Validating the Use of Gaussian Process Regression for Adaptive Mapping of Residual Stress Fields

Probing the stress state using a high density of measurement points is time intensive and presents a limitation for what is experimentally feasible. Alternatively, individual strain fields used for determining stresses can be reconstructed from a subset of points using a Gaussian process regression (GPR). Results presented in this paper evidence that determining stresses from reconstructed strain fields is a viable approach for reducing the number of measurements needed to fully sample a component's stress state. The approach was demonstrated by reconstructing the stress fields in wire-arc additively manufactured walls fabricated using either a mild steel or low-temperature transition feedstock. Effects of errors in individual GP reconstructed strain maps and how these errors propagate to the final stress maps were assessed. Implications of the initial sampling approach and how localized strains affect convergence are explored to give guidance on how best to implement a dynamic sampling experiment.