A novel approach to detect anomalies in superconducting radio-frequency cavities is presented, based on the parity space method with the goal to detect quenches and distinguish them from other anomalies. The model-based parity space method relies on analytical redundancy and generates a residual signal computed from measurable RF waveforms. The residual is a sensitive indicator of deviation from the model and provides different signatures for different types of anomalies. This new method not only helps with detecting faults, but also provides a catalogue of unique signatures, based on the detected fault. The method was experimentally verified at the European X-ray Free Electron Laser (EuXFEL). Various types of anomalies incorrectly detected as quenches by the current quench detection system are analysed using this new approach.