FE-aided Kalman Filter for nonlinear state estimation with unknown input

A Kalman Filter-Finite Element (KF-FE) framework for joint input-state estimation of nonlinear systems is proposed in the current study. The KF-FE framework has been developed aiming to estimate the nonlinear structural behavior induced by excessive loading such as earthquake-induced ground motions or strong waves, during which a limited number of responses can be measured. The proposed framework involves the use of a Bayesian recursive filter, namely the Kalman Filter, in conjunction with a nonlinear Finite Element (FE) model, which allows to update the state space model formulation at each time step. The proposed KF-FE framework builds its novelty for nonlinear systems on the basis of existing methods for online state estimation of linear systems. The application of such a framework can be suitable for nonlinear state estimation when only output measurements are available. A numerical testbed is adopted herein consisting of a 2D steel moment resisting frame structure subjected to earthquake ground motions. The KF-FE results from the nonlinear numerical analysis scheme indicate estimation performance of high accuracy for both global (e.g., nodal displacements and rotations) and local (moment-curvature relationships) demand parameters while the computational cost is kept low.