Aerospace and Electronic Systems Magazine April 2017 - 33

Nassar, Hussein, and Medhat
and the kernel methods coded in MATLAB are used for the SVMs
training and testing.

RESULTS AND ANALYSIS

Based on the observations from Egyptian remote sensing spacecraft, a series of numerical experiments were conducted in this
SELECTION OF KERNEL FUNCTION AND KERNEL
study, using the PLS-DA algorithm, nonlinear SVMs algorithm,
and soft independent modeling for class analogy (SIMCA-P)
PARAMETERS
software model to monitor the spacecraft behavior during the
The SVMs classification technique is generalized to the ADCS
nominal and anomalous operation periods via the telemetry actelemetry by testing the two different polynomial and Gaussian
quired. The scenario of spacecraft operations uses a total of 16
RBF kernel functions during the training process. The algorithm
analogue variables and 1080 observations for both nominal and
requires a feasible point to start. If the initial point is not feasible,
faulty data acquired from ADCS sensory orbit to generate the
then one can find a feasible point by solving the linear programinput matrix-X, which means that the original data has dimension
ming problem. According to the performance of these kernel
D = 16. These features represent the root mean square of the time
functions, the suitability of the SVMs as an intelligent classifier
domain records of the sensory signals measurements regarding
is judged. The selection of the optimum parameters for SVMs
spacecraft roll, pitch, yaw angles, angular velocity and quateris done during the training process (Set-T). The SVM classifier
nions, etc.
with the best performance is obtained by testing different values
The models are established using a set of ADCS telemetry
of the kernel parameters. These parameters are varied in the folacquired from the operations for three days in the course of 12
lowing manner: γ is varied with values of 0.1, 0.2, 0.3, 0.5, 1, 3,
communication sessions that represent the nominal and off- nomi5. The order of the polynomial kernel n is varied with steps of 2.
nal status. During this period and by the end of the second day a
The penalty due to the error C is also varied with values of 1, 10,
system anomaly was reported due to angular velocity meter in
100, 500, and 1000. The tolerance condition for the trust-region
Z-direction (AVMz) and the redundant one (AVMr) was used inmethods for nonlinear minimization QP solver is 0.0000001. The
stead of a faulty device. Also, during the function of AVMr its teperformance of the two SVMs is assessed on each of these vallemetry sometimes indicated improper reading during these days.
ues by calculating the training percentage performance efficiency
In addition spacecraft miss-stabilization mode (tumbling mode)
defined by
occurs. If the aforementioned fault is repeated, the spacecraft will
acquire the tumbling mode to a critical extent, and from experts
No. of samples correct classified


 100
experience this mode is extremely severe
because it could lead to
(10)
Total No. of samples
spacecraft losses.
There are several evaluation schemes for selection of trainFrom these results, the SVM classifier with the highest training
ing and testing sets including hold-out, leave-one-out, cross-valpercentage performance efficiency is selected. The testing process
idation, and bootstrap. In our article the selection is based on the
is then performed, during which the generalization performance of
hold-out method. So, the 1080 observations are divided into 810
the classifier is examined using the testing set (Set-T) by evaluatobservations as the training set and 270 observations as the testing
ing the testing percentage performance efficiency.
set. The division percentage is 75% for the training set to 25% for
the testing set.

EFFECT OF THE SIZE OF THE TRAINING DATA ON THE
CLASSIFIER'S PERFORMANCE

NONLINEAR SVM RESULTS
In this section, the generalization of the nonlinear SVMs classification algorithm to the ADCS SOH telemetry data and its performance are investigated. The training technique generated in this
design work is adapted to train 810 observations (777 nominal,
33 faulty) as training set (Set-1). Subsequently, the model is tested
and validated on a subset (Set-T) of the remaining 270 observations (239 nominal, 31 faulty) and their corresponding normalized
values are directly used as the input features for SVMs. The corresponding output y1 is −1 for a normal condition and +1 for a fault
condition.

SVM MODELS DESIGN
The SVM models are designed during the training process using
trial and error. The training process involves different kernel functions as well as several values of each kernel's parameters in order
to obtain the SVM classifier with the best performance. The SVM
APRIL 2017

The main training data set (Set-1) of the 810 observations is reduced to 500 observations in order to obtain a new training data
set (Set-2), which is also used for training the proposed classifiers.
After training all the SVM classifiers with these two sets, they are
tested with a different data set (Set-T) of 270 observations in order
to evaluate the efficiency of the proposed approach when subjected
to a reduced size of training data.

TRAINING AND TESTING THE RESULTS
Figure 6 shows the best performance of kernel functions during the
training process of the training set (Set-1). The best performance is
introduced in terms of the percentage training efficiency of equation (10), with respect to the variation of the kernel parameters γ,
and n as well as the penalty due to the error C. The corresponding
number of support vectors (SVs) and the training time are also illustrated.

IEEE A&E SYSTEMS MAGAZINE

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