Composite overwrapped pressure vessels are increasingly used for hydrogen storage because of their lightweight construction. Ensuring their structural integrity therefore becomes an important requirement for safe operation. Ultrasonic guided waves are well suited for this task because they are highly sensitive to structural changes in thin-walled pressure vessels. In this work, we developed a machine learning framework based on interpretable Best Daubechies Wavelet features and k-Nearest Neighbors novelty detection. The framework identifies a persistent transition in the UGW response during overpressurization that is indicative of a permanent structural change and occurs prior to burst failure. It was validated using measurements acquired from a real-world pressure vessel. For the a priori selected sensor pair 11–12, located in the highly stressed cylindrical section, the method achieved a balanced accuracy of 98.28% and a true negative rate of 100%. In addition, the proposed methodology identified the pressure level at which the persistent structural transition first became detectable and showed that this transition remained detectable after the vessel had returned to its normal operating pressure.