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: detection, localization, classification, and quantification. In this paper, SHM quantification step is addressed. Particularly, we approach delamination quantification as a classification problem whereby each class corresponds to a certain damage extent. Starting from the assumption that damage causes a structure to exhibit nonlinear response, we investigate whether the use of nonlinear model based features increases classification performance. A support Vector Machine (SVM) is used to perform multi-class classification task. Two types of features are used to feed the SVM algorithm: Signal Based Features (SBF) and Nonlinear Model Based Features (NMBF). SBF are rooted in a direct use of response signals and do not consider any underlying model of the test structure. NMBF are computed based on parallel Hammerstein models which are identified with an Exponential Sine Sweep (ESS) signal. Dimensionality reduction of features vector using Principal Component Analysis (PCA) is also carried out in order to find out if it allows robustifying the quantification process suggested in this work. Experimental results on Carbon Fiber Reinforced Polymer (CFRP) composite plates equipped with piezoelectric elements and containing various delamination severities are considered for demonstration. Delamination-type damage is introduced into samples in a calibrated way using Laser Shock Wave Technique (LSWT) and more particularly symmetrical laser shock configuration. LSWT is chosen as an alternative to conventional damage generation techniques such as conventional impacts and Teflon inserts since it allows for a better calibration of damage in type, depth and size. Results show that by introducing NMBF, classification performance is improved. Furthermore, PCA allows for higher recognition rates while reducing features vector dimension.