Simultaneous Exploration of Geometric Features and Performance in Design Optimization

Topology optimization (TO) algorithms generate novel concepts to inspire and propel the design iteration process. LS-TaSC® is an industrial tool that implements TO algorithms and generates designs optimized for performance objectives such as maximum stiffness or energy absorption, under specified constraints e.g. allowed mass fraction of material in the design space. A multi-objective design exploration framework based on LS-OPT® and LS-TaSC to generate designs is already available. The framework yields a Pareto set of designs by varying a parameter representing the relative preference of the user among the different objectives. A challenge persists as to how potentially large datasets of designs, generated using such an approach, can be reviewed efficiently by a designer. In this paper, we propose a method to identify a few representative design prototypes, which can be more easily reviewed by a designer. More concretely, the approach identifies classes of designs that look significantly different from a geometric point of view. For this purpose, we encode the information about the geometry using a voxel representation of the design. Subsequently, we use Principal Component Analysis (PCA), to reduce the high dimensionality of the representation, and extract features that encapsulate the geometric variation in the set of designs. Design prototypes are derived based on clustering algorithms using weights of principal components as features. To evaluate the proposed approach, we consider a solid beam model that is optimized for high stiffness under a static load case and high-energy absorption in a crash load case. Similar design problems are especially common in the car body design. We generate a Pareto set of designs for this test case and identify design prototypes. An interesting application of this method is to find designs with similar geometric appearance but very different performances. This can help us to estimate the robustness of a design. By helping in design exploration and selection, the proposed approach shows promise in large-scale industrial applications.