Damage detection by finite element model updating using modal flexibility residual

A sensitivity-based finite element (FE) model updating is carried out for damage detection in this paper. The objective function consisting of the modal flexibility residual is formulated and its gradient is derived. The optimization algorithm used to minimize the objective function and damage detection procedures are explained. The proposed procedure is firstly illustrated with a simulated example of the simply supported beam. The effect of noise on the updating algorithm is studied. It is demonstrated that the behavior of proposed algorithm on noise is satisfactory and the identified damage patterns are good. Afterwards, the procedure is applied for the tested reinforced concrete beam, which is damaged in the laboratory. Despite all the elements in the FE model are used as updating parameters which is considered as the extreme adverse condition in FE model updating, the identified damage pattern is comparable with those obtained from the tests. It is verified that the modal flexibility is sensitive to damage and the proposed procedure of FE updating using the modal flexibility residual is promising for the detection of damaged elements.