Bayesian sensitivity analysis of the millimetre-wave ablation process of geological materials

Abstract

Thermophysical granular properties exhibit large uncertainties which have a significant effect on the performance of millimetre wave beam energy ablation. To analyse these effects, we present a sensitivity analysis algorithm. This algorithm combines a high-fidelity thermal PDE solver, Gaussian process modelling, and variance-based sensitivity analysis to reduce the computational cost of evaluating global sensitivity indices. First, a response metamodel of a non-linear physics simulator is constructed using noisy observations and small sample sizes. It is trained using a Gaussian Process with spectral mixture kernels, which are a wide kernel family capable of capturing complex patterns. Bayesian quadrature for the calculation of conditional expectations and uncertainty sampling is used to compute the sensitivity indices of the response model, using analytical integral formulae we derive. This combination produces significantly more accurate sensitivity indices compared to standard Monte-Carlo integration. Finally, the algorithm is applied on a range of cases to quantify the effects of rock thermophysical properties and heterogeneities on the performance of the millimetre wave drilling process.