基于Gibbs抽样的马尔科夫蒙特卡罗方法在结构物理参数识别及损伤定位中的研究
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摘要
通过对结构动力特征方程进行的一系列变化,得到了线性结构识别模型,并由贝叶斯更新理论得到其后验分布形式。利用结构的模态参数,并考虑其随机性,应用基于Gibbs抽样的马尔科夫蒙特卡罗方法对线性结构识别模型中各参数的条件后验分布进行了抽样,成功地实现了结构物理参数识别及损伤定位。数值算例表明:Gibbs抽样结果可以以不同的方式标识结构的损伤程度及位置且识别的误差较小。
At first,A linear structural identification model was obtained based on a series of conversion of dynamic characteristic equations.Then,the posterior distribution of the model was achieved by using Bayesian updating theory.Utilizing the structural modal parameters,and taking their randomness into consideration,the samples of the parameters from the conditional posterior distribution of the linear structural identification model were achieved.During the process,Markov chain Monte Carlo method based on Gibbs sampling was used.The numerical examples showed that Gibbs sampling can not only identify damage level and locations in different ways with less error,but also can make a probability measurement of the identified values.
At first,A linear structural identification model was obtained based on a series of conversion of dynamic characteristic equations.Then,the posterior distribution of the model was achieved by using Bayesian updating theory.Utilizing the structural modal parameters,and taking their randomness into consideration,the samples of the parameters from the conditional posterior distribution of the linear structural identification model were achieved.During the process,Markov chain Monte Carlo method based on Gibbs sampling was used.The numerical examples showed that Gibbs sampling can not only identify damage level and locations in different ways with less error,but also can make a probability measurement of the identified values.
引文
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[2]张坤,罗绍湘,段忠东.基于动态响应灵敏度同步反演结构物理参数与输入的算法[J].振动与冲击,2009,28(9):143-148,167.
[3]Muto M M.Application of stochastic simulation methods tosystem identification[D].California Institute of Technology,Pasadena,California,2007.
[4]Cheung S H,Beck J L.Bayesian Model Updating UsingHybrid Monte Carlo Simulation with Application to StructuralDynamic Models with Many Uncertain Parameters[J].Journal of Engineering Mechanics,2009,135(4):243-255.
[5]李小华.结构参数识别的贝叶斯方法及应用研究[D].中国地震局工程力学研究所,2009.
[6]Beck J L,Katafygiotis L S.Updating models and theiruncertainties I:Bayesian statistical[J].Journal ofEngineering Mechanics,1998,124(4):455-461.
[7]Beck J L,Au S K.Bayesian updating of structural modelsand reliability using Markov chain Monte Carlo simulation[J].Journal of Engineering Mechanics,2002,128:380-391.
[8]Ching J,Chen Y J.Transitional markov chain monte carlomethod for bayesian model updating,model class selection,and model averaging[J].Journal of Engineering Mechanics,2007,133(7):816-832.
[9]Ching J,Muto M,Beck J L.Structural model updating andhealth monitoring with incomplete modal data using Gibbssampler[J].Computer-Aided Civil and InfrastructureEngineering,2006,21:242-257.
[10]易伟建,吴高烈,徐丽.模态参数不确定性分析的贝叶斯方法研究[J].计算力学学报,2006,26(6):700-705.
[11]Scott M L.Introduction to applied bayesian statistics andestimation for social scientists[M].Springer,2007.
[12]任宜春,张杰峰,易伟建.基于改进L-P小波的时变模态参数识别方法[J].振动与冲击,2009,28(3):144-148.
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