Structural Damage Detection Based on Improved Sensitivity Function of Modal Flexibility and Iterative Reweighted lp Regularization

The l2 regularization is usually used to deal with the problems of under-determinacy and measurement noise for the conventional sensitivity-based model updating damage detection methods. However, the l2 regularization technique often provides overly smooth solutions and thus cannot exhibit the sparsity of the structural damage due to the promotion of the 2-norm term on smoothness. In the study, a structural damage detection method is proposed based on an improved modal flexibility sensitivity function and an iterative reweighted lp (IRlp) regularization. Specifically, the sensitivity function is established by introducing changes in the mode shapes into the derivative of eigenvalue and can be applied to identify the localized damage more accurately. Additionally, IRlp regularization is proposed to deal with the ill-posed problem of damage detection in a noisy environment. The proposed IRlp regularization is compared with the l1 and l2 regularizations through a numerical and an experimental examples. The numerical and experimental results indicate that the IRlp regularization can more accurately locate and quantify the single and multiple damages under the noise situation. The maximum identification errors are only 5.16% and 5.67%, respectively. Moreover, compared to the basic modal flexibility sensitivity function, the improved function is more sensitive to the damage. The maximum identification error of the improved function is less than 6%, while the relative errors are significantly larger in the basic function.