基于贝叶斯网的结构延性需求分析
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摘要
概率延性需求分析是基于性能的结构抗震评估与设计中的重要一环。根据搜集到的1918条地震记录,对具有不同屈服水平系数及周期的单自由度体系作了弹塑性时程分析,通过拟合得到简化的延性需求计算公式;针对单一地面峰值加速度作为地震强度指标的不足,根据回归分析构造一个新的参数用于描述地震频谱特性对延性需求的影响;以地面峰值加速度和此新参数作为地震强度指标向量,建立给定地震强度条件下结构延性需求的概率关系,并形成相应的贝叶斯网。引进马尔科夫链蒙特卡罗模拟方法,用于更新给定地震强度观察值条件下延性需求的后验分布,从而实现延性需求计算的本地化。通过算例分析了各地震强度参量、给定观测值条件下对延性需求计算结果的影响。
Ductility demand probabilistic analysis is important for performance based seismic evaluation and design.Nonlinear time history analysis of SDOF with various yield strength coefficients and periods are performed using 1918 earthquake ground motion records to obtain simplified formula for ductility demand through curve fitting.Considering the insufficiency of PGA for being as single intensity measure,a new parameter is constructed through regression analysis to quantify the effect of earthquake spectrum characteristics on the ductility demand.With PGA and the new parameter being as IM vector,the relationship of ductility demand probabilistic with given earthquake intensity is formulated,and a Bayesian network is established.Markov Chain Monte Carlo method is introduced to update the ductility demand posterior probabilistic distribution with given observation of earthquake intensity,thus localizing the calculation of the ductility demand.Examples analyze how the parameters of earthquake intensity and the condition of given observations affect the calculation result.
Ductility demand probabilistic analysis is important for performance based seismic evaluation and design.Nonlinear time history analysis of SDOF with various yield strength coefficients and periods are performed using 1918 earthquake ground motion records to obtain simplified formula for ductility demand through curve fitting.Considering the insufficiency of PGA for being as single intensity measure,a new parameter is constructed through regression analysis to quantify the effect of earthquake spectrum characteristics on the ductility demand.With PGA and the new parameter being as IM vector,the relationship of ductility demand probabilistic with given earthquake intensity is formulated,and a Bayesian network is established.Markov Chain Monte Carlo method is introduced to update the ductility demand posterior probabilistic distribution with given observation of earthquake intensity,thus localizing the calculation of the ductility demand.Examples analyze how the parameters of earthquake intensity and the condition of given observations affect the calculation result.
引文
[1]Cornell C A,Krawinkler H.Progress and challenges inseismic performance assessment[EB/OL].PEER CenterNews,2000.http://peer.berkeley.edu/news/2000spring/performance.html
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[3]Yi Weijian,Zhang Haiyan,Kunnath S K.Probabilisticconstant-strength ductility demand spectra[J].Journal ofStructural Engineering,2007,133(4):567-575
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[7]Yuen K V,Au S K,Beck J L.Two-stage structural healthmonitoring approach for phase I benchmark studies[J].Journal of Engineering Mechanics,2004,130(1):16-33
[8]Shome N,Cornell C A,Bazzurro P,et al.Earthquake,records,and nonlinear responses[J].Earthquake Spectra,1998,14(3):469-500
[9]Baker J W,Cornell C A.A vector-valued ground motionintensity measure consisting of spectral acceleration andepsilon[J].Earthquake Engineering and StructuralDynamics,2005,34(10):1193-1217
[10]Malhotra P K.Response of buildings to near-field pulse-like ground motions[J].Earthquake Engineering andStructural Dynamics,1999,28(11):1309-1326
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[12]刘恢先,卢荣俭,陈达生,等.修订我国地震烈度的一个建议方案[C]//地震工程研究报告集,第四集.北京:科学出版社,1981
[13]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑大学学报,1994,27(5):1-10(Ou Jinping,Duan Yubo,Liu Huiyi.Structural randomearthquake action and its statistical parameters[J].Journalof Harbin University of Civil Engineering and Architecture,1994,27(5):1-10(in Chinese))
[14]Geweke J F.Evaluating the accuracy of sampling-basedapproaches to the calculation of posterior moments[C]//Bayesian Statistics.Oxford:Oxford University Press,1991:169-193
[15]Raftery A E,Lewis S.How many iterations in the Gibbssampler[C]//Bayesian Statistics.Oxford:OxfordUniversity Press,1992:763-773
[16]Cowles M K,Carlin B P.Markov chain Monte Carloconvergence diagnostics:a comparative review[J].Journal of the American Statistical Association,1996,91(434):883-904
[2]吕西林,周定松.考虑场地类别与设计分组的延性需求谱和弹塑性位移反应谱[J].地震工程与工程振动,2004,24(1):39-48(LüXilin,Zhou Dingsong.Ductilitydemand spectra and inelastic displacement spectraconsidering soil conditions and design characteristic periods[J].Earthquake Engineering and Engineering Vibration,2004,24(1):39-48(in Chinese))
[3]Yi Weijian,Zhang Haiyan,Kunnath S K.Probabilisticconstant-strength ductility demand spectra[J].Journal ofStructural Engineering,2007,133(4):567-575
[4]Jordan M I.Learning in graphical models[M].USA:MITPress,1998
[5]Geyskens P,Kiureghian A D,Monteiro P.Bayesianprediction of elastic modulus of concrete[J].Journal ofStructural Engineering,1998,124(1):89-95
[6]Beck J L,Katafygiotis L S.Updating models and theiruncertainties.Part I:Bayesian statistical framework[J].Journal of Engineering Mechanics,1998,124(4):455-461
[7]Yuen K V,Au S K,Beck J L.Two-stage structural healthmonitoring approach for phase I benchmark studies[J].Journal of Engineering Mechanics,2004,130(1):16-33
[8]Shome N,Cornell C A,Bazzurro P,et al.Earthquake,records,and nonlinear responses[J].Earthquake Spectra,1998,14(3):469-500
[9]Baker J W,Cornell C A.A vector-valued ground motionintensity measure consisting of spectral acceleration andepsilon[J].Earthquake Engineering and StructuralDynamics,2005,34(10):1193-1217
[10]Malhotra P K.Response of buildings to near-field pulse-like ground motions[J].Earthquake Engineering andStructural Dynamics,1999,28(11):1309-1326
[11]黄建文,朱晞.近震作用下单自由度结构的非弹性响应分析研究[J].中国安全科学学报,2003,13(11):59-65(Huang Jianwen,Zhu Xi.Inelastic response analysisfor the SDOF structures under near-field earthquakes[J].China Safety Science Journal,2003,13(11):59-65(inChinese))
[12]刘恢先,卢荣俭,陈达生,等.修订我国地震烈度的一个建议方案[C]//地震工程研究报告集,第四集.北京:科学出版社,1981
[13]欧进萍,段宇博,刘会仪.结构随机地震作用及其统计参数[J].哈尔滨建筑大学学报,1994,27(5):1-10(Ou Jinping,Duan Yubo,Liu Huiyi.Structural randomearthquake action and its statistical parameters[J].Journalof Harbin University of Civil Engineering and Architecture,1994,27(5):1-10(in Chinese))
[14]Geweke J F.Evaluating the accuracy of sampling-basedapproaches to the calculation of posterior moments[C]//Bayesian Statistics.Oxford:Oxford University Press,1991:169-193
[15]Raftery A E,Lewis S.How many iterations in the Gibbssampler[C]//Bayesian Statistics.Oxford:OxfordUniversity Press,1992:763-773
[16]Cowles M K,Carlin B P.Markov chain Monte Carloconvergence diagnostics:a comparative review[J].Journal of the American Statistical Association,1996,91(434):883-904
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