What question did this study set out to answer?

The research aims to improve bearing fault diagnosis by integrating chaos theory and machine learning to capture nonlinear dynamics.

March 29, 2026Journal of the Brazilian Society of Mechanical Sciences and Engineering1 citationsOpen Access

Validated chaos theory for robust bearing fault diagnosis

PAPaulo R. L. AlmeidaUniversidade Federal da Paraíba TLThyago L. V. LimaInstituto Federal de Educação Ciência e Tecnologia da Paraíba ABAlisson V. BritoUniversidade Federal da Paraíba

Key Points

The research aims to improve bearing fault diagnosis by integrating chaos theory and machine learning to capture nonlinear dynamics.
Integrated chaos theory and multifractal analysis with machine learning.
Extracted nonlinear features from vibration data for analysis.
Utilized surrogate testing, 0–1 test, and Lyapunov analysis for validation.
Conducted leave-one-bearing-out cross-validation for generalization assessment.
Tested the robustness of the method under various signal-to-noise conditions.
Achieved perfect classification accuracy (100%) on controlled tests.
Demonstrated realistic generalization with 83.2% accuracy on unseen data.
Validated chaos through rigorous statistical tests with p < 0.001.
Maintained high accuracy (86.54%) at 0 dB signal-to-noise ratio.
Facilitated real-time processing in 8.3 ms for industrial applications.

Abstract

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 0.7), 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.

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