Recent advancements in sensing technologies have significantly enhanced the deployment of sensors for real-time monitoring of systems and structures. By integrating sensor data with numerical models, it is possible to create a digital twin of a structure that facilitates damage detection, localization, and control—potentially in real time. This study leverages experimental data from distributed optical fiber sensors (DOFS) within a modified dual Kalman filter (MDKF) framework for damage identification. The MDKF improves upon the classical Kalman filter by incorporating the modified constitutive relation error (mCRE), an effective identification functional that maintains physical relevance even in the presence of measurement noise. This leads to a robust and sequential methodology vital for the development of digital twins in engineering applications. The algorithm is employed on the measurement data acquired from a concrete beam that has been instrumented by optic fibers and has been subjected to 4-point bending test, in order to identify and localize damage using the Cartesian grid finite element method (CgFEM).