report 2 posted

_posts/2022-04-03-machine-learning-directed-study-report-2/citations.bib

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+
+@misc{eberlyPolyhedralMassProperties2002,
+  title = {Polyhedral {{Mass Properties}} ({{Revisited}})},
+  author = {Eberly, David},
+  year = {2002},
+  month = dec,
+  copyright = {CC BY 4.0},
+  url = "https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf"
+}
+
+

_posts/2022-04-03-machine-learning-directed-study-report-2/machine-learning-directed-study-report-2.Rmd

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+---
+title: "Machine Learning Directed Study Report 2"
+description: |
+  Advanced processing of 3D meshes using Julia, and data science in Matlab.
+author:
+  - name: Anson Biggs
+    url: https://ansonbiggs.com
+repository_url: https://gitlab.com/orbital-debris-research/directed-study/report-2
+date: 2022-04-03
+output:
+  distill::distill_article:
+    self_contained: false
+categories:
+  - Matlab
+  - Orbital Debris
+  - Julia
+preview: Figures/final_scatter.png
+bibliography: citations.bib
+draft: false
+---
+
+## 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 of 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.
+
+![Example CubeSat Used for Analysis](Figures/assembly.jpg)
+
+## 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 able to be implemented in the Julia programming
+language. The current implementation of the algorithm calculates a
+moment of inertia tensor, volume, and center of gravity in a few
+milliseconds per part.
+
+![Current Process](Figures/current_process.svg)
+
+The algorithm's speed is critical not only for the eventually 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. I have decided that it makes the most sense to
+normalize the dataset based on volume. I chose volume for a few reasons,
+namely because it was easy to implement an efficient algorithm to
+calculate volume, and currently, volume seems to be the least essential
+property for the data analysis. Unfortunately, scaling a model to have 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
+     │ Symbol    Float64      Float64       Float64      Float64
+─────┼────────────────────────────────────────────────────────────
+   1 │ volume     0.00977609   1.05875e-10   2.0558e-5   0.893002
+   2 │ cx        -0.836477    -3.13272      -0.00135877  0.0866989
+   3 │ cy        -1.52983     -5.07001      -0.101678    0.177574
+   4 │ cz         0.162855    -6.83716       0.00115068  7.60925
+   5 │ Ix         0.00425039  -5.2943e-7     9.10038e-9  0.445278
+   6 │ Iy         0.0108781    1.05468e-17   1.13704e-8  1.14249
+   7 │ Iz         0.0111086    1.05596e-17   2.1906e-8   1.15363
+```
+
+Above is a summary of the current 108 part dataset without scaling. The
+max values are well above the median, and given the dataset's small
+size, there are still significant outliers in the dataset. For now, any
+significant outliers will be removed, with more explanation below, but
+hopefully, this will not become as necessary or shrink the dataset as
+much as the dataset grows. As mentioned before, a raw and a normalized
+dataset were prepared, and the data can be found below:
+
+-   [dataset.csv](https://gitlab.com/orbital-debris-research/directed-study/report-2/-/blob/main/dataset.csv)
+-   [scaled_dataset.csv](https://gitlab.com/orbital-debris-research/directed-study/report-2/-/blob/main/scaled_dataset.csv)
+
+## Characterization
+
+The first step toward characterization is to perform a principal
+component analysis to determine the essential properties. In the past,
+moments of inertia have been the most important for capturing the
+variation in the data. However, since this dataset is significantly
+different from the previous one, it is essential to ensure inertia is
+still the most important. We begin by using the `pca` function in Matlab
+on our scaled dataset.
+
+``` {.matlab}
+[coeff,score,latent] = pca(scaled_data);
+```
+
+We can then put the `coeff` and `score` returned by the `pca` function
+into a biplot to visualize what properties are the most important
+easily. Unfortunately, we exist in a 3D world, so the centers of gravity
+and moments of inertia have to be analyzed individually.
+
+![3D BiPlots for PCA](Figures/biplots.png)
+
+The components of all six properties are represented in each of the
+biplots by the blue lines, and the red dots represent the scores of each
+property for each part. The data variation is captured pretty well for
+the current dataset by both the inertia and the center of gravity. I
+will continue using inertia since it performed slightly better here and
+was the best when it was performed on just a single satellite. As the
+dataset grows and the model ingestion pipeline becomes more robust, more
+time will be spent analyzing the properties.
+
+Now that it has been determined that inertia will be used, k-means
+clustering can be performed on the raw, unscaled dataset.
+
+``` {.matlab}
+[IDX, C] = kmeans(inertia,3);
+
+histcounts(IDX) % Get the size of each cluster
+    89    10     8
+```
+
+![Scatter of all Data](Figures/first_scatter.png)
+
+This data has four distinct groups, with much overlap in the larger
+groups. Therefore, to get a better view, only the smallest magnitude
+group will be kept since it seems to have the most variation and k-means
+will be performed again to understand the data better.
+
+``` {.matlab}
+inertia = inertia(IDX == 1,:);
+[IDX, C] = kmeans(inertia,3);
+
+histcounts(IDX) % Get the size of each cluster
+    76     6     7
+```
+
+![Scatter of Smallest Group](Figures/final_scatter.png)
+
+This brings the dataset down to 89 parts from the original 108 and still
+leaves some small clusters. This highlights the need to grow the dataset
+by around 10x so that, hopefully, there will not be so many small,
+highly localized clusters.
+
+## 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. Characteristic length is being used heavily by NASA
+Debrisat and seems straightforward to implement so that will be the next
+goal for the mesh processing code. Before the next report, I would like
+to see this dataset grow closer to one thousand pieces.

_posts/2022-04-03-machine-learning-directed-study-report-2/machine-learning-directed-study-report-2_files/header-attrs-2.13/header-attrs.js

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+// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
+// be compatible with the behavior of Pandoc < 2.8).
+document.addEventListener('DOMContentLoaded', function(e) {
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_posts/2022-04-03-machine-learning-directed-study-report-2/machine-learning-directed-study-report-2_files/tippy-6.2.7/tippy-light-border.css

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_posts/2022-04-03-machine-learning-directed-study-report-2/machine-learning-directed-study-report-2_files/webcomponents-2.0.0/webcomponents.js

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+Copyright (c) 2018 The Polymer Project Authors. All rights reserved.
+This code may only be used under the BSD style license found at http://polymer.github.io/LICENSE.txt
+The complete set of authors may be found at http://polymer.github.io/AUTHORS.txt
+The complete set of contributors may be found at http://polymer.github.io/CONTRIBUTORS.txt
+Code distributed by Google as part of the polymer project is also
+subject to an additional IP rights grant found at http://polymer.github.io/PATENTS.txt
+*/
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+
+ Copyright (c) 2016 The Polymer Project Authors. All rights reserved.
+ This code may only be used under the BSD style license found at http://polymer.github.io/LICENSE.txt
+ The complete set of authors may be found at http://polymer.github.io/AUTHORS.txt
+ The complete set of contributors may be found at http://polymer.github.io/CONTRIBUTORS.txt
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