基于增秩Kalman滤波的动态荷载识别和结构响应重构

针对传统的荷载识别方法受不适定性问题影响导致识别误差较大，且受传感器数上的限制也无法监测所有结构易损伤位置处振动响应的问题，提出了一种基于增秩Kalman滤波（augmented Kalman filter, AKF）算法的动态荷载识别和结构响应重构方法.基于结构状态空间方程，形成由荷载向量和状态向量组成的增秩状态向量（augmented-rank state vector,ASV），利用Kalman滤波算法获得增秩状态向量的最小方差无偏（minimum variance unbiased， MVU）估计，实现了状态和荷载向量的同时识别.结合最优状态估计和观测矩阵，实现了未布置传感器处的结构动力响应重构.通过三个有限元案例，初步验证了该方法的可行性和有效性.结果表明，当荷载位置固定或移动时，所提方法均能有效地识别荷载和重构响应，精度较高且对测量噪声不敏感.传感器的种类、数量和布置位置对荷载识别和响应重构精度会有一定影响.

Dynamic Load Identification and Structural Response Reconstruction Based on the Augmented Kalman Filter

For traditional load identification methods the ill-posedness problem brings about relatively large errors, and due to the insufficiency of monitoring sensors, the structural vibration responses at the damage points can’t be exhaustively monitored. Therefore, an augmented Kalman filter (AKF) algorithm-based dynamic load identification and response reconstruction method was proposed. Based on the structural state space formulation, the load vector and the state vector were combined into the augmented-rank state vector（ASV）, and the Kalman filter algorithm was employed to obtain the minimum-variance unbiased (MVU) estimation of the augmented state vector to realize the simultaneous identification of the state and the load vectors. Furthermore, the dynamic response reconstruction of the structure parts without sensors was realized through combination of the optimal state estimation and the observation matrix. Three finite element cases were studied to verify the feasibility and effectiveness of the proposed method. The results show that, this method can well identify the load and reconstruct the response regardless of moving or fixed loads with high accuracy, and is insensitive to measurement noise. The types, the number and the locations of the sensors have some impact on the accuracy of load identification and response reconstruction.