蒋水华;李典庆;方国光;

• 1:武汉大学水资源与水电工程科学国家重点实验室
• 2:武汉大学水工岩石力学教育部重点实验室
• 3:新加坡国立大学土木与环境工程系

摘要(Abstract)：

从拟合功能函数方法、计算精度与效率、收敛性等方面对响应面法和随机响应面法进行了系统地分析.算例表明:与响应面法相比,随机响应面法实现了真正意义上的非侵入式分析.响应面法采用二次多项式响应面函数仅仅在验算点附近能较好地拟合真实功能函数,而随机响应面法采用高阶Hermite随机多项式,能在整个空间上很好地拟合真实功能函数.当随机变量个数较少时,随机响应面法的计算精度和效率均优于响应面法.并且随机响应面法可进行自身的收敛性分析,确定最优阶次的计算结果作为精确解,其收敛性也优于响应面法.

关键词(KeyWords)： 可靠度;响应面法;随机响应面法;功能函数;收敛性

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(编号:51079112,51028901);; 中央高校基本科研业务费专项资金项目(编号:2103001)

作者(Authors): 蒋水华;李典庆;方国光;

参考文献(References)：

• [1]张明.结构可靠度分析方法与程序[M].北京:科学出版社,2009.
• [2]Bucher C G,Bourgund U.A fast and efficient re-sponse surface approach for structural reliability prob-lems[J].Structrual Safety,1990,7:57-66.
• [3]Kim S H,Na S W.Response surface method usingvector projected sampling points[J].Structrual Safety,1997,19:3-19.
• [4]Kaymaz I,McMahon C A.A response surface methodbased on weighted regression for structural reliabilityanslysis[J].Probabilistic Engineering Mechanics,2004,20:11-17.
• [5]Gomes H M.,Awruch A M.Comparison of responsesurface method and neural network with other methodsfor structural reliability analysis[J].Structrual Safe-ty,2006,26:49-67.
• [6]Gavin H P,Yau S C.High-order limit state functionsin the response surface method for structural reliabilityanalysis[J].Structrual Safety,2008,30:162-179.
• [7]Wong F S.Slope reliability and response surface meth-od[J].Journal of Geotechnical Engineering,1995,111(1):32-53.
• [8]赵国藩.工程结构可靠性理论与应用[M].大连:大连理工大学出版社,1996.
• [9]苏永华,赵明华,邹志鹏,等.边坡稳定性分析的Sar-ma模式及其可靠度计算方法[J].水利学报,2006,37(4):457-463.
• [10]Isukapalli S S.Uncertainty analysis of transport trans-formation models[D].New Brunswick,New Jersey,USA:The State University of New Jersey,1999.
• [11]Huang S P,Mahadevan S,Rebba R.Collocation-based stochastic finite element analysis for randomfield problems[J].Probabilistic Engineering Mechan-ics,2007,22(2):194-205.
• [12]Li D Q,Chen Y F,Lu W B,Zhou C B.Stochastic re-sponse surface method for reliability analysis of rockslopes involving correlated non-normal variables[J].Computers and Geotechnics,2011,38(1):58-68.
• [13]Mollon G,Dias D,Soubra A H.Probabilistic analysisof pressurized tunnels against face stability using collo-cation-based stochastic response surface method[J].Journal of Geotechnical and Geoenvironmental Engi-neering,2011,137(4):385-397.
• [14]李典庆,周创兵,陈益峰,等.边坡可靠度分析的随机响应面法及程序实现[J].岩石力学与工程学报,2010,29(8):1-11.
• [15]Lin K,Qiu H B,Gao L,Sun Y F.Comparison of sto-chastic response surface method and response surfacemethod for structure reliability analysis[C]//SecondInternational Conference on Intelligent ComputationTechnology and Automation,Changsha,China,2009:172-175.
• [16]Grooteman F.Adaptive radial-based importance sam-pling method for structural reliability[J].StructrualSafety,2008,30:533-542.
• [17]Cameron R,Martin W.The orthogonal developmentof nonlinear functional in series of Fourier Hermitefunctional[J].The Annals of Mathematics,1947,48(2):385-392.
• [18]Guan X L,Melchers R E.Effect of response surfaceparameter variation on structural reliability estimates[J].Structrual Safety,2001,23:533-542.