Damage identification by the Kullback-Leibler divergence and hybrid damage index

The hybrid damage index (HDI) is presented as a mean for the damage identification in this paper, which is on the basis of the Kullback-Leibler divergence (KLD) and its approximations. The proposed method is suitable for detecting damage in one-dimensional structure and delamination in laminated composite. The first step of analysis includes obtaining the mode data of the structure before and after the damage, and then the KLD and its approximations are obtained. In addition, the HDI is obtained on the basis of the KLD and its approximations, utilizing the natural frequencies and mode shape at the same time. Furthermore, the modal strain energy (MSE) method is employed to verify the efficiency of the proposed method. Finally, to demonstrate the capability of the proposed method, examples of the beam and laminated composite are applied for checking the present approaches numerically, and the final results validate the effective and accurate performance of the present technique.