Intrinsic localized modes (ILMs) are localized vibrational responses that may occur in a variety of nonlinear periodic systems. Many investigations have characterized the existence and stability of ILMs and they have been realized in systems representing numerous domains and length scales. Previous studies indicate that ILMs strongly interact with an impurity via attraction or repulsion from the damage location. In this research to exploit such phenomena for structural damage identification, we analyze the interaction of an ILM with multiple impurities, where a steered impurity strategically guides the ILM towards another, static impurity representative of damage. We discover and catalog the distinct phenomenological interaction types between steered ILMs and damage. For some interaction types, the ILM propagation rate temporarily exceeds a threshold, a behavior that is shown to consistently coincide with ILM interaction with damage (the static impurity). The quantitatively distinct interaction types are used to devise a method to effectively identify damage in the nonlinear periodic structure. Numerous studies are performed to assess the viability and accuracy of the proposed damage identification method and to examine its robustness to random structural heterogeneity. Beyond stiffness change, the proposed method is applicable to monitoring other system characteristics, such as changing mass or multi-field features, which may be representative of damage or static impurity.