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 (αf=0.43±0.37, corresponding to Hurst exponent H≈0.22) reflecting stable mechanical equilibrium, while faulted bearings demonstrate persistent regime (αf=1.18±0.39, H≈0.59) driven by periodic defect-induced excitation, with threshold crossing at αf=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 (η2=0.685, p=0.001) on naturally-degraded bearings, dramatically outperforming multifractal spectrum width (η2=0.087, p=0.579) despite both exhibiting genuine multifractality validated through rigorous MF-DFA (mean h(q) linearity R2=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.