Data-driven multifidelity topology design with multi-channel variational auto-encoder for concurrent optimization of multiple design variable fields

Abstract

Topology optimization can generate high-performance structures with a high degree of freedom. Regardless, it generally confronts entrapment in undesirable local optima especially in problems characterized by strong non-linearity. This study aims to establish a gradient-free topology optimization framework that facilitates more global solution searches to avoid the entrapment. The framework utilizes a data-driven multifidelity topology design (MFTD), where solution candidates initially generated by solving low-fidelity (LF) optimization problems are iteratively updated by a variational auto-encoder (VAE) and high-fidelity (HF) evaluation. A key procedure of the solution update is to construct HF models by extruding material distributions obtained by the VAE to thickness distribution, which is spcatially constant across all solution candidates in the conventional data-driven MFTD. This constant assignment leads to no exploration of the thickness space, which necessitates extensive parametric studies outside the optimization loop. To enable a more comprehensive optimization in a single run, we propose a multi-channel image data architecture that stores material distributions in the first channel and other design variable fields like thickness distribution in the second or subsequent channels. This significant shift enables a thorough exploration of the additional design variable fields space with no necessity of parametric studies afterwards, by simultaneously optimizing both material distributions and those variable fields. We apply the framework to a maximum stress minimization problem, where the LF optimization problem is formulated with approximation techniques, whereas the HF evaluation is conducted by accurately analyzing the stress field, bypassing any approximation techniques. We first validate that the framework can successfully identify high-performance solutions superior to the reference solutions by effectively exploring both material and thickness distributions in a fundamental stiffness maximization. Then we demonstrate the framework can identify promising solutions for the original maximum stress minimization problems.