Damage identification of structural systems by modal strain energy and an optimization-based iterative regularization method

Sensitivity-based methods using modal data are effective and reliable tools for damage localization and quantification. However, those may fail in obtaining reasonable and accurate results due to low damage detectability of sensitivity functions and the ill-posedness problem caused by noisy modal data. To address these major challenges, this article proposes a new method for locating and quantifying damage by developing a new sensitivity function of modal strain energy and solving an ill-posed inverse problem via an optimization-based iterative regularization method called Iteratively Reweighted Norm-Basis Pursuit Denoising (IRN-BPD). A stopping condition based on the residual of the solution and an improved generalized cross-validation function are proposed to terminate the iterative algorithm of IRN-BPD and determine an optimal regularization value. The major contributions of this article include getting an idea from the first-order necessary condition of the optimization problem for deriving a sensitivity formulation and proposing a new regularized solution. The great advantages of these methods are increasing damage detectability, determining an optimal regularization value, and obtaining an accurate solution. A simple mass–spring system and a full-scale bridge structure are considered to verify the accuracy and effectiveness of the proposed methods in numerical studies. Results demonstrate that the methods presented in this article succeed in locating and quantifying damage under incomplete noisy modal data.