Topological dimensionality reduction-based machine learning for efficient gradient-free 3D topology optimization

Powerful gradient-free topology optimization methods are needed for structural design concerning complex responses. In this paper, a novel gradient-free optimization method is proposed by integrating the material-field series expansion topological parameterization and the deep neural networks, providing two-fold advances: firstly, it generally reduces the massive topological design variables to fewer than 200, while keeps the capability to represent relative complex 3D topologies and clear boundaries; secondly, by constructing a sequential neural network surrogate model, it sufficiently explores the reduced design space and is capable of handling multi-peak and discontinuous optimization problems. The effectiveness of this method is illustrated via several design problems, among which the optimized material effective bulk modulus achieves 98% of the H-S bound and the highly-nonlinear peak weld stress in a phone dropping process is decreased by 16.59%. This method reduces the computational time by 1–4 orders of magnitude compared with the coarse-mesh-based gradient-free methods, and it is the first time to successfully conduct gradient-free 3D topology optimization with thousands of finite elements. The method's ease of implementation and compatibility with various simulation software, brings topology optimization into complex industrial applications and proves that gradient-free technology represents an effective optimization benchmark for improving structural performance.