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。
Here,aiming at phenomena of decreased accuracy and even larger deviation in reconstruction results when using Kalman filter(KF)algorithm for response reconstruction under non-Gaussian noise,a non-Gaussian Kalman filter(NGKF)algorithm was proposed for structural response reconstruction.Firstly,L1 Kalman filter(L1KF)algorithm was introduced into structural response reconstruction,and the loss function in L1KF algorithm was reconstructed.Secondly,the coefficient matrices derived from loss function were used to penalize noise covariance matrices of state equation and observation equation,and make KF algorithm suitable for non-Gaussian noise.Finally,acceleration,velocity and displacement responses of the structure were calculated using limited amount of acceleration measurement signals and reconstruction equation.Both numerical simulation and overhanging beam tests showed that the proposed method can have good noise robustness when using only limited amount of acceleration sensors for structural response reconstruction,effectively reduce reconstruction errors and improve phenomena of larger deviations when using KF algorithm for response reconstruction under various non-Gaussian noises.
作者
祁义博
彭珍瑞
QI Yibo;PENG Zhenrui(School of Mechanical Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2024年第11期206-216,共11页
Journal of Vibration and Shock
基金
国家自然科学基金(62161018)。
