Sensor Fault Diagnosis in Wind Turbines - Wind Turbine Control and Monitoring - page 271

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Fig. 10.2 Detection of excessive noise on the incremental encoder for the generator speed, X g :
the estimated speed; d 2 X g

d t 2 : the estimated second derivative of the generator speed; g ð k Þ and
g dis ð k Þ : decision functions of the presence and disappearance of excessive noise, respectively; A:
alarm signal indicating the presence of excessive noise

y m ð k Þ¼ Cx ð k Þþ v ð k Þþ f ð k Þ

ð 10 : 22 Þ

with x 2 R ; y ð k Þ2 R p ; v ð k Þ2 R p ; f ð k Þ2 R p . y m ð k Þ denotes the vector made of
the p sensor measurements. v ð k Þ stands for the measurement noise vector. It is a
zero mean white noise vector with variance R. f ð k Þ is a vector of additive faults
that can notably represent a bias or a drift on the sensors. Finally C is a p 1
matrix of sensor gains. If the measurement noises on the different sensors are
assumed to be independent, matrix R takes the form R ¼ diag j ¼ 1 ; p f r j g and the
scalars r j

can be chosen in accordance with the precision class of the instrument

notably.