A flexibility-based continuum damage identification approach

The present work presents a flexibility-based continuum damage identification approach. Here, it is considered that the current integrity state of a structure is described by means of a continuum damage model. This model enables one to parameterize the stiffness matrix of the finite element (FE) model of the system, such that, in an updating process, properties such as symmetry and sparsity of the original FE model are naturally preserved. The damage identification is accomplished by minimizing the Frobenius norm of the difference between the experimental and analytical flexibility matrix only related to the measured degrees of freedom (DOF) of the structure. By utilizing an error only related to the measured DOF one avoids the need for model expansion or model reduction, difficulties commonly present in the model updating process. The modal information required for the experimental flexibility matrix calculation are obtained by means of Eigensystem Realization Algorithm (ERA) and common-based structure identification (CBSI). The assessment of the present approach has been performed by means of simulations on a beam-like structure considering typical shortcomings occurring in real applications such as small number of sensors, different levels of signal to noise ratio and limited spectral information. It has also been analyzed the use of a regularization term in the error function to be minimized, in order to improve the performance of the proposed method.