基于对数回归模型的结构易损性分析
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摘要
综合考虑结构物理参数的随机性和响应的统计相关性,提出了基于对数回归模型的结构易损性分析方法。以蒙特卡罗模拟和随机时程分析法考虑物理参数的随机性,采用β-二项分布探讨响应统计相关性,并建立对数回归模型计算结构易损性。以某一钢筋混凝土两跨连续梁高速公路桥为算例,根据设计图获取其物理参数作为均值,选取合适的标准差做蒙特卡罗模拟,随机采样得到参数样本,通过随机时程分析获得最大响应样本,利用矩估计、最小二乘分别求得β-二项分布和对数回归模型未知参数,最终获得各等级破坏状态下的易损性曲线,并与提出的基于累积极限状态阈值的结构易损性相比较。结果表明:所提出的易损性分析方法,能够达到对结构易损性的保守估计,保证预测结果的合理性,为检测桥梁构件是否过度老化或意外损坏提供理论依据。
A fragility evaluation methodology for bridge is proposed,based on logistic regression model.The methodology incorporates randomness of structural physical parameters and statistical dependence among response values.Using Monte Carlo simulation and random time history analysis,randomness of structural physical parameters was considered.Statistical dependence among response values was plored by Beta-binomial distribution,then logistic regression model was set up to analyse structure fragility.A two-span continuous concrete girder bridge was used as an example to illustrate the approach.Structure physical parameters with design drawings were taken as mean,and an appropriate standard deviation was selected for Monte Carlo simulation which can obtain parameter samples.Random time history analysis was done to get the sample of maximum values of responses,moment estimation and least square were used to obtain respectively Beta-binomial distribution and the unknown parameters of the logistic regression model,then the structure fragility curve under each level failure state was got and compared with fragility curve based on cumulative limit state valve.The results show that the proposed method can achieve a conservative fragility estimation,and better ensure the rationality of the prediction results,providing theoretical evidence for bridge damage detection.
A fragility evaluation methodology for bridge is proposed,based on logistic regression model.The methodology incorporates randomness of structural physical parameters and statistical dependence among response values.Using Monte Carlo simulation and random time history analysis,randomness of structural physical parameters was considered.Statistical dependence among response values was plored by Beta-binomial distribution,then logistic regression model was set up to analyse structure fragility.A two-span continuous concrete girder bridge was used as an example to illustrate the approach.Structure physical parameters with design drawings were taken as mean,and an appropriate standard deviation was selected for Monte Carlo simulation which can obtain parameter samples.Random time history analysis was done to get the sample of maximum values of responses,moment estimation and least square were used to obtain respectively Beta-binomial distribution and the unknown parameters of the logistic regression model,then the structure fragility curve under each level failure state was got and compared with fragility curve based on cumulative limit state valve.The results show that the proposed method can achieve a conservative fragility estimation,and better ensure the rationality of the prediction results,providing theoretical evidence for bridge damage detection.
引文
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[10]Daniel S,Armen D K.Seismic Fragility Modeling from Empirical Data[J].Structural Safety,2008,30(4):320-336.
[11]Wang Q,Wu Z,Liu S.Seismic Fragility Analysis of Highway Bridges Considering Multi-Dimensional Performance Limit State[J].Earthquake Engineering and Engineering Vibration,2012,11(2):185-193.
[12]Serdar S.Health Monitoring of Existing Structure[D].California:University of California,Irvine,2007.
[13]Shinozuka M,Banerjee S.Damage Modeling of Reinforced Concrete Bridges[D].Las Vegas,NV:University of California,Irvine,2005.
[14]Dutta A,Mander J B.Rapid and Detailed Seismic Fragility Analysis of Highway Bridges[R].New York:Multidisciplinary Center for Earthquake Engineering Research,2001.
[2]Shinozuka M,Feng M Q,Lee J,et al.Statistical Analysis of Fragility Curves[J].Journal of Engineering Mechanics,ASCE,2000,126(12):1224-1231.
[3]Tanaka S,Kameda H,Nojima N,et al.Evaluation of Seismic Fragility for Highway Transportation Systems[C]∥Proceedings of the12th World Conference on Earthquake Engineering.New Zealand:2000:2-6.
[4]Cimellaro G P,Reinhorn A M,Bruneau M,et al.Multi-Dimensional Fragility of Structure Formulation and Evaluation[R].Report No.MCEER-06-0002,New York:Multidisciplinary Center for Earthquake Engineering Research,2006.
[5]Hwang H,刘晶波.地震作用下钢筋混凝土桥梁结构易损性分析[J].土木工程学报,2004,37(6):48-51.
[6]Daniel S,Armen D K.Seismic Reliability Assessment of Infrastructure Systems Based on Fragility Models[C]∥Applications of Statistics and Probability in Civil Engineering-Proceedings of the10th International Conference on Applications of Statistics and Probability.2007:435-436.
[7]Williams D A.Extra-Binomial Variation in Logistic Linear Models[J].Applied Statistics,1982,31(2):144-148.
[8]Poortema K.On Modelling Overdispersion of Counts[J].Statistica Neerlandica,1999,53(1):5-20.
[9]张新培.钢筋混凝土抗震结构非线性分析[M].北京:科学出版社,2003:99-101.
[10]Daniel S,Armen D K.Seismic Fragility Modeling from Empirical Data[J].Structural Safety,2008,30(4):320-336.
[11]Wang Q,Wu Z,Liu S.Seismic Fragility Analysis of Highway Bridges Considering Multi-Dimensional Performance Limit State[J].Earthquake Engineering and Engineering Vibration,2012,11(2):185-193.
[12]Serdar S.Health Monitoring of Existing Structure[D].California:University of California,Irvine,2007.
[13]Shinozuka M,Banerjee S.Damage Modeling of Reinforced Concrete Bridges[D].Las Vegas,NV:University of California,Irvine,2005.
[14]Dutta A,Mander J B.Rapid and Detailed Seismic Fragility Analysis of Highway Bridges[R].New York:Multidisciplinary Center for Earthquake Engineering Research,2001.
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