Damage identification of composite structures is a major ongoing challenge for a secure operational life-cycle due to the complex, gradual damage behaviour of composite materials. Especially for composite rotors in aero-engines and wind-turbines, a cost-intensive maintenance service has to be performed in order to avoid critical failure. A major advantage of composite structures is that they are able to safely operate after damage initiation and under ongoing damage propagation. Therefore, a robust, efficient diagnostic damage identification method would allow monitoring the damage process with intervention occurring only when necessary. This study investigates the structural vibration response of composite rotors by applying machine learning methods and the ability to identify, localise and quantify the present damage. To this end, multiple fully connected neural networks and convolutional neural networks were trained on vibration response spectra from damaged composite rotors with barely visible damage, mostly matrix cracks and local delaminations using dimensionality reduction and data augmentation. A databank containing 720 simulated test cases with different damage states is used as a basis for the generation of multiple data sets. The trained models are tested using k-fold cross validation and they are evaluated based on the sensitivity, specificity and accuracy. Convolutional neural networks perform slightly better providing a performance accuracy of up to 99.3% for the damage localisation and quantification.