非高斯测量噪声下的结构响应重构

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振动与冲击 ›› 2024, Vol. 43 ›› Issue (11) : 206-216.

论文

非高斯测量噪声下的结构响应重构

祁义博，彭珍瑞

作者信息 +

Structural response reconstruction under non-Gaussian measurement noise

QI Yibo, PENG Zhenrui

Author information +

文章历史 +

摘要

针对非高斯噪声下使用卡尔曼滤波(Kalman Filter, KF)算法进行响应重构时精度下降，甚至重构结果偏差较大的现象，提出一种非高斯卡尔曼滤波(Non-Gaussian Kalman Filter, NGKF)算法进行结构响应重构。首先将L1卡尔曼滤波(L1KF)算法引入结构响应重构，并重新构造了L1卡尔曼滤波算法中的损失函数，其次根据损失函数导出的系数阵惩罚状态方程和观测方程的噪声协方差阵，使KF算法适用于非高斯噪声。最后通过有限的加速度测量信号，结合重构方程计算结构的加速度、速度和位移响应。数值仿真和外伸梁试验均表明所提方法在仅使用有限数量的加速度传感器进行结构响应重构时具有良好的噪声鲁棒性，能有效降低重构误差，改善多种非高斯噪声下使用KF算法进行响应重构时偏差较大的现象。

Abstract

The accuracy of response reconstruction using the Kalman Filter (KF) algorithm is degraded under non-Gaussian noise. To tackle this issue, a non-Gaussian Kalman filter algorithm for structural response reconstruction is proposed. Firstly, the L1 Kalman Filter (L1KF) algorithm is introduced to structural response reconstruction, followed by a revised definition of the loss function within the L1KF. Secondly, the coefficient matrix derived according to the loss function penalizes the noise covariance matrix of the state equation and the observation equation, making the KF algorithm applicable to non-Gaussian noise. Finally, the acceleration, velocity, and displacement responses of the structure are computed from a limited number of acceleration measurements. Both numerical simulations and an overhanging beam test show that the proposed method has good noise robustness using only a limited number of accelerometers, effectively reducing the reconstruction error. The large bias in response reconstruction using KF algorithm under multiple non-Gaussian noises is improved.

导出引用

祁义博，彭珍瑞. 非高斯测量噪声下的结构响应重构[J]. 振动与冲击, 2024, 43(11): 206-216

QI Yibo, PENG Zhenrui. Structural response reconstruction under non-Gaussian measurement noise[J]. Journal of Vibration and Shock, 2024, 43(11): 206-216

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