
% $Id:$

\section{Problem Domain}

The data mining techniques discussed in this paper have been applied to
an existing spacecraft re-entry simulation.  The simulation is used to evaluate 
algorithms 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
determine the margins of the simulation from the nominal operating points relative
to the failure front.

At launch, multiple settings can be made to various command control variables.
The goal of this simulation+data mining study was to 
\begin{quote}
Find {\em margins}
of those parameters 
that cause the spacecraft to reliably land {\em close} to the target site.
\end{quote}
Initial attempts to determine the margins were thwarted by the resilience of the
simulation around the nominal operating points.  The data ranges utilized for
this study are far outside the normal operating bounds of the simulation, but
this expansion is necessary to determine the margin to failure.

A standard Monte Carlo technique was used, where dispersion shapes and ranges were
defined for a group of 24 different input parameters.  One thousand cases were run,
with random values chosen for each of the input parameters from their respective
distributions.  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.
%
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.}

\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}

The Monte Carlo simulations can generate any amount of output. Two
data miners (\TAR and \AB)
were hence applied to simplify
the analysis of that data.
%Even when regarding only the most important variables that are recorded
%during the simulation (e.g., like deviation from landing target,
%fuel consumption, or maximal G-forces), a high-dimensional data set
%is produced.
%Due to the physical nature of the simulation and the Monte Carlo 
%execution model,
%which uses Gaussian distributed random parameters, many of the output
%variables can be modeled as Gaussian distributed statistical variables
%that are i.i.d.\ over all simulation runs. %We can write $x_i  \sim N(\mu,\sigma^2)$.
%

