Flame describing function mapping with machine learning to predict instabilities in an annular combustor

One important issue that arises in the engineering application of reduced-order models of thermoacoustic instabilities is that of obtaining a comprehensive representation of the multidimensional combustion dynamics in the form of a flame describing functions (FDFs) that cover the whole domain of operation. By systematically measuring FDFs over this domain, it was recently shown that it was possible to delineate the unstable region of operation of an annular combustor. However, this instability prediction process requires a comprehensive sweep of operational conditions, which can be challenging and costly in practice. The present study explores the use of a supervised Machine Learning method, specifically Gaussian Process Regression (GPR), to predict FDFs from a subset of experimentally determined FDFs. It is shown that a small number of FDF datasets (typically 7 out of 35) can be used for training to predict the remaining datasets and forecast the FDF ensemble corresponding to the whole domain of operation. The method achieves high accuracy, with R2 scores exceeding 0.9 for the FDF gain and 0.99 for the phase. A physics-based reduced-order model is then employed to calculate instability growth rate maps, thereby inferring the domain of azimuthal instability of an annular combustor. Comparisons with measured FDFs across all operating points indicate that this method, which requires only a few measured FDFs, suitably determines the growth rates in the domain of operation of the system so that the uncertainties associated with FDF prediction by GPR only have a minor impact on the prediction of the instability domain layout.