Bayesian inference of physics-based models of acoustically-forced laminar premixed conical flames

TL;DR

This paper develops a Bayesian inference framework to create a physics-based reduced-order model of acoustically-forced laminar premixed flames, accurately capturing flame dynamics with minimal data and computational cost.

Contribution

It introduces a Bayesian inference method using Laplace's approximation for efficient parameter estimation in flame modeling, enabling accurate extrapolation and uncertainty quantification.

Findings

Achieved quantitatively accurate flame models with seven parameters.

Successfully extrapolated model predictions beyond training data.

Provided MATLAB code for broader application of the method.

Abstract

We perform twenty experiments on an acoustically-forced laminar premixed Bunsen flame and assimilate high-speed footage of the natural emission into a physics-based model containing seven parameters. The experimental rig is a ducted Bunsen flame supplied by a mixture of methane and ethylene. A high-speed camera captures the natural emission of the flame, from which we extract the position of the flame front. We use Bayesian inference to combine this experimental data with our prior knowledge of this flame's behaviour. This prior knowledge is expressed through (i) a model of the kinematics of a flame front moving through a model of the perturbed velocity field, and (ii) a priori estimates of the parameters of the above model with quantified uncertainties. We find the most probable a posteriori model parameters using Bayesian parameter inference, and quantify their uncertainties using Laplace's method combined with first-order adjoint methods. This is substantially cheaper than other common Bayesian inference frameworks, such as Markov Chain Monte Carlo. This process results in a quantitatively-accurate physics-based reduced-order model of the acoustically forced Bunsen flame for injection velocities ranging from 1.75 m/s to 2.99 m/s and equivalence ratio values ranging from 1.26 to 1.47, using seven parameters. We use this model to evaluate the heat release rate between experimental snapshots, to extrapolate to different experimental conditions, and to calculate the flame transfer function and its uncertainty for all the flames. Since the proposed model relies on only seven parameters, it can be trained with little data and successfully extrapolates beyond the training dataset. Matlab code is provided so that the reader can apply it to assimilate further flame images into the model.