A Physics-Informed Stability-Driven Approach to Wavelet Packet Band Selection for Crack Severity Classification Across Operating Conditions

Accurate crack severity classification in rotating shafts remains a challenging task due to the strong spectral overlap between adjacent damage levels and the absence of distinct fault-specific frequency components. In such conditions, conventional vibration-based approaches relying on global spectral descriptors often fail to provide sufficient discriminatory information. This work proposes a stability-driven multi-resolution framework for crack severity classification based on the Wavelet Packet Transform (WPT). The approach aims to identify frequency bands that exhibit consistent diagnostic relevance across multiple decomposition levels while maintaining a monotonic relationship with crack severity. To this end, an interpretability-driven analysis based on Random Forest feature importance is combined with a frequency stability criterion and a monotonicity constraint, enabling the selection of physically meaningful and consistent spectral regions. The proposed framework has been evaluated on vibration data acquired from a rotating shaft test bench under multiple operating speeds and damage conditions. The results have shown that crack progression is characterised by distributed energy variations across specific frequency regions rather than by the emergence of isolated spectral peaks. It can be concluded that the proposed stability-driven band selection approach enables the identification of these regions in a consistent manner across spectral resolutions and operating conditions. Furthermore, the integration of WPT-based features with conventional time- and frequency-domain descriptors leads to a hybrid multi-scale representation that improves classification performance, particularly in intermediate severity regimes where spectral overlap is most pronounced. Overall, the proposed methodology provides a physically interpretable and consistent framework for vibration-based crack severity classification, with potential applicability to a wide range of rotating machinery diagnostics problems.