Method for monitoring a degradation in an on-board device of an aircraft with automatic determination of a decision threshold

1. A method for monitoring a degradation in an on-board device of an aircraft, implemented by a computer, the method comprising:

measuring physical parameters from a plurality of sensors on the on-board device of the aircraft;

transforming, using the computer, the measured physical parameters to obtain an abnormality score for a given flight of the aircraft;

comparing the abnormality score obtained for the given flight of the aircraft to a decision threshold; and

transmitting an alert when the decision threshold is exceeded,

wherein the decision threshold is automatically determined for a given probability of alert Pa, corresponding to a probability of an alert being transmitted during the monitoring method when the on-board device is undamaged, by:

computing a plurality of abnormality scores for a plurality of flights of the aircraft without degradation;

obtaining a distribution of a probability density of the plurality of abnormality scores, with the distribution being specific to a physical nature of the on-board device;

obtaining a continuous adjusted distribution function by adjusting the distribution using a non-parametric estimator of the probability density;

computing a continuous adjusted division function based on the continuous adjusted distribution function; and

determining the decision threshold by reading an antecedent of the continuous adjusted division function for a given value, the antecedent corresponding to the decision threshold,

wherein the given value is 1−Peac, where Peac is an elementary probability of exceeding the decision threshold for confirmation per k exceedances of the decision threshold during n consecutive flights and is obtained by the following formula:

Peac=B −1 (k, n−k+1) (Pa)

wherein B −1 (k, n−k+1) is an inverse Beta division function of parameters k and n−k+1 and Pa is the probability of alert.

2. The method for monitoring according to claim 1 , wherein the non-parametric estimator of the probability density is a Parzen window estimator.

3. The method for monitoring according to claim 2 , wherein the distribution is formed from a number N of abnormality scores for the plurality of flights of the aircraft without degradation, the distribution having an estimated standard deviation {circle around (σ)}, and a width h of the Parzen window is defined according to the following formula:

h

=

σ

^

⁡

(

4

3

*

N

)

1

/

5

4. The method for monitoring according to claim 1 , wherein the probability of alert Pa is obtained by the following formula:

Pa

=

Pe

(

1

-

Pe

)

·

(

1

-

β

)

a

⁢

⁢

priori

·

Pd

(

1

-

Pd

)

wherein:

Pe corresponds to the probability of the on-board device being undamaged when the alert is transmitted;

Pd corresponds to the probability of the degradation for the given flight; and

(1β) a priori corresponds to the probability of detecting an a priori degradation.

5. The method for monitoring according to claim 4 , further comprising:

deducing the probability of detecting the a posteriori degradation (1β) a posteriori by implementing the method for monitoring the degradation in the on-board device with the previously determined decision threshold for the plurality of abnormality scores formed for the plurality of flights of the aircraft with degradation (1β) a posteriori ;

determining a new probability of alert Pa as a function of the probability of detecting the a posteriori degradation (1β) a posteriori ;

determining the elementary probability of exceeding the threshold Peac based on the new probability of alert Pa; and

determining a new decision threshold that is refined based on the new elementary probability of exceeding the threshold Peac.

6. The method for monitoring according to claim 1 , further comprising:

predetermining values of k and n.

7. The method for monitoring according to claim 6 , wherein the value of n is selected before that of k and the value of k is selected as a function of that of n.

8. The method for monitoring according to claim 7 , wherein the value of n is selected in order to maximise the detection probability.