Validated chaos theory for robust bearing fault diagnosis

Abstract Bearing fault diagnosis is essential for preventing catastrophic failures in rotating machinery, yet traditional linear methods fail to capture nonlinear fault dynamics. This work integrates chaos theory, multifractal analysis, and machine learning with rigorous theoretical and robustness validation. From vibration data, we extract comprehensive nonlinear features quantifying dynamical complexity. Rigorous validation proves genuine chaos: surrogate testing ( p < 0.001), 0–1 test ( K > 0.7), and Lyapunov analysis (73.4% positive exponents) converge mathematically. Perfect test classification (100%, 12/12) validates feature quality, while leave-one-bearing-out cross-validation demonstrates realistic generalization (83.2%) on unseen equipment without calibration. The framework maintains extreme industrial robustness: 86.54% accuracy at 0 dB signal-to-noise ratio, 89.62% with 30% missing data, and > 76% with three sensor groups failed. Real-time processing (8.3 ms) enables deployment in industrial monitoring. Novel contributions: first rigorous chaos validation in bearing diagnostics; transparent dual-reporting distinguishing controlled (100%) from realistic (83.2%) performance; comprehensive industrial robustness; edge deployment capability.