Multiscale symbolic hellinger spectral entropy: A novel nonlinear metric for feature extraction of mechanical signals

Entropy-based methods have been widely used for feature measurement and condition assessment of mechanical vibration signals. Addressing the instability of traditional entropy measures in noisy environments and the limited ability of classical spectral entropy to characterize subtle spectral structure changes, this paper proposes a nonlinear spectral-structure divergence measure termed Symbolic Hellinger Spectral Entropy and its multiscale extension. This method first maps spectral information to symbol sequences through energy weighting and an adaptive quantile strategy. Then, it utilizes Hellinger distance to quantify the differences between symbol probability distributions, thereby quantifying the non-uniformity of symbolic spectral probability distributions. To further improve robustness and nonlinear separability, a logarithmic mapping is introduced to stabilize and smooth feature representations. Experimental results show that SHSE exhibits competitive and stable performance compared with the evaluated baseline entropy methods in data length sensitivity, consistency, and noise robustness. By combining multi-scale analysis and the SOFBIS classifier, the proposed intelligent diagnostic framework achieves stable and satisfactory results on three typical wind turbine datasets and a real factory bearing dataset. It is worth noting that under low signal-to-noise ratio conditions, MSHSE provides stronger discriminative features than traditional entropy methods on the tested datasets, providing an efficient and robust solution for the detection, extraction, and diagnosis of fault features in rotating machinery in noisy environments.