Benefits of Mann–Kendall trend analysis for vibration-based condition monitoring

Abstract

Rank-based statistics offer an appealing framework to non-parametric robust trend detection. Especially, the Mann–Kendall test detects the presence of a trend in a series. This paper investigates the benefits of using the Mann–Kendall test, which seems to have remained largely unnoticed in the context of vibration-based condition monitoring. Two contributions structure the present paper. First, theoretical foundations of rank-statistics are reminded and the Z-score is introduced, a statistical metric measuring the presence of a trend in a given series. The performance of the Mann–Kendall test is investigated and confronted to different numerical cases involving series of increasing condition indicators. Second, based on this understanding, the Z-score metric is exploited to design two trend-oriented signal processing tools dedicated to vibration-based condition monitoring. Namely, a new tool named the Mannagram is introduced as a dyadic filterbank representation of the trend of indicators series. It shows effective in the informative band selection problem and unveils more interpretable indicators. Besides, a concise representation of trend by frequency bin is introduced and coined the Kendrum. This representation is shown to help the diagnosis by summarising the trend information of series of spectra. Both methods are demonstrated on run-to-failure series of vibration signals from industrial wind turbines.