改进的强追踪平方根无迹卡尔曼滤波时变结构参数识别

Time-varying structural parametric identification with MSTSRUKF

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(MSTSRUKF)方法。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。

Time-varying structural parameter identification under earthquake is always concerned by researchers.Traditional extended Kalman filter(EKF)and unscented Kalman filter(UKF)have problems of lower tracking and recognition ability of time-varying structural parameters,and numerical instability caused by matrix singularity during extracting the square root matrix of covariance matrix.Here,based on the square root unscented Kalman filter(SRUKF),a modified strong tracing square root unscented Kalman filter(MSTSRUKF)algrithm was proposed.Firstly,QR decomposition method was used to improve the method of extracting the square root matrix of covariance matrix in SRUKF,and make the calculation process be unconditional numerical stable.Secondly,the method to calculate the square root matrix of covariance matrix was modified in filtering update.Meanwhile,the equivalent form of observation matrix was introduced to ensure the stability of the proposed algorithm,and avoid solving Jacobian matrix of complicated system.Finally,the strong tracking filter technique was introduced to update the time prediction covariance matrix,and make the proposed algorithm have the ability to track time-varying parameters.Numerical analysis results showed that the proposed MSTSRUKF algorithm can effectively identify mutation parameters of linear and nonlinear systems,and more accurately predict the structural state;MSTSRUKF can have numerical stability in calculation and stronger anti-noise ability.