"This dissertation proposes a vibration-based approach to detect and monitor structural damage by tracking the instantaneous modal parameters. A change in the instantaneous modal parameters indicates change in the structural health condition. In contrast to many existing structural health monitoring schemes, the proposed approach is less model dependent and works well for both sudden and evolving damage, general loading conditions and complex structures. The instantaneous modal parameters, including modal frequency, mode shape vector and modal damping ratio, are introduced as a bridge between the system properties and time varying vibration modes. The theoretical background of the time-varying vibration modes is developed. It has been shown that for slowly time-varying systems such modes exist and the instantaneous modal parameters have a clear physical interpretation and can be identified from free and forced vibration responses. A set of known techniques are used in an innovative way to identify the instantaneous modal parameters. Applicability of the identification techniques depends on the nature and availability of measurement data. Wavelet ridge method is used to identify the instantaneous modal frequencies and normalized instantaneous mode shape vectors from free vibration data. Wavelet packet sifting technique in conjunction with Hilbert transform and confidence index is proposed to identify the normalized instantaneous mode shape vector from both free and forced vibration data. Time-varying Kalman filter is integrated with the wavelet packet sifting technique to identify the instantaneous modal frequencies and the instantaneous modal damping ratios from free and forced vibration data. The proposed approach has been validated using both simulation and experimental data. The simulation data is obtained from a multi-degree-of-freedom system with time varying stiffness under different loading conditions. Experimental data include both impact testing data from the ASCE benchmark study and shaking-table test data of a full-size two-story wooden building structure, conducted at DPRI, Kyoto University, Japan. It has been shown that the proposed approach can successfully detect and monitor damage and, therefore, has great potential for real applications."

"In this work an innovative wavelet packet based sifting process for signal decomposition has been developed and its application for health monitoring of time-varying structures is presented. With the proposed sifting process, a signal can be decomposed into its mono-frequency components by examining the energy content in the wavelet packet components of a signal, and imposing certain decomposition criteria. The method is illustrated for simulation data of a linear three degree-of-freedom spring-mass-damper system and the results are compared with those obtained using the empirical mode decomposition (EMD) method. Both methods provide good approximations, as compared with the exact solution for modal responses from a conventional modal analysis. Incorporated with the classical Hilbert transform, the proposed sifting process may be effectively used for structural health monitoring by monitoring instantaneous modal parameters of the structure for both, cases of abrupt structural stiffness loss and progressive stiffness degradation. The effectiveness of this method for practical application is evaluated by applying the methodology for experimental data and the results obtained matched with the field observations. The proposed methodology has shown better results in a comparison study which is done to evaluate performance of the proposed approach with other available SHM techniques, namely EMD technique and Continuous Wavelet Transform (CWT) method, for cases characterized by different damage scenarios and noise conditions."