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Improved Kalman filter damage detection approach based on l p regularization
Author(s) -
Huang Jiezhong,
Li Dongsheng,
Zhang Chun,
Li Hongnan
Publication year - 2019
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.2424
Subject(s) - extended kalman filter , tikhonov regularization , regularization (linguistics) , inverse problem , backus–gilbert method , norm (philosophy) , optimization problem , kalman filter , mathematical optimization , mathematics , control theory (sociology) , regularization perspectives on support vector machines , computer science , algorithm , artificial intelligence , mathematical analysis , political science , law , control (management)
Summary The conventional extended Kalman filter (EKF) for detecting structural damage with measured responses is a dynamic inverse problem. With the increase in size of the extended state vector, EKF suffers from low accuracy and convergence difficulty due to the ill‐condition of the inverse problem and increased computational error. To overcome the aforementioned drawbacks, an improved EKF method based on l p regularization (EKF‐ l p ) is proposed in this paper. In the proposed method, the sparse characteristic on the distribution of local damage, as a priori information, is introduced into EKF by the l p regularization technique. Then, the unconstrained optimization problem of EKF becomes the optimization problem with the l p ‐norm constraint. To obtain a recursive solution of the constrained optimization, a pseudo‐measurement equation is used to embed the l p ‐norm constraint into the recursive EKF steps. In addition, a precise integration method is employed in the time update step to improve the accuracy of state prediction. To select an appropriate p value in the EKF‐ l p method, a novel L‐surface approach is proposed. Finally, the proposed EKF‐ l p method is compared with the existing EKF with Tikhonov regularization method and EKF with l 1 regularization method on a beam example and an experiment of a three‐story shear building. It is shown that the proposed method is stable and reliable, and its identification precision is higher than the other methods. Moreover, it requires significant less measurements than conventional methods.