Simultaneous excitation and parameter identification for non-linear structural systems

In this paper, an algorithm is proposed for simultaneous excitation and parameter identification for non-linear system in state space. The algorithm is based on the sequential application of extended Kalman estimator for non-linear structural parameters and the weighted least squares estimation for unknown excitations. The state and parameter are reformed into the augmented state, and the state space equations are non-linear associated with the augmented state. With the first-order Taylor expansion for nonlinear system and approximately linear minimum-variance unbiased estimation, a recursive algorithm is derived where the identification of the augmented state and the excitation are interconnected. Two numerical examples which identify uncertain parameters of a 3-DOF Duffing-type system and a four-story hysteretic shear-beam building subject to unknown random excitation respectively, are conducted to demonstrate the effectiveness of the proposed approach.