Sensor Fault Diagnosis in Wind Turbines - Wind Turbine Control and Monitoring - page 266

10.2.3 Practical Issues

Two issues have to be discussed, namely the setting of the parameters of the
recursive algorithm and the actions to be taken once an alarm has been generated,
in order to detect a possible fault disappearance.
As far as the setting of the parameters is concerned, one should distinguish the
choices of h 0 ; h ' ;'¼ 1 ; ... ; n f and the thresholds h ' . h 0 is normally determined
from a set of data obtained in healthy operation. These data are processed by the
residual generators to be described next, in order to generate a residual set
f r ð 1 Þ; ... ; r ð N Þg . h 0 is then determined as an empirical estimate of the corre-
sponding characteristics (mean or variance for instance), of the probability density
function of the residual. For what regards h ' ;'¼ 1 ; ... ; n f , the fault magnitude is
usually not known; yet one has to quantify the effect of the fault on the residual in
order to set h ' ;'¼ 1 ; ... ; n f . This is achieved typically by considering the fault
'; ' ¼ 1 ; ... ; n f with the smallest magnitude one wishes to detect and isolate. This
magnitude will depend in the end on its effect on the technical-economic perfor-
mance of the system, which is yet to be determined, and is outside the framework
of this chapter. The fault is superimposed to the recorded measurements (provided
the sensor is not used within a closed loop) or simulated via a model of the
supervised process; a residual vector is computed from these data and the
parameter vector of the residual probability density function, namely h ' ; is esti-
mated from this residual sequence.
The choice of the threshold can be performed in two steps. An a priori setting of
the threshold values can be determined from analytical expressions of the mean
detection/isolation delays in terms of the thresholds and a measure of the distance
between the statistical distribution of the residual in fault free and faulty modes
[ 10 , 11 ]. This a priori value can be fine tuned from a set of experimental data in
fault free mode, and possibly in faulty mode. By processing the residual generated
from these data with the decision system, one should notably check that the mean
time between false alarms meets the specifications and possibly increase the
threshold if too many false alarms are observed.
As far as detection of a possible fault disappearance is concerned, two
approaches can be distinguished. In the case of the CUSUM algorithm given by
Eqs. 10.5 - 10.8 aimed at fault detection, once a change from H 0 to H 1 has been
detected, it is natural to look for the opposite change, namely:
Choose between the following two hypotheses:

H 0 L ð r ð i ÞÞ ¼ p h 1 ð r ð i ÞÞ for i ¼ t a ; ... ; k

H 1 L ð r ð i ÞÞ ¼ p h 1 ð r ð i ÞÞ for i ¼ t a ; ... ; k 1 1

¼ p h 0 ð r ð i ÞÞ for i ¼ k 1 ; ... ; k

where k 1 is the unknown fault disappearance time, and t a is the alarm time instant.