钢框架结构抗震可靠度的概率重要性分析
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摘要
概率重要度是一类特殊的参数灵敏度,对于结构可靠度设计、优化和评定等具有重要的价值。本文引进四类重要性测度,即重要性向量α、γ、δ和η。前两个测度分别描述标准正态空间内和原始空间内随机变量的本质特征和相对重要性程度以及可靠指标对设计点变化的灵敏性;后两个测度分别描述可靠指标对随机变量均值和标准差变化的灵敏性。采用基于FORM的有限元可靠度方法对钢框架结构进行抗震可靠度分析和概率重要性分析,以一个实际工程结构为例,分析了承载能力和变形能力极限状态抗震可靠度的概率重要性,结果表明:四类重要性测度的变化规律基本一致,将概率重要度很小的随机变量作为确定性变量处理,可以显著地提高大型复杂结构可靠度分析的计算效率。
As a special type of parametric sensitivity,probability importance is very valuable for reliability design,optimization and evaluation for large complex structures.In this paper,four measures of probability importance are introduced,which include importance vectors α,γ,δ and η.Importance vectors α and γ character the degree of relative importance in standard normal space and original space respectively,while importance vectors δ and η are the sensitivities of reliability index with respect to the variations of mean values and standard deviations of random variables respectively.The seismic reliability and the corresponding probability importance of plane steel frames are analyzed by using the finite element reliability method based on FORM.By taking a practical engineering structure as an example,the probability importance of seismic reliability both in ultimate limit state and deformation limit state is computed.The analysis results demonstrate that the changing rule of the four measures of probability importance is consistent,and that replacing the unimportant random variables by deterministic values can greatly improve the computation efficiency of reliability analysis for large complex structures.
As a special type of parametric sensitivity,probability importance is very valuable for reliability design,optimization and evaluation for large complex structures.In this paper,four measures of probability importance are introduced,which include importance vectors α,γ,δ and η.Importance vectors α and γ character the degree of relative importance in standard normal space and original space respectively,while importance vectors δ and η are the sensitivities of reliability index with respect to the variations of mean values and standard deviations of random variables respectively.The seismic reliability and the corresponding probability importance of plane steel frames are analyzed by using the finite element reliability method based on FORM.By taking a practical engineering structure as an example,the probability importance of seismic reliability both in ultimate limit state and deformation limit state is computed.The analysis results demonstrate that the changing rule of the four measures of probability importance is consistent,and that replacing the unimportant random variables by deterministic values can greatly improve the computation efficiency of reliability analysis for large complex structures.
引文
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[8]Hohenbichler M,Rackwitz R.Sensitivities and importancemeasures in structural reliability[J].Civil EngineeringSystems,1986,3:203-209.
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[13]Sorensen J D,Enevoldsen I.Sensitivity weaknesses inapplication of some statistical distributions in first orderreliability methods[J].Structural Safety,1993,12(4):315-325.
[14]Melchers R E,Ahammed M.A fast approximate method forparameter sensitivity estimation in Monte Carlo structuralreliability[J].Computers and Structures,2004,82:55-61.
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[18]O迪特莱夫森[丹麦],HO麦德森[挪威]著.结构可靠度方法[M].何军译.上海:同济大学出版社,2005.
[19]刘宁,吕泰仁.三维结构可靠度对随机变量的敏感性分析[J].工程力学,1995,12(2):119-128.
[20]刘宁,吴海斌,方军.地下洞室围岩可靠度的敏感性计算[J].岩石力学与工程学报(专辑),2000:1-6.
[21]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001.
[22]Brenner C E,Bucher C G.A contribution to the SFE-basedreliability assessment of nonlinear structures under dynamicloading[J].Probabilistic Engineering Mechanics,1995,10(4):265-273.
[23]Mansour A E,Wirsching P H.Sensitivity factors and theirapplication to marine structures[J].Marine Structures,1995,8:229-255.
[24]Enevoldsen I,Sorensen J D.Reliability-based optimizationin structural engineering[J].Structural Safety,1994,15(3):169-196.
[25]Faber M H,Kroon I B,Sorensen J D.Sensitivities instructural maintenance planning[J].Reliability Engineeringand System Safety,1996,51:317-329.
[26]Chaudhuri A,Chakraborty S.Sensitivity evaluation inseismic reliability analysis of structures[J].ComputerMethods in Applied Mechanics and Engineering,2004,193:59-68.
[27]Boland P J,El-Neweihi E.Measures of componentimportance in reliability theory[J].Computers Ops.Res.1995,22(4):455-463.
[28]Edeland T.Two trends in reliability[J].Structural Safety,1991,9(4):261-268.
[29]Cornell C A.A Probability-based structural code[J].Journal of American Concrete Institute,1969,66:974-985.
[30]Hohenbichler M,Rackwitz R.Non-normal dependent vectorsin structural safety[J].ASCE Journal of EngineeringMechanics,1981,107(6):1227-1238.
[31]Der Kiureghian A,Ke J-B.The stochastic finite elementmethod in structural reliability[J].Probabilistic EngineeringMechanics,1988,3(2):83-91.
[32]Liu P L,Lin HZ,Der Kiureghian A.CALREL user manual[R].Report No.UCB/SEMM-89/18,StructuralEngineering,Mechanics and Materials,Department of CivilEngineering,University of California,Berkeley,CA,April,1989.
[33]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑工程学院学报,1994,27(5):1-10.
[34]Rackwitz R,Fiessler B.Structural reliability undercombined load sequence[J].Computer and Structures,1978,114(12):2195-2199.
[35]吕大刚,李晓鹏,胡晓琦等.钢框架结构的非线性静力抗震可靠性分析:I有限元反应及其灵敏度[J].地震工程与工程振动,2007,27(5):55-60.
[2]Madsen H O,Krenk S,Lind N C.Methods of structuralsafety[M].Englewood Cliffs(NJ):Prentice Hall,1986.
[3]Enevoldsen I,Sorensen J D.Reliability-based optimizationof series systems of parallel systems[J].ASCE Journal ofStructural Engineering,1993,119(4):1069-1084.
[4]Enevoldsen I.Sensitivity analysis of reliability-based optimalsolution[J].ASCE Journal of Structural Engineering,1994,120(1):198-205.
[5]Madsen H O.Model updating in reliability theory[C]//Proceeding of ICASP-5.Vancouver,Canada,1987:564-577.
[6]Der Kiureghian A.Structural reliability methods for seismicsafety assessment:A review[J].Engineering Structures,1996,18(6):412-424.
[7]Der Kiureghian A.Measures of structural safety underimperfect states of knowledge[J].ASCE Journal ofStructural Engineering,1989,115(5):1119-1140.
[8]Hohenbichler M,Rackwitz R.Sensitivities and importancemeasures in structural reliability[J].Civil EngineeringSystems,1986,3:203-209.
[9]Madsen H O.Omission sensitivity factors[J].StructuralSafety,1988,5(1):35-45.
[10]Bjerager P,Krenk S.Parametric sensitivity in first orderreliability theory[J].ASCE Journal of EngineeringMechanics,1989,115(7):1577-1582.
[11]Bjerager P.On computation methods for structural reliabilityanalysis[J].Structural Safety,1990,9(2):79-96.
[12]Karamchandani A,Cornell C A.Sensitivity estimation withinfirst and second order reliability methods[J].StructuralSafety,1992,11(2):95-107.
[13]Sorensen J D,Enevoldsen I.Sensitivity weaknesses inapplication of some statistical distributions in first orderreliability methods[J].Structural Safety,1993,12(4):315-325.
[14]Melchers R E,Ahammed M.A fast approximate method forparameter sensitivity estimation in Monte Carlo structuralreliability[J].Computers and Structures,2004,82:55-61.
[15]Sues R H,Cesare M A.System reliability and sensitivityfactors via the MPPSS method[J].Probabilistic EngineeringMechanics,2005,20(2):148-157.
[16]Ditlevsen O,Madsen H O.Structural reliability methods[M].New York:John Wiley and Sons,1996.
[17]Ditlevsen O,Madsen HO.Structural reliability methods[M/OL].[2005-06]http://www.mek.dtu.dk/staff/od/books.htm.2005.
[18]O迪特莱夫森[丹麦],HO麦德森[挪威]著.结构可靠度方法[M].何军译.上海:同济大学出版社,2005.
[19]刘宁,吕泰仁.三维结构可靠度对随机变量的敏感性分析[J].工程力学,1995,12(2):119-128.
[20]刘宁,吴海斌,方军.地下洞室围岩可靠度的敏感性计算[J].岩石力学与工程学报(专辑),2000:1-6.
[21]刘宁.可靠度随机有限元法及其工程应用[M].北京:中国水利水电出版社,2001.
[22]Brenner C E,Bucher C G.A contribution to the SFE-basedreliability assessment of nonlinear structures under dynamicloading[J].Probabilistic Engineering Mechanics,1995,10(4):265-273.
[23]Mansour A E,Wirsching P H.Sensitivity factors and theirapplication to marine structures[J].Marine Structures,1995,8:229-255.
[24]Enevoldsen I,Sorensen J D.Reliability-based optimizationin structural engineering[J].Structural Safety,1994,15(3):169-196.
[25]Faber M H,Kroon I B,Sorensen J D.Sensitivities instructural maintenance planning[J].Reliability Engineeringand System Safety,1996,51:317-329.
[26]Chaudhuri A,Chakraborty S.Sensitivity evaluation inseismic reliability analysis of structures[J].ComputerMethods in Applied Mechanics and Engineering,2004,193:59-68.
[27]Boland P J,El-Neweihi E.Measures of componentimportance in reliability theory[J].Computers Ops.Res.1995,22(4):455-463.
[28]Edeland T.Two trends in reliability[J].Structural Safety,1991,9(4):261-268.
[29]Cornell C A.A Probability-based structural code[J].Journal of American Concrete Institute,1969,66:974-985.
[30]Hohenbichler M,Rackwitz R.Non-normal dependent vectorsin structural safety[J].ASCE Journal of EngineeringMechanics,1981,107(6):1227-1238.
[31]Der Kiureghian A,Ke J-B.The stochastic finite elementmethod in structural reliability[J].Probabilistic EngineeringMechanics,1988,3(2):83-91.
[32]Liu P L,Lin HZ,Der Kiureghian A.CALREL user manual[R].Report No.UCB/SEMM-89/18,StructuralEngineering,Mechanics and Materials,Department of CivilEngineering,University of California,Berkeley,CA,April,1989.
[33]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑工程学院学报,1994,27(5):1-10.
[34]Rackwitz R,Fiessler B.Structural reliability undercombined load sequence[J].Computer and Structures,1978,114(12):2195-2199.
[35]吕大刚,李晓鹏,胡晓琦等.钢框架结构的非线性静力抗震可靠性分析:I有限元反应及其灵敏度[J].地震工程与工程振动,2007,27(5):55-60.
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