工程力学 ›› 2019, Vol. 36 ›› Issue (4): 221-230.doi: 10.6052/j.issn.1000-4750.2018.03.0139

• 土木工程学科 • 上一篇    下一篇

基于扩展卡尔曼滤波的结构参数和荷载识别研究

张肖雄, 贺佳   

  1. 湖南大学土木工程学院, 工程结构损伤诊断湖南省重点实验室, 湖南, 长沙 410082
  • 收稿日期:2018-03-13 修回日期:2018-10-24 出版日期:2019-04-25 发布日期:2019-04-15
  • 通讯作者: 贺佳(1983-),男,湖南人,副教授,博士,主要从事结构损伤诊断和动力识别的研究(E-mail:jiahe@hnu.edu.cn). E-mail:jiahe@hnu.edu.cn
  • 作者简介:张肖雄(1995-),男,湖北人,硕士生,主要从事结构健康监控及动力识别的研究(E-mail:zhangxiaoxiong95@163.com).
  • 基金资助:
    国家自然科学基金青年基金项目(51708198);湖南大学青年教师成长计划项目(531107050912)

IDENTIFICATION OF STRUCTURAL PARAMETERS AND UNKNOWN EXCITATIONS BASED ON THE EXTENDED KALMAN FILTER

ZHANG Xiao-xiong, HE Jia   

  1. College of Civil Engineering, Hunan University, Hunan Provincial Key Lab on Damage Diagnosis for Engineering Structures, Changsha, Hu'nan 410082, China
  • Received:2018-03-13 Revised:2018-10-24 Online:2019-04-25 Published:2019-04-15

摘要: 经典的扩展卡尔曼滤波(Extend Kalman Filter,EKF)方法可有效识别结构参数,但却需要已知外部激励,然而,在工程实际中,有些外激励往往难以实时获取。为此,该文提出了一种基于EKF的未知激励下的结构参数和荷载识别方法。通过在观测方程中引入投影矩阵,实现了结构参数的识别,同时,利用最小二乘估计实时识别了未知的外激励。为了验证该方法的有效性和鲁棒性,文中采用了三个数值算例:四层的Benchmark模型、分段线性系统和非线性Duffing系统。数值分析的结果表明,该方法不仅能够准确识别线性和非线性结构的参数,还能有效识别作用于这些结构的外激励。

关键词: 未知外激励, 线性和非线性参数识别, 扩展卡尔曼滤波, 投影矩阵, 最小二乘估计

Abstract: The classical extended Kalman filter (EKF) method is capable of accurately identifying structural parameters with known external excitations. However, in some practical situations, the excitations are difficult or impossible to measure. A time-domain approach based on EKF is proposed in this paper for the simultaneous identification of structural parameters and unknown inputs. A projection matrix is introduced in the observation equation, based on which the structural parameters are identified. The unknown inputs are determined by means of least squares estimation using the estimated parameters. The effectiveness and robustness of the proposed approach is verified through three numerical examples including a four-story benchmark model, a piecewise linear structure and a Duffing hysteretic structure. The numerical results show that the proposed approach can not only accurately identify the parameters of linear and nonlinear structures, but also satisfactorily estimate the unknown external excitations.

Key words: unknown external excitation, linear and nonlinear structural parameter identification, extended Kalman filter, projection matrix, least squares estimation

中图分类号: 

  • TU311.3
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