Abstract
Setting optimal alarm thresholds in vibration based condition monitoring system is inherently difficult. There are no established thresholds for many vibration based measurements. Most of the time, the thresholds are set based on statistics of the collected data available. Often times the underlying probability distribution that describes the data is not known. Choosing an incorrect distribution to describe the data and then setting up thresholds based on the chosen distribution could result in sub-optimal thresholds. Moreover, in wind turbine applications the collected data available may not represent the whole operating conditions of a turbine, which results in uncertainty in the parameters of the fitted probability distribution and the thresholds calculated. In this study, Johnson, Normal, and Weibull distributions are investigated; which distribution can best fit vibration data collected from a period of time. False alarm rate resulted from using threshold determined from each distribution is used as a measure to determine which distribution is the most appropriate. This study shows that using Johnson distribution can eliminate testing or fitting various distributions to the data, and have more direct approach to obtain optimal thresholds. To quantify uncertainty in the thresholds due to limited data, implementations with bootstrap method and Bayesian inference are investigated.
Highlights
Wind turbines are generally subject to aleatory uncertainty due to stochastic nature of the weather and the wind itself
Thresholds based on Johnson and Weibull distributions generally result in the lowest false alarm rates
A method to set alarm thresholds automatically based on fitting different distributions to vibration data has been presented
Summary
Wind turbines are generally subject to aleatory uncertainty due to stochastic nature of the weather and the wind itself. (Bechhoefer & Bernhard, 2005) have presented a case where Gaussian distribution is not appropriate to describe the probability distribution of first order magnitude (1X) of a helicopter shaft They further explained that it is important that the underlying distribution of a measurement is correct so that the threshold can be determined based on low probability of false alarm. This condition is widely known, there has not been much work or study in this area Another contribution of this paper is to present the effects of having limited data available (e.g. a few days, a few weeks, or a few months) in wind turbine thresholds setting and the possible false alarms generated. Bootstrap method and Bayesian inference are investigated for uncertainty quantification with possible industrial applications in mind
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