Performance of an observer state-space identification in the presence of mild nonlinearities

The Eigensystem Realization Algorithm with an Observer Kalman Filter (ERA-OKID) operates under the assumption that the system is linear and time invariant. Most practical engineering structures, however, behave in a nonlinear fashion to a certain extent. The aim of the investigation reported in this paper is to examine how the system parameters identified by the ERA-OKID algorithm vary as nonlinearity is introduced in the system that generates the response data. The paper presents a brief review of the ERA-OKID approach and discusses the results of two numerical examples. The first example is a two-dimensional, four-story shear building and the second is a three-dimensional building with plan eccentricity, also with four stories in elevation. In all cases, the excitation is taken as horizontal ground acceleration with bidirectionality considered in the three-dimensional case. In the cases considered, the nonlinear hysteretic behavior is reflected in an increase in the damping of the fundamental mode, with little effect on the identified eigenvalues. Identification of the underlying linear systems is shown possible using small amplitude data from the early part of the response. The difference between the response predicted with the realization obtained from the early portion and the computed response is explored as a potential source of information in characterizing the nonlinear behavior.