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Clustering Topologically-Optimized Designs based on Structural Deformation

Ernest Hutapea, Nivesh Dommaraju, Mariusz Bujny, Fabian Duddeck, "Clustering Topologically-Optimized Designs based on Structural Deformation", Munich Symposium on Lightweight Design 2021, 2022.


Topology optimization can be used to generate a large set of lightweight structural solutions either by changing the constraints or the weights for different objectives in multi-objective optimization. Engineers must analyze and review the designs to select solutions according to their preference towards objectives such as structural compliance and crash performance. However, the sheer number of solutions challenge the engineers' decision-making process. An automated way of summarizing solutions is to cluster groups of similar designs based on a suitable metric. For example, with the Euclidean metric in the objective vector, design groups with similar performance can be identified and only the representative designs from the different clusters may be analyzed. Since the deformation behavior of a structure is an important design feature, in this work, we investigate the use of manifold learning algorithms to identify and group similar designs using the nodal displacement data. The proposed approach can process the volumetric deformation of geometries with completely different topologies. In this study, we couple the manifold learning techniques, t-distributed Stochastic Neighbor Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP), with the clustering algorithms, $k$-means and Ordering Points To Identify the Clustering Structure (OPTICS), to identify the representative deformation modes. Using Gaussian Random Fields (GRF) to create artificial displacement fields, we generate a labeled dataset with different modes, which enabled us to evaluate our method using classification accuracy, precision, recall, and F1-score. Finally, using our approach, we successfully distinguished between similar and non-similar designs in the results from topology optimization.

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