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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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description-meta: This report details advanced 3D mesh processing for orbital debris characterization using Julia and MATLAB. It covers data gathering from online 3D models, data preparation using a custom Julia library for efficient property extraction, and characterization using Principal Component Analysis (PCA) and k-means clustering. The report also includes visualizations and discusses next steps for dataset expansion and property derivation.
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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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date-modified: 2024-02-29
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@@ -25,7 +26,7 @@ excellent source of high-quality 3D models, and all the models have, at worst, a
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license making them suitable for this study. The current dataset uses three separate satellite
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assemblies found on GrabCAD, below is an example of one of the satellites that was used.
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{fig-alt="A 3D model of a satellite with deployed solar panels. The satellite bus is a rectangular structure with exposed framework. The solar panels are arranged in a cross-like configuration, with blue and gold panels. The model is shown against a light gray background with a reflective surface."}
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## Data Preparation
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@@ -47,7 +48,7 @@ project. The characteristic length takes the maximum orthogonal dimension of a b
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dimensions then divides by 3 to produce a single scalar value that can be used to get an idea of
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thesize of a 3D object.
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{fig-alt="A diagram illustrating the current mesh processing pipeline. The pipeline begins with a satellite image and converts it into a mesh. The mesh is brought into code represented by summation symbols over x, y, and z. Finally, properties labeled Ix, Iy, and Iz are extracted from the mesh."}
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The algorithm's speed is critical not only for the eventual large number of debris pieces that have
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to be processed, but many of the data science algorithms we plan on performing on the compiled data
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@@ -105,7 +106,7 @@ lambda_ratio = cumsum(lambda) ./ sum(lambda)
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Then plotting `lambda_ratio`, which is the `cumsum`/`sum` produces the following plot:
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{fig-alt="A line graph depicting the cumulative variance of different components. The x-axis represents the components (Iz, Iy, Ix, body z, body y, body x, Lc, and Surface Area), and the y-axis represents the cumulative variance ranging from 0.988 to 1. The variance is calculated as ∑i=1Mλi/∑λ, where λ represents the eigenvalues. The plot shows a rapid increase in cumulative variance for the first few components, followed by a plateau."}
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The current dataset can be described incredibly well just by looking at `Iz`, which again the models
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are rotated so that `Iz` is the largest moment of inertia. Then including `Iy` and `Iz` means that a
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Which produces the following plot:
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{fig-alt="A line graph illustrating the sum of distances to centroids for different numbers of clusters (K). The x-axis represents the number of clusters, ranging from 2 to 20, and the y-axis represents the sum of distances to the centroid. The plot shows a sharp decrease in the sum of distances as the number of clusters increases initially, followed by a gradual flattening of the curve, suggesting diminishing returns with increasing K."}
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As can be seen in the above elbow plot, at 6 clusters there is an "elbow" which is where there is a
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large drop in the sum distance to the centroid of each cluster which means that it is the optimal
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number of clusters. The inertia's can then be plotted using 6 k-means clusters produces the
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following plot:
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{fig-alt="A 3D scatter plot showing clusters of data points. The plot's axes represent Inertia x, Inertia y, and Inertia z. Six distinct clusters are represented by different colors and labeled accordingly in a legend."}
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From this plot it is immediately clear that there are clusters of outliers. These are due to the
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different shapes and the extreme values are slender rods or flat plates while the clusters closer to
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