write matlab code for me Task

$1\mathrm{.}1$

$$Develop algorithms to plot confidence ellipsoids to detect anomaly detection of the

$50$

$$pumps$.$ Assume parameter uncertainty as a

$99$

$\%$

$$confidence region.List which of the

$50$

$$pumps do not require immediate maintenance to avoidfailing in the nearfuture. You do not need to plot the Mahalanobis distances, only measure them.

Task

$1\mathrm{.}2$

$$ Repeat your results for a parameter uncertainty of

$64$

$\%$

$$confidence region.

Can you briefly explain the changes in the results, and which of the two results would you prefer to make your final decision on

$?$

$$

$($

~

$200$

$$words

$)$clear all, close all;

load SensorData $\%$ manufacturer supplied data for pump's delivery head

$[$HealthyTheta$1,$ HealthyTheta$2]=$ linearFit$(1,$ HealthyEnsemble$)$;

M $=$ mean$($HealthyTheta$1,1)$;$\%$Mean of h parameters

C $=$ cov$($HealthyTheta$1)$;$\%$Covariance of h parameters

color$=1\mathrm{.}5\%$ Gives surface colour to ellipsoid

$[$U$,$L$]=$ eig$($C$)$;

$\%$ For n standard deviation spread of data, the radii of the ellipsoid will

$\%$ be given by n$*$SQRT$($eigenvalues$)$

n$=2$;

l $=50$;$\%$ No of faces

radii $=$ n$*$sqrt$($diag$($L$))$;

$[$xc$,$yc$,$zc$]=$ ellipsoid$(0,0,0,$radii$(1),$radii$(2),$radii$(3),$l$)$;

$\%$

a $=$ kron$($U$($:$,1),$xc$)$; b $=$ kron$($U$($:$,2),$yc$)$; c $=$ kron$($U$($:$,3),$zc$)$;

data $=$ a$+$b$+$c;

nc $=$ size$($data$,2)$;

x $=$ data$(1$:nc$,$:$)+$M$(1)$;

y $=$ data$($nc$+1$:$2*$nc$,$:$)+$M$(2)$;

z $=$ data$(2*$nc$+1$:end,:$)+$M$(3)$;

if isscalar$($color$),$ color $=$ color$*$ones$(1,3)$; end

ColorMap$($:$,$:$,1)=$ color$(1)*$ones$($l$+1)$;

ColorMap$($:$,$:$,2)=$ color$(2)*$ones$($l$+1)$;

ColorMap$($:$,$:$,3)=$ color$(3)*$ones$($l$+1)$;

sc $=$ surf$($x$,$y$,$z$,$ColorMap$)$;

shading interp

alpha$($sc$,0\mathrm{.}4)$;

camlight headlight

lighting phong