Identification of hysteretic dynamic systems by using hybrid extended kalman filter and wavelet multiresolution analysis with limited observation

The availability ofmethods for the identification of nonlinear hysteretic systems is crucial for the assessment of the health and the repair of civil infrastructures during and after severe earthquakes. However, most methods used to identify hysteretic systems suffer from two problems: (1) the structural responses at all dynamic degrees of freedom(DOFs) must be measured, which is obviously impractical for real applications; and (2) the nonlinear model of a system is assumed to be known, and only the model parameters are to be identified, meaning that the nonlinear characteristics of the underlying structures may not be captured accurately. To overcome these two problems, this paper proposes a novel method that does not assume a nonlinear model and that does not require measurements at all DOFs. The new approach alternately uses the extended Kalman filter (EKF) and wavelet (W) multiresolution analysis. Within each time step, the identification can then be divided into two stages. In stage one, based on limited-state observations and the structural model at previous step, the structural responses at all DOFs are estimated using the EKF method. In stage two, based on the estimated full states, wavelet multiresolution analysis is used to identify the tangent stiffness matrix and the hysteresis-restoring force curves of the structure (i.e., the structural model is updated using the estimated full states). Two model structures with various nonlinearities at different locations, and with various state-observation schemes, are employed to conduct the numerical study. The numerical results verify the efficiency and accuracy of the proposedmethod. The best location for state observation is also discussed in the numerical study.