In this article, newmethods for detecting damage in structural systems are presented. These methods are categorized as damage localization and damage quantification, respectively. Hence, direct changes of modal strain energy are applied to identify locations of damage. Moreover, some restraints such as incomplete measured modes and simple assumptions in structural modeling may cause failure in the results of damage localization. Therefore, a correlation-based method is utilized to obviate these limitations and precisely detect damage sites. Subsequently, an improved sensitivity of modal strain energy is generated to determine damage severities. To achieve appropriate results in damage quantification, Tikhonov regularization approach is utilized instead of classical methods such as applying penalty function and current inverse problem techniques. Applicability and effectiveness of proposed methods are numerically verified using two practical examples consisting of a planner truss and a portal frame, respectively. Eventually, numerical results indicate that the proposed damage localization approach provides an influential algorithm for precisely identifying damage sites. Furthermore, obtained damage severities show that utilizing the sensitivity of modal strain energy and also solving the damage equation by Tikhonov regularization makes it possible to accurately determine damage extents in the case of incomplete modal data.

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