基于改进稀疏正则化的扩展卡尔曼滤波损伤识别研究

基于传统扩展卡尔曼滤波方法（EKF）的损伤识别过程是一个典型的反问题求解，反问题的不适定性使EKF识别结果容易受噪声干扰，导致EKF算法收敛困难、识别精度下降。基于l₁正则化的EKF算法在一定程度上可以缓解此问题，但其不能获得足够准确的稀疏解。为此，提出了一种改进稀疏正则化的EKF方法。该方法采用Arctangent罚函数代替l₁范数以施加损伤稀疏性约束；通过伪测量技术将稀疏性约束嵌入到EKF中，获得施加约束方程后的递推解。采用3层剪切结构和悬臂梁2个试验算例验证了该方法的有效性。研究结果表明：即使在噪声干扰下，所提方法也可以准确识别出结构损伤；相比传统l₁正则化EKF方法，该方法需要的观测信息更少，能获得更准确的稀疏解。

Structural Damage Identification Based on Improved Sparse Regularization Extended Kalman Filter

Damage identification based on the conventional extended Kalman filter (EKF) was a typical inverse problem. Due to the ill-posedness of the inverse problem, the identification results of EKF were susceptible to noise interference, which caused the convergence difficulty and low identification accuracy of EKF algorithm. The EKF algorithm based on l₁ regularization can alleviate this problem to a certain extent, but it cannot obtain a sufficiently accurate sparse solution. Therefore, a novel EKF method based on improved sparse regularization was proposed in this paper. In the proposed method, the Arctangent penalty function was used to introduce damage sparsity constraint into EKF by replacing ||·||₁ with a function Arctangent. Then, to obtain an EKF recursive solution, a pseudo-measurement equation was used to embed the sparsity constraint into EKF. To verify the effectiveness of the proposed algorithm, two experiment examples were employed:a three-story shear structure and a cantilever beam structure. The results show that, even if the noise interference exists, the proposed method can achieve an accurate damage identification. Compared with the conventional l₁ regularized EKF method, the proposed method requires less observation information and can obtain a sparser solution.