Aerospace and Electronic Systems Magazine April 2017 - 38

Supervised Learning Algorithms for Spacecraft Attitude Determination and Control System Health Monitoring

Figure 15.

PLS-DA algorithm and SIMCA-P Shewhart control charts for process
shifts.

Figure 14.

PLS-DA algorithm and SIMCA-P/DModX model residual contribution
plots.

critical in determining the overall health status of the process operation and shows that the aforementioned variables (ωx), (ωy), (ωz),
(q2), and (Theta) are most critical and also responsible for the fault.
More analysis was carried out using model residuals named distance to model X (DModX). DModX can be used to define a control limit in a direction perpendicular to the PC-model hyperplane
and to detect process upsets (spikes in telemetry data that couldn't
be observed by scatter plots) by determining moderate outliers.
Figure 14 illustrates that most of the observations from "1 to 777"
used to train the model are inside or nearly inside the model critical
distance (D-Critical 0.05). This indicates that in this time interval
the process is fairly stable and no new process event is recognized.
However, the last observations from "778 to 810" don't fit the
model well, and indicate that a new process behavior has become
established and ought to be scrutinized more closely.
Further study using multivariate control charts is crucial because the DModX will not explicitly indicate the cause of this shift
[17]. Control charts provide good insight into plausible causes or
variables related to the causes. They adhere to a state of statistical
control, unless a special event occurs. A state of statistical control
exits when certain critical process variables and or product attributes remain close to target values and don't change perceptibly
[17]. In order to detect special events, control charts are routinely
used to monitor key process variables and quality over time. So, the
proposed algorithm has the capability to detect large changes like
a shift in average or general drift over time via investigating the
telemetry data over time. Figure 15 shows that the process shifts
could be tackled using the control charts. Both the PLS-DA algorithm control chart and the Shewhart control used by SIMCA-P are
used to give an early warning trend monitor. Gathering both control
38

charts and residual DModX is very informative and enables strong
and moderate process outliers to be considered simultaneously.
Eventually, analysis results obtained by applying the aforementioned algorithms to detect anomaly and classify between
normal and faulty data of spacecraft have a significant accuracy
percentage. Nonlinear Gaussian and polynomial functions of the
SVMs technique show a high accuracy with percentage of 96.98%
Gaussian and 96.13% polynomial, respectively. Subsequently, applying both the PLS-DA algorithm and SIMCA-P software gives
accuracy with percentage of 97.9% for our PLS-DA algorithm and
96.4% SIMCA-P software, respectively. Furthermore, the most
significant result of using the PLS-DA algorithm over the SVMs
algorithm is that it is a dimensionality reduction technique and
that means we reduce the dimensions of data matrix-X from its
original space to a lower dimensions space new variables t1 and
t2 (in our case the dimensional of the matrix is now reduced from
(D16) to (2D) only by applying projection philosophy). Moreover,
the SVMs technique gives more than one model by changing the
parameters used in the model development, but both the PLS-DA
algorithm and SIMCA-P software give only one model. Additionally, spacecraft models involve a massive number of variables that
are often difficult to interpret together, especially when we want
to model more than one spacecraft subsystem in one monitoring chart. As a result, a better alternative is to group the data into
blocks with logically related variables and apply hierarchical data
analysis. So, the main advantage of our proposed algorithm over
other statistical multivariate software such as SIMCA-P is that in
SIMCA-P, one can't create blocks of variables in order to automatically create hierarchical base models of type PLS-DA. Finally, the
most important attribute is that the PLS-DA technique overcomes
the black-box problem that SVMs and ANNs suffer from because
the model gives significant information about the system outputs
as well as adding more insight into physical explanations and inter-

IEEE A&E SYSTEMS MAGAZINE

APRIL 2017



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