Investigation of dimension reduction for Bayesian calibration of a Ti-6Al-4V crystal plasticity model

Abstract

Numerical simulation models that accurately predict the behavior of complex materials such as the aerospace-grade Ti-6Al-4V are often highly computationally expensive and contain a large number of model parameters that must be inferred by comparing the model predictions with experimental observations. Often, such calibration is carried out using deterministic optimization procedures, but these methods do not account for physical, data, or modeling uncertainties and may produce results that cannot be meaningfully extrapolated to new operating conditions not covered by the calibration experiments. On the other hand, uncertainty-aware calibration using the Bayesian framework is more robust, but it is difficult to carry out for a large number of parameters because of the curse of dimensionality and the computational expense of evaluating the simulation model many times. With this context, the contributions of this work are twofold. First, we investigate the application of Bayesian calibration, enhanced with active subspace-based dimension reduction and surrogate modeling, to a crystal plasticity finite element model that predicts the mechanical properties of a forged Ti-6Al-4V alloy. In particular, we demonstrate how dimension reduction can enable calibration in high dimensions without the use of sophisticated sampling techniques or heuristic down-selecting of parameters. Next, we study the impact of the latent space dimension (constructed through dimension reduction) on the calibrated posteriors. Most importantly, we examine how optimal single-value estimates of the model parameters differ between deterministic calibration algorithms and Bayesian point estimates, underscoring the necessity of appropriately incorporating all physical, modeling, and approximation uncertainties to ensure robust calibration outcomes.