Structural health monitoring (SHM) is an emerging technology designed to automate the inspectionprocess undertaken to assess the health condition of structures. The SHM process is classically decom-posed into four sequential steps: damage detection, localization, classification, and quantification. Thispaper addresses damage type classification and severity quantification issues as classification problemswhereby each class corresponds to a given damage type or a certain damage extent. A Support VectorMachine (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, start-ing from the assumption that damage causes a structure to exhibit nonlinear response, it is investigatedwhether the use of Nonlinear Model Based Features (NMBF) increases classification performance. NMBFare computed based on parallel Hammerstein models which are identified with an Exponential SineSweep (ESS) signal. A study of the sensitivity of classification performance to the noise contained in out-put 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 processsuggested in this work. Simulated data on a cantilever beam with various damage types and severitiesas well as experimental data coming from a composite aeronautic plate with various damage severitiesgenerated with a unique and original laser process are considered for demonstration. For both applicationcases, results show that by introducing NMBF, classification performance is improved. Furthermore, PCAallows for high recognition rates while reducing features vector dimension.