Online damage detection via a synergy of proper orthogonal decomposition and recursive Bayesian filters

In this paper, an approach based on the synergistic use of proper orthogonal decomposition and Kalman filtering is proposed for the online health monitoring of damaged structures. The reduced-order model of a structure is obtained during an (offline) initial training stage of monitoring; afterward, effective estimations of a possible structural damage are provided online by tracking the evolution in time of stiffness parameters and projection bases handled in the model order reduction procedure. Such tracking is accomplished via two Kalman filters: a first (extended) one to deal with the time evolution of a joint state vector, gathering the reduced-order state and the stiffness terms degraded by damage; a second one to deal with the update of the reduced-order model in case of damage evolution. Both filters exploit the information conveyed by measurements of the structural response to the external excitations. Results are reported for a (pseudo-experimental) benchmark test on an eight-story shear building. Capability and performance of the proposed approach are assessed in terms of tracked variation of the stiffness terms of the reduced-order model, identified damage location and speed-up of the whole health monitoring procedure.