基于新息自适应卡尔曼滤波算法的多类型结构响应重构

Multi-type structural response reconstruction based on innovation adaptive Kalman filtering algorithm

为改善传统卡尔曼滤波KF(Kalman filter)算法在过程噪声方差和测量噪声方差未知的情况下响应重构精度降低甚至发散的问题,提出了一种基于新息自适应卡尔曼滤波IAKF(innovation-based adaptive Kalman filter)算法的多类型响应重构方法。首先根据新息统计特性对卡尔曼滤波增益和状态估计误差协方差矩阵进行实时自适应调整;然后利用有限测点的加速度传感器的测量数据,结合模态法对结构各个位置的加速度、速度、位移以及应变进行响应重构;最后对起重机桁架和简支梁分别进行数值模拟和试验分析。结果表明,该方法能够有效地调整过程噪声方差并估计测量噪声方差,未测点的重构响应时程曲线与计算响应或测量响应时程曲线吻合良好。

In order to improve the problem of low reconstruction precision and even divergence when the process noise variance and measurement noise variance are unknown in the traditional Kalman filter(KF)algorithm,a multi-type response reconstruction method based on the innovation-based adaptive Kalman filter(IAKF)algorithm is proposed.Firstly,the Kalman filter gain matrix and state estimation error covariance matrix are adjusted according to the statistical characteristics of innovation.Then,the acceleration,velocity,displacement and strain of each position of the structure are reconstructed using the measurement data of the acceleration sensors at a limited number of measuring points and combined with the modal method.Finally,the numerical simulation and experimental analysis are carried out on crane truss and a simply supported beam respectively.The results show that the method can effectively adjust the process noise variance and estimate the measurement noise variance,and the reconstructed response time-history curves of the unmeasured points are in good agreement with the calculated response time-history curves or the measured response time-history curves.