基于移动窗卡尔曼滤波算法的结构响应重构

Structural response reconstruction based on moving window Kalman filtering algorithm

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。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。

Here,to overcome the problem of using traditional Kalman filtering(KF)algorithm needing known measurement noise variance and process noise variance and assuming they being constant when reconstructing a structure’s unmeasured point response,a structural response reconstruction method based on moving-window Kalman filtering(MWKF)algorithm was proposed.The feature of this method was not needing to set variances of measurement noise and process noise according to experience in advance.Firstly,the moving-window technique was used to estimate variances of measurement noise and process noise in real time.Then,based on KF algorithm,responses of structure at positions without sensors were reconstructed by using response information of limited measuring points.Finally,a plane single-span frame structure was taken as an example to do numerical simulation and test analysis.The analysis results showed that the proposed method can be used to effectively estimate measurement noise variance and process noise variance in real time;the reconstructed dynamic response time history of unmeasured points agrees well with the calculated response time history or the measured one.