Online damage detection in structural systems via dynamic inverse analysis: A recursive Bayesian approach

In this paper, a framework is presented for the joint state tracking and parameter estimation of partially observed structural systems characterized by a relatively large number of degrees of freedom. To pursue this aim in real-time, the order of the system is reduced via an optimal set of bases, or proper orthogonal modes (POMs) obtained through proper orthogonal decomposition. Since the aforementioned POMs are sensitive to damage, which is defined as a change in the stiffness of the structural model, the variation in the characteristics of the POMs themselves is also tracked online. Taking advantage of the linear relationship between the observation process and the components of the POMs, a solution to the whole problem is obtained with an extended Kalman filter or a hybrid extended Kalman particle filter for the joint tracking-estimation purposes, and with a further Kalman filter for the model update purposes. The efficiency of the proposed method is assessed through simulated experiments on a 8-story shear type building.