System PHM Algorithm Maturation

Abstract

The maturation of PHM functions is focused on two Key Performance Indicators (KPI): The NFF, No Fault Found ratio, P(No degradation|Detection), and the Probability Of Detection POD, P(Detection|Degradation). The estimation of the second KPI can be done by counting the global abnormality threshold trespassing when each different kind of degradation is simulated. The  estimation of the first KPI can be done through the following formula using the Bayes rule:
( )
( | )* ( )
( | )
P Detection
P Detection NoDegradation P NoDegradation
P NoDegradation Detection 
P(Degradation) may be known through FMEA or field experience. Typically, for a probability of 10-7, a specified NFF ratio of 1%, and an expected POD of 90%, the order of magnitude of P(Detection| No degradation) should be 10-9. The estimation of such extreme level of probability needs some parametric adjustment of the distribution of the global abnormality score with no degradation. Two PHM functions are considered as case studies: Turbofan engine start capability (ESC) and turbofan engine lubrication oil consumption (EOC). In ESC the global abnormality score is a norm of a vector of specific abnormality scores. The specific scores are centered and reduced residues between expected values and observed values. Some specific scores are devoted to starter air supply. Examples are duration of phase 1 from starter air valve open command to ignition speed. Other scores are devoted to fuel metering. Examples are duration of phase 2 from ignition to cut off speed. The expected values are estimations through regression relations using as inputs the other specific scores and context parameters such as lubrication oil temperature at start. The regression relations are learnt on start records with no degradations. Impact simulations of degradations on specific scores are learnt on a phase 1 simulator based on torques balance and on start test records including fuel metering biases. In EOC, the global abnormality score is the daily weekly or monthly consumption estimations on a daily basis. Consumption estimations use linear regressions of oil level measurements versus time at an invariable ground idle speed corrected according to oil fill detections and oil temperature. The over consumptions are simulated by drifts in mean of the consumption estimations.
To reach acceptable POD at the specified NFF ratio three improvements are needed for ESC:
 Adjust the abnormality decision threshold according to each candidate degradation using extreme value quantiles on the global abnormality score distribution
 Average the global abnormality score on five consecutive starts
 Learn the regression relations specifically on each engine.
The first improvement is a novelty. It is successfully applied to both ESC and EOC functions. It is generic to all airborne system PHM functions based on abnormality scores.