扩展卡尔曼滤波对时变参数追踪性能的影响研究
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作者单位:

南京航空航天大学机械结构力学及控制国家重点实验室,南京 210016

作者简介:

通讯作者:

姜金辉,男,副教授,E-mail: jiangjinhui@nuaa.edu.cn。

中图分类号:

TB124

基金项目:

国家自然科学基金(51775270)。


Research on Tracking Performance of Extended Kalman Filter for Time Varying Parameters
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Affiliation:

State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China

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    摘要:

    扩展卡尔曼滤波(Extended Kalman filter, EKF)理论由线性卡尔曼滤波理论发展而来。在结构的物理参数未知的情况下,扩展卡尔曼滤波理论将结构的物理参数与其状态向量组成增广状态向量,对增广状态向量进行识别,从而得到修正的结构参数。本文引入扩展卡尔曼滤波理论,对结构参数进行识别。为了验证该方法的有效性,引入1个时变参数三自由度系统作为仿真算例,分别探讨扩展卡尔曼滤波中的各项滤波参数(模型噪声的协方差矩阵Q,测量噪声的协方差矩阵R)对结构的时变参数追踪性能的影响。结果表明,合适的滤波参数能使得算法更迅速,准确地识别出结构中的时变参数变化趋势。还通过一个悬臂梁仿真算例,证明了即使在部分测点没有测量的情况下,EKF算法也能识别出结构参数。

    Abstract:

    Extended Kalman filter(EKF) theory is developed from linear Kalman filter theory. When the physical parameters of the structure are unknown, the unknown parameters of the structure are combined with the state vector of the structure to form an augmented state vector, which is called extended Kalman filter theory. The unknown structural parameters are obtained through the augmented state vector. This paper introduces EKF theory to identify structural parameters. In order to verify the effectiveness of this method, a three-degree of freedom system with time-varying parameters is introduced as a simulation example to investigate the influence of various parameters (covariance matrix Q of model noise, covariance matrix R of measurement noise, influence of observation points) on tracking performance of time-varying parameters of structure. The results show that the algorithm with appropriate filter parameters (QR) can identify the time-varying parameters in the structure more quickly and accurately. And a cantilever beam simulation example is also introduced to show that the EKF algorithm can identify structural parameters even if some measuring points are not measured.

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引用本文

唐宏志,姜金辉.扩展卡尔曼滤波对时变参数追踪性能的影响研究[J].南京航空航天大学学报,2022,54(2):304-310

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  • 收稿日期:2020-08-07
  • 最后修改日期:2021-04-07
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  • 在线发布日期: 2023-02-22
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