Damage identification from static tests by eigenparameter decomposition and sparse regularization

Identifying the damages from test data is central to assuring the structural safety. The static model is the simplest model to describe the mechanical behavior of the structure where only the stiffness is involved and it is independent of the mass and the complex damping. As a result, damage identification based on the static data will not be deteriorated by the inexact damping and the possible error in the mass. Notwithstanding, the major difficulty regarding damage identification with static test data is that the amount of the static data is quite limited and insufficient with respect to the amount of damage parameters, rendering the identification very sensitive to the measurement noise. Attempting to circumvent this difficulty, a novel damage identification approach is developed in this article where the sparse regularization is introduced to implicitly enforce the sparsity constraint of the damage locations. Moreover, in order to work well with the sparse regularization, a new goal function is established by resorting to the eigenparameter decomposition for which the decoupling feature would make the sparse regularization be tackled immediately with closed-form solutions. Then, the alternating minimization approach is used to get the solution of the new goal function and the threshold setting method is simply called to determine a proper regularization parameter. Numerical and experimental examples are studied to testify the feasibility, accuracy, and robustness of the proposed damage identification approach.