Includes abstract. ; Includes bibliographical references (leaves 108-112). ; Literature was reviewed with an aim to identify research needs in vibration based damage detection techniques and the quantification of the uncertainty in these techniques. It was discovered that the literature lacked examples of the explicit propagation of measurement uncertainty through damage detection algorithms. Instrumentation errors and variable environmental and operational conditions were identified as sources of uncertainties. It was established that in order to ensure reliability of the damage detection techniques and to assess their robustness, a damage detection framework which, accounting for sources of error in the measurements, propagates the uncertainty through the algorithms of the damage detection techniques. Standard methods of uncertainty quantification and propagation were reviewed and summarized, thus identifying the tools available for developing the desired framework for the inclusion of uncertainty quantification in damage detection techniques. Frameworks for the application of non-model-based vibration-based damage detection techniques, incorporating uncertainties, were developed. The frameworks consisted of data collection, feature extraction, feature discrimination and damage diagnosis with a quantitative measure of confidence in the diagnosis. The adopted feature extraction technique consisted of an algorithm that compared the residual errors of an ARX model fitted to a reference dynamic system with the residual errors of the same model fitted to a potentially damaged dynamic system. The damage-sensitive feature was chosen as the ratio between the standard deviation of the residual errors for the ARX model applied to the reference data and the standard deviation of the residual errors when the same model is fitted to data from an unknown structural state. Two feature discrimination techniques were investigated, namely a probability density approach and an outlier analysis approach. These feature discrimination techniques were statistical models that involved Monte Carlo simulations for uncertainty quantification. The frameworks for the application of non-model-based vibration-based damage detection techniques, incorporating uncertainties, were tested using experimental data. The test structures were steel-reinforced concrete beams. Damage was gradually introduced into the beams by the accelerated corrosion of their steel reinforcement. Vibration tests were conducted on the beams at various degrees of corrosion and different core temperatures of the beams. The results of the application of the proposed damage detection frameworks to the test data revealed a high correlation between the degree of corrosion and the probability that the structure was damaged. The chosen damagesensitive feature proved to be insensitive to changes in the core temperature of the beams. It was concluded that the ARX damage detection technique was capable of detecting the damage brought about by corrosion of the longitudinal steel reinforcement in concrete beams. By including uncertainty quantification, the damage detection frameworks proposed in this thesis were able to output quantitative measures of the certainty in their diagnoses. The frameworks accounted for instrumentation errors and errors due to changes in temperature. They can however be generalised to account for other environmental and operational effects by developing a comprehensive reference database of the adopted damage sensitive features. Civil infrastructure suffers from subtle and complex forms of damage, such as the deterioration brought about by steel reinforcement corrosion in concrete structures and due to the problems brought about by uncontrollable environmental and operational conditions. The frameworks developed in this thesis for the detection of damage address these complexities and are therefore applicable to the structural health monitoring of civil infrastructure.