改进的强追踪平方根无迹卡尔曼滤波时变结构参数识别

杨纪鹏1,夏烨1,闫业祥1,孙利民1,2

振动与冲击 ›› 2021, Vol. 40 ›› Issue (23) : 74-82.

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (23) : 74-82.
论文

改进的强追踪平方根无迹卡尔曼滤波时变结构参数识别

  • 杨纪鹏1,夏烨1,闫业祥1,孙利民1,2
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Time-varying structural parametric identification with MSTSRUKF

  • YANG Jipeng1, XIA Ye1, YAN Yexiang1, SUN Limin1,2
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摘要

地震作用下时变结构参数识别一直为研究者所关心,传统扩展卡尔曼滤波(EKF)、无迹卡尔曼滤波(UKF)等方法存在时变结构参数跟踪识别能力弱、协方差矩阵开方时矩阵奇异导致计算不稳定等问题。基于平方根无迹卡尔曼滤波(SRUKF),提出一种改进的强追踪平方根无迹卡尔曼滤波方法(MSTSRUKF)。首先使用QR分解改进平方根无迹卡尔曼滤波算法中协方差矩阵平方根计算方法,使计算过程无条件数值稳定;其次改进滤波更新中协方差矩阵平方根的计算方法,同时引入观测矩阵的等价形式,保证算法的稳定性的同时,避免求解复杂系统的Jacobian矩阵;最后引入强追踪滤波技术,更新时间预测协方差矩阵,使算法具备时变参数跟踪能力。数值分析结果表明,MSTSRUKF算法能有效识别线性和非线性系统突变参数,同时能较准确地预测结构状态,计算过程中数值稳定,算法具有较强的抗噪性。

Abstract

Time-varying structural parameter identification under earthquake is always concerned by researchers. Traditional extended Kalman filter (EKF) and unscented Kalman filter (UKF) have some problems, such as weak tracking ability of time-varying structural parameter, numerical instability when the square root matrix of covariance matrix was calculated due to matrix singularity. Based on the stand square root unscented Kalman filter (SRUKF), a modified strong tracing square root unscented Kalman filter (MSTSRUKF) was proposed. Firstly, the decomposition method of the square root matrix in SRUKF was improved, and QR decomposition method was used to make the calculation process unconditional numerical stability. Secondly, the calculation method of square root matrix in filtering update was improved to ensure the stability of the algorithm. At the same time, the equivalent form of observation matrix was introduced to avoid solving Jacobian matrix. Finally, strong tracking filter technique was introduced to update the time prediction covariance matrix, so that the proposed algorithm has the ability to trace time-varying parameters. Numerical analysis results demonstrated the proposed MSTSRUKF algorithm can effectively identify the mutation parameters of linear and nonlinear systems, and accurately predict the structural state. The proposed method also has strong noise resistance.

关键词

地震 / 平方根无迹卡尔曼滤波(SRUKF) / QR分解 / 时变参数识别

Key words

 seismic / square root unscented Kalman filter(SRUKF) / QR decomposition / time-varying parameter identification

引用本文

导出引用
杨纪鹏1,夏烨1,闫业祥1,孙利民1,2. 改进的强追踪平方根无迹卡尔曼滤波时变结构参数识别[J]. 振动与冲击, 2021, 40(23): 74-82
YANG Jipeng1, XIA Ye1, YAN Yexiang1, SUN Limin1,2. Time-varying structural parametric identification with MSTSRUKF[J]. Journal of Vibration and Shock, 2021, 40(23): 74-82

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