We extend the Bloch wave-based reduced order models in the Wave Finite Element Method (WFEM) framework for fast wave-damage interaction analysis. It aims at fault detection and diagnosis of periodic structures. A finned tube heat exchanger, which can be seen as a 1D system, is used as a numerical application. Reduced model results and performance are compared to a standard WFEM model. Diffusion curves are obtained more than a hundred times faster with the proposed scheme, moving toward massive generation of wave-damage scenarios and indicators to perform damage detection.