Improvements in the Wavelet Transform and Its Variations: Concepts and Applications in Diagnosing Gearbox in Non-Stationary Conditions

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Abstract
Wavelet transform is a powerful time-frequency-based analysis method often used in gear fault diagnostics. The development of wavelet transform is closely linked to the improvement of resolution. When the high-frequency resolution allows for easy observation of different frequency components, it is a symptom of damage to an individual part of the machine. This study effectively applied the Wavelet analysis technique to diagnose faulty gearboxes operated in non-stationary conditions. This is a complex problem that usual diagnostic approaches need help to solve due to its non-linear character. This work conducted a simulation and real-world testing to show that the newest wavelet analysis techniques work well, showing that they can accurately find gear faults in gearboxes in non-stationary conditions. A thorough overview of the cutting-edge applications of wavelet transform in diagnosing faults in industrial gearbox systems was also given. This work also explained in detail the mathematical ideas behind the continuous wavelet transform, discrete wavelet transforms, and wavelet packet transform.

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