Automatic Threshold Setting and Its Uncertainty Quantification in Wind Turbine Condition Monitoring System
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.
Uncertainty Quantification, Johnson distribution, Alarm Threshold, Wind turbine condition monitoring
Bechhoefer, E., & Bernhard, A. P. (2004). Setting HUMS condition indicator thresholds by modeling aircraft and torque band variance. In Aerospace conference, 2004. proceedings. 2004 IEEE (Vol. 6, pp. 3590–3595).
Bechhoefer, E., & Bernhard, A. P. (2005). Use of nongaussian distribution for analysis of shaft components. In Aerospace conference, 2006 IEEE (pp. 9–pp).
Bechhoefer, E., & Bernhard, A. P. (2007). A generalized process for optimal threshold setting in HUMS. In Aerospace conference, 2007 IEEE (pp. 1–9).
Bechhoefer, E., He, D., & Dempsey, P. (2011, September 25–20). Gear health threshold setting based on a probability of false alarm. In Annual Conference of the Prognostics and Health Management Society. Montreal, Canada.
Box, G. E. P., & Tiao, G. C. (1973). Bayesian inference in statistical analysis. Addision-Wesley Publishing Company.
Cempel, C. (1987). Simple condition forecasting techniques in vibroacoustical diagnostics. Mechanical Systems and Signal Processing, 1(1), 75–82.
Cempel, C. (1990). Limit value in the practice of machine vibration diagnostics. Mechanical systems and signal processing, 4(6), 483–493.
Chernick, M. R. (1999). Bootstrap methods, a practitioners guide. John Wiley & Sons.
Crabtree, C. (2011). Condition monitoring techniques for wind turbines. Unpublished doctoral dissertation, Durham University.
DeBrota, D. J., Dittus, R. S., Swain, J. J., Roberts, S. D., & Wilson, J. R. (1989). Modeling input processes with johnson distributions. In Proceedings of the 21st conference on winter simulation (pp. 308–318).
DeBrota, D. J., Roberts, S. D., Swain, J. J., Dittus, R. S.,Wilson, J. R., & Venkatraman, S. (1988). Input modeling with the johnson system of distributions. In Proceedings of the 20th conference on winter simulation (pp. 165–179).
Enterprises, S. (2012). Scilab: Free and open source software for numerical computation [Computer software manual]. Orsay, France. Retrieved from http://www.scilab.org
Green, E. J., Roesch Jr., F. A., Smith, A. F. M., & Strawderman, W. E. (1994, March). Bayesian estimation for the three-parameter weibull distribution with tree diameter data. Biometrics, 50(1), 254–269.
Hill, I., Hill, R., & Holder, R. (1976). Algorithm AS 99: Fitting Johnson curves by moments. Applied Statistics, 180–189.
Jablonski, A., Barszcz, T., Bielecka, M., & Breuhaus, P. (2013). Modeling of probability distribution functions for automatic threshold calculation in condition monitoring systems. Measurement, 46(1), 727–738.
Johnson, N. L. (1949). Systems of frequency curves generated by methods of translation. Biometrika, 16, 149–176.
MacKay, D. J. C. (2003). Information theory, inference, and learning algorithms. Cambridge University Press.
Marhadi, K. (2015, 10–12 March). Condition monitoring of offshore wind turbines with multi-level severity assessment of potential faults to help plan maintenance. In EWEA Offshore 2015 Conference Proceeding. Copenhagen, Denmark.
Marhadi, K., & Hilmisson, R. (2013, 11–13 June). Simple and effective technique for early detection of rolling element bearing fault: A case study in wind turbine application. In International congress of condition monitoring and diagnostic engineering management (COMADEM). Helsinki, Finland.
Marhadi, K., Venkataraman, S., & Pai, S. S. (2012). Quantifying uncertainty in statistical distribution of small sample data using bayesian inference of unbounded johnson distribution. International Journal of Reliability and Safety, 6(4), 311–337.
Tavner, P. (2012). Offshore wind turbines. The Institution of Engineering and Technology.