An adaptive extended Kalman filter for structural damage identifications II: unknown inputs

After a major event, such as a strong earthquake, a rapid assessment of the state (or damage) of the structure, including buildings, bridges and others, is important for post-event emergency responses, rescues and management. Time domain analysis methodologies based on measured vibration data, such as the least squares estimation and the extended Kalman filter (EKF), have been studied and shown to be useful for the on-line tracking of structural damages. The traditional EKF method requires that all the external excitation data (input data) be measured or available, which may not be the case for many structures. In this paper, an EKF approach with unknown inputs (excitations), referred to as EKF-UI, is proposed to identify the structural parameters, such as the stiffness, damping and other nonlinear parameters, as well as the unmeasured excitations. Analytical solution for the proposed EKF-U1 approach is derived and presented. Such an analytical solution for EKF-UI is not available in the previous literature. An adaptive tracking technique recently developed is also implemented in the proposed EKF-UI approach to track the variations of structural parameters due to damages. Simulation results for linear and nonlinear structures demonstrate that the proposed approach is capable of identifying the structural parameters, their variations due to damages, and unknown excitations. Copyright (c) 2006 John Wiley & Sons, Ltd.