华南理工大学学报(自然科学版) ›› 2019, Vol. 47 ›› Issue (7): 49-57.doi: 10.12141/j.issn.1000-565X.180429

• 土木建筑工程 • 上一篇    下一篇

基于环境振动和贝叶斯定理的有限元模型 自动修正方法及应用

刘佩 朱海鑫 连鹏宇 杨维国   

  1. 北京交通大学 土木建筑工程学院,北京 100044
  • 收稿日期:2018-08-25 修回日期:2019-02-20 出版日期:2019-07-25 发布日期:2019-06-01
  • 通信作者: 刘佩(1982-),女,博士,副教授,主要从事结构健康监测研究. E-mail:peiliu@ bjtu.edu.cn
  • 作者简介:刘佩(1982-),女,博士,副教授,主要从事结构健康监测研究.
  • 基金资助:
    国家自然科学基金资助项目(51878034);北京交通大学中央高校基本科研业务费专项资金资助项目 (2019JBM085)

Automatic Updating Method of Finite Element Model and Its Application Based on Ambient Vibration and Bayesian Theorem

 LIU Pei ZHU Haixin LIAN Pengyu YANG Weiguo   

  1. School of Civil Engineering,Beijing Jiaotong University,Beijing 100044,China
  • Received:2018-08-25 Revised:2019-02-20 Online:2019-07-25 Published:2019-06-01
  • Contact: 刘佩(1982-),女,博士,副教授,主要从事结构健康监测研究. E-mail:peiliu@ bjtu.edu.cn
  • About author:刘佩(1982-),女,博士,副教授,主要从事结构健康监测研究.
  • Supported by:
    Supported by the National Natural Science Foundation of China(51878034)

摘要: 传统的有限元模型修正方法通常没有定量考虑测试误差和模型误差的不确定性 对修正结果的影响,并且难以用于复杂结构. 针对上述问题,提出了一种基于环境振动测 试和商业软件交互访问的贝叶斯有限元模型修正方法. 该方法以环境振动测试和快速贝 叶斯方法识别所得模态参数为已知数据,基于贝叶斯定理得到修正参数的后验概率密度 函数,利用单纯形法最小化修正参数的负对数似然函数,得到其最有可能值及后验变异系 数,并通过 SAP2000 有限元模型和 MATLAB 修正程序的交互访问,实现复杂结构有限元 模型参数的自动修正. 对某两层大跨楼板结构进行了环境振动测试和模态参数识别,利用 所提方法直接对混凝土楼板和钢梁的弹性模量进行修正,修正后的自振频率和振型与识 别值吻合较好.

关键词: 环境振动测试, 贝叶斯定理, 模型修正, 模态参数识别, 有限元模型, 大跨楼板结构

Abstract: The effects of uncertainties due to test and model errors on the updated model parameters are not consi- dered in the traditional finite element model updating methods. These methods are difficult to be applied to compli- cated structures. To solve the above problems,a Bayesian finite element model updating method based on ambient vibration test and interactive access of commercial software was proposed. Modal parameters were identified by a fast Bayesian FFT method with the ambient vibration test data. Taking the identified modal parameters as known data,the posterior probability density function of the updated parameters was obtained by Bayesian theorem. By minimizing the negative log-likelihood function with the simplex method,the most probable values and coefficients of variation of the updated parameters were obtained. A data-exchange algorithm was employed to integrate the Bayesian structural model updating method in MATLAB with the finite element analysis results in SAP2000 to up- date the finite element model parameters automatically. Ambient vibration tests and modal parameter identification were conducted on two long-span floor structures. The proposed method is employed to update the values of elastic modulus of concrete floors and steel beams. The modal analysis results from the updated finite element model agree well with the identified ones.

Key words: ambient vibration test, Bayesian theorem, model updating, modal parameter identification, finite element model, long-span floor structure

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