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. 1. Introduction As evidenced by the vast literature in the damage detection, the structural health monitoring has become an increasingly crucial issue. To data, significant efforts have been made by researchers in the damage identification. The presence of damage generally produces changes in the structural stiffness matrix. Meanwhile, these changes are accompanied with changes in the structural modal parameters. This phenomenon has been widely noted and used by researchers in distinguishing the damage. However, using different modal parameters correlated with other relevant information in the damage identification may get very various results with varying accuracy. For this reason, seeking a proper selection or combination of dynamic parameters is an imperative purpose. From the perspective of the damage detection, Park et al. [1] reviewed the piezoelectric impedance-based structural health monitoring and applied it in the damage detection of civil structural components [2]. Sekhar [3] provided an excellent review on research advances in damage detection areas over the twenty years. Fan and Qiao [4] reviewed vibration-based damage identification methods and gave a comparative study on the damage detection, and the strain-based damage index for the structural damage identification was reviewed by Li [5]; the recurrence quantification analysis has emerged as a useful tool for detecting subtle nonstationarities and changes in the time-series data; Nichols et al. [6] extended the recurrence quantification analysis method to multivariate observations for the damage detection. Sun et
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