Global sensitivity analysis (GSA) is widely used in engineering design to study the inner workings of complex models by analyzing how model inputs contribute to the model response. This proves especially beneficial in materials design for characterizing material systems, guiding experiments, and extracting physical knowledge. So far, GSA studies have been limited to design spaces with individual quantitative (numerical) design variables. However, many material systems also contain different types of variables such as qualitative (categorical) design variables. In this work, we introduce two new methods that incorporate both quantitative and qualitative variables into GSA studies with applications to materials design.
Qualitative variables could play a crucial role in design of engineered materials. However, a challenge remains in quantifying their influence on the material properties. To overcome this challenge, we present the first metamodel-based mixed-variable GSA method. Specifically, we integrate Latent Variable Gaussian Process (LVGP) with Sobol’ analysis for knowledge discovery. We also incorporate our method with Bayesian optimization to create a sensitivity-aware design framework for accelerating the design exploration of materials with many-level combinatorial design spaces.
Furthermore, common GSA methods use analytical or surrogate models, the accuracy of which depends on the complete conformance to all model assumptions. Even so, such system models are not flexible and fail to capture nonlinear behaviors in complex systems. We introduce a flexible, interpretable artificial neural network model to perform data-driven GSA in mixed design spaces. The employed model allows the investigation of the main effects and pairwise interaction effects in GSA according to functional analysis of variance decomposition. The knowledge extracted from the method lays the foundation for deriving experimental guidelines and rules for next-generational material design