mirror of
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setting up quarto
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# .prettierrc.toml
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@misc{eberlyPolyhedralMassProperties2002,
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title = {Polyhedral {{Mass Properties}} ({{Revisited}})},
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author = {Eberly, David},
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year = {2002},
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month = dec,
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copyright = {CC BY 4.0},
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url = {https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf}
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}
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@inproceedings{DebriSat2019,
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title = {Analysis of the DebriSat Fragments and Comparison to the NASA Standard Satellite Breakup Model},
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author = {Murray, James and Cowardin, Heather and Liou, J-C and Sorge, Marlon and Fitz-Coy, Norman and Huynh, Tom},
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booktitle = {International Orbital Debris Conference (IOC)},
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number = {JSC-E-DAA-TN73918},
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year = {2019},
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url = {https://ntrs.nasa.gov/citations/20190034081}
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}
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@online{interfluo6UCubeSatModel,
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title = {{{6U CubeSat}} Model | {{3D CAD Model Library}} | {{GrabCAD}}},
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author = {{Interfluo}},
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url = {https://grabcad.com/library/6u-cubesat-model-1},
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urldate = {2022-02-15}
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}
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This is XeTeX, Version 3.141592653-2.6-0.999993 (MiKTeX 21.8) (preloaded format=xelatex 2021.10.31) 23 APR 2022 00:47
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entering extended mode
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108i,1n,108p,10631b,270s stack positions out of 5000i,500n,10000p,200000b,80000s
|
||||
|
||||
No pages of output.
|
||||
151
report.qmd
Normal file
151
report.qmd
Normal file
@ -0,0 +1,151 @@
|
||||
---
|
||||
title: "Characterization of Space Debris using Machine Learning Methods"
|
||||
subtitle: "Advanced processing of 3D meshes using Julia, and data science in Matlab."
|
||||
author: Anson Biggs
|
||||
date: "4/30/2022"
|
||||
latex-auto-install: true
|
||||
format:
|
||||
html:
|
||||
self-contained: true
|
||||
pdf: default
|
||||
|
||||
# reference-location: margin
|
||||
citation-location: margin
|
||||
bibliography: citations.bib
|
||||
---
|
||||
|
||||
## Gathering Data
|
||||
|
||||
To get started on the project before any scans of the actual debris are made available, I opted to
|
||||
find 3D models online and process them as if they were data collected by my team. GrabCAD is an
|
||||
excellent source of high-quality 3D models, and all the models have, at worst, a non-commercial
|
||||
^[This is a test] license making them suitable for this study. The current dataset uses three
|
||||
separate satellite assemblies found on GrabCAD, below is an example of one of the satellites that
|
||||
was used.
|
||||
|
||||
|
||||
|
||||
## Data Preparation
|
||||
|
||||
The models were processed in Blender, which quickly converted the assemblies to `stl` files, giving
|
||||
108 unique parts to be processed. Since the expected final size of the dataset is expected to be in
|
||||
the magnitude of the thousands, an algorithm capable of getting the required properties of each part
|
||||
is the only feasible solution. From the analysis performed in
|
||||
[Report 1](https://gitlab.com/orbital-debris-research/directed-study/report-1/-/blob/main/README.md),
|
||||
we know that the essential debris property is the moments of inertia which helped narrow down
|
||||
potential algorithms. Unfortunately, this is one of the more complicated things to calculate from a
|
||||
mesh, but thanks to a paper from [@eberlyPolyhedralMassProperties2002] titled
|
||||
[Polyhedral Mass Properties](https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf),
|
||||
his algorithm was implemented in the Julia programming language. The current implementation of the
|
||||
algorithm calculates a moment of inertia tensor, volume, center of gravity, characteristic length,
|
||||
and surface body dimensions in a few milliseconds per part. The library can be found
|
||||
[here.](https://gitlab.com/MisterBiggs/stl-process) The characteristic length is a value that is
|
||||
heavily used by the NASA DebriSat project [@DebriSat2019] that is doing very similar work to this
|
||||
project. The characteristic length takes the maximum orthogonal dimension of a body, sums the
|
||||
dimensions then divides by 3 to produce a single scalar value that can be used to get an idea of
|
||||
thesize of a 3D object.
|
||||
|
||||
|
||||
|
||||
The algorithm's speed is critical not only for the eventual large number of debris pieces that have
|
||||
to be processed, but many of the data science algorithms we plan on performing on the compiled data
|
||||
need the data to be normalized. For the current dataset and properties, it makes the most sense to
|
||||
normalize the dataset based on volume. Volume was chosen for multiple reasons, namely because it was
|
||||
easy to implement an efficient algorithm to calculate volume, and currently, volume produces the
|
||||
least amount of variation out of the current set of properties calculated. Unfortunately, scaling a
|
||||
model to a specific volume is an iterative process, but can be done very efficiently using
|
||||
derivative-free numerical root-finding algorithms. The current implementation can scale and process
|
||||
all the properties using only 30% more time than getting the properties without first scaling.
|
||||
|
||||
```txt
|
||||
Row │ variable mean min median max
|
||||
─────┼───────────────────────────────────────────────────────────────────
|
||||
1 │ surface_area 25.2002 5.60865 13.3338 159.406
|
||||
2 │ characteristic_length 79.5481 0.158521 1.55816 1582.23
|
||||
3 │ sbx 1.40222 0.0417367 0.967078 10.0663
|
||||
4 │ sby 3.3367 0.0125824 2.68461 9.68361
|
||||
5 │ sbz 3.91184 0.29006 1.8185 14.7434
|
||||
6 │ Ix 1.58725 0.0311782 0.23401 11.1335
|
||||
7 │ Iy 3.74345 0.178598 1.01592 24.6735
|
||||
8 │ Iz 5.20207 0.178686 1.742 32.0083
|
||||
```
|
||||
|
||||
Above is a summary of the current 108 part with scaling. Since all the volumes are the same it is
|
||||
left out of the dataset, the center of gravity is also left out of the dataset since it currently is
|
||||
just an artifact of the `stl` file format. There are many ways to determine the 'center' of a 3D
|
||||
mesh, but since only one is being implemented at the moment comparisons to other properties doesn't
|
||||
make sense. The other notable part of the data is the model is rotated so that the magnitudes of
|
||||
`Iz`, `Iy`, and `Ix` are in descending order. This makes sure that the rotation of a model doesn't
|
||||
matter for characterization. The dataset is available for download here:
|
||||
|
||||
- [scaled_dataset.csv](https://gitlab.com/orbital-debris-research/directed-study/report-3/-/blob/main/scaled_dataset.csv)
|
||||
|
||||
## Characterization
|
||||
|
||||
The first step toward characterization is to perform a principal component analysis to determine
|
||||
what properties of the data capture the most variation. `PCA` also requires that the data is scaled,
|
||||
so as discussed above the dataset that is scaled by `volume` will be used. `PCA` is implemented
|
||||
manually instead of the Matlab built-in function as shown below:
|
||||
|
||||
```matlab
|
||||
% covaraince matrix of data points
|
||||
S=cov(scaled_data);
|
||||
|
||||
% eigenvalues of S
|
||||
eig_vals = eig(S);
|
||||
|
||||
% sorting eigenvalues from largest to smallest
|
||||
[lambda, sort_index] = sort(eig_vals,'descend');
|
||||
|
||||
|
||||
lambda_ratio = cumsum(lambda) ./ sum(lambda)
|
||||
```
|
||||
|
||||
Then plotting `lambda_ratio`, which is the `cumsum`/`sum` produces the following plot:
|
||||
|
||||
|
||||
|
||||
The current dataset can be described incredibly well just by looking at `Iz`, which again the models
|
||||
are rotated so that `Iz` is the largest moment of inertia. Then including `Iy` and `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:
|
||||
|
||||
```matlab
|
||||
for ii=1:20
|
||||
[idx,~,sumd] = kmeans(inertia,ii);
|
||||
J(ii)=norm(sumd);
|
||||
end
|
||||
```
|
||||
|
||||
Which produces the following plot:
|
||||
|
||||
|
||||
|
||||
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:
|
||||
|
||||
|
||||
|
||||
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.
|
||||
|
||||
## 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.
|
||||
460
report.tex
Normal file
460
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Normal file
@ -0,0 +1,460 @@
|
||||
% Options for packages loaded elsewhere
|
||||
\PassOptionsToPackage{unicode}{hyperref}
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\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
|
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\documentclass[
|
||||
letterpaper,
|
||||
DIV=11,
|
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numbers=noendperiod,
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|
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\usepackage{amsmath,amssymb}
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
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|
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|
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|
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|
||||
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|
||||
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|
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|
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|
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|
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\usepackage{color}
|
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\usepackage{fancyvrb}
|
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\newcommand{\VerbBar}{|}
|
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|
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\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
|
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% Add ',fontsize=\small' for more characters per line
|
||||
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|
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|
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|
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|
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|
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|
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|
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|
||||
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|
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|
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|
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|
||||
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|
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|
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|
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\makeatother
|
||||
% Allow footnotes in longtable head/foot
|
||||
\IfFileExists{footnotehyper.sty}{\usepackage{footnotehyper}}{\usepackage{footnote}}
|
||||
\makesavenoteenv{longtable}
|
||||
\usepackage{graphicx}
|
||||
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|
||||
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth\else\Gin@nat@width\fi}
|
||||
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|
||||
\makeatother
|
||||
% Scale images if necessary, so that they will not overflow the page
|
||||
% margins by default, and it is still possible to overwrite the defaults
|
||||
% using explicit options in \includegraphics[width, height, ...]{}
|
||||
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|
||||
% Set default figure placement to htbp
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
{% don't indent paragraphs
|
||||
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|
||||
% turn on hanging indent if param 1 is 1
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\usepackage{calc}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
\KOMAoption{captions}{tableheading}
|
||||
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|
||||
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|
||||
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|
||||
\@ifpackageloaded{caption}{}{\usepackage{caption}}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\renewcommand*\listfigurename{List of Figures}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\renewcommand*\listtablename{List of Tables}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\ifdefined\tablename
|
||||
\renewcommand*\tablename{Table}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
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|
||||
|
||||
\title{Characterization of Space Debris using Machine Learning Methods}
|
||||
\usepackage{etoolbox}
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
\makeatother
|
||||
\subtitle{Advanced processing of 3D meshes using Julia, and data science
|
||||
in Matlab.}
|
||||
\author{Anson Biggs}
|
||||
\date{4/30/2022}
|
||||
|
||||
\begin{document}
|
||||
\maketitle
|
||||
|
||||
\ifdefined\Shaded\renewenvironment{Shaded}{\begin{tcolorbox}[interior hidden, borderline west={3pt}{0pt}{shadecolor}, boxrule=0pt, enhanced, breakable, sharp corners, frame hidden]}{\end{tcolorbox}}\fi
|
||||
|
||||
\hypertarget{gathering-data}{%
|
||||
\subsection{Gathering Data}\label{gathering-data}}
|
||||
|
||||
To get started on the project before any scans of the actual debris are
|
||||
made available, I opted to find 3D models online and process them as if
|
||||
they were data collected by my team. GrabCAD is an excellent source of
|
||||
high-quality 3D models, and all the models have, at worst, a
|
||||
non-commercial license making them suitable for this study. The current
|
||||
dataset uses three separate satellite assemblies found on GrabCAD, below
|
||||
is an example of one of the satellites that was used.
|
||||
|
||||
\begin{figure}
|
||||
|
||||
{\centering \includegraphics{Figures/assembly.jpg}
|
||||
|
||||
}
|
||||
|
||||
\caption{Example CubeSat Used for Analysis}
|
||||
|
||||
\end{figure}
|
||||
|
||||
\hypertarget{data-preparation}{%
|
||||
\subsection{Data Preparation}\label{data-preparation}}
|
||||
|
||||
The models were processed in Blender, which quickly converted the
|
||||
assemblies to \texttt{stl} files, giving 108 unique parts to be
|
||||
processed. Since the expected final size of the dataset is expected to
|
||||
be in the magnitude of the thousands, an algorithm capable of getting
|
||||
the required properties of each part is the only feasible solution. From
|
||||
the analysis performed in
|
||||
\href{https://gitlab.com/orbital-debris-research/directed-study/report-1/-/blob/main/README.md}{Report
|
||||
1}, we know that the essential debris property is the moments of inertia
|
||||
which helped narrow down potential algorithms. Unfortunately, this is
|
||||
one of the more complicated things to calculate from a mesh, but thanks
|
||||
to a paper from (Eberly
|
||||
2002)\marginpar{\begin{footnotesize}\leavevmode\vadjust pre{\protect\hypertarget{ref-eberlyPolyhedralMassProperties2002}{}}%
|
||||
Eberly, David. 2002. {``Polyhedral {Mass Properties} ({Revisited}).''}
|
||||
\url{https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf}.\vspace{2mm}\par\end{footnotesize}}
|
||||
titled
|
||||
\href{https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf}{Polyhedral
|
||||
Mass Properties}, his algorithm was implemented in the Julia programming
|
||||
language. The current implementation of the algorithm calculates a
|
||||
moment of inertia tensor, volume, center of gravity, characteristic
|
||||
length, and surface body dimensions in a few milliseconds per part. The
|
||||
library can be found
|
||||
\href{https://gitlab.com/MisterBiggs/stl-process}{here.} The
|
||||
characteristic length is a value that is heavily used by the NASA
|
||||
DebriSat project (Murray et al.
|
||||
2019)\marginpar{\begin{footnotesize}\leavevmode\vadjust pre{\protect\hypertarget{ref-DebriSat2019}{}}%
|
||||
Murray, James, Heather Cowardin, J-C Liou, Marlon Sorge, Norman
|
||||
Fitz-Coy, and Tom Huynh. 2019. {``Analysis of the DebriSat Fragments and
|
||||
Comparison to the NASA Standard Satellite Breakup Model.''} In
|
||||
\emph{International Orbital Debris Conference (IOC)}. JSC-E-DAA-TN73918.
|
||||
\url{https://ntrs.nasa.gov/citations/20190034081}.\vspace{2mm}\par\end{footnotesize}}
|
||||
that is doing very similar work to this project. The characteristic
|
||||
length takes the maximum orthogonal dimension of a body, sums the
|
||||
dimensions then divides by 3 to produce a single scalar value that can
|
||||
be used to get an idea of thesize of a 3D object.
|
||||
|
||||
\begin{figure}
|
||||
|
||||
{\centering \includegraphics{Figures/current_process.pdf}
|
||||
|
||||
}
|
||||
|
||||
\caption{Current mesh processing pipeline}
|
||||
|
||||
\end{figure}
|
||||
|
||||
The algorithm's speed is critical not only for the eventual large number
|
||||
of debris pieces that have to be processed, but many of the data science
|
||||
algorithms we plan on performing on the compiled data need the data to
|
||||
be normalized. For the current dataset and properties, it makes the most
|
||||
sense to normalize the dataset based on volume. Volume was chosen for
|
||||
multiple reasons, namely because it was easy to implement an efficient
|
||||
algorithm to calculate volume, and currently, volume produces the least
|
||||
amount of variation out of the current set of properties calculated.
|
||||
Unfortunately, scaling a model to a specific volume is an iterative
|
||||
process, but can be done very efficiently using derivative-free
|
||||
numerical root-finding algorithms. The current implementation can scale
|
||||
and process all the properties using only 30\% more time than getting
|
||||
the properties without first scaling.
|
||||
|
||||
\begin{Shaded}
|
||||
\begin{Highlighting}[]
|
||||
\NormalTok{ Row │ variable mean min median max}
|
||||
\NormalTok{─────┼───────────────────────────────────────────────────────────────────}
|
||||
\NormalTok{ 1 │ surface\_area 25.2002 5.60865 13.3338 159.406}
|
||||
\NormalTok{ 2 │ characteristic\_length 79.5481 0.158521 1.55816 1582.23}
|
||||
\NormalTok{ 3 │ sbx 1.40222 0.0417367 0.967078 10.0663}
|
||||
\NormalTok{ 4 │ sby 3.3367 0.0125824 2.68461 9.68361}
|
||||
\NormalTok{ 5 │ sbz 3.91184 0.29006 1.8185 14.7434}
|
||||
\NormalTok{ 6 │ Ix 1.58725 0.0311782 0.23401 11.1335}
|
||||
\NormalTok{ 7 │ Iy 3.74345 0.178598 1.01592 24.6735}
|
||||
\NormalTok{ 8 │ Iz 5.20207 0.178686 1.742 32.0083}
|
||||
\end{Highlighting}
|
||||
\end{Shaded}
|
||||
|
||||
Above is a summary of the current 108 part with scaling. Since all the
|
||||
volumes are the same it is left out of the dataset, the center of
|
||||
gravity is also left out of the dataset since it currently is just an
|
||||
artifact of the \texttt{stl} file format. There are many ways to
|
||||
determine the `center' of a 3D mesh, but since only one is being
|
||||
implemented at the moment comparisons to other properties doesn't make
|
||||
sense. The other notable part of the data is the model is rotated so
|
||||
that the magnitudes of \texttt{Iz}, \texttt{Iy}, and \texttt{Ix} are in
|
||||
descending order. This makes sure that the rotation of a model doesn't
|
||||
matter for characterization. The dataset is available for download here:
|
||||
|
||||
\begin{itemize}
|
||||
\tightlist
|
||||
\item
|
||||
\href{https://gitlab.com/orbital-debris-research/directed-study/report-3/-/blob/main/scaled_dataset.csv}{scaled\_dataset.csv}
|
||||
\end{itemize}
|
||||
|
||||
\hypertarget{characterization}{%
|
||||
\subsection{Characterization}\label{characterization}}
|
||||
|
||||
The first step toward characterization is to perform a principal
|
||||
component analysis to determine what properties of the data capture the
|
||||
most variation. \texttt{PCA} also requires that the data is scaled, so
|
||||
as discussed above the dataset that is scaled by \texttt{volume} will be
|
||||
used. \texttt{PCA} is implemented manually instead of the Matlab
|
||||
built-in function as shown below:
|
||||
|
||||
\begin{Shaded}
|
||||
\begin{Highlighting}[]
|
||||
\CommentTok{\% covaraince matrix of data points}
|
||||
\VariableTok{S}\OperatorTok{=}\VariableTok{cov}\NormalTok{(}\VariableTok{scaled\_data}\NormalTok{)}\OperatorTok{;}
|
||||
|
||||
\CommentTok{\% eigenvalues of S}
|
||||
\VariableTok{eig\_vals} \OperatorTok{=} \VariableTok{eig}\NormalTok{(}\VariableTok{S}\NormalTok{)}\OperatorTok{;}
|
||||
|
||||
\CommentTok{\% sorting eigenvalues from largest to smallest}
|
||||
\NormalTok{[}\VariableTok{lambda}\OperatorTok{,} \VariableTok{sort\_index}\NormalTok{] }\OperatorTok{=} \VariableTok{sort}\NormalTok{(}\VariableTok{eig\_vals}\OperatorTok{,}\SpecialStringTok{\textquotesingle{}descend\textquotesingle{}}\NormalTok{)}\OperatorTok{;}
|
||||
|
||||
|
||||
\VariableTok{lambda\_ratio} \OperatorTok{=} \VariableTok{cumsum}\NormalTok{(}\VariableTok{lambda}\NormalTok{) }\OperatorTok{./} \VariableTok{sum}\NormalTok{(}\VariableTok{lambda}\NormalTok{)}
|
||||
\end{Highlighting}
|
||||
\end{Shaded}
|
||||
|
||||
Then plotting \texttt{lambda\_ratio}, which is the
|
||||
\texttt{cumsum}/\texttt{sum} produces the following plot:
|
||||
|
||||
\begin{figure}
|
||||
|
||||
{\centering \includegraphics{Figures/pca.png}
|
||||
|
||||
}
|
||||
|
||||
\caption{PCA Plot}
|
||||
|
||||
\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}
|
||||
Loading…
x
Reference in New Issue
Block a user