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\section{Problem Domain}

The data mining techniques discussed in this paper have been applied to
an existing spacecraft re-entry simulation.  The Advanced NASA Technology 
Architecture for Exploration Studies (ANTARES) code~\cite{Antares} was used 
in this study.  ANTARES contains many types of models including
environmental, propulsion, effector and Guidance Navigation and Control (GNC) 
algorithms.  ANTARES is built on the Trick Simulation Environment~\cite{Trick},
which
is an executive for assembling and running the models in both real-time
and fast-time environments.

The simulation is used to design algorithms and evaluate 
trajectories for targeted return from various orbital insertion points.  
Numerous parameter variations are considered in order to determine the 
resilience of the algorithms to dispersions in mass properties, 
aerodynamic properties, atmospheric properties,
and insertion points.  The data mining techniques discussed here are intended 
to characterize the operational envelop of the simulation and to 
find the ranges of parameters that lead to the closest landings to the
target.  The margin between the best ranges to the failure points of
each parameter can then be determined.

Both standard Monte Carlo and three-factor combinatorial techniques were used
in this study.  The number of parameters for this series of test cases varied from 24 to 61.  
For the Monte Carlo cases, one thousand cases were run,
with random values chosen for each of the input parameters from their respective
probability distributions.  Here, the parameter ranges are greatly expanded such that
they are likely to include failure cases.  The output data encompass a wide range of variables that are
saved
at each iteration point.  Data representing key parameters such as trajectories, 
mass properties and consumption, G-loads and aerodynamic properties
were extracted from the simulation for the analysis that follows.
%
Figure~\ref{fig:3D} shows a 3D representation of all 1000 simulated
trajectories%
\footnote{In this paper, colors encode the class membership as
determined by the clustering algorithm. (Section 4.3, \AB)}

\begin{figure}[h]
  \centerline{\includegraphics[width=0.45\textwidth]{figures/Norm_Traj}}
  \caption{\label{fig:3D}3D representation of spacecraft re-entry trajectories
for 1000 simulation runs with different simulation parameters.}
\end{figure}

