基于贝叶斯傅里叶动态模型的桥梁极值应力预测
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摘要
研究了基于健康监测应力数据的桥梁极值应力动态预测.考虑到监测应力的周期性、随机性和动态性等特点,首先初次建立了桥梁监测极值应力的傅里叶动态非线性模型(Fourier Dynamic Nonlinear Model,FDNM),结合Taylor级数展开技术,将FDNM近似转化为傅里叶动态线性模型(Fourier Dynamic Linear Model,FDLM);然后采用贝叶斯方法,基于动态监测极值应力数据,建立了无先验信息的贝叶斯傅里叶动态线性模型(Bayesian Fourier Dynamic Linear Model:BFDLM),进而对监测极值应力的一步向前预测分布参数和后验应力状态分布参数进行了预测分析;最后通过实际桥梁监测极值应力数据对本文所建模型和方法的合理性及适用性进行了验证分析,结果表明本文所建BFDLM能够反映桥梁极值应力的周期性、随机性以及动态性等特点.研究成果将为桥梁监测极值应力预测提供理论基础和应用方法.
The dynamic prediction of bridge extreme stress based on health monitoring stress data was studied.Considering the monitored stresses' periodicity, randomness, dynamic characteristics and so forth,firstly,the Fourier Dynamic Nonlinear Model(FDNM)of bridge monitored extreme stress was built,and, with Taylor series expansion technology, FDNM was approximately transferred into the Fourier Dynamic Linear Model(FDLM);secondly, with Bayes method, the Bayesian FDLM(BFDLM)was built based on the monitored extreme stress data,and the one-step forward prediction distribution parameters of monitored extreme stress and distribution parameters of posterior stress state were dynamically predicted; finally, the monitored extreme stress data of an actual bridge was provided to illustrate the application and feasibility of the proposed models and methods.The results show that the proposed BFDLM can reflect bridge extreme stresses' periodicity, randomness, dynamics and so forth,which can provide the theoretical foundation and application approach for bridge monitoring extreme stress prediction.
The dynamic prediction of bridge extreme stress based on health monitoring stress data was studied.Considering the monitored stresses' periodicity, randomness, dynamic characteristics and so forth,firstly,the Fourier Dynamic Nonlinear Model(FDNM)of bridge monitored extreme stress was built,and, with Taylor series expansion technology, FDNM was approximately transferred into the Fourier Dynamic Linear Model(FDLM);secondly, with Bayes method, the Bayesian FDLM(BFDLM)was built based on the monitored extreme stress data,and the one-step forward prediction distribution parameters of monitored extreme stress and distribution parameters of posterior stress state were dynamically predicted; finally, the monitored extreme stress data of an actual bridge was provided to illustrate the application and feasibility of the proposed models and methods.The results show that the proposed BFDLM can reflect bridge extreme stresses' periodicity, randomness, dynamics and so forth,which can provide the theoretical foundation and application approach for bridge monitoring extreme stress prediction.
引文
[1]李顺龙.基于健康监测技术的桥梁结构状态评估和预警方法研究[D].哈尔滨:哈尔滨工业大学土木工程学院,2009:18-39.LI S L.Approached of condition assessment and damage alarming of bridges based on structural health monitoring[D]. Harbin:School of Civil Engineering,Harbin Institute of Technology,2009:18—39.(In Chinese)
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[9]STRAUSS A,FRANGOPOL D M,Kim S Y. Use of monitoring extreme data for the performance prediction of structures:Bayesian updating[J].Engineering Structures,2008,30:3654—3666.
[10]赵卓.基于ARMA模型的伊通河桥监测数据建模与可靠度分析[D].哈尔滨:哈尔滨工业大学土木工程学院,2012:35—93.ZHAO Z.Health monitoring data modeling and reliability analysis for Yitong river bridge based on ARMA model[D].Harbin:School of Civil Engineering,Harbin Institute of Technology,2012:35—93.(In Chinese)
[11]LUD G,FAN X P. Bayesian forecasting of structural bending capacity of aging bridges based on dynamic linear model[J].Journal of Harbin Institute of Technology,2012,44(12):13—17.
[12]樊学平,吕大刚.基于多个BDLM的桥梁结构可靠度实时预测[J].华南理工大学学报(自然科学版),2013,41(3):70—75.FAN X P,L(U|¨)D G. Real-time reliability forecast of bridge structures based on multiple BDLMs[j].Journal of South China University of Technology,2013,41(3):70—75.(In Chinese)
[13]樊学平.基于验证荷载和监测数据的桥梁可靠性修正与贝叶斯预测[D].哈尔滨:哈尔滨工业大学土木工程学院,2014:39-84.FAN X P. Bridge reliability updating and Bayesian prediction based on proof loads and monitored data[D]. Harbin:School of Civil Engineering,Harbin Institute of Technology,2014:39—84.(In Chinese)
[14]WEST M,HARRISON J.Bayesian forecasting and dynamic models[M].2nd ed.New York:Springer Series,1997:32—37.
[15]PETRIS G,PETRONE S,CAMPAGNOLI P.Dynamic linear models with R[M].New York:Springer Series,2009:31—84.
[2]宗周红,钟儒勉,郑沛娟,等.基于健康监测的桥梁结构损伤预后和安全预后研究进展及挑战[J].中国公路学报,2014,27(12):46—57.ZONG Z H,ZHONG R M,ZHENG P J,et al.Damage and safety prognosis of bridge structures based on structural health monitoring:progress and challenges[J].China Journal of Highway and Transport,2014,27(12):46—57.(In Chinese)
[3]魏锦辉,任伟新.基于响应面方法的桥梁静动力有限元模型修正[J].公路交通科技,2015,32(2):68—73.WEI J H,REN W X. Static and dynamic bridge finite element model updating based on response surface method[J].Journal of Highway and Transportation Research and Development,2015,32(2):68—73.(In Chinese)
[4]焦美菊,孙利民,李清富.基于监测数据的桥梁结构可靠度评估[J].同济大学学报(自然科学版),2011,39(10):1452-1457.JIAO M J,SUN L M,LI Q F. Bridge structural reliability assessment based on health monitoring data[J].Journal of Tongji University(Natural Science), 2011, 39(10):1452—1457.(In Chinese)
[5]FRANGOPOL D M,STRAUSS A,KIM S. Bridge reliability assessment based on monitoring[J]. Journal of Bridge Engineering,2008,13(3):258—270.
[6]WALSH S B,BORELLO D J,GULDUR B,et al.Data processing of point clouds for object detection for structural engineering applications[J]. Computer-Aided Civil and Infrastructure Engineering,2013,28(7):495—508.
[7]CATBAS F N,SUSOY M,FRANGOPOL D M. Structural health monitoring and reliability estimation:long span truss bridge application with environmental monitoring data[J].Engineering Structures,2008,30(9):2347—2359.
[8]FRANGOPOL D M,STRAUSS A,KIM S Y. Use of monitoring extreme data for the performance prediction of structures:general approach[J].Engineering Structures,2008,30:3644—3653.
[9]STRAUSS A,FRANGOPOL D M,Kim S Y. Use of monitoring extreme data for the performance prediction of structures:Bayesian updating[J].Engineering Structures,2008,30:3654—3666.
[10]赵卓.基于ARMA模型的伊通河桥监测数据建模与可靠度分析[D].哈尔滨:哈尔滨工业大学土木工程学院,2012:35—93.ZHAO Z.Health monitoring data modeling and reliability analysis for Yitong river bridge based on ARMA model[D].Harbin:School of Civil Engineering,Harbin Institute of Technology,2012:35—93.(In Chinese)
[11]LUD G,FAN X P. Bayesian forecasting of structural bending capacity of aging bridges based on dynamic linear model[J].Journal of Harbin Institute of Technology,2012,44(12):13—17.
[12]樊学平,吕大刚.基于多个BDLM的桥梁结构可靠度实时预测[J].华南理工大学学报(自然科学版),2013,41(3):70—75.FAN X P,L(U|¨)D G. Real-time reliability forecast of bridge structures based on multiple BDLMs[j].Journal of South China University of Technology,2013,41(3):70—75.(In Chinese)
[13]樊学平.基于验证荷载和监测数据的桥梁可靠性修正与贝叶斯预测[D].哈尔滨:哈尔滨工业大学土木工程学院,2014:39-84.FAN X P. Bridge reliability updating and Bayesian prediction based on proof loads and monitored data[D]. Harbin:School of Civil Engineering,Harbin Institute of Technology,2014:39—84.(In Chinese)
[14]WEST M,HARRISON J.Bayesian forecasting and dynamic models[M].2nd ed.New York:Springer Series,1997:32—37.
[15]PETRIS G,PETRONE S,CAMPAGNOLI P.Dynamic linear models with R[M].New York:Springer Series,2009:31—84.