Learning the relationship between operating condition and flame response from acoustic data

Predicting how the thermoacoustic response of a combustor changes across operating conditions is a long-standing challenge because small uncertainties in the flame response lead to large uncertainties in the thermoacoustic response. In this paper, we address this challenge for the Rolls-Royce SCARLET test rig using a combination of Bayesian inference, Gaussian process regression, and information-theoretic experiment design. Starting from a physics-based acoustic network model whose flame parameters are inferred at several operating conditions using Bayesian inference (described in a companion paper), we use Gaussian process regression in Part A to learn how the five parameters of a flame model vary with six operating condition parameters. The resulting Gaussian process model predicts the flame response at unseen conditions with quantified uncertainty, and, when coupled into the acoustic network, produces operating maps of the full thermoacoustic response. In Part B, we use metrics from information theory to identify the small number of forcing frequencies that are most informative about the flame parameters. For the SCARLET rig, three optimally chosen frequencies recover the flame transfer function to the same fidelity as the full dataset of around 20 frequencies forced from both upstream and downstream, reducing the data required by up to 90%.