基于贝叶斯理论的大坝体系可靠度计算方法
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摘要
提出了大坝体系可靠度的改进计算方法.首先,通过响应面法拟合极限状态函数,进而通过JC法求出大坝单元的失效概率.然后,通过设定失效模式,以复合极限状态函数为准则,搜索出相应的失效路径;基于贝叶斯公式和Cauchy-Schwarz不等式,通过推导得出大坝以某种失效模式失效时的失效概率的上限,从而得出大坝整个体系的可靠度.最后,结合规范,施加地震荷载、静水压力和动水压力进行了实例验证,并对各种荷载进行了敏感性分析.结果表明,与常规求解大坝体系可靠度方法相比,其优点为考虑了多条失效路径,使用的为其失效概率的上限,计算偏于保守.
An improved calculation method for system reliability of dam is proposed.Firstly,through fitting limit state function by response surface method,the failure probability of dam units was obtained by JC method.Then,the failure paths were searched by setting failure mode according to composite limit state function,and based on Bayes formula and Cauchy-Schwarz inequality,the upper limit of failure probability for failure mode and system reliability of dam were deduced.Finally,according to the criterion,seismic load,hydrostatic pressure and hydrodynamic pressure were applied to the gravity dam model to verify the example and sensitivities of these loads were analyzed.Compared with other conventional algorithms,this method has some strong points:more failure paths are considered and the upper limit of failure probability is used for greater security.
An improved calculation method for system reliability of dam is proposed.Firstly,through fitting limit state function by response surface method,the failure probability of dam units was obtained by JC method.Then,the failure paths were searched by setting failure mode according to composite limit state function,and based on Bayes formula and Cauchy-Schwarz inequality,the upper limit of failure probability for failure mode and system reliability of dam were deduced.Finally,according to the criterion,seismic load,hydrostatic pressure and hydrodynamic pressure were applied to the gravity dam model to verify the example and sensitivities of these loads were analyzed.Compared with other conventional algorithms,this method has some strong points:more failure paths are considered and the upper limit of failure probability is used for greater security.
引文
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[13]CHENG Jin,LI Q S,XIAO Ru-cheng.A newartificial neural network-based response surfacemethod for structural reliability analysis[J].Probabilistic Engineering Mechanics,2008,23:51-63
[14]KAYMAZ I,MCMAHON C A.A response surfacemethod based on weighted regression for structuralreliability analysis[J].Probabilistic EngineeringMechanics,2005,20:11-17
[15]GAVIN H P,YAU Siu-chung.High-order limitstate functions in the response surface method forstructural reliability analysis[J].Structural Safety,2008,30:162-179
[16]WONG S M,HOBBS R E,ONOF C.An adaptiveresponse surface method for reliability analysis ofstructures with multiple loading sequences[J].Structural Safety,2005,27:287-308
[17]ZOU Tong,MOURELATOS Z P,TU Jian.Anindicator response surface method for simulation-based reliability analysis[J].Journal of MechanicalDesign,2008,130:071401-1-11
[18]LGER P,LARIVIRE R,PALAVICINI F,et al.Performance of gated spillways during the1996Sanguinity flood(Que'bec,Canada)andevolution of related design criteria[C]//Proceedingof ICOLD 20th Congress.Beijing:[s n],2000:417-438
[19]CASTILLO E,MINGUEZ R,CASTILLO C.Sensitivity analysis in optimization and reliabilityproblems[J].Reliability Engineering and SystemSafety,2008,93:1788-1800
[20]SONG Jun-ho,KANG Won-hee.System reliabilityand sensitivity under statistical dependence bymatrix-based system reliability method[J].Structural Safety,2009,31:148-156
[21]范书立,陈健云,范武强,等.地震作用下碾压混凝土重力坝的可靠度分析[J].岩石力学与工程学报,2008(3):564-571
[2]曹晖,林学鹏.地震动非平稳特性对结构非线性响应影响的分析[J].工程力学,2006,23(12):30-35
[3]林家浩.随机地震响应的确定性算法[J].地震工程与工程振动,1986,5(1):89-93
[4]汪梦甫.非比例阻尼线性体系平稳随机地震响应计算的虚拟激励法[J].计算力学学报,2008,25(1):94-99
[5]汪梦甫.用虚拟激励法求解非比例阻尼线性体系的非平稳随机地震响应[J].力学季刊,2006,27(4):598-605
[6]孙建梅,叶继红,程文瀼.多点输入下大跨空间索结构的虚拟激励法[J].振动与冲击,2005,24(4):107-119
[7]龚文俊,刘扬,张建仁.基于虚拟变量法的结构可靠度参数敏感性分析[J].长沙交通学院学报,2006,22(1):12-16
[8]MOORE L J,SA Ping.Comparisons with the best inresponse surface methodology[J].Statistics&Probability,1999,44:189-194
[9]ZHENG Y,DAS P K.Improved response surfacemethod and its application to stiffened plate reliabilityanalysis[J].Engineering Structures,2000,22:544-551
[10]GUAN X L,MELCHERS R E.Effect of responsesurface parameter variation on structural reliabilityestimates[J].Structural Safety,2001,23(4):429-444
[11]GUPTA S,MANOHAR C S.Improved responsesurface method for time variant reliability analysis ofnonlinear random structures under no stationaryexcitations[J].Nonlinear Dynamics,2004,36:267-280
[12]GOMES H M,AWRUCH A M.Comparison ofresponse surface and neural network with othermethods for structural reliability analysis[J].Structural Safety,2004,26:49-67
[13]CHENG Jin,LI Q S,XIAO Ru-cheng.A newartificial neural network-based response surfacemethod for structural reliability analysis[J].Probabilistic Engineering Mechanics,2008,23:51-63
[14]KAYMAZ I,MCMAHON C A.A response surfacemethod based on weighted regression for structuralreliability analysis[J].Probabilistic EngineeringMechanics,2005,20:11-17
[15]GAVIN H P,YAU Siu-chung.High-order limitstate functions in the response surface method forstructural reliability analysis[J].Structural Safety,2008,30:162-179
[16]WONG S M,HOBBS R E,ONOF C.An adaptiveresponse surface method for reliability analysis ofstructures with multiple loading sequences[J].Structural Safety,2005,27:287-308
[17]ZOU Tong,MOURELATOS Z P,TU Jian.Anindicator response surface method for simulation-based reliability analysis[J].Journal of MechanicalDesign,2008,130:071401-1-11
[18]LGER P,LARIVIRE R,PALAVICINI F,et al.Performance of gated spillways during the1996Sanguinity flood(Que'bec,Canada)andevolution of related design criteria[C]//Proceedingof ICOLD 20th Congress.Beijing:[s n],2000:417-438
[19]CASTILLO E,MINGUEZ R,CASTILLO C.Sensitivity analysis in optimization and reliabilityproblems[J].Reliability Engineering and SystemSafety,2008,93:1788-1800
[20]SONG Jun-ho,KANG Won-hee.System reliabilityand sensitivity under statistical dependence bymatrix-based system reliability method[J].Structural Safety,2009,31:148-156
[21]范书立,陈健云,范武强,等.地震作用下碾压混凝土重力坝的可靠度分析[J].岩石力学与工程学报,2008(3):564-571
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