The paper aims to extend the definition of Digital Twin (DT) concept to be able to identify small severity damages by incorporating mathematical formulations in construction of neural networks. Advanced modelling techniques such as Reduced Basis (RB) method and artificial neural networks were used during the offline stage to develop a DT model to detect abnormal changes in structural behaviour during the online monitoring stage. Finite element model was used with RB model order reduction technique for construction of a low-dimensional space to speed the analysis during the online stage. Different damage scenarios were implemented by reducing the effective stiffness of several structural members to test the ability of the established DT model to detect damages once they have appeared in the structure. In addition, the RB model was used to choose the optimal location of displacement sensors in a physical structure. The RB model was validated against experimental test results for a two-dimensional truss. A neural network was developed and trained to identify the location of damage once it has appeared during the operational stage. The constructed RB model was used again for identification of severity of damage identified by the optimized neural network. It was found that the developed method showed high accuracy in identifying small severity damages during the online stage.