Autoregressive model-based gear shaft fault diagnosis using the Kolmogorov–Smirnov test

Vibration behavior induced by gear shaft crack is different from that induced by gear tooth crack. Hence, a fault indicator used to detect tooth damage may not be effective for monitoring shaft condition. This paper proposes an autoregressive model-based technique to detect the occurrence and advancement of gear shaft cracks. An autoregressive model is fitted to the time synchronously averaged signal of the gear shaft in its healthy state. The order of the autoregressive model is selected using Akaike information criterion and the coefficient estimates are obtained by solving the Yule–Walker equations with the Levinson–Durbin recursion algorithm. The established autoregressive model is then used as a linear prediction filter to process the future signal. The Kolmogorov–Smirnov test is applied on line for the prediction of error signals. The calculated distance is used as a fault indicator and its capability to diagnose shaft crack effectively is demonstrated using a full lifetime gear shaft vibration data history. The other frequently used statistical measures such as kurtosis and variance are also calculated and the results are compared with the Kolmogorov–Smirnov test.