Auto-regressive model based input and parameter estimation for nonlinear finite element models

A novel framework to accurately estimate nonlinear structural model parameters and unknown external inputs (i.e., loads) using sparse sensor networks is proposed and validated. The framework assumes a time-varying auto-regressive (TAR) model for unknown loads and develops a strategy to simultaneously estimate those loads and parameters of the nonlinear model using an unscented Kalman filter (UKF). First, it is confirmed that a Kalman filter (KF) allows to estimate TAR parameters for a measured, earthquake, acceleration time-history. The KF-based framework is then coupled to an UKF to jointly identify unmeasured inputs and nonlinear finite element (FE) model parameters. The proposed approach systematically assimilates different structural response quantities to estimate TAR and FE model parameters and, as a result, updates the FE model and unknown external excitation estimates. The framework is validated using simulated experiments on a realistic three-dimensional nonlinear steel frame subjected to unknown seismic ground motion. It is demonstrated that assuming relatively low order TAR model for the unknown input leads to precise reconstruction and unbiased estimation of nonlinear model parameters that are most sensitive to measured system response.