Efficient structural damage detection via the l regularization and randomized extended Kaczmarz algorithm

Structural damage detection (SDD) is an important aspect of structural health monitoring. This study aimed to explore a new method IT omega -REK theta (omega = 1, 1/2; theta = 1,2,3) for SDD based on the l omega sparse regularization model and the randomized extended Kaczmarz (REK) type algorithms. When omega = 1/2, the l1/2 sparse regularization model was applied to enhance the ill-posedness of the damage identification problem and ensure the sparsity of the solution. The REK, theta = 1, partially randomized extended Kaczmarz (theta = 2), and fast maximum-distance extended Kaczmarz (theta = 3) algorithms with different threshold operators were used to solve the l omega regularization model. These algorithms could obtain optimal identification results and significantly improve computational efficiency by randomly and partially selecting the data of the sensitivity equations. Numerical and experimental studies on different structures showed that the proposed method could fast locate structural damage and accurately identify the damage extents, which was robust to the SDD problem with noise.