Formulation of equation error estimator using measured displacement de-noised by temporal–spatial filter for system identification of elastic solids

Abstract

ABSTRACT This paper presents a new class of the equation error estimator using de-noised displacement by the temporal–spatial filter for the system identification in an elastic solid. The finite element method is employed to discretize the equation of motion for an elastic solid, and the Young’s modulus of each finite element is estimated by the proposed approach. The temporal–spatial filter is applied to de-noise measured nodal displacements and to reconstruct nodal accelerations. The equation of motion modified for the de-noised dynamic responses is derived, and the equation error estimator (EEE) for the system identification is defined with the modified equation of motion. The proposed EEE represents the residual error of the modified equation of motion over a measurement interval, and results in a nonlinear equation, which is solved by the successive substitution method. The sensitivity of the temporal–spatial filter required to solve the nonlinear equation is derived by the direction differentiation of the analytical expressions of the filter. The validity and accuracy of the proposed approach are tested through numerical simulation studies. It is shown that the proposed method yields accurate and stable solutions without regularization for all cases tested in this study.