Aerospace and Electronic Systems Magazine April 2017 - 37
Nassar, Hussein, and Medhat
SIMCA-P variables VIP plot.
Validation of the PLS-DA model using the training set (Set-1) and testing/prediction set (Set-T).
testing observations are indicated by the gray triangle points
named (No Class) in the score plot as shown in Figure 11.
From the figure, the PLS-DA model succeeds in classifying
the new observations to nominal and faulty data.
Figure 12 represents the score contribution bar plot,
which is used to understand which variables contribute
most strongly to an observed process change. By investigation of the dissimilarity between faulty observations such
as (F1) and the rest of the faulty observations such as (F2),
we conclude that the unique trend of faulty telemetry (F1)
is because of the higher effect of the pitch angle (Theta)
instead of the reverse effect in the others faulty telemetry.
From ground operations experience and deep anaylsis this
is reasonable, due to the beginning of the occurrence of
the high rate damping (detumbling) mode of the spacecraft
(miss-stabilization mode). One can notice that, the angular
velocity of spacecraft (ωy), quaternion element (q2) and the
pitch angle (Theta) giving an alarm on the occurrence of
the faulty state due to high angler velocity which caused by
the beginning of detumbling mode occurs.
Further investigation is carried out by using the contribution plot known as variables importance to projection (VIP)
bar plot. A very interesting aspect of modeling the inputs (Xmatrix) is that one can test and examine changes happening
in them by managing their values and the model weights.
One of these interesting features is the variable VIP plot. A
VIP ranks the variable by their relative importance to explain both the Y-matrix and the projection in the X-space. It
shows an average (cumulative) measure of the influence of
each x-variable on the output y-variables. Mathematically it
is expressed as follows :
wak2 · Ry2 a
VIP k a 2
Score contribution to variables weight bar plot.
where (a) is the number of effective PCs, k is the number
of x-variables, Ry2 is the coefficient of explanation of the yvariable, and wak2 is the weight matrix. Figure 13 explains
the anomaly identification across the features deemed most
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