Self-similarity in vibration time series: Application to gear fault diagnostics

The vibration time series of gear systems exhibit self-similarity. The time-series behavior is characterized by an exponent, known as the scaling exponent. An algorithm is proposed for the estimation of both global and local exponents, thus providing a means of examining the time-series fine structure. The proposed algorithm is applied to experimental data recorded from gear pairs with localized defects in the form of bending fatigue cracks. It is shown that an examination of the exponent empirical histogram allows detection of damage at an early stage and also provides an estimate of the defect magnitude.