Nonlinear Identification of Lumped-Mass Buildings Using Empirical Mode Decomposition and Incomplete Measurement

Most structures exhibit some degrees of nonlinearity such as hysteretic behavior especially under damage. It is necessary to develop applicable methods that can be used to characterize these nonlinear behaviors in structures. In this paper, one such method based on the empirical mode decomposition (EMD) technique is proposed for identifying and quantifying nonlinearity in damaged structures using incomplete measurement. The method expresses nonlinear restoring forces in semireduced-order models in which a modal coordinate approach is used for the linear part while a physical coordinate representation is retained for the nonlinear part. The method allows the identification of parameters from nonlinear models through linear least-squares. It has been shown that the intrinsic mode functions (IMFs) obtained from the EMD of a response measured from a nonlinear structure are numerically close to its nonlinear modal responses. Hence, these IMFs can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known. Two procedures are developed for identifying nonlinear damage in the form of nonhysteresis and hysteresis in a structure. A numerical study on a seven-story shear-beam building model with cubic stiffness and hysteretic nonlinearity and an experimental study on a three-story building model with frictional magnetoreological dampers are performed to illustrate the proposed method. Results show that the method can quite accurately identify the presence as well as the severity of different types of nonlinearity in the structure.