The motivation for this article is to propose new damage classifiers based on a supervised learning problem for locating and quantifying damage. A new feature extraction approach using time series analysis is introduced to extract damage-sensitive features from auto-regressive models. This approach sets out to improve current feature extraction techniques in the context of time series modeling. The coefficients and residuals of the AR model obtained from the proposed approach are selected as the main features and are applied to the proposed supervised learning classifiers that are categorized as coefficient-based and residual-based classifiers. These classifiers compute the relative errors in the extracted features between the undamaged and damaged states. Eventually, the abilities of the proposed methods to localize and quantify single and multiple damage scenarios are verified by applying experimental data for a laboratory frame and a four-story steel structure. Comparative analyses are performed to validate the superiority of the proposed methods over some existing techniques. Results show that the proposed classifiers, with the aid of extracted features from the proposed feature extraction approach, are able to locate and quantify damage; however, the residual-based classifiers yield better results than the coefficient-based classifiers. Moreover, these methods are superior to some classical techniques.