Optimal sinusoidal modelling of gear mesh vibration signals for gear diagnosis and prognosis

► Optimal model of gear mesh vibration signal is developed with batch learning type of least squares. ► All components of a gear mesh vibration signal are identified with insight of gear tooth crack. ► Impulsive resonance vibration signal is sufficient for diagnosing tooth cracking. ► The excellent performance of the new methodologies is validated with a set of rig test data.