Optimisation of the hydrogen bake-out treatment in steels via Gaussian processes

Abstract

The presence of hydrogen in structural alloys reduces their ductility, a phenomenon called hydrogen embrittlement. Bake-out heat treatments are employed during processing to allow hydrogen trapped in microstructural features to effuse from the samples, but the optimal times and temperatures depend on the kinetics of hydrogen diffusion in the material. In this work, Gaussian process surrogate models are employed to emulate the outputs of microstructure-sensitive diffusion differential equations in steel. Training the models by sequentially increasing the number of dimensions results in better performances and shorter training times. Two main approaches are developed: single output models with experimental design for the prediction of optimal bake-out times, and multi-output principal component analysis models for the prediction of hydrogen concentration evolution. A novel approach is implemented to shorten the training times of multi-trap models by exploiting the symmetry of the equations with respect to different kinds of traps. The resulting models pave the way for the implementation of Gaussian processes on more computationally expensive diffusion simulations for the optimisation of heat treatments and other applications.