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171 lines
7.7 KiB
Plaintext
---
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title: "Machine Learning Directed Study Report 2"
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description: |
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Advanced processing of 3D meshes using Julia, and data science in Matlab.
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author:
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- name: Anson Biggs
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url: https://ansonbiggs.com
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repository_url: https://gitlab.com/orbital-debris-research/directed-study/report-2
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date: 2022-04-03
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output:
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distill::distill_article:
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self_contained: false
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categories:
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- Matlab
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- Orbital Debris
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- Julia
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preview: Figures/final_scatter.png
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bibliography: citations.bib
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draft: false
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---
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## 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 of 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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## Data Preparation
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The models were processed in Blender, which quickly converted the
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assemblies to `stl` files, giving 108 unique parts to be processed.
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Since the expected final size of the dataset is expected to be in the
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magnitude of the thousands, an algorithm capable of getting the required
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properties of each part is the only feasible solution. From the analysis
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performed in [Report
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1](https://gitlab.com/orbital-debris-research/directed-study/report-1/-/blob/main/README.md),
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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 [@eberlyPolyhedralMassProperties2002] titled [Polyhedral
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Mass
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Properties](https://www.geometrictools.com/Documentation/PolyhedralMassProperties.pdf),
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his algorithm was able to be 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, and center of gravity in a few
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milliseconds per part.
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The algorithm's speed is critical not only for the eventually large
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number of debris pieces that have to be processed, but many of the data
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science algorithms we plan on performing on the compiled data need the
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data to be normalized. I have decided that it makes the most sense to
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normalize the dataset based on volume. I chose volume for a few reasons,
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namely because it was easy to implement an efficient algorithm to
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calculate volume, and currently, volume seems to be the least essential
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property for the data analysis. Unfortunately, scaling a model to have a
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specific volume is an iterative process, but can be done very
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efficiently using derivative-free numerical root-finding algorithms. The
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current implementation can scale and process all the properties using
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only 30% more time than getting the properties without first scaling.
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``` {.txt}
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Row │ variable mean min median max
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│ Symbol Float64 Float64 Float64 Float64
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─────┼────────────────────────────────────────────────────────────
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1 │ volume 0.00977609 1.05875e-10 2.0558e-5 0.893002
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2 │ cx -0.836477 -3.13272 -0.00135877 0.0866989
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3 │ cy -1.52983 -5.07001 -0.101678 0.177574
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4 │ cz 0.162855 -6.83716 0.00115068 7.60925
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5 │ Ix 0.00425039 -5.2943e-7 9.10038e-9 0.445278
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6 │ Iy 0.0108781 1.05468e-17 1.13704e-8 1.14249
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7 │ Iz 0.0111086 1.05596e-17 2.1906e-8 1.15363
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```
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Above is a summary of the current 108 part dataset without scaling. The
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max values are well above the median, and given the dataset's small
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size, there are still significant outliers in the dataset. For now, any
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significant outliers will be removed, with more explanation below, but
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hopefully, this will not become as necessary or shrink the dataset as
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much as the dataset grows. As mentioned before, a raw and a normalized
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dataset were prepared, and the data can be found below:
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- [dataset.csv](https://gitlab.com/orbital-debris-research/directed-study/report-2/-/blob/main/dataset.csv)
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- [scaled_dataset.csv](https://gitlab.com/orbital-debris-research/directed-study/report-2/-/blob/main/scaled_dataset.csv)
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## Characterization
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The first step toward characterization is to perform a principal
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component analysis to determine the essential properties. In the past,
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moments of inertia have been the most important for capturing the
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variation in the data. However, since this dataset is significantly
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different from the previous one, it is essential to ensure inertia is
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still the most important. We begin by using the `pca` function in Matlab
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on our scaled dataset.
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``` {.matlab}
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[coeff,score,latent] = pca(scaled_data);
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```
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We can then put the `coeff` and `score` returned by the `pca` function
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into a biplot to visualize what properties are the most important
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easily. Unfortunately, we exist in a 3D world, so the centers of gravity
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and moments of inertia have to be analyzed individually.
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The components of all six properties are represented in each of the
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biplots by the blue lines, and the red dots represent the scores of each
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property for each part. The data variation is captured pretty well for
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the current dataset by both the inertia and the center of gravity. I
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will continue using inertia since it performed slightly better here and
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was the best when it was performed on just a single satellite. As the
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dataset grows and the model ingestion pipeline becomes more robust, more
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time will be spent analyzing the properties.
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Now that it has been determined that inertia will be used, k-means
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clustering can be performed on the raw, unscaled dataset.
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``` {.matlab}
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[IDX, C] = kmeans(inertia,3);
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histcounts(IDX) % Get the size of each cluster
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89 10 8
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```
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This data has four distinct groups, with much overlap in the larger
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groups. Therefore, to get a better view, only the smallest magnitude
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group will be kept since it seems to have the most variation and k-means
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will be performed again to understand the data better.
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``` {.matlab}
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inertia = inertia(IDX == 1,:);
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[IDX, C] = kmeans(inertia,3);
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histcounts(IDX) % Get the size of each cluster
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76 6 7
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```
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This brings the dataset down to 89 parts from the original 108 and still
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leaves some small clusters. This highlights the need to grow the dataset
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by around 10x so that, hopefully, there will not be so many small,
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highly localized clusters.
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## Next Steps
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The current dataset needs to be grown in both the amount of data and the
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variety of data. The most glaring issue with the current dataset is the
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lack of any debris since the parts are straight from satellite
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assemblies. Getting accurate properties from the current scans we have
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is an entire research project in itself, so hopefully, getting pieces
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that are easier to scan can help bring the project back on track. The
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other and harder-to-fix issue is finding/deriving more data properties.
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Properties such as cross-sectional or aerodynamic drag would be very
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insightful but are likely to be difficult to implement in code and
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significantly more resource intensive than the current properties the
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code can derive. Characteristic length is being used heavily by NASA
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Debrisat and seems straightforward to implement so that will be the next
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goal for the mesh processing code. Before the next report, I would like
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to see this dataset grow closer to one thousand pieces.
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