The “s or more threshold trespassings out of N consecutive watch periods” detection verification strategy is known to offer advantages in terms of threshold value not too extreme under the constraint of low false alert rate, PFA. Typically PFA < 5%. The definition of PFA here considered is P(No degradation|Alert). It means the probability that there is no degradation given that degradation has been detected. The alert threshold placement has previously been addressed in the case where the abnormality score with no degradation has a stationary distribution and may be approached with a continuous non parametric Parzen distribution. This is illustrated on an abnormality score of the daily lubricant consumption estimation of an aircraft engine. The watch period is a day. The N consecutive watch periods are seven consecutive service days. The s or more trespassings are six or more trespassings out of seven consecutive days. In such configuration, the threshold is 0.21 l/h, which is inside the observed distribution. With an abnormality alert strategy with no verification, i.e. s = N = 1, the threshold is a more extreme value of 0.31 l/h which is outside the observed distribution. Two steps were considered. Step 1: Learning of the abnormality score distribution with no degradation by a non parametric Parzen fit. Step 2: Threshold set by quintile interpolation on the adjustment. This is extended to the case where the abnormality score with no degradation has a discrete distribution close to a Dirac distribution. This is typically the case for abnormality scores based on “out of range” counts for measurement chains along M clock increments of a watch period, corresponding to a flight cycle. With no degradation, most of the counts during a flight, but not all, are zero. Another example is an abnormality score based on a rough quantification of the time, “t SAV open”, between the open command and the start of movement of a starter air valve, during a watch period corresponding to a start sequence. With no degradation, most of the t SAV open of a start sequence are reported “zero”. Only a few start sequences trespass the few first quantification times. In these discrete cases close to Dirac the Parzen adjustment is no longer acceptable. A discrete degradation detection threshold, l, is set as a “l events or more count out of M” clock increments of a watch period, at each watch period for an “s out of N watch periods” confirmation strategy under the same constraint of P(No degradation| Alert) < PFA. This is done according to a binomial as well as a Poisson distribution on the number of events. Like in the continuous case two steps are considered. Step 1: Estimation of the ratio of discrete events with α confidence level based on the number, r, of events during a learning phase of I time increments over watch periods with no degradation. Step 2: Alert threshold set as the limit, l, on a watch period of size M for a “s out of N limit trespassings” detection strategy.
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Abnormality Detection Threshold
Demaison F., Flandrois X., Massé J.R., Massot G., Hmad O. & Ricordeau J. (2010). Méthode de suivi de la consommation d’huile dans un système de lubrification de turbomachine. Patent # 1H105790 1093FR, WO 2011131892 (A1).
Beauseroy P., Boulet X., Grall-Maes E., Hmad O., Massé J.R. Procédé de surveillance d’une dégradation d’un dispositif embarqué d’un aéronef avec détermination automatique d’un seuil de décision (2013) Patent # FR 2990725 (A1).
Foiret G. (2013) Système de surveillance d’une chaine de mesure d’un turboréacteur, Patent # WO 2013038091 (A1)
Hmad O., Grall E., Beauseroy P., Masse J.R. & Mathevet A., (2011). A comparison of distribution estimators used to determine a degradation decision threshold for very low first order error. ESREL conference, September 18-22, Troyes, France.
Hmad O., Masse J.R, Beauseroy P., Grall-Maës E., & Mathevet (2013). A. Maturation of Detection Functions by Performances Benchmark. Application to a PHM Algorithm. Prognostics and System Health Management Conference, September 9-11, Milan. Chemical Engineering Transactions , Vol. 33.
Lacaille J (2009) Standardized Failure Signature for a Turbofan Engine. IEEE Aerospace Conference, March 7-19, Big Sky, Montana, USA.
Masse J.R., Hmad O., & Boulet X. (2012) System PHM algorithm maturation, First European Conference of the Prognostics and Health Management Society, July 3-5, Dresden, Germany.
Massé J.R., Hmad O., Grall E., Beauseroy P. (2013). System PHM Algorithm Maturation. Prognostics and System Health Management Conference, September 9-11, Milan. Chemical Engineering Transactions , Vol. 33.
Pipe, K., & Culkin, B., (2011). Dynamic alert generation technology for condition monitoring systems. The Eighth International Conference on Condition Monitoring and Machinery Failure Prevention
Technologies, June 20-22, Cardiff, UK.
Sheppard, J.W., M.A. Kaufman, and T.J. Wilmer. "IEEE Standards for Prognostics and Health Management." Aerospace and Electronic Systems Magazine 24, no. 9 (2009): 34–41.
Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. London: Chapman and Hall.
Wickens, T.D. (2002). Elementary Signal Detection Theory USA: Oxford University Press.
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