Multifractal characterization of bearing fault progression: Persistent-to-anti-persistent dynamics transition and cross-dataset validation of complexity-based features

Bearing vibration signatures during fault progression exhibit complex multiscale temporal correlations quantifiable through fractal and entropy-based analysis. We demonstrate systematic persistent-to-anti-persistent dynamics transition characterizing fault development through multifractal detrended fluctuation analysis (MF-DFA) and variogram-based fractal index analysis across 15 naturally-degraded bearings spanning 1217 operating hours from the Paderborn University dataset. Healthy bearings exhibit anti-persistent dynamics ( α f = 0 . 43 ± 0 . 37 , corresponding to Hurst exponent H ≈ 0 . 22 ) reflecting stable mechanical equilibrium, while faulted bearings demonstrate persistent regime ( α f = 1 . 18 ± 0 . 39 , H ≈ 0 . 59 ) driven by periodic defect-induced excitation, with threshold crossing at α f = 1 ( H = 0 . 5 ) providing universal degradation signature. Cross-dataset validation comparing artificial defects (Case Western Reserve University) against natural fault progression reveals classical amplitude-based features (RMS, kurtosis) suffer severe performance degradation (11.3-fold mean reduction, RMS: 19.7-fold), while complexity-based measures maintain robustness (2.4-fold degradation). Spectral entropy emerges as optimal diagnostic feature achieving large effect size for fault-type discrimination ( η 2 = 0 . 685 , p = 0 . 001 ) on naturally-degraded bearings, dramatically outperforming multifractal spectrum width ( η 2 = 0 . 087 , p = 0 . 579 ) despite both exhibiting genuine multifractality validated through rigorous MF-DFA (mean h ( q ) linearity R 2 = 0 . 963 ± 0 . 037 ). The persistent-to-anti-persistent transition represents a physics-based degradation criterion generalizable to rotating machinery systems exhibiting complexity reduction during fault progression, while benchmark bias quantification establishes mandatory cross-dataset validation before deployment certification in industrial condition monitoring applications.