Generative Adversarial Design Analysis of Non-Convexity in Topology Optimization

Nathan Hertlein, A. Gillman, P. Buskohl
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Abstract

Material penalization and filtering schemes are key strategies applied to topology optimization (TO) to promote more discrete and manufacturable designs. However, these modifications introduce fluctuations in the design landscape that amplify non-convexity and influence the local minima identified by TO. Harnessing the machine learning approach of generative adversarial networks (GAN), we investigate the role of penalization and filtering by comparing the designs between TO and GAN-based TO surrogates. A total of 17 GANs were constructed to predict 2D minimum compliance topologies across a set of penalization factors and filters, each interpolating a design space of 270,000 boundary condition and loading scenarios. The prevalence of GAN-predicted topologies with better compliance than TO-calculated topologies was estimated via a random sampling of the design space. GAN ‘over-performance’ occurs across material penalization and filtering conditions, where the frequency tends to increase as penalization increases. Analysis of this test set is leveraged to highlight trends regarding the conditions under which this ‘over-performance’ occurs, and the geometric characteristics these designs exhibit. Collectively, this study presents an alternative method to characterize the effects of penalization and filtering on design outcomes and motivates the use of data-driven surrogates to augment traditional approaches.
拓扑优化中的非凸性生成对抗设计分析
材料惩罚和滤波方案是应用于拓扑优化(to)的关键策略,以促进更离散和可制造的设计。然而,这些修改引入了设计景观的波动,放大了非凸性并影响了由TO确定的局部最小值。利用生成对抗网络(GAN)的机器学习方法,我们通过比较基于TO和基于GAN的TO替代品的设计来研究惩罚和过滤的作用。共构建了17个gan,通过一组惩罚因子和滤波器预测二维最小顺应性拓扑,每个gan插值27万个边界条件和加载场景的设计空间。通过对设计空间的随机抽样,估计gan预测的拓扑比to计算的拓扑具有更好的顺应性。GAN“性能过剩”发生在材料惩罚和滤波条件下,其中频率倾向于随着惩罚的增加而增加。通过对该测试集的分析,可以突出显示与这种“性能超常”发生的条件有关的趋势,以及这些设计所表现出的几何特征。总的来说,本研究提出了一种替代方法来表征惩罚和过滤对设计结果的影响,并激励使用数据驱动的替代方法来增强传统方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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