Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process
Data-Driven Topology Optimization with Multiclass Microstructures using Latent Variable Gaussian Process
复制标题
DOI：
10.1115/1.4048628
复制
发表时间：
2020-06
期刊：
影响因子：
--
通讯作者：
Liwei Wang;Siyu Tao;Ping Zhu;Wei Chen
中科院分区：
文献类型：
--
作者：
Liwei Wang;Siyu Tao;Ping Zhu;Wei Chen
数据驱动方法正在成为一种有前途的方法，可以更高效地进行多尺度结构的拓扑设计。然而，现有的数据驱动方法主要关注单一类别的微观结构，而不考虑多个类别来适应空间变化的所需属性。关键的挑战是不同类别的微观结构之间缺乏内在的排序或“距离”度量来满足一系列性能。为了克服这一障碍，我们扩展了新开发的潜变量高斯过程（LVGP）模型，为超材料的微观结构库创建多响应 LVGP（MR-LVGP）模型，将定性微观结构概念和定量微观结构设计变量作为混合变量输入。 MR-LVGP 模型根据混合变量对响应的集体影响将混合变量嵌入到连续设计空间中，从而为不同几何类别和微观结构材料参数之间的相互作用提供了深入的见解。通过该模型，我们可以轻松获得不同微观结构概念之间的连续且可微的过渡，从而为多尺度拓扑优化提供梯度信息。我们通过非周期性微观结构的多尺度拓扑优化展示了其优势。设计实例表明，由于微观和宏观结构的载荷传递路径一致，考虑多类微观结构可以提高性能。
The data-driven approach is emerging as a promising method for the topological design of multiscale structures with greater efficiency. However, existing data-driven methods mostly focus on a single class of microstructures without considering multiple classes to accommodate spatially varying desired properties. The key challenge is the lack of an inherent ordering or “distance” measure between different classes of microstructures in meeting a range of properties. To overcome this hurdle, we extend the newly developed latent-variable Gaussian process (LVGP) models to create multi-response LVGP (MR-LVGP) models for the microstructure libraries of metamaterials, taking both qualitative microstructure concepts and quantitative microstructure design variables as mixed-variable inputs. The MR-LVGP model embeds the mixed variables into a continuous design space based on their collective effects on the responses, providing substantial insights into the interplay between different geometrical classes and material parameters of microstructures. With this model, we can easily obtain a continuous and differentiable transition between different microstructure concepts that can render gradient information for multiscale topology optimization. We demonstrate its benefits through multiscale topology optimization with aperiodic microstructures. Design examples reveal that considering multiclass microstructures can lead to improved performance due to the consistent load-transfer paths for micro- and macro-structures.