基于移动窗卡尔曼滤波算法的结构响应重构

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摘要为了克服传统卡尔曼滤波(Kalman filter, KF)算法在重构结构未测点响应时，需要已知测量噪声方差和过程噪声方差以及需假定二者为恒值的问题，提出了一种基于移动窗卡尔曼滤波(moving-window Kalman filter, MWKF)算法的结构响应重构方法。该方法的特点在于：无需预先按经验设定测量和过程噪声方差值，利用移动窗技术，首先实时估计二者的数值，然后基于KF算法，利用有限测点的响应信息重构结构未安装传感器位置的响应。文中以一个平面单跨框架结构为例进行数值模拟和试验分析。分析结果表明：该方法能有效地实时估计测量噪声方差和过程噪声方差，未测点的重构动力响应时程与计算响应时程或者测量响应吻合良好。

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	张笑华
	吴志彪
	吴圣斌
	黄梅萍

关键词 ：噪声方差未知, 卡尔曼滤波算法, 移动窗, 有限测点, 响应重构

Abstract：The classical Kalman filter (KF) algorithm is a powerful tool to reconstruct the unmeasured responses but needing available process and measurement noise covariance and always assuming to be constants. However, it is generally difficult to determine in advance the noise covariance and they are time-varied. This paper thus investigates responses reconstruction by using the moving-window Kalman filter (MWKF) with unknown measurement and process noise covariance. The measurement and process noise covariance was firstly evaluated by utilizing the moving-window estimation technique and measurements. Then the structural responses at unmeasured locations were reconstructed based on KF algorithm with limited measurements. Numerical and experimental investigations were conducted by using a three-storey frame structure to verify the effectiveness and feasibility of the MWKF in response reconstruction. The results indicate that the measurement and process noise covariance can be well estimated and the reconstructed responses agree well with the real or measured responses.

Key words： unknown noise variance Kalman filer moving-window limited measurements response reconstruction

收稿日期: 2020-05-21 出版日期: 2021-11-15

引用本文:

张笑华，吴志彪，吴圣斌，黄梅萍. 基于移动窗卡尔曼滤波算法的结构响应重构[J]. 振动与冲击, 2021, 40(21): 90-96.
ZHANG Xiaohua, WU Zhibiao, WU Shengbin, HUANG Meiping. Structural response reconstruction based on moving window Kalman filtering algorithm. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(21): 90-96.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I21/90

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