Structural health monitoring (SHM) is an emerging technology designed to automate the inspection process undertaken to assess the health condition of structures. The SHM process is classically decomposed into four sequential steps: damage detection, localization, classification, and quantification. This paper addresses damage type classification and severity quantification issues as classification problems whereby each class corresponds to a given damage type or a certain damage extent. A Support Vector Machine (SVM) is used to perform multi-class classification task. Classically, Signal Based Features (SBF) are used to train SVMs when approaching SHM from a machine learning perspective. In this work, starting from the assumption that damage causes a structure to exhibit nonlinear response, it is investigated whether the use of Nonlinear Model Based Features (NMBF) increases classification performance. NMBF are computed based on parallel Hammerstein models which are identified with an Exponential Sine Sweep (ESS) signal. A study of the sensitivity of classification performance to the noise contained in output signals is also conducted. Dimension reduction of features vector using Principal Component Analysis (PCA) is carried out in order to find out if it allows robustifying the classification/quantification process suggested in this work. Simulated data on a cantilever beam with various damage types and severities as well as experimental data coming from a composite aeronautic plate with various damage severities generated with a unique and original laser process are considered for demonstration. For both application cases, results show that by introducing NMBF, classification performance is improved. Furthermore, PCA allows for high recognition rates while reducing features vector dimension. (C) 2018 Elsevier Ltd. All rights reserved.