Detection, localization and quantification of damages in structures have received a considerable attention over the past two decades. These processes are utilized to decrease the probability of failure, improve the performance, and increase the useful lifetime of the structural systems. This thesis presents a number of basic techniques to detect, localize, and quantify multi-damage levels in damaged structures. First, the first three Markov parameters of the collocated multi-input/multi-output structure, before and after the presence of the damage, are used to examine how the system matrices change. The relationship between the change in the Markov parameter matrices and the change in the system matrices is shown. This method could also be used in on-line monitoring of the structures by recursive algorithms. Second, a new approach is presented for simultaneous assessment of the degree of damages in structures. Before and after a damage, some system digital pulse response data related tosome selected collocated sensor-actuator DOFs are used to assess the extension of damages. By this method, an Equivalent Virtual Damped Single Degree of Freedom (EVDSDOF) system is identified through the pulse responses extracted from the instrumented DOFs.Monitoring changes, in mass and stiffness properties, results in identifying the size of that damage. The Differential Evolution algorithm is used as an intelligent optimizer performing a curve fitting by introducing an EVDSDOF system.In the third place, an inverse problem is configured to compute the physical property matrices from the identified modal parameters. We obtain some elements of the mass matrix directly from the state-space model, and then we solve an optimization problem to find the full mass, stiffness, and damping matrices, without any assumption about either normalizing eigenvectors or orthogonality conditions.Two time-domain system identification algorithms, i.e., ERA/DC and SRIM, are comprehensively surveyed. Also, based on identified state-space models of an assembled structure and its substructures, a joint identification procedure is explained which may be utilized in order to joint monitoring. Eventually, depends on modal parameters extracted from structural testing, three approaches are explained for model-order reduction. Two methods find a reduced mass/stiffness/damping model where one of them realizes the characteristic equation of the reduced model; and the other decreases the modal energies of the reduced model. The third method reduced the identified modal matrix by curve fitting of frequency response function. Key Words: System Identification; Structural Health Monitoring; SRIM; ERA/DC; Markov Parameter; EVDSDOF; Model-Order Reduction; Structural Joint Identification.
