor Pract,1988,8:6-13[王光远,王文泉,欧进萍.系统的广义可靠度.系统工程理论与实践,1988,8:6-13]
4 Wang G Y.Unascertained information and its mathematical treatment(in Chinese).J Harbin Univ Civil Eng Architect,1990,4:1-9[王光远.未确知信息及其数学处理.哈尔滨建筑大学学报,1990,4:1-9]
5 Wang G Y.Software Design of Engineering.Beijing:Science Press,1992.239-264[王光远.工程软件设计.北京:科学出版社,1992.239-264]
6 Wang G Y,Liu Y B.Practical calculation method for fuzzy random reliability of structures(in Chinese).Earthq Eng Eng Vibrat,1995,15:38-46[王光远,刘玉彬.结构模糊随机可靠度的实用计算方法.地震工程与工程振动,1995,15:38-46]
7 Zhang A L,Zhao G F,Wang G Y.Practical method for the fuzzy dynamic reliability assessment of existing structures(in Chinese).J Basic Sci Eng,1998,6:83-90[张爱林,赵国藩,王光远.现役结构模糊动态可靠度评估实用方法.应用基础与工程科学学报,1998,6:83-90]
8 Wang G Y,Zhang P.Reliability analysis for engineering systems with intermediate state(in Chinese).China Civil Eng J,2001,34:13-17[王光远,张鹏.具有中介状态的工程系统的可靠性分析.土木工程学报,2001,34:13-17]
9 Liu Y B,Wang G Y.Generalized Reliability Theory of Engineering Structures.Beijing:Science Press,2005[刘玉彬,王光远.工程结构广义可靠性理论.北京:科学出版社,2005]
10 Cai K Y,Wen C Y,Zhang M L.Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context.Fuzzy Sets Syst,1991,42:145-172
11 Huang H Z.Research on the method of reliability analysis in the presence of fuzziness attached to the operating time(in Chinese).Chin J Mech Eng,1993,29:1-8[黄洪钟.关于模糊可靠性若干基本问题的讨论——将清晰工作时间拓广到模糊工作时间.机械工程学报,1993,29:1-8]
12 Guo S X,Lu Z Z.Procedure for computing the fuzzy probability of failure of mechanical structures when parameters of probabilistic models are fuzzy(in Chinese).J Mech Strength,2003,25:527-529[郭书详,吕震宙.概率模型含模糊分布参数时的模糊失效概率计算方法.机械强度,2003,25:527-529]
13 Ben-Haim Y,Elishakoff I.Convex of Uncertainty in Applied Mechanics.Amsterdam:Elsevier,1990
14 Jiang C,Ni B Y,Han X,et al.Non-probabilistic convex model process:A new method of time-variant uncertainty analysis and its application to structural dynamic reliability problems.Comput Meth Appl Mech Eng,2014,268:656-676
15 Bi R G.Non-probabilistic Uncertainty Convex Model and Reliability Analysis Method Incorporating Correlation(in Chinese).Dissertation for Doctoral Degree.Changsha:Hunan University,2015[毕仁贵.考虑相关性的不确定凸集模型与非概率可靠性分析方法.博士学位论文.长沙:湖南大学,2015]
16 Ferson S,Kreinovich V,Ginzburg L,et al.Constructing probability boxes and Dempster-Shafer structures.Reprot,Sandia National Laboratories,Sand2002-4015,2003
17 Zhang H,Mullen R L,Muhanna R L.Interval Monte Carlo methods for structural reliability.Struct Saf,2010,32:183-190
18 Qiu Z,Yang D,Elishakoff I.Probabilistic interval reliability of structural systems.Int J Solids Struct,2008,45:2850-2860