Data-Driven Topology Optimization With Multiclass Microstructures Using Latent Variable Gaussian Process

Abstract

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.

Data‐Driven Approaches Toward Smarter Additive Manufacturing

“…[133] Furthermore, data-driven TO models could also generate multiclass microstructures (i.e., structures that have more than one type of unit cell in their microstructure) which have important applications in the biomedical and aerospace industry as they can be designed to have specific properties that cannot be found naturally. [136] Integration of data-driven approaches with design tools like TO and GD allows designers to efficiently generate novel complex structures with minimal computational cost. A crucial aspect is to construct a thorough reference dataset that can generate output designs similar to those generated by FE-based models.…”

Decomposition and optimization of linear structures using meta models

“…For this purpose, a regression model based on a reduced basis description was established, where the microstructure properties are determined by samples of parametrized unit cells. Furthermore, Wang et al (2021) carried out a multi-scale topology optimization where meta models of different parameterized microstructures were considered with respect to material properties as stiffness matrix or thermal conductivity. However, due to prescribed parametrization of the geometry, the design freedom in the presented approaches is limited and hence one does not exploit the full lightweight potential.…”

Latent variable Gaussian process models: A rank‐based analysis and an alternative approach

“…15 Leveraging the BO framework, it has been applied to a plethora of material design problems and yielded improved results. [19][20][21][22] It has also been extended to topology optimization 23 and enables full-rank correlation matrices for the qualitative factors. The distinction in correlation function's rank is important because GP models with full-rank correlation functions can always perfectly interpolate any set of response surface data and thus represent any response surface no matter how complex it is.…”

“…Leveraging the BO framework, it has been applied to a plethora of material design problems and yielded improved results 19‐22 . It has also been extended to topology optimization 23 and variable‐design‐space problems 24 . The effectiveness of this LVGP model motivates our further investigation into it in this article.…”