基于Bayesian证据推断与信息增益的参数化有限元修正模型选择

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (12) : 159-166.

论文

尹涛王祥宇周越

作者信息 +

Model selection in updating of parametric FE model based on Bayesian evidence inference and information divergence#br#

YIN Tao ZHOU Yue WANG Xiang-yu

Author information +

文章历史 +

摘要

在概率论和信息论框架下，建立一种基于Bayesian证据推断与马尔科夫链蒙特卡洛（MCMC）方法的有限元参数化修正模型选择分析方法，以解决有限元模型修正中的待定模型参数选择问题。引入信息增益（Information divergence）指标，定量表征有限元模型修正过程中需要从测量数据中提取用于修正待定模型参数的信息量多少，以惩罚有限元模型待修正参数的复杂程度，能过权衡有限元参数化模型复杂度与其相应信息论表述的复杂度，获得满足模型与实测数据吻合度要求且待定参数相对简单的有限元参数化修正模型，有效避免由于待修正参数过多而导致的模型过拟合问题。通过对某两层螺栓连接钢框架有限元模型半刚性连接刚度参数修正的数值仿真与模型实验研究，对本文方法进行验证。

Abstract

Within the framework of probability and information theory, this paper presents a methodology for finiteelement (FE) modelclass selection for selecting suitable modeling parameters to update FE models based on Bayesian evidence inference and Markov chain Monte Carlo (MCMC) method. The amount of information needed to be extracted from the measurement data is explicitly quantified during the procedure of FE model updating by introducing the concept of information divergence. This is then employed for penalizing the complexity of FE parameterization with a tradeoff between the complexity of a given FE model class and that of its corresponding informationtheoretic interpretation, in order to obtain a relatively simple FE parameterization scheme for keeping similar modeldata matching and avoid the overfitting problem arisen from excessive modeling parameters efficiently. The validity of the presented methodology was verified through both numerical simulation and experimental verification carried out for a twostory boltconnected steel frame.

导出引用

尹涛王祥宇周越. 基于Bayesian证据推断与信息增益的参数化有限元修正模型选择[J]. 振动与冲击, 2018, 37(12): 159-166

YIN Tao ZHOU Yue WANG Xiang-yu. Model selection in updating of parametric FE model based on Bayesian evidence inference and information divergence#br#[J]. Journal of Vibration and Shock, 2018, 37(12): 159-166

参考文献

[1] Friswell MI, Mottershead JE. Finite element model updating in structural dynamics[M]. Kluwer Academic Publishers, 1995.
[2] 张德文, 魏阜旋. 模型修正与破损诊断[M]. 北京：科学出版社, 1999.
ZHANG De-wen, WEI Fu-xuan.Model updating and damage detection[J]. Beijing: Science Press, 1999.
[3] 魏来生. 结构有限元动态模型修正方法综述[J]. 振动与冲击, 1998, 17(3): 43-46.
WEI Lai-sheng.A review on the updating methods of finite element model[J]. Journal of Vibration and Shock, 1998, 17(3): 43-46.
[4] 尹涛, 余岭, 朱宏平. 一种基于模型修正的结构损伤识别方法[J]. 振动与冲击, 2007, 26(6): 59-62.
YIN Tao, YU Ling, ZHU Hong-ping.Model updating based approach for structural damage detection[J]. Journal of Vibration and Shock, 2007, 26(6): 59-62.
[5] Yu L，Yin T. Damage identification in frame structures based on FE model updating[J]. Journal of Vibration and Acoustics, 2010, 132(5): 1741-1757.
[6] Beck J L. Bayesian system identification based on probability logic[J]. Structural Control and Health Monitoring, 2010, 17(7): 825-847.
[7] Friswell MI, Mottershead JE, Ahmadian H. Combining subset selection and parameter constraints in model updating[J]. Journal of Vibration and Acoustics, 1998, 120(4): 854-859.
[8] 宋汉文, 王丽炜, 王文亮. 有限元模型修正中若干重要问题[J]. 振动与冲击, 2003, 22(4): 68-71.
SONG Han-wen, WANG Li-wei, WANG Wen-liang.Several important problems for updating finite element model[J]. Journal of Vibration and Shock, 2003, 22(4): 68-71.
[9] 费庆国, 张令弥, 李爱群, 郭勤涛. 基于统计分析技术的有限元模型修正研究[J]. 振动与冲击, 2005, 24(3): 23-26.
FEI Guo-qing, ZHANG Ling-mi, LI Ai-qun, GUO Qin-tao.Finite element model updating using statistics analysis[J]. Journal of Vibration and Shock, 2005, 24(3): 23-26.
[10] 李延强, 杜彦良. 基于最敏感设计参数的斜拉索有限元动力模型修正[J]. 振动与冲击, 2009, 28(3): 141-143.
LI Yan-qiang, DU Yan-liang. Dynamic finite element model updating of stay-cable based on the most sensitivity design variable[J]. Journal of Vibration and Shock, 2009, 28(3): 141-143.
[11] Mottershead JE, Link M, Friswell MI. The sensitivity method in finite element model updating: A tutorial[J]. Mechanical Systems and Signal Processing, 2011, 25(7): 2275-2296.
[12] Wan HP, Ren WX. Parameter selection in finite-element-model updating by global sensitivity analysis using Gaussian process metamodel[J]. Journal of Structural Engineering, 2014, 141(6): 04014164.
[13] 姜东, 丁继锋, 费庆国，韩晓林. 一种有限元模型修正中的参数选择方法[J]. 固体力学学报, 2011(s1): 88-92.
JIANG Dong, DING Ji-feng, FEI Guo-qing, HAN Xiao-lin. A method for parameter selection in finite element model updating[J]. Chinese Journal of Solid Mechanics, 2011(s1): 88-92.
[14] Gull S F. Bayesian inductive inference and maximum entropy[C]. In Maximum Entropy and Bayesian Methods, Skilling J (ed.). Kluwer Academic Publishers: Dordrecht, Holland, 1989, 53–74.
[15] Haario H, Laine M, Mira A, Saksman E. DRAM: Efficient adaptive MCMC[J]. Statistics and Computing, 2006, 16(4): 339-354.
[16] Yuen K V. Bayesian methods for structural dynamics and civil engineering[M]. John Wiley & Sons, Ltd, 2010.
[17] Yin T, Jiang QH, Yuen KV. Vibration-based damage detection for structural connections using incomplete modal data by Bayesian approach and model reduction technique[J]. Engineering Structures, 2017, 132(1): 260-277.
[18] Yin T, Lam HF, Chow HM, Zhu HP. Dynamic reduction based structural damage detection of transmission tower utilizing ambient vibration data[J]. Engineering Structures, 2009, 31(9): 2009-2019.
[19] Lam H F, Yin T. Dynamic reduction based structural damage detection of transmission towers: practical issues and experimental verification[J]. Engineering Structures, 2011, 33(5): 1459-1478.