An effective approach for damage identification in beam-like structures based on modal flexibility curvature and particle swarm optimization

In this paper, a computationally simple approach for damage localization and quantification in beam-like structures is proposed. This method is based on using modal flexibility curvature (MFC) and particle swarm optimization (PSO) algorithm. Analytical studies in the literature have shown that changes in the modal flexibility curvature can be considered as a sensitive and suitable criterion for identifying damage in the beam-like structures. Modal flexibility curvature can be calculated utilizing central difference approximation, based on entries of the modal flexibility matrix. The PSO algorithm, as a powerful optimization tool, is used to minimize the error function which is formulated as an error function between the measured modal flexibility curvatures of the damaged structure and those calculated from the analytical structure. To demonstrate the efficiency of the method, two beam-like structures under different damage scenarios are studied. In addition, the robustness of presented method is investigated when only the first several modal data are available. It is observed that the proposed approach is able to localize and quantify various damage cases only by a few lower vibrational modes and also, it is low-sensitive to measurement noise.