Abstract
Abstract This paper examines and compares the commonly used machine learning algorithms in their performance in interpolation and extrapolation of flame describing function (FDFs), based on experimental and simulation data. Algorithm performance is evaluated by interpolating and extrapolating FDFs and then the impact of errors on the limit cycle amplitudes are evaluated using the extended FDF (xFDF) framework. The best algorithms in interpolation and extrapolation were found to be the widely used cubic spline interpolation, as well as the Gaussian processes (GPs) regressor. The data itself were found to be an important factor in defining the predictive performance of a model; therefore, a method of optimally selecting data points at test time using Gaussian processes was demonstrated. The aim of this is to allow a minimal amount of data points to be collected while still providing enough information to model the FDF accurately. The extrapolation performance was shown to decay very quickly with distance from the domain and so emphasis should be put on selecting measurement points in order to expand the covered domain. Gaussian processes also give an indication of confidence on its predictions and are used to carry out uncertainty quantification, in order to understand model sensitivities. This was demonstrated through application to the xFDF framework.
Highlights
Increasing regulation on NOx emissions in aero and power turbines is necessitating a move to lean premixed combustion
It has been found that the cubic and linear spline interpolation is matched only by Gaussian processes in interpolating flame describing function (FDF), while the latter is preferred due to its inherent ability to provide an uncertainty with its prediction
It was demonstrated that satisfying the metric for enough data points was sufficient to give good agreement between the full dataset and the reduced dataset
Summary
Increasing regulation on NOx emissions in aero and power turbines is necessitating a move to lean premixed combustion With this comes increased exposure to thermoacoustic instabilities requiring better tools for their modeling and prediction. In order to determine FDFs, either experimental measurements are carried out by forcing a flame using a loudspeaker or numerical measurements are made of how the flame responds to different frequencies and levels of forcing in a simulation Collecting data from both of these methods can be costly and is often subject to a restriction on the domain (range of frequencies and amplitudes) that can be tested, e.g., the maximum amplitude of forcing in an experimental rig can be limited by the loudspeaker. The importance of intelligently selecting data points is demonstrated, and the impact of interpolation errors on a system model is evaluated, wherein the limit cycle oscillation of a laminar slit burned is calculated utilizing the extended FDF (xFDF) framework
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
