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工程设计学报
工程设计学报  2016, Vol. 23 Issue (3): 206-211    DOI: 10.3785/j.issn. 1006-754X.2016.03.002
设计理论与方法学     
一种基于Bayes方法的随机模型修正方法
马天政, 吕昊, 张义民
东北大学 机械工程与自动化学院, 辽宁 沈阳 110819
Stochastic model updating based on Bayesian method
MA Tian-zheng, LÜ Hao, ZHANG Yi-min
School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China
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摘要：

提出了一种随机模型的修正方法用以估计结构参数的统计特性.基于Bayes方法的参数估计原理,将需要修正的结构参数的均值和方差看作符合一定先验概率分布的随机变量,根据核密度估计原理构建得到似然函数,进而使用基于差分进化的MCMC方法估计参数的后验概率密度,并根据最大后验概率密度准则估计结构参数的均值和方差.同时使用Kriging方法建立了结构输入和输出之间的代理模型,保证计算精度的同时极大地节约了计算时间.数值算例验证了本方法的可行性.
关键词： 随机模型修正;  Kriging代理模型;  Bayes方法;  MCMC抽样    
Abstract:

A new method for stochastic model updating was proposed to estimate the statistical information of the structural parameters.According to the principle of Bayesian method,the parameters' mean value and variance to be estimated were regarded as random variables and the likelihood functions were constructed by using kernel density estimation method.The posterior distribution of the parameters were calculated by utilizing the population-based MCMC simulation method and then the parameters' mean value and variance could be obtained based on MAP (maximum a posterior) principle.A surrogate model based on Kriging method was established,which greatly saved the computational cost.Numerical example demonstrated the effectiveness of the method.
Key words: stochastic model updating    Kriging agent model    Bayesian method    MCMC sampling
收稿日期: 2016-01-06 出版日期: 2016-06-28
CLC:  O327  
基金资助:

国家自然科学基金重点资助项目(51135003);国家自然科学基金资助项目(U1234208);国家重点基础研究发展计划(973计划)项目(2014CB046303);中央高校基本科研业务费资助项目(02090022115014);“高档数控机床与基础制造装备”科技重大专项课题(2013ZX04011011).
作者简介: 马天政(1987-),男,辽宁鞍山人,博士,从事随机模型修正及动力学可靠性研究,E-mail:zpaprecv@sohu.com.http://orcid.org//0000-0002-9509-9802
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引用本文:

马天政, 吕昊, 张义民. 一种基于Bayes方法的随机模型修正方法[J]. 工程设计学报, 2016, 23(3): 206-211.

MA Tian-zheng, LÜ Hao, ZHANG Yi-min. Stochastic model updating based on Bayesian method. Chinese Journal of Engineering Design, 2016, 23(3): 206-211.

链接本文:

https://www.zjujournals.com/gcsjxb/CN/10.3785/j.issn. 1006-754X.2016.03.002    或    https://www.zjujournals.com/gcsjxb/CN/Y2016/V23/I3/206

[1] BAO Nuo,WANG Chun-jie.A Monte Carlo simulation based inverse propagation method for stochastic model updating[J].Mechanical Systems and Signal Processing,2015(60/61):928-944.

[2] MOTTERSHEAD J E,MARES C,FRISWELL M I.Stochastic model updating:part 1:theory and simulated example[J].Mechanical Systems and Signal Processing,2006,20(7):1674-1695.

[3] 陈志国,邓忠民,毕司峰.基于Monte Carlo法的结构动力学模型确认[J].振动与冲击,2013,32(16):76-81. CHEN Zhi-guo,DENG Zhong-min,BI Si-feng.Structural dynamics model validation based on Monte Carlo method[J].Journal of vibration and shock,2013,32(16):76-81.

[4] FANG Shen-gen,REN Wei-xin,PERERA R.A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation[J].Mechanical Systems and Signal Processing,2012,33:83-96.

[5] KHODAPARAST H H,MOTTERSHEAD J E,FRISWELL M I.Perturbation methods for the estimation of parameter variability in stochastic model updating[J].Mechanical Systems and Signal Processing,2008,22(8):1751-1773.

[6] GOVERS Y,LINK M.Stochastic model updating-Covariance matrix adjustment from uncertain experimental modal data[J].Mechanical Systems and Signal Processing,2010,24(3):696-706.

[7] KHODAPARAST H H,MOTTERSHEAD J E,BADCOCK K J.Interval model updating with irreducible uncertainty using the Kriging predictor[J].Mechanical Systems and Signal Processing,2011,25(4):1204-1226.

[8] FANG Shen-gen,ZHANG Qiu-hu,REN Wei-xin.An interval model updating strategy using interval response surface models[J].Mechanical Systems and Signal Processing,2015(60/61):909-927.

[9] JASRA A,STEPHENS D A,HOLMES C C.On population-based simulation for static inference [J].Statistics and Computing,2015(60/61):909-927.

[10] NICHOLS J M,MOORE E Z,MURPHY K D.Bayesian identification of a cracked plate using a population-based Markov chain Monte Carlo method[J].Computers & Structures,2011,89(13/14):1323-1332.

[11] 黄章俊,王成恩.基于Kriging模型的涡轮盘优化设计方法[J].计算机集成制造系统,2010,16(5):905-911. HUANG Zhang-jun,WANG Cheng-en.Turbine discs optimization design based on Kriging model[J].Computer Integrated Manufacturing Systems,2010,16(5):905-911.

[12] 方圣恩,林友勤,夏樟华.考虑结构参数不确定性的随机模型修正方法[J].振动、测试与诊断,2014,34(5):832-837. FANG Sheng-en,LIN You-qin,XIA Zhang-hua.Stochastic model updating method considering the uncertainties of strucutral parameters[J].Journal of Vibration,Measurement & Diagnosis,2014,34(5):832-837.
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