Automatic Postprocessing of Topology Optimization Solutions by Using Support Vector Machines

The postprocessing step from the density result in topology optimization to a parametric CAD model is typically most time consuming and usually involves several hands on maneuvers by an engineer. In this paper we propose an approach in order to automate this step by using soft non-linear support vector machines (SVM). Our idea is to generate the boundaries separating regions of material (elements with densities equal to one) and no material (elements with densities equal zero) obtained from topology optimization automatically by using SVM. The hyper-surface of the SVM can then in the long run be explicitly implemented in any CAD software. In this work we generate these hypersurfaces by solving the dual formulation of the SVM with soft penalization and nonlinear kernel functions using quadratic programming or the sequential minimal optimization approach. The proposed SVM-based postprocessing approach is studied on topology optimization results of orthotropic elastic design domains with mortar contact conditions studied most recently in a previous work. The potential energy of several bodies with nonmatching meshes is maximized. In such manner no extra adjoint equation is needed. Intermediate density values are penalized using SIMP or RAMP, and the regularization is obtained by applying sensitivity or density filters following the approaches of Sigmund and Bourdin. The study demonstrates that the SVM-based postprocessing approach automatically generates proper hypersurfaces which can be used efficiently in the CAD modelling.