Evaluation of geometric similarity metrics for structural clusters generated using topology optimization

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.