Topology optimization problems involving structural mechanics are highly dependent on the design constraints and boundary conditions. Thus, even small alterations in such parameters require a new application of the optimization routine. To address this problem, we examine the use of known solutions for predicting optimal topologies under a new set of design constraints. In this context, we explore the feasibility and performance of a data-driven approach to structural topology optimization problems. Our approach takes as input a set of images representing optimal 2-D topologies, each resulting from a random loading configuration applied to a common boundary support condition. These images represented in a high dimensional feature space are projected into a lower dimensional space using component analysis. Using the resulting components, a mapping between the loading configurations and the optimal topologies is learned. From this mapping, we estimate the optimal topologies for novel loading configurations. The results indicate that when there is an underlying structure in the set of existing solutions, the proposed method can successfully predict the optimal topologies in novel loading configurations. In addition, the topologies predicted by the proposed method can be used as effective initial conditions for conventional topology optimization routines, resulting in substantial performance gains. We discuss the advantages and limitations of the presented approach and show its performance on a number of examples.
Erva Ulu, Rusheng Zhang, Levent Burak Kara. (2015). A Data-Driven Investigation and Estimation of Optimal Topologies Under Variable Loading Configurations. Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization.