In the early stages of engineering design, multitudes of feasible designs can be generated using structural optimization methods by varying the design requirements or user preferences for different performance objectives. Data mining such potentially large datasets is a challenging task. An unsupervised data-centric approach for exploring designs is to find clusters of similar designs and recommend only the cluster representatives for review. Design similarity can be defined not only on a purely functional level but also based on geometric properties, such as size, shape, and topology. While metrics such as chamfer distance measure the geometrical differences intuitively, it is more useful for design exploration to use metrics based on geometric features, which are extracted from high-dimensional 3D geometric data using dimensionality reduction techniques. If the Euclidean distance in the geometric features is meaningful, the features can be combined with performance attributes resulting in an aggregate feature vector that can potentially be useful in design exploration based on both geometry and performance. We propose a novel approach to evaluate such derived metrics by measuring their similarity with the metrics commonly used in 3D object classification. Furthermore, we measure clustering accuracy, which is a state-of-the-art unsupervised approach to evaluate metrics. For this purpose, we use a labeled, synthetic dataset with topologically complex designs. From our results, we conclude that Pointcloud Autoencoder is promising in encoding geometric features and developing a comprehensive design exploration method.

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In an engineering design process, multitudes of feasible designs can be automatically generated using structural optimization methods by varying the design requirements or user preferences for different performance objectives. Design exploration of such potentially large datasets is a challenging task. An unsupervised data-centric approach for exploring designs is to find clusters of similar designs and recommend only the cluster representatives as designs for review. Similarity can be defined on a purely functional level but also based on the geometric properties, such as size, shape, and topology, which are important at the early stages of design engineering. Different metrics exist to measure geometrical differences, e.g., voxel distance, chamfer distances, or Euclidean distance in the reduced representation of the high-dimensional 3D geometric data. It is not clear which of the numerous metrics is best suited for exploring designs obtained in structural optimization. For example, chamfer distance intuitively measures the geometrical differences but is expensive. Euclidean distance with low-dimensional geometric features, when meaningful, provides features that can be associated with designs, which eases the visualization and exploration of a design dataset. To evaluate different metrics in the context of design exploration, we propose a novel approach to quantify certain useful properties of a metric such as the ability to capture intuitive geometrical differences and to identify similar designs in topologically-complex synthetic datasets using clustering, an unsupervised machine learning method. From our results, we conclude that dimensionality reduction techniques, namely, UMAP (Uniform Manifold Approximation and Projection), and PCAE (Pointcloud Autoencoder) are promising in encoding geometric features that enable us to integrate geometrical properties with performance attributes.

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