Aerospace and Electronic Systems Magazine April 2017 - 28
Supervised Learning Algorithms for Spacecraft Attitude Determination and Control System Health Monitoring
preventive actions to avoid the expected faulty condition. Moreover, their work describes a study on a possible proactive model
to deal with failures based on techniques from statistics, machine
learning, and data mining to identify future trends of the object to
foresee the behavior of the system. But, the research work didn't
assist the predictions in real-time that can be checked against a set
of predefined failure probabilities thresholds.
MacGregor et al.  established the potential of applying
multivariate latent space methods in monitoring and fault diagnosis by comparing it with many other data-driven techniques. The
authors declared that black-box models such as artificial neural
networks (ANNs), hidden Markov models (HMM), and SVMs fall
within the class of regression methods/classifiers that provides no
allowance for modeling the X-space. Also, these techniques have a
limited capability to interpret full rank data, to handle missing data,
and to test for outliers in new data, even though they recognize that
these methods can be useful in some cases.
Peng et al.  proposed a fault diagnosis method for key components of satellites called anomaly monitoring method (AMM),
which is made up of state estimation based on multivariate state
estimation techniques (MSETs). The method was applied to satellite power supply subsystems and the analysis of failure was conducted on lithium-ion batteries (LIBs). The authors selected only
two parameters as key parameters of AMM, so neither an in-depth
analysis failure of LIBs was conducted nor more influencing parameters were considered.
Upadhyaya et al.  provided a structured and comprehensive
overview of the research on classification-based outlier detection.
The authors listed various techniques that are applicable to the area of
research, focusing on the underlying approach adopted by each technique. Also, they have identified key assumptions, which are used by
the techniques to differentiate between normal and outlier behavior.
The study has been conducted in an unstructured manner without relying on a unified notion of outliers. So the theoretical understanding
of the outlier detection problem still becomes a difficult task.
Schwabacher et al.  utilized data-driven methods to automatically detect and isolate faults in the J-2X rocket engine. It was
decided to use a decision tree algorithm known as C4.5, since it
tends to be easier to interpret than other data-driven methods. The
decision tree algorithm automatically learns a decision tree by performing a search through the space of possible decision trees to
find the one that fits the training data. But, they didn't use other
algorithms for validation and compression motivation.
Many of the existing approaches to supervised learning for systems health monitoring have used ANNs to model the system .
He and Shi  found that SVMs produced better accuracy than
ANNs when applied to a pump diagnosis problem. One significant
disadvantage of neural network approaches is that most humans
are unable to understand or interpret the ANNs models and also
SVMs models suffer from a similar lack of comprehensibility.
The proposed monitoring and anomaly detection system is based
on the data-driven approach. The powerful feature of using this
approach is the ability to analyze multivariate parameters simulta28
neously. This feature allows us to discover and model interactions
between related parameters that might be difficult to observe when
monitoring the parameters individually.
The data-driven approach includes unsupervised and supervised
anomaly detection algorithms. Unsupervised anomaly detection algorithms are trained using a single set of unlabeled data, partially or
totally composed by nominal data . They are also called one-class
learning algorithms because they represent a data-driven system that
is provided with data for a single type (class) of behavior, typically
nominal operation. They learn a model of the nominal data, which can
be used to signal an anomaly when new data fails to match the model
. They are useful when hardly any examples of failure data are
available. Supervised anomaly detection algorithms require training
data consisting of a set of examples of both anomalies and nominal
data. From the data, the algorithms learn a model that distinguishes
between the nominal and the faulty data points. Supervised anomaly
detection algorithms typically require tens or hundreds of labeled
examples of anomalies, plus a similar number of labeled examples
of nominal data points, in order to obtain adequate performance .
They are able to go beyond the capabilities of unsupervised anomaly
detection algorithms by identifying the fault mode, rather than just
detecting anomalies. The most popular data-driven health monitoring approaches include Fisher discriminant analysis (FDA), canonical variate analysis (CA), principal component analysis (PCA), partial least squares (PLS) method and its extension PLS-DA, ANNs,
decision trees, and SVMs -. Among these, we decided to
use both multivariate statistical methods such as the supervised PLSDA statistical algorithm and machine learning techniques such as
nonlinear SVMs for the first time in space operations.
MULTIVARIATE PLS-DA BASIC THEORY
From the latent projection philosophy, when PCA is used for classification problems with a set of observations representing one or
several classes, knowledge related to class membership is not used
to find the location of the principle components. It must be realized
that PCA finds the directions in multivariate space that represent
the largest sources of variations, the so-called principle components. However, it is not necessarily the case that these maximum
variation directions coincide with the maximum separation directions among the classes. Rather it may be that other directions are
more pertinent for discrimination among classes of observations. It
is in this perspective that a PLS-DA becomes vital .
PLS-DA methodology is based on projection philosophy that
aims to find a line, a plane or hyperplane "latent direction" which
maximizes the separation between classes of observations based on
their X-variable of the projection (Figure 1). PLS-DA is a dimensionality reduction technique that transforms or maps the correlated variables from its original space to a lower dimensional space
"new variables" that are uncorrelated with each other and are linear
combinations of the original variables (preserving the correlation
structure between the original features). The main discrepancy between PCA and PLS-DA is the principle applied when estimating
the principal components (PCs) (latent variables or eigenvectors).
While the unsupervised learning PCA finds latent directions that
maximize the variance of the projection, the supervised learning
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