System identification and damage detection of structures with unknown excitations

System identification and damage detection, based on measured vibration data, have received considerable attention recently. Frequently, the damage of a structure may be reflected by a change of some parameters in structural elements, such as a degradation of the stiffness. Hence it is important to develop data analysis techniques that are capable of detecting the parametric changes of structural elements during a severe event, such as the earthquake.; Time domain analysis methodologies based on measured vibration data, such as the least squares estimation and the extended Kalman filter, have been studied and shown to be useful for the on-line tracking of structural damages. The traditional recursive least squares estimation (RLSE) and extended Kalman filter (EKF) require that all the external excitation data (input data) be measured or available, which may not be the case for many structures. The purpose of this dissertation is to propose an adaptive recursive least squares estimation with unknown inputs (excitations) and an adaptive extended Kalman filter with unknown inputs (excitations), to identify the structural parameters, such as the stiffness, damping and other nonlinear parameters, the variation of structural parameters due to damages and the unmeasured excitations.; In this dissertation, analytical recursive solutions for the proposed recursive least squares estimation with unknown inputs (RLSE-UI) and extended Kalman filter with unknown inputs (EKF-UI) are first derived and presented. An adaptive tracking technique recently developed is implemented in the proposed approaches to track the variations of structural parameters due to damages. Simulation results based on linear and nonlinear structures, as well as plane frames with finite-element model (FEM) demonstrate that the proposed approaches are quite effective and accurate in: (i) identifying the structural parameters, (ii) tracking the variations of these parameters due to damages, and (iii) identifying the unknown external excitations.