mirror of
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setting up quarto
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pdftitle={Characterization of Space Debris using Machine Learning Methods},
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pdfauthor={Anson Biggs},
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\title{Characterization of Space Debris using Machine Learning Methods}
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\usepackage{etoolbox}
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\makeatletter
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\providecommand{\subtitle}[1]{% add subtitle to \maketitle
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\apptocmd{\@title}{\par {\large #1 \par}}{}{}
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}
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\makeatother
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\subtitle{Advanced processing of 3D meshes using Julia, and data science
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in Matlab.}
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\author{Anson Biggs}
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\date{4/30/2022}
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\begin{document}
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\maketitle
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\ifdefined\Shaded\renewenvironment{Shaded}{\begin{tcolorbox}[interior hidden, borderline west={3pt}{0pt}{shadecolor}, boxrule=0pt, enhanced, breakable, sharp corners, frame hidden]}{\end{tcolorbox}}\fi
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\hypertarget{gathering-data}{%
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\subsection{Gathering Data}\label{gathering-data}}
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To get started on the project before any scans of the actual debris are
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made available, I opted to find 3D models online and process them as if
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they were data collected by my team. GrabCAD is an excellent source of
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high-quality 3D models, and all the models have, at worst, a
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non-commercial license making them suitable for this study. The current
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dataset uses three separate satellite assemblies found on GrabCAD, below
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is an example of one of the satellites that was used.
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\begin{figure}
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{\centering \includegraphics{Figures/assembly.jpg}
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}
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\caption{Example CubeSat Used for Analysis}
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\end{figure}
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\hypertarget{data-preparation}{%
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\subsection{Data Preparation}\label{data-preparation}}
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The models were processed in Blender, which quickly converted the
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assemblies to \texttt{stl} files, giving 108 unique parts to be
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processed. Since the expected final size of the dataset is expected to
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be in the magnitude of the thousands, an algorithm capable of getting
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the required properties of each part is the only feasible solution. From
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the analysis performed in
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\href{https://gitlab.com/orbital-debris-research/directed-study/report-1/-/blob/main/README.md}{Report
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1}, we know that the essential debris property is the moments of inertia
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which helped narrow down potential algorithms. Unfortunately, this is
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one of the more complicated things to calculate from a mesh, but thanks
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to a paper from (Eberly
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2002)\marginpar{\begin{footnotesize}\leavevmode\vadjust pre{\protect\hypertarget{ref-eberlyPolyhedralMassProperties2002}{}}%
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Eberly, David. 2002. {``Polyhedral {Mass Properties} ({Revisited}).''}
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\url{https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf}.\vspace{2mm}\par\end{footnotesize}}
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titled
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\href{https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf}{Polyhedral
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Mass Properties}, his algorithm was implemented in the Julia programming
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language. The current implementation of the algorithm calculates a
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moment of inertia tensor, volume, center of gravity, characteristic
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length, and surface body dimensions in a few milliseconds per part. The
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library can be found
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\href{https://gitlab.com/MisterBiggs/stl-process}{here.} The
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characteristic length is a value that is heavily used by the NASA
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DebriSat project (Murray et al.
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2019)\marginpar{\begin{footnotesize}\leavevmode\vadjust pre{\protect\hypertarget{ref-DebriSat2019}{}}%
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Murray, James, Heather Cowardin, J-C Liou, Marlon Sorge, Norman
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Fitz-Coy, and Tom Huynh. 2019. {``Analysis of the DebriSat Fragments and
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Comparison to the NASA Standard Satellite Breakup Model.''} In
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\emph{International Orbital Debris Conference (IOC)}. JSC-E-DAA-TN73918.
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\url{https://ntrs.nasa.gov/citations/20190034081}.\vspace{2mm}\par\end{footnotesize}}
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that is doing very similar work to this project. The characteristic
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length takes the maximum orthogonal dimension of a body, sums the
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dimensions then divides by 3 to produce a single scalar value that can
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be used to get an idea of thesize of a 3D object.
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\begin{figure}
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{\centering \includegraphics{Figures/current_process.pdf}
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}
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\caption{Current mesh processing pipeline}
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\end{figure}
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The algorithm's speed is critical not only for the eventual large number
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of debris pieces that have to be processed, but many of the data science
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algorithms we plan on performing on the compiled data need the data to
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be normalized. For the current dataset and properties, it makes the most
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sense to normalize the dataset based on volume. Volume was chosen for
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multiple reasons, namely because it was easy to implement an efficient
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algorithm to calculate volume, and currently, volume produces the least
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amount of variation out of the current set of properties calculated.
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Unfortunately, scaling a model to a specific volume is an iterative
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process, but can be done very efficiently using derivative-free
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numerical root-finding algorithms. The current implementation can scale
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and process all the properties using only 30\% more time than getting
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the properties without first scaling.
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\begin{Shaded}
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\begin{Highlighting}[]
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\NormalTok{ Row │ variable mean min median max}
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\NormalTok{─────┼───────────────────────────────────────────────────────────────────}
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\NormalTok{ 1 │ surface\_area 25.2002 5.60865 13.3338 159.406}
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\NormalTok{ 2 │ characteristic\_length 79.5481 0.158521 1.55816 1582.23}
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\NormalTok{ 3 │ sbx 1.40222 0.0417367 0.967078 10.0663}
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\NormalTok{ 4 │ sby 3.3367 0.0125824 2.68461 9.68361}
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\NormalTok{ 5 │ sbz 3.91184 0.29006 1.8185 14.7434}
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\NormalTok{ 6 │ Ix 1.58725 0.0311782 0.23401 11.1335}
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\NormalTok{ 7 │ Iy 3.74345 0.178598 1.01592 24.6735}
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\NormalTok{ 8 │ Iz 5.20207 0.178686 1.742 32.0083}
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\end{Highlighting}
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\end{Shaded}
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Above is a summary of the current 108 part with scaling. Since all the
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volumes are the same it is left out of the dataset, the center of
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gravity is also left out of the dataset since it currently is just an
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artifact of the \texttt{stl} file format. There are many ways to
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determine the `center' of a 3D mesh, but since only one is being
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implemented at the moment comparisons to other properties doesn't make
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sense. The other notable part of the data is the model is rotated so
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that the magnitudes of \texttt{Iz}, \texttt{Iy}, and \texttt{Ix} are in
|
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descending order. This makes sure that the rotation of a model doesn't
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matter for characterization. The dataset is available for download here:
|
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\begin{itemize}
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\tightlist
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\item
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\href{https://gitlab.com/orbital-debris-research/directed-study/report-3/-/blob/main/scaled_dataset.csv}{scaled\_dataset.csv}
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\end{itemize}
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\hypertarget{characterization}{%
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\subsection{Characterization}\label{characterization}}
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The first step toward characterization is to perform a principal
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component analysis to determine what properties of the data capture the
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most variation. \texttt{PCA} also requires that the data is scaled, so
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||||
as discussed above the dataset that is scaled by \texttt{volume} will be
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used. \texttt{PCA} is implemented manually instead of the Matlab
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built-in function as shown below:
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\begin{Shaded}
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\begin{Highlighting}[]
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\CommentTok{\% covaraince matrix of data points}
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\VariableTok{S}\OperatorTok{=}\VariableTok{cov}\NormalTok{(}\VariableTok{scaled\_data}\NormalTok{)}\OperatorTok{;}
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\CommentTok{\% eigenvalues of S}
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\VariableTok{eig\_vals} \OperatorTok{=} \VariableTok{eig}\NormalTok{(}\VariableTok{S}\NormalTok{)}\OperatorTok{;}
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\CommentTok{\% sorting eigenvalues from largest to smallest}
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\NormalTok{[}\VariableTok{lambda}\OperatorTok{,} \VariableTok{sort\_index}\NormalTok{] }\OperatorTok{=} \VariableTok{sort}\NormalTok{(}\VariableTok{eig\_vals}\OperatorTok{,}\SpecialStringTok{\textquotesingle{}descend\textquotesingle{}}\NormalTok{)}\OperatorTok{;}
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\VariableTok{lambda\_ratio} \OperatorTok{=} \VariableTok{cumsum}\NormalTok{(}\VariableTok{lambda}\NormalTok{) }\OperatorTok{./} \VariableTok{sum}\NormalTok{(}\VariableTok{lambda}\NormalTok{)}
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\end{Highlighting}
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\end{Shaded}
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Then plotting \texttt{lambda\_ratio}, which is the
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\texttt{cumsum}/\texttt{sum} produces the following plot:
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\begin{figure}
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{\centering \includegraphics{Figures/pca.png}
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}
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\caption{PCA Plot}
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\end{figure}
|
||||
|
||||
The current dataset can be described incredibly well just by looking at
|
||||
\texttt{Iz}, which again the models are rotated so that \texttt{Iz} is
|
||||
the largest moment of inertia. Then including \texttt{Iy} and
|
||||
\texttt{Iz} means that a 3D plot of the principle moments of inertia
|
||||
almost capture all the variation in the data.
|
||||
|
||||
The next step for characterization is to get only the inertia's from the
|
||||
dataset. Since the current dataset is so small, the scaled dataset will
|
||||
be used for rest of the characterization process. Once more parts are
|
||||
added to the database it will make sense to start looking at the raw
|
||||
dataset. Now we can proceed to cluster the data using the k-means method
|
||||
of clustering. To properly use k-means a value of k, which is the number
|
||||
of clusters, needs to be determined. This can be done by creating an
|
||||
elbow plot using the following code:
|
||||
|
||||
\begin{Shaded}
|
||||
\begin{Highlighting}[]
|
||||
\KeywordTok{for} \VariableTok{ii}\OperatorTok{=}\FloatTok{1}\OperatorTok{:}\FloatTok{20}
|
||||
\NormalTok{ [}\VariableTok{idx}\OperatorTok{,\textasciitilde{},}\VariableTok{sumd}\NormalTok{] }\OperatorTok{=} \VariableTok{kmeans}\NormalTok{(}\VariableTok{inertia}\OperatorTok{,}\VariableTok{ii}\NormalTok{)}\OperatorTok{;}
|
||||
\VariableTok{J}\NormalTok{(}\VariableTok{ii}\NormalTok{)}\OperatorTok{=}\VariableTok{norm}\NormalTok{(}\VariableTok{sumd}\NormalTok{)}\OperatorTok{;}
|
||||
\KeywordTok{end}
|
||||
\end{Highlighting}
|
||||
\end{Shaded}
|
||||
|
||||
Which produces the following plot:
|
||||
|
||||
\begin{figure}
|
||||
|
||||
{\centering \includegraphics{Figures/kmeans.png}
|
||||
|
||||
}
|
||||
|
||||
\caption{Elbow method to determine the required number of clusters.}
|
||||
|
||||
\end{figure}
|
||||
|
||||
As can be seen in the above elbow plot, at 6 clusters there is an
|
||||
``elbow'' which is where there is a large drop in the sum distance to
|
||||
the centroid of each cluster which means that it is the optimal number
|
||||
of clusters. The inertia's can then be plotted using 6 k-means clusters
|
||||
produces the following plot:
|
||||
|
||||
\begin{figure}
|
||||
|
||||
{\centering \includegraphics{Figures/inertia3d.png}
|
||||
|
||||
}
|
||||
|
||||
\caption{Moments of Inertia plotted with 6 clusters.}
|
||||
|
||||
\end{figure}
|
||||
|
||||
From this plot it is immediately clear that there are clusters of
|
||||
outliers. These are due to the different shapes and the extreme values
|
||||
are slender rods or flat plates while the clusters closer to the center
|
||||
more closely resemble a sphere. As the dataset grows it should become
|
||||
more apparent what kind of clusters actually make up a satellite, and
|
||||
eventually space debris in general.
|
||||
|
||||
\hypertarget{next-steps}{%
|
||||
\subsection{Next Steps}\label{next-steps}}
|
||||
|
||||
The current dataset needs to be grown in both the amount of data and the
|
||||
variety of data. The most glaring issue with the current dataset is the
|
||||
lack of any debris since the parts are straight from satellite
|
||||
assemblies. Getting accurate properties from the current scans we have
|
||||
is an entire research project in itself, so hopefully, getting pieces
|
||||
that are easier to scan can help bring the project back on track. The
|
||||
other and harder-to-fix issue is finding/deriving more data properties.
|
||||
Properties such as cross-sectional or aerodynamic drag would be very
|
||||
insightful but are likely to be difficult to implement in code and
|
||||
significantly more resource intensive than the current properties the
|
||||
code can derive.
|
||||
|
||||
|
||||
|
||||
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user